I managed the girls softball team in high school, which my algebra instructor coached - or I'd have been royally fucked.
One time I remember she called on me and asked me to solve for "x" in an equation - three times. Finally, in desperation, when she was begging me to answer "What's X???", I told her "x" was a fucking letter, and not a number.
Got to visit my favorite vice-principal over that one . . .
@DonberKon An engineering student? Ok, I'm going to be the person I always wanted to hate. When I was doing my Marine Engineering undergrad, we didn't have them fancy calculator things. We had slide rules and we liked it! I'm not sure if schools now continue on to Advanced Math for Engineers but that comes after Differential Equations, 2 semesters. Just some advice from someone that has gone through it, go on to an MBA after you finish. You won't believe how easy it is. I did my doctorate in Information Systems and other than the writing, engineering is much harder. Good luck with your education. Question, what school are you studying at and what do you want to do? Curious and best wishes.
@bsci87 I go to Iowa State. They don't require any "hard math" after DE, and they even let us use a program that solves diff eq's for you. I'm not sure what I want to do yet. Second year Mechanical major. I think I want to be involved in testing, verification; you know, the exciting stuff. Also, I'm a gearhead, so automotive interests me.
@DonberKon No hard math after DE? And they let you use computers for that? Yikes! I think I hate you now. Well that or I'm just an idiot for putting myself through that. Iowa State is a good school but once you finish don't take a break. Take one class toward your masters. That one class gives you another line for your resume. Your a candidate for a masters degree and that could make a difference. Take your break after that. Always remember, engineering is the hardest undergraduate program there is and if you can make it through there, you can make it through anything. I work with ships now at a major port and there are always things to do that you have to think on your feet and figure out. When I first got out of school I was working with submarines. Very cool work and people turned to me and asked what do we do next. I was like, why are you asking me, I'm just some punk kid but someone had to figure it out because it wasn't going away. If you look you'll find a job that fits you and makes you feel like you didn't work so hard for nothing. If any business majors ever give you any grief just know they couldn't have made it through your first engineering class. It really is that special. Keep my handle if you ever want to talk further. Keep your head down and push to the finish. Best Wishes.
@DonberKon My f'ing undergrad school made us learn how to program a computer to solve calculus programs while taking calculus. OMG. First I was taking calculus without having taken trig second of all I was having enough trouble with calculus let alone learning how to program on top of that to solve stupid problems. Fortunately my roommate was dating a junior engineering student. Then a zillion years later I had to relearn calculus enough to solve stupid, idiotic, there is no earthly reason why I need to know how to do this econ proofs in a doctoral seminar those of us in a different business field were being tortured with.
@DonberKon Weird. it truncated what I was saying and said "forbidden" when I hit send for the first time... here is the rest of the message (back button picked it up).
You are right. Stats is way easier (I did take an engineering class at one point, for reasons I no longer remember, except that the class sounded interesting). Stats is way easier than Calculus too. You only need basic high school algebra to solve those problems. Unless of course you are forced to learn matrix algebra while doing third semester (PhD program) stats. Matrix algebra is a pain in the ass when you are having to learn how to do that before you can figure out the homework problems. This is why they invented SAS (or SPSS or r or whatever your favorite stats program is).
I discovered with one program you could get it to print the maxtrix algebra solution to something you just ran using a menu (can't remember which program it was - we had to learn 5 of them, one using unix, the rest PC, one of which is pretty much DOA at this point). Made my life easier. And then I found the 1975 textbook my prof was using to teach from in the obsolete stacks of the library (eg the "old" stacks vs the ones that had books much newer - in desperation I was looking for a book that taught this crap in matrix algebra since our book used vectors). Bingo. Turned everything into a piece of cake. Just followed along. Found all the homework problems there, the exam problems in there. Got the highest grade in the class of around 80, including those getting a PhD in stats, because of that little book. They wanted to know if was going to change my major and get my PhD in stats. Were they out of their freaking mind? I was so glad to be done done done with all that crap. Of course the joke is on me. I got stuck teaching stats to undergrads who were allergic to math and turned their brains off even before they started to think about it. LOL
@DonberKon You go to Iowa State?! Holy Shit another Iowan...i didnt know anymore really existed. I figured that everyone buying from Iowa was some sort of a glitch.
I decided to go back to school recently, and while I am earning A's in nearly every subject, math has been killing me. I earned my first D ever in math last semester, and I am currently re-taking the class. I have a big test on Saturday and I am convinced I will fail. This class is the only thing keeping me from completing two degrees.
@PocketBrain Very true. Math is such a sensitive topic for me, I should of graduated last semester, but you must earn a C or better in Math in order for it to count towards graduation. English and Math are the only subjects that require that.
@conandlibrarian To the people who are having a tough time with math and need to pass. I taught adjunct for almost 20 years while running my company and doing a doctorate. Not bragging at all, that was my stupidity and what I chose to do. My advice is to break down the math you're doing to smaller pieces that you can relate to. If you take it in larger chunks, you'll never get through it. Baby steps and relate it to the real world and what you do everyday. There isn't anything that's hard about it and trust me, you can pass it. You just need just turn it around and have it make sense to you. Once you do that, you'll pass it with no problem. It is easier than you are making it. Best wishes.
@conandlibrarian Hey, if I can offer some advice: try reaching out not only to fellow students, but to the teachers. If there are open office hours go to them, there's a good chance you won't be alone and it'll be a group study session semi- or fully-directed by a prof and/or TA. You may make some friends that can help you study there, too. If there aren't regular open sessions like that, ask your prof for an appointment for extra help and come armed with questions. See if they'll meet with you regularly throughout the quarter/semester to help - if they don't offer first, ask. Don't be afraid - most profs (in my experience) are more than willing to help people who put forth the effort to at least show that they're trying, and for the ones that aren't, hell, it's probably part of their contract to fake it.
Between doing those things and studying my tail off like never before, that's how I survived both organic chem and biochem. You can do it, don't give up!
@conandlibrarian Go to the undergrad math lab for tutoring. They saved my ass in a PhD econ seminar. And others are right. Having a homework study group, going to see the prof... all help.
@jiltant I actually am in communication weekly with the instructor. While nice, she is not that helpful. I typically cannot get the answers to the questions I need, and just leave confused.
I got a minor in math with my B.S.E.E.T. Went all the way through differential calc, multi variable calc, linear algebra, the whole shebang. Don't remember much of it now though.
@PocketBrain B.E.M.E. That's 152 credits minimum to graduate but I was stupid and did 172 with only 3 or 4, 4 credit classes. Lots of math, science and engineering but if you can survive that course load, you can survive anything.
In college I took Math 102, which covered things like voting systems, fair division (such as with inheritances), and Euler circuits. It was actually really interesting, and tests were open note so it was really easy, too!
@jqubed When I taught that class, I called it "Math for people who think they don't need math". The university called it "Quantative reasoning". I loved teaching it.
I sucked at Math in High School. I took an independent study class in college for Intermediate Algebra ( work at your own pace showing up for tests and lab only) and got a B. Then I took College Algebra in a typical classroom with students. Got another B. It was as if the mathematics in college had meaning and inspired me to improve.
I'd love to go back to school, get my AA (most of what's left are science classes), and move towards a better job than the retail occupation I've had for the past 11 years.
@JT954 Never too late to go back. I went back at 37, and finished my A.A. stuff in about 18 months. I took about 15 units a semester, including summer. It was so worth it.
@conandlibrarian Good for you! I didn't graduate from community college until I was 27, then a couple of bachelor degrees when I was 30. Time passed, waiting tables, bartending, small business ownership...
And now, back in school at 42 working on my Master's to teach bio to high schoolers. It's truly never too late. I anticipate I'll go back to school in another 15 or 20 years for something new.
As a CSCI student, I went through Calc early (Calc 1 in high school,) and then did Statistics, Discrete Math and Numeric Analysis. I should have taken Linear Algebra and Differential Equations so I could play around more in the Computer Graphics space, but never did. I might buy some books for those at some point and just learn it on my own.
I was an engineering major for a while, so lots of math. Then I quit and became a chef. So more practical, everyday math involved in that. I also taught Applied Math at Le Cordon Bleu for some years.
Upper level statistics. It was that or calculus, and statistics were a better choice for biodemographic research. And it wasn't calculus, so there's that.
I started junior college in "you still count on your fingers" remedial math as a high school dropout, and I worked my way up through calculus and later upper division stats at a 4-year. I got a BS in sciencey stuff and regret nothing.. but my secret love was probably really English classes, where I could just read and write stuff all day. Words are easier than math.
@jiltant I heartily disagree. With math, even when the teacher hated me, I could still pass, because the answers are definite, absolute. When I made the mistake of upsetting a fascist English teacher, I found my grades started to dip. Even outside of classrooms, words can be problematic due to how people take things differently and how much is based on personal taste. Math is constant. I can know the right answer to a math problem. With words, best I can do is know an answer that is right enough for now, with this person. Unless you me grammar and punctuation. Then we just open doors for grammar nazis, who would likely have plenty to say about my mess here.
@simplersimon Haha, yeah, admittedly English profs can be real SOBs. Their grading systems are often horrifically subjective, their mysterious rubriks obeying no known Earthly laws. Most of the ones I met seemed to be frustrated by receiving endless students that were nearly functionally illiterate, and there's no way that they could imagine reversing the (in their eyes) bad habits ingrained by years of prior bad teaching. So they all kind of had this grim despair with a touch of a brutal streak, and a thousand yard stare.
But, that being said, I always had fun learning what the profs expected and trying to duck around it as much as I could and entertain the reader. In a lit. analysis class, I once wrote a Marxist-style analysis of a play, turning it into a hilariously wrong but internally consistent diatribe about class warfare, and enjoyed a pretty good grade as a result. Other times I'd argue specifically against myself in pieces, trying to justify crap I don't really believe in. I'd "psychoanalyse" famous characters and tie some supposed neurosis back to the author's own (completely made up by me) complexes. Stuff like that. I had a lot of fun with it.
Math was also fun and interesting in a different way, but I didn't often get the full swing of the creative momentum with numbers as I did with letters. Other people can do that, and that's awesome too. :)
@simplersimon@AnnaB@jiltant I wouldn't say that words are easier, just that they're more fun and flexible. They're probably easier chiefly in the sense that they're easier to be creative with. My understanding is that the deeper you get into math the answer isn't necessarily the answer and there's more creative potential. What gets me about this is that kids even just a few years old start to get this and enjoy it.
I always liked that algebra and grammar (in particular sentence structure and conjugations and such) are so similar. Both math and language are symbolic systems.
What's especially fascinating about language is that it's multilayered and multifaceted; even in ordinary conversation (let alone poetry) you have several strands of meaning superimposed and in fact interacting with each other. Even just the visual and auditory elements and the denotative and connotative senses can create enough tension to make the whole fucking thing explode. Seriously, that shit's crazy. And I mean awesome. Also, perspective (background, culture, etc.) is so much more a factor.
@simplersimon@AnnaB@jiltant My kid had some bad English teachers. I don't think I had any that I wasn't able to get a good grade out of or earn the respect of. And when you learn an English instructor's expectations and how to play with them, you're learning not just the material per se, you're learning a person. That "the answer is the answer" is fine, but that "an answer is their answer" is arguably more meaningful. Both are necessary in any case.
@joelmw My college freshman english teacher fell for all sorts of "creative" BS. We had to read Labyrinths and I wrote my paper in a spiral. Not much content and would have been a pain in the ass to read (was a pain in the ass to write it out that way -but less of a pain in the ass than if I had created more content for the book or whatever it was, that I hated) - he was duped and gave me an A on that. Since he fell for the creativity distractor I played that to the hilt. Made that class way less work.
@joelmw Don't get me wrong - I adore the beauty of a well written thought. What I don't like is a teacher telling me what words are supposed to mean to me. Part of what I love about reading is that an author's words can hold different truths for different people, not unlike a painting or a piece of music. I just really dislike having to determine what those words mean to my instructor and then parroting their truth back to them. This makes the whole experience lose its joy for me.
@Kidsandliz Alas, I was usually creating more work for myself. Sigh. I wanted everything I did to be original and undeniably substantive. I didn't learn until later in life to just do what I needed to do and/or game the system.
Actually, to clarify what I said before, I think I was always demonstrably capable of doing the kind of work that each of my instructors wanted, but sometimes on big assignments I would over-complicate things or set the standards too high or procrastinate to the point that I ended up screwing myself over.
@AnnaB I was much more of a sycophant and general people-pleaser as a kid. But in my defense, I often, OFTEN, (maybe usually) took a position contrary either to my instructor or to the established orthodoxy or both, just because that's how I am. The trick--and it is a trick--is to frame that contrariness in such a way as to still meet the requirements and earn the respect.
It's funny, because at this point in my life, I really don't give much of a fuck about fitting into other people's world views. I mean, I do it sometimes and think I still can, but it's too much effort to conform to the Procrustes' Bed of someone else's expectations and limited imagination, because usually it will involve the chopping off of a good bit of both my legs and skull. I do still have a tendency to please English prof types and other freaks. Except the ones that absolutely demand brevity above all. Again, sometimes, maybe. But fuck those guys.
Of course at work I try to make a point of pleasing my bosses with both written and graphic documents. I do have a tendency to go long with the written, but I eventually bring it down--all by my lonesome if needed. I have a great system worked out with my immediate supervisor, because she usually wants me to start by rambling and including everything; then she decides what she wants to highlight and I (or--her call--we) work on honing it. It feels like she understands my process and the value of beginning with a more comprehensive view and just kind of get it all spread out.
I see the need to communicate and the sometimes necessity and/or value of brevity, but I contend that a big part of our problem as a society is that we over-value brevity.
@AnnaB The other thing I'd say is that I definitely want to understand and, if possible, contain where the other person is coming from. I just inevitably want to add to it.
@joelmw Agreed. I do want to understand the other person's viewpoint. That expands everything - the meaning of the words, my mind, etc. I just really loathed, particularly in Lit classes, being told THE way I was supposed to be thinking about a particular topic. Especially since I am/was often not.
@AnnaB Yeah, I agree with you. It might even be stubborn defiance that drove me to undermine them more subtly and not give them any excuse--aside from my contrary (and obviously superior ) way of thinking. I think it was one of those deals where if I perceived any doubt on their part I was determined to prove that I understood their stupid little thoughts and could contain them. Maybe not totally emotionally healthy, but it kept me motivated.
@joelmw@simplersimon@AnnaB@jiltant I dont think one is easier than the other. I think math is more intuitive for some people and words/language come more naturally for others. We're all wired differently. Language is more of an artform, but there is incredible beauty and a lot of room for creativity in math, as well.
For the record (@joelmw!), math can be very fun and flexible. Especially when you get into higher level proofs. Structure often enhances creativity more than it supresses it. There are axioms and absolutes, but infinite ways to put those pieces together. It's like playing with legos. The pieces are what they are, but have limitless potential when you put them together. Well... it's like words.
This statement made me pretty happy, though: "My understanding is that the deeper you get into math the answer isn't necessarily the answer and there's more creative potential." I'm telling myself that I am at least partially responsible for that understanding.
The parallels you (again, @joelmw) draw between math and language are very accurate. The math most people know is essentially the equivalent of spelling and grammar. Creativity and expression build from that foundation. Words and mathematics can be used to describe the world around us and our experiences in it.
Math is "multilayered and multifaceted" comminication. It is a language. You just have to get beyond the "spelling" and "grammar" stages of that language to enjoy those aspects. Most people don't need to become fluent in mathematics, so they never pursue it that far.
I'm gonna forgo any objections just because I love what you said and how you said it even if I might slightly disagree with a few details. I might mostly agree anyway, but I can't tell, because I'm doing that proud dad thing.
You certainly deserve some credit. Though I had some of that feeling and desire for math before you came along. I just ended up being seduced by other forms of thought and expression. I've often wondered what might have been on both sides--if I'd have pursued math (which I almost did) or if you'd pursued English (which you've more than sufficiently demonstrated you easily could have; you're certainly a writer). Your mom and I of course shared the writing thing and we sometimes wondered why the math and not the words were your primary passion--but it wasn't long after that that you showed that you had it under control, despite some awful English teachers and not having done the journalism.
It was probably inevitable that I'd fall mostly into words. And there's always been something more precise and objective and organized (and I mean that as an unambiguous compliment--at least in this case), even if still extremely imaginative and admirably bizarre, about your way of looking at the world. I think I've always had a bit of a squishy world view (not that I'm ashamed of that) and a fondness for the fog and grey spaces.
@joelmw I think the decision to study math also had a lot to do with how much was out there for me to learn. I felt like I had the basic tools to explore language and literature and the power of words. But there was so much more for me to be introduced to when it came to math. And, without getting a lot of that exposure from my classes, I could not have gotten very far with it. Does that make sense? There are so many fundamentals and basics of mathematics that we don't even begin to explore in K-12. I had mathematical curiosity I didn't know how to pursue in any other way.
@christinewas Yeah, that makes sense. Yaknow, I guess as I think about it, I didn't really see Math that way when I was coming out of high school. I did think of Physics like that, and of course, I thought I'd find something in Philosophy.
And I'm still infatuated with Poetry.
I think that's the nature of love. It's something I started to realize in those last wonderful years with your mother. We speak in terms of commitment and sacrifice, but I think the way that love works is that we're committed and we continue to pursue because we don't lose that sense of fascination and wonder. For me, if ever my love wanes, that's where I find it, in the reawakening of the truth that that other is as yet mostly undiscovered. I think every human is that undiscovered country (and that's my rationale for monogamy--and I think it's biblical, fwiw). I also think that for many of us we find that passion in some or a few or many other forms of knowledge.
Was a biochem student, so they were okay with basic freaking algebra. Come on, I did that in fourth grade.
The calculus class I took in high school started to count for college credit two years later. Where did it fall short? There wasn't enough "math history." Teacher said he had to cut a third of actual math he taught to teach about the lives of Newton an Leibniz and a couple others.
When I retook calc in college, I was the only non-math major. Even the math ed majors didn't need it. Of the five of us, three had failed in previous years and were retaking, and the last was supposed to be some math prodigy. And I was the best in the class, both in high school and college. College had three of the classes scheduled for the final so we could party during the actual scheduled time. I finished halfway through the first day. The rest needed to use the scheduled final time and two still failed, one of whom was the prodigy.
In short, I went to school with sucky math majors and owned them. The math professor hated me for it. And yes, I did grab DiffCalc and a couple more, though they were at better schools with better students, so not as fun for the stories. Though I will admit, I haven't used anything higher than basic algebra since college, with a few recreational exceptions.
Highest math I've done is HS Algebra II, and that was a C class... something just never clicked for me...my brain still just locks up sometimes when presented with figures... now most of my friends were in all the advanced classes, one (who is now a Thoracic surgeon somewhere) could do, I wanna say Integral calculus?, in his head.
@lumpthar I took physics of music just for fun. For my final project a friend borrowed strain gages out of the gravity lab (they were looking for gravitational waves - I see that someone finally found them) and the three of us used them to measure overtones on bell tower bells (rather expensive over kill - luckily we didn't ruin those little buggers).
I got frustrated in physics lab. There was one stupid lab assignment with projectiles and mine were landing all over the place. So I figured out where they were supposed to land, took away all the carbon paper except under where they were suppose to land and shot off enough balls to get the requisite number landing in the right place. LOL. Nope you don't want me in a physics lab doing research for you. Of course the joke was on me later when I ran a science enrichment program for high school students at a linear beam accelerator facility. Physics of amusement park rides was part of the program as well - Bush Gardens has a canned program for that complete with instructions on how to make gravity measuring devises so you spend time on roller coasters measuring the force of gravity while upside down, going around corners, etc.
First semester in college they planned your schedule for you. Gave me Calculus and Finite Math that semester. I was always proficient in math but those classes absolutely fucking killed me. Sure fire way to turn a student off from college.
I was the math award winner at my high school. Took Calc as a freshman, Differential equations as a soph. Changed majors from engineering to accounting (thanks to physical chemistry) and took two high level stats courses. When I went back to school after 8 years in accounting to study computers, took linear algebra. Calc and differentials were a much higher level of math than linear. Stats was too easy compared to either of them. Never used any of them working with computers, formulas were second year algebra level.
I was really good at math in high school and took the highest that we had (we didn't have AP or calculus, just trig and pre-calc, back in the day, at least at my school). We had this actuaries' sponsored test that I used to kick ass on. And I saved my grade in Geometry (which had fallen because I just didn't do my homework, because I'm lazy and undisciplined like that) by setting the curve on the final; and yes, this fucked up other people's grades, which--I won't lie, I thought was a little funny, because I'm an asshole like that and it was an honors class and some of those kids were a little snooty.
When I went off to college, I didn't have to take any math. I wanted to, but couldn't fit it in and it just really didn't make any sense for my humanities-focused studies. In retrospect, I wish I'd taken some formal statwistics, just because, well, yaknow, it's a cool tool; I've picked up enough to be dangerous along the way. I do a fair degree of the maths at work (geospatial is a sort of geometry and we've got the budgets and shit like that, which I always get roped into). I kind of think it's important to understand how and why calculations that are done automatically work.
Alas, @christinewas was probably better than me at math by the time she was in the eighth grade (not because I'm stupid, but because she's that smart) and a couple of jobs ago, I had her help me with a formula to determine some kind of coordinate transposition or something or other; she did the math and I translated it into Excel. I remember trying to help her with her math once in junior high or high school and I got the answer, but took a super convoluted way to get to it. She lost patience with me and I think that was the last time she asked me for that kind of help, which she didn't really need anyway. I take winding paths; studying philosophy, theology and literature helped me perfect this gift.
I've forgotten most of the formulas and methods I learned in high school. Now it's mostly about Excel functions and Google searches and if I really get lost, I bug the kid. This is one of the reasons we have kids, right?
@joelmw Why we have kids? Hmm I thought it was hormones. And then later so we'd have someone to fight with about dishes and raking pine needles (that they then earn $3/ bag on craigslist for and then decide to rake half the neighborhood for free because orders were pouring in and in the end clear close to $300 - I paid for all those bags - but still hates me for making her rake our yard for pay plus selling the pine needles) and no you can't have an advance on next month's allowance the first day of this month; so we could wreck our evenings and nights because there was a mattress on the floor in the bedroom because brat child snuck out the window to party and got caught when she was trying to sneak back in like a giant cockroach... There are good reasons why some species eat their young you know (and yes I know DHS and the law both would take a dim view of a dinner of roasted kid - but it can be oh so tempting at times LOL).
@Kidsandliz Having raked my share of pine needles as a kid, I'm afraid I might be on the kid's side. But, yeah, I get you on the rest (even though we didn't have that particular struggle).
I think I got pretty lucky in the offspring department.
Oh, and hormones are definitely part of the equation too. Lotsa parts.
@joelmw My brother, a Yalie lawyer and an totally wonderful person, used to read his kids assignments and make suggesions if they wished, or were struggling.
So one day he's visiting his oldest, a UVA chem engineering major, they are out for pizza, father/son bonding. And kid asks dad to look over a paper he just finished. The topic of the paper was somewhere between chem eng and diff eq's.
Brother looked at paper, frowned, then laughed, and bought his son another beer. Admitted his days as a friendly critic were done.
Calculus, in High School. 1st period at 7:45am. I slept through the first two 6week periods. Then audited the rest of the course (already had my HS math credits, was taking it just for the AP credit.) Got a 2 on the AP exam, like the rest of the class. 8/10 - would sleep through and audit again.
Took Calc again at uni - but it was some weird almagamation of calculus, stats, and biology. The called it Calculus for the Life Sciences. The course was applied calculus following trends and creating projections in Mathlab and Maple for environments/ecosystems/genetic diversions. Neat course, remember very little of it. Except I hate Mathlab. Maple was OK. 6/10 for retention and disliking Mathlab.
Also took Stats 1 and 2, they were super easy. 9/10 with rice.
I haven't understood any of it since 5th grade. My husband was taking calculus as his elective when I met him! Still don't understand that. Endless choices of subjects and he picked math????? Weird.
Aerospace engineering major in college (Go Illini!). Got credit for my first 2 semesters of calculus via AP credit in HS; still had to take 3? 4? more advanced math classes for my degree. These turned out to mostly be a waste of time for my career, but supremely important for my roommate who went into computational fluid dynamics and eventually became a math researcher/professor.
I didn't take that many math courses, but I did end up taking Symbolic Logic and a low-level Discrete Mathematics course (more than the business students, less than the Comp Sci people). The logic class kind of sucked (although it is really just puzzle solving once you get far enough in), but the other course did leave an impression on me. One of the coolest parts was sets and cardinality- you learn the sort of mind-blowing fact that infinity isn't the same everywhere, that there are actually larger infinite sets than others, and you can prove this yourself with just the knowledge you learned from the course
BS in Mathematics with an emphasis in pure math. (Changed my major from EE when I realized I was in it for the math.)
I've taken the math classes mentioned here and then some. Topology was one of my more enjoyable/challenging classes that I didn't notice in the above comments. Another I didn't see up there, Complex Variables was... baffling in that they dedicated an entire course to the subject. But, I guess that's what you should expect when you choose pure math over applied math or statistics. The rest were mostly things like Abstract Algebra II or Partial Differential Equations (throw words or numbers onto other course names and study more things).
I could tell you almost nothing about all of those classes, but it comes back pretty quickly.
One of my favorite professors let me sit in on his graduate Knot Theory class (a topology thing), until I realized I was too busy. I'd love to really study Knot Theory someday.
I was recently looking at a master's program in Colorado and realized I had already taken most of the courses and that my classes had probably been much more rigorous. That was a little disheartening. (If I get healthier, realize money is cool, and decide to become an actuary, I might see how they would handle my situation.)
@christinewas If the program in Colorado is at a "name" school, dont worry about the course listings, those are the same, uni to uni, and the content at a good grad program is not undergrad content. Those profs will hand you the material, lecture a bit, make you prove you know it, and encourage you to take it as far as you can. So will your fellow students, if they're good.
The q is, if you are paying, what's the masters for? Those programs are profit-makers for the uni, if you're not rich and are shelling out, how will you make it pay for itself?
If you're rich and paying, is this how you wanna spend your time? If yes, go to the best program you can get into. The atmosphere is much richer when you are surrounded by people much more skilled than you may be, since they started earlier, and are more immersed.
If you have a grant, that can be great if you can be happy with that life and get the most out of it, and make it pay to better your life in the long run. If it doesnt better your life, you just spent a few years on a wonderful intellectual journey and now have to come back to earth. Can you afford those years? If so, it can be a treasure, esp at a really good school.
Btw, student get to spend far more time/energy "at play in the fields of the Lord", as opposed to drudgery or assigned stuff, and get way better faculty and student interaction, the better the school. Good grad program really matters.
@f00l I don't have a good reason to pursue an MS, so it is unlikely that I would (especially after all this time). Unless someone else really wanted to pay for it.
To be honest, I wasn't looking at a particularly great school. And I drew as many conclusions from the undergrad program and limited faculty as I did the graduate program. (I briefly looked at another Colorado school this morning and their math programs looked much more solid.
I think I was just... a little bit spoiled at my school. They had professors who were researching and publishing in fields that I found interesting. Which meant they offered learning opportunities that were appealing (like the Knot Theory course). The graduate program (where they started, before beginning to offer undergrad courses) actually seemed interesting. But I had decided, at that point, to take my life in a different direction. I didn't even bother with a senior thesis.
@christinewas Cool. You seem to have a lot going on, and a bunch of energy to go with. Few get to "follow their bliss" but you may. Hope so. And if you wind up doing something because it pays, suspect you will find a way to turn it into something more.
They keep trying to get me to comeback to do a Masters, but the masters courses are the same as my bs courses with an added paper and discussion period.Plus I only plan to work for another 5 years, so where's the payback. so Meh
@connorbush from what I've seen of the masters programs available near me (at least for math), the courses are actually less rigorous than my undergrad classes. My school had options, variety, and quality that actually made it look like an actual step forward. (The local BS requirements also looked like... well, total BS.)
@connorbush For whatever reason, this reminds me of the highest grade I ever achieved in any course, ever. I took a financial math course in college to meet a requirement, and the teacher was a brand new, terrified of failure adjunct. She let us take quizzes in groups, discuss and revise homework before turning it in, and gave out absurd amounts of extra credit (maybe all homework was extra credit? memory fuzzy), often potentially nearly 100% worth. My final grade in that class was 183%.
I never liked the way I was taught math, which largely made me think I didn't like math. Now that I can explore it on my own with no repercussions, I enjoy it pretty well. And, in school, I enjoyed it in my own way, which largely involved screwing with the relevant teacher but ultimately taught me more important things. Like using a slide rule on my standardized tests (in the late 90s or early 00s) — actually taught (and continues to teach) me a lot about the relationships among numbers, logs, etc. Or like somehow convincing the folks in charge to essentially let me pull an independent study on boolean algebra, which helped me far more than the regular old dull kind ever has.
I saw this thread yesterday, but yesterday was a huge FU day in my life, so put it off till now.
Once upon a time i wanted to be a professional mathematician, research job, PhD, the whole deal. I took it pretty far.
So i have a very nice show-off list on courses and seminars (dont have transcripts handy, just from memory and google, missing quite a bit....)
Differential Equations Multivariate Calculus Real Analysis Complex Analysis Linear Algebra Abstract Algebra Probability Topology Algebraic Topology Number Theory Fourier Series Differential Geometry Algebraic Geometry Combinatorial Mathematics Game Theory Hilbert Spaces Commutative Algebra Riemann Surfaces Lie Groups and Lie Algebras Logic and Foundations Galois Representations Functional Analysis Knot Theory Chaos Theory Stochastic Calculus Set Theory Mathematical Logic
None of this involved computers, slide rules, calculators, and after calculus and diff eq, no calculation. Pencil/paper, blackboard/chalk. This has changed: the increasing importance of statistics, big data, mathematical modeling, and computer modeling of symbolic language has transformed the field, i suspect you can no longer get thru any degree program without a lot of machine time.
I remember almost none of the content. The topics i found most fascinating were foundations, logic, topology, algebraic topology.
I thought i wanted to be a PhD mathematician, the way teenagers think they've found a calling when they are 17. And followed this thru college. Only i choose a grad school in Manhattan, and i think the movie and music schedules posted in The New Yorker and The Village Voice called out to me as much as the math. When this happens to a would-be mathematician, it's not usually a good sign, because you need to be pretty intense to get thru the coursework. The other bad thing, intellectually, that happens to a lot of grad students, is that you can get stuck, thru fascination, in a particular area, when your broad mathematical education is not yet sufficiently advanced, and you become so wrapped up in it that you can't be bothered to pay attention to the other material you have yet to master. Which means if you dont pull yourself out of it, you wont finish your degree.
I think most students who do well as math majors in a good undergrad school and do well in the first 2 years of a decent graduate program are perfectly capable of handling the material, doing the work to get PhDs. What gets in the way is burnout, undisciplined fascination, and the increasing importance of the rest of life.
The material is so abstract that you cant give a casual/informal description of what you are doing to anyone outside of other mathematicians, plus some physicists and engineers if the study area is applicable to those disciplines. And later on, when the work is more advanced, you cant even give a casual discription of your work to the mathematician in the next office without taking much time unless your areas of work have a lot of overlap. At the highest levels, even that becomes difficult, unless the other party has time to really absorb your work, as most math is done is done on such incredibly sprecialized topics.
My own perception of math is that calculus and 1st year diff eq are where the math experience starts to change, tho there are early glimpses of what mathematicians do along the way, particularly in high school geometry. But you are just a beginner, in high school and the first year of college. Those (calculus etc) are prep courses for how you will start to think differently as the years pass. I arrived at what i think of as the beginnings of the mathematical experience after diff eq, when i started real analysis and abstract algebra. Not that earlier courses, particularly trig, calc, geometry, set theory, diff eq arent real mathematics - they are, and diff eq in particular is notoriously difficult.
But after a my 1st and 2nd years in college, i looked back on the earlier-studied material with different eyes. Something about the endless practice of definitions, theorems, proofs, examples, counter-examples, was a bit like (in my imagination, anyway) being in an immersive experience in martial-arts - some sort of endless discipline until it's all second nature. (Have no martial arts, have a blown knee.) You start to swim in the water and then learn to breathe the way a fish does.
In spite of the logic, or because of it, it can at times feel a big magical, almost zen. You see (somewhat literally), with your mind. At least i did. Once the problems i dealt with passed beyond what could be resolved thru any form of computation, I would always try to go forward thru a very personal visual imagination - once i had the essential logical elements in my head, to create an symbolic-image-representation of the mathetical environs, and then create a visual symbolic transformation toward a solution, and then try to transform the vision back into mathematical symbolic language, and to see if i could then create a rigorous connection on paper. This failed far more often than it succeeded, but i would try again and again, till i had something.
Different mathematicians work in different ways, i have no idea how common my approach is, tho i have heard of other mathematicians speak of it. If i looked at a publication in a math journal, i would bet that the work was not done in the language that's in the page - it's done in an imaginative state akin to "logical daydreaming". Then you try to make it real and bring it home.
And i burned out, or got close to using up the broad spectrum of my msthematical curiosity. I suspect more than half of grad students, perhaps far more, do that. The work is so very intense and focused and takes such energy, and you get tired of not being able to talk about your work with anyone, you might have kids or other family members to deal with, debt, life, housing....you get curious about normal interests.
Or you live in Manhattan halfway between CBGB's and the Mudd Club, with reperatory cinema and Merce Cunningham and spicy noodles and the Blue Note and Carnegie Hall all around. And i had friends in film, music, dance, holography, journalists, who lived aboard the QE2, who were getting PhDs in something "sane" like economics, friends who were coding, and i didnt want to live and breath only math anymore. And someone with my state of mind at that time is prob a goner for grad school.
I coded for a few years in New York City, then due in part to a domestic situation, wanted out of the city. I've lost touch with almost all my math friends and city friends - didnt put enough time into keeping those connections over the decades. And aside from following own interests, have messed with almost no serious math and only miniscule coding since then. Because math is an enormous and complex structure, and if you dont see the structure, you cant interpret the pieces of it.
But some of the thinking habits stay. Matheticians fall in love with that world, and then most of them, when young adults, want to use their mathematical thinking to resolve problems of relationships, survival, income and prosperity, family, life choices. Particularly relationships. Hmmm. This doesnt go so well. They get over it, laugh at themselves, learn a bit more humility, courtesy, empathy. Most mathematicians are good at admitting when their own reasoning has limits. And they learn to make choices in something resembling the normal way.
Mathematics itself looks more perculiar and perhaps fascinating the more one lives in it. Esp the simple stuff such as logic and simple definitions>theorems>proofs starts to look more and more like an infinitely transforming beast the more one studies it. There's simply so much undiscovered stuff even in the areas that are well-studied (this is provable), let alone the areas where very little is known. And stuff keeps transforming into other stuff in the most unexpected ways. And there keeps being logical space and wiggle room where you thought there was none.
And you can try to applying strictly rigorous methods to real issues posed in normal human languages, which works (imo) poorly, but the results are interesting. And this can impinge into philosophy and other areas (which to my mind use different habits of thinking).
It changes how you think, for life. I dont know how to clarify it to a non-mathematician, but could, i suspect, talk with any mathematician about it. My sense of possible complexity changed completely. My sense of "the space between the words, the echos behind the sentences" changed, the more math i did. Like i became aware of how much possibility of meaning and fact were out there, and how one might tease a little of it out.
And now i'm way off the deep end and beyond earshot in the "incoherence sweepstakes", no doubt. Apologies.
I suspect this mental transformation occurs in the lives of many adults who have studied something using high intellectual energy and rigorous thinking - within other academic disciplines, or out in the real world: the combo of knowledge and practice and repetition and constant challenge changes the brain forever, in ways unforeseeable to those who havent worked that hard with their minds. To me it's a gift to have had the chance.
One math friend (who taught and published for decades in a long, excellent career) said something like this to me: "mathematicians get to see the things and visit the places that are part of why many people drop acid."
All the math prople i knew during those years had done drugs, that era, and tho my friend's point is a bit facile, every one of those math prople would have gotten the sense in which he meant it.
FWIW (me being silly), i think our species is just getting started with math, and during my years, i saw only the tiniest part of it.
@mfladd I thought i was the luckiest person ever, for a while....
;)
Byw i make that facial expression, lots of times, every day, over the simplest shit. Math people are not famous for great decision making and common sense. Given many individual exceptions, the lack of stellar rep is for a reason.
@f00l I'm only about half way through this comment, but I'm loving it so much that I just had to pause for a moment to say THIS IS AWESOME. I'm ridiculously tired today and having trouble with... sentences. So I might not end up saying a lot of the things I'm thinking after I read the rest. But... again... I love this.
@f00l I like the way you describe the earlier courses. In geometry, I thought I hated proofs. What I hated was spending so much time on such basic, simple proofs. All of those early classes were often mindnumbingly boring. But the disciplines you need to learn to think mathematically, to conceptualize, comprehend, and then articulate higher mathematics, become second nature through that kind of repetition.
I think the thing that frustrates me most about my love of math is my general inability to articulate the beauty I've seen in it to someone who has not studied math. I can say things about unexpected order or surprising connections. But that doesn't convey much. And then there are all of those beautiful things that I dont even know how to put into words for myself.
It's fun to watch a mathematician get excited about math. I still vividly remember the first time I saw one of my professors flip out over something he was teaching us. I was just a Freshman and it was my first class with that professor. Out of nowhere, he came to life. He left his (unreadable) scribbles on the board and became very animated as he gushed about how beautiful it was and drew connections to topics we wouldn't be covering in that class.
Regarding the process, I can definitely relate to the way you described it. I have found that some of the best descriptions of how I do math (not computations, but the really mathy stuff) have actually been books and articles written about the creative process. I would also say that a startling amount of my mathematical problem solving happened on a subconscious level. I would often be driving, showering, eating, or engaged in some other random task when I would suddenly connect the dots. It happened all the time when I wasn't consciously focusing on the proof or whatever it was that suddenly became clear to me.
I didn't exhaust my mathematical curiosity. I don't think I even came close. Which is probably why I occasionally find myself looking at graduate programs nearby or in places I'd like to live. But, by the time I graduated, there were other things that were just... higher priorities and more important to me. (That "increasing importance of the rest of life" thing you mentioned.) So I went in a different direction. But there were constant moments, in the first few years, that made me long for it. Things like hearing from an old college professor. Having a conversation about math. Those triggers don't happen as often as they used to, but they still happen.
Math definitely changed me. I love the way you described its impact on your understanding of... the true complexity of things and a broadening sense of possibility. So, so true.
It makes me sad to think of mathematics shifting more toward machine time, statistics, and computation. I think the heart of mathematics is on the more abstract end, though that certainly isn't the "math" most people think of. That's where progress happens and our understanding of the world expands. Advances in mathematics enable more accurate models and expanded applications. But you have to get abstract to get there.
Once again, I really enjoyed reading all of that. Thanks for taking the time to post!
@christinewas Since i'm not a practicing mathematician or math student now, i dont know exactly how the curriculum has change except for sometimes hearing a comment. I'm not sure machine time gets in the way of the stuff that's wildly beautiful and unexpected - it may increase the drudgery, or open doors.
All i did was strictly theorectical pure stuff, in part because i was fascinated by the aesthetics. And in part because that's what my liberal arts college taught. A differential equation may appear beautiful to its mother, but not to me. There is a certain joy in wrestling with them to get a little control. I have enormous respect for the researchers in that area.
But mathematical thinking, as practicing mathematicians experience it, syarts after diff eq. When you talk about the solution and discovery process as being intuitive, that's right on. Only easy delimmas can be solved or reaolves by computation. You gain knowledge suddenly, with fits and spurts and dry spells,
Every mathematician i've spoken with has described the work as being kinda "part drudgery, part the stuff that dreams are made of." An every mathematician i've known had read books on the creative process, and found a sort of mirror therein.
If you wanna keep messing with it....well if i were doing that, if my skills weren't recently honed, i'd do a buncha remedial stuff to get back in the swing. Then i'd try out Coursera, Edx, or similar. I'd try to pick something that doesn't entertwine itself too tightly with the rest of the theorectical structure, because less to keep up with and keep track of. Say number theory or probability, tho i'm decades out of date here, and perhaps wrong about these.
It could be a lot of fun.
I was (perhaps!!) fortunate in my undergrad work, done at a place w no grades, no requirements, didnt even have to take courses if you could come up with an alternative. My 1st term freshman classes contained perhaps 10-20 students. After that, they shrank to 5-10 students, then 2 -5, as we learned to work the system and did everything by custom tutorial. One of my fav profs has pets snakes and brought them to class for us to play with during brainstorming.
The best times were when 2-4 of us grabbed a classroom after hours and just worked all might, feeding ideas to each other. Or when we did the same in a prof's office. It was a very intense place, most students put in 60-80 hours a week, some more, but you were studying exactly what you had chosen to study.
It comes close to me perfect ideal environment.
The downsides: first, that this method unwittingly encouraged the idea of knowledge for self-actualization to the degree that some students faced nasty shocks in their later lives and careers, esp in political or manipulative circumstances, and in dealing with the practicalities of making a living.
Second, that the college no longer exists in the quite the same form. It was a wonderful experiment and it also had to faced the real world. So the school is now part of a state system, tho much is unchanged. It's perhaps not quite as impractical as when a student got 2 terms credit for walking from one ocean to the other, while journalling and making local community contacts. Or perhaps it is. I'm not up on that, my 2 fav profs are no longer living.
Sometimes i wish i'd gone to a normal place, with grades and requirements. Perhaps i would have achieved more, instead of living an eclectic and often foolish life.
And since regret does not re-order the past into a better config, and since i cherish what i was given, i put that away. And apart from family/friends/pets, math had my best, and gave me its best, for many years. I do feel lucky. Like there's this treasure, and most people dont know its there, or get to see it. And i did, i got to live and play and dream there, and thats a gift.
I'm going to reply in this thread, despite only tangentially responding to it, as I suspect only @christinewas, @f00l, and possibly @joelmw will take much of an interest. Or, maybe not, but now I tagged all of you and you're stuck reading this.
Your comment on the inability to articulate the beauty of math resonated with me on several levels, cw. I am the sort of hopeless artistic romantic who constantly finds that struggle in the things that I love. I don't necessarily have that struggle with math, because it's not as important to me, but I definitely understand it.
To me, the beauty or the romance in math is that of a puzzle. You have one outcome, a ton of pieces, and a journey. If someone doesn't understand the magic of math, just tell them it's all a bigger version of Sudoku. A much, much bigger version of sudoku. Or a crossword, but in base 10 (maybe, probably) instead of base 26.
I started programming computers (and calculators - my formative years were on the Commodore 64 and the HP 41C) basically as soon as I could read and understand how to poke buttons. I gave up making a career of this later in life because there's a very clear divide between those who know and are good at syntax, and those who are clever and good at math. The algorithm queens. These sorts of people. And I couldn't hack that. I can knock out an NYT Monday crossword in about 5 minutes, but if it were my job I'd be fighting it all week.
So, to me, numbers are largely a diversion. One of my favorite diversions is Viète's formula. And, assuming I can key it in correctly on whatever calculator happens to be nearest me, it's a great answer to 'why are there calculators everywhere and you paid how much for them!?' It's… beautiful. It's a bunch of 2s, it's (ultimately) a bunch of polygons, and then magically it's pi. Seriously, anyone who is reading this on a Mac or Linux box, go to your terminal and type in dc -e "12k25si2ddvdsz2/[lz2+vdsz2/*lid1-si2<v]svlvx/p" and watch something resembling pi show up (dc has no guard digits, so the operating precision and shown precision are the same — error in the last few digits is a given). It's dumb, but it's fun.
I don't really know what the point of this ramble is. I know that it's easy to look at these ten characters and only be reminded that our taxes are due in like a week and holy crap that's not a lot of time. To a lot of folks, numbers come into play for… nasty nuisance reasons, mostly. But sometimes, even if you can't convince someone they need an HP 42S in their life, showing them how one number becomes another truly is like a magic trick. I guess that, to me, is the beauty.
@brhfl@f00l@christinewas What I like about this is that ultimately we're talking about passion and beauty and art and the human creative impulse. I completely agree that Math can be the focus and the venue and the muse and goal for human imagination. What pleases me is that the playground of the imagination isn't bound as we conventionally believe it to be--in its domain any more than, well, any other way.
And aside from loving others (not that I in fact consider it distinct from what I'm about to say, as I've implied in a comment above), I'm not sure I think there's anything more fundamentally human and sublime than the joy of discovery and creation that y'all are talking about.
@WTFhqwhgads There are 10 types of people in this world, those who understand base 3, those who don't, and those who realize this joke actually falls horribly flat beyond binary.
I managed the girls softball team in high school, which my algebra instructor coached - or I'd have been royally fucked.
One time I remember she called on me and asked me to solve for "x" in an equation - three times. Finally, in desperation, when she was begging me to answer "What's X???", I told her "x" was a fucking letter, and not a number.
Got to visit my favorite vice-principal over that one . . .
I'm an engineering student, so I've done all the calculus and then some differential equation solving, now I'm working on statistics, which is easier.
@DonberKon An engineering student? Ok, I'm going to be the person I always wanted to hate. When I was doing my Marine Engineering undergrad, we didn't have them fancy calculator things. We had slide rules and we liked it! I'm not sure if schools now continue on to Advanced Math for Engineers but that comes after Differential Equations, 2 semesters. Just some advice from someone that has gone through it, go on to an MBA after you finish. You won't believe how easy it is. I did my doctorate in Information Systems and other than the writing, engineering is much harder. Good luck with your education. Question, what school are you studying at and what do you want to do? Curious and best wishes.
@bsci87 I go to Iowa State. They don't require any "hard math" after DE, and they even let us use a program that solves diff eq's for you. I'm not sure what I want to do yet. Second year Mechanical major. I think I want to be involved in testing, verification; you know, the exciting stuff. Also, I'm a gearhead, so automotive interests me.
@DonberKon No hard math after DE? And they let you use computers for that? Yikes! I think I hate you now. Well that or I'm just an idiot for putting myself through that. Iowa State is a good school but once you finish don't take a break. Take one class toward your masters. That one class gives you another line for your resume. Your a candidate for a masters degree and that could make a difference. Take your break after that. Always remember, engineering is the hardest undergraduate program there is and if you can make it through there, you can make it through anything. I work with ships now at a major port and there are always things to do that you have to think on your feet and figure out. When I first got out of school I was working with submarines. Very cool work and people turned to me and asked what do we do next. I was like, why are you asking me, I'm just some punk kid but someone had to figure it out because it wasn't going away. If you look you'll find a job that fits you and makes you feel like you didn't work so hard for nothing. If any business majors ever give you any grief just know they couldn't have made it through your first engineering class. It really is that special. Keep my handle if you ever want to talk further. Keep your head down and push to the finish. Best Wishes.
@DonberKon My f'ing undergrad school made us learn how to program a computer to solve calculus programs while taking calculus. OMG. First I was taking calculus without having taken trig second of all I was having enough trouble with calculus let alone learning how to program on top of that to solve stupid problems. Fortunately my roommate was dating a junior engineering student. Then a zillion years later I had to relearn calculus enough to solve stupid, idiotic, there is no earthly reason why I need to know how to do this econ proofs in a doctoral seminar those of us in a different business field were being tortured with.
@DonberKon Weird. it truncated what I was saying and said "forbidden" when I hit send for the first time... here is the rest of the message (back button picked it up).
You are right. Stats is way easier (I did take an engineering class at one point, for reasons I no longer remember, except that the class sounded interesting). Stats is way easier than Calculus too. You only need basic high school algebra to solve those problems. Unless of course you are forced to learn matrix algebra while doing third semester (PhD program) stats. Matrix algebra is a pain in the ass when you are having to learn how to do that before you can figure out the homework problems. This is why they invented SAS (or SPSS or r or whatever your favorite stats program is).
I discovered with one program you could get it to print the maxtrix algebra solution to something you just ran using a menu (can't remember which program it was - we had to learn 5 of them, one using unix, the rest PC, one of which is pretty much DOA at this point). Made my life easier. And then I found the 1975 textbook my prof was using to teach from in the obsolete stacks of the library (eg the "old" stacks vs the ones that had books much newer - in desperation I was looking for a book that taught this crap in matrix algebra since our book used vectors). Bingo. Turned everything into a piece of cake. Just followed along. Found all the homework problems there, the exam problems in there. Got the highest grade in the class of around 80, including those getting a PhD in stats, because of that little book. They wanted to know if was going to change my major and get my PhD in stats. Were they out of their freaking mind? I was so glad to be done done done with all that crap. Of course the joke is on me. I got stuck teaching stats to undergrads who were allergic to math and turned their brains off even before they started to think about it. LOL
@DonberKon You go to Iowa State?! Holy Shit another Iowan...i didnt know anymore really existed. I figured that everyone buying from Iowa was some sort of a glitch.
@bsci87 Thank you. I really appreciate your kind and encouraging words.
@bsci87
Hard undergrad programs...agree engineering hardest, but would throw in physics & math majors as well.
I decided to go back to school recently, and while I am earning A's in nearly every subject, math has been killing me. I earned my first D ever in math last semester, and I am currently re-taking the class. I have a big test on Saturday and I am convinced I will fail. This class is the only thing keeping me from completing two degrees.
@conandlibrarian You need a study buddy!
@PocketBrain Very true. Math is such a sensitive topic for me, I should of graduated last semester, but you must earn a C or better in Math in order for it to count towards graduation. English and Math are the only subjects that require that.
@conandlibrarian To the people who are having a tough time with math and need to pass. I taught adjunct for almost 20 years while running my company and doing a doctorate. Not bragging at all, that was my stupidity and what I chose to do. My advice is to break down the math you're doing to smaller pieces that you can relate to. If you take it in larger chunks, you'll never get through it. Baby steps and relate it to the real world and what you do everyday. There isn't anything that's hard about it and trust me, you can pass it. You just need just turn it around and have it make sense to you. Once you do that, you'll pass it with no problem. It is easier than you are making it. Best wishes.
@conandlibrarian Hey, if I can offer some advice: try reaching out not only to fellow students, but to the teachers. If there are open office hours go to them, there's a good chance you won't be alone and it'll be a group study session semi- or fully-directed by a prof and/or TA. You may make some friends that can help you study there, too. If there aren't regular open sessions like that, ask your prof for an appointment for extra help and come armed with questions. See if they'll meet with you regularly throughout the quarter/semester to help - if they don't offer first, ask. Don't be afraid - most profs (in my experience) are more than willing to help people who put forth the effort to at least show that they're trying, and for the ones that aren't, hell, it's probably part of their contract to fake it.
Between doing those things and studying my tail off like never before, that's how I survived both organic chem and biochem. You can do it, don't give up!
@conandlibrarian Go to the undergrad math lab for tutoring. They saved my ass in a PhD econ seminar. And others are right. Having a homework study group, going to see the prof... all help.
@jiltant I actually am in communication weekly with the instructor. While nice, she is not that helpful. I typically cannot get the answers to the questions I need, and just leave confused.
I got a minor in math with my B.S.E.E.T. Went all the way through differential calc, multi variable calc, linear algebra, the whole shebang. Don't remember much of it now though.
In university I got to, and was then ungraciously defeated by, the evil Calculon.
@curtise
@jqubed dramatic pause...
BSEE so trig, calc, diff, partial d.e., linear, statistics and NEW MATH!
@PocketBrain B.E.M.E. That's 152 credits minimum to graduate but I was stupid and did 172 with only 3 or 4, 4 credit classes. Lots of math, science and engineering but if you can survive that course load, you can survive anything.
I ran out of AP calculus classes to take in high school.
(Don't remember any of it nowadays, though!)
In college I took Math 102, which covered things like voting systems, fair division (such as with inheritances), and Euler circuits. It was actually really interesting, and tests were open note so it was really easy, too!
@jqubed When I taught that class, I called it "Math for people who think they don't need math". The university called it "Quantative reasoning". I loved teaching it.
I sucked at Math in High School. I took an independent study class in college for Intermediate Algebra ( work at your own pace showing up for tests and lab only) and got a B. Then I took College Algebra in a typical classroom with students. Got another B. It was as if the mathematics in college had meaning and inspired me to improve.
I'd love to go back to school, get my AA (most of what's left are science classes), and move towards a better job than the retail occupation I've had for the past 11 years.
@JT954 Never too late to go back. I went back at 37, and finished my A.A. stuff in about 18 months. I took about 15 units a semester, including summer. It was so worth it.
@conandlibrarian Good for you! I didn't graduate from community college until I was 27, then a couple of bachelor degrees when I was 30. Time passed, waiting tables, bartending, small business ownership...
And now, back in school at 42 working on my Master's to teach bio to high schoolers. It's truly never too late. I anticipate I'll go back to school in another 15 or 20 years for something new.
Oops...How for can I edit poll choice?
I guess I did take college algebra, but it was a summer course and my cousin was the teacher, so... I got a B+.
hoo boy
Got a C in Calc I and a D- in Calc II. Switched majors to Criminal Justice.
i was always pretty good at math, but was much gooder at english.
@carl669 snort.
As a CSCI student, I went through Calc early (Calc 1 in high school,) and then did Statistics, Discrete Math and Numeric Analysis. I should have taken Linear Algebra and Differential Equations so I could play around more in the Computer Graphics space, but never did. I might buy some books for those at some point and just learn it on my own.
I was an engineering major for a while, so lots of math. Then I quit and became a chef. So more practical, everyday math involved in that. I also taught Applied Math at Le Cordon Bleu for some years.
Upper level statistics. It was that or calculus, and statistics were a better choice for biodemographic research. And it wasn't calculus, so there's that.
I started junior college in "you still count on your fingers" remedial math as a high school dropout, and I worked my way up through calculus and later upper division stats at a 4-year. I got a BS in sciencey stuff and regret nothing.. but my secret love was probably really English classes, where I could just read and write stuff all day. Words are easier than math.
@jiltant I heartily disagree. With math, even when the teacher hated me, I could still pass, because the answers are definite, absolute. When I made the mistake of upsetting a fascist English teacher, I found my grades started to dip. Even outside of classrooms, words can be problematic due to how people take things differently and how much is based on personal taste. Math is constant. I can know the right answer to a math problem. With words, best I can do is know an answer that is right enough for now, with this person. Unless you me grammar and punctuation. Then we just open doors for grammar nazis, who would likely have plenty to say about my mess here.
@simplersimon Haha, yeah, admittedly English profs can be real SOBs. Their grading systems are often horrifically subjective, their mysterious rubriks obeying no known Earthly laws. Most of the ones I met seemed to be frustrated by receiving endless students that were nearly functionally illiterate, and there's no way that they could imagine reversing the (in their eyes) bad habits ingrained by years of prior bad teaching. So they all kind of had this grim despair with a touch of a brutal streak, and a thousand yard stare.
But, that being said, I always had fun learning what the profs expected and trying to duck around it as much as I could and entertain the reader. In a lit. analysis class, I once wrote a Marxist-style analysis of a play, turning it into a hilariously wrong but internally consistent diatribe about class warfare, and enjoyed a pretty good grade as a result. Other times I'd argue specifically against myself in pieces, trying to justify crap I don't really believe in. I'd "psychoanalyse" famous characters and tie some supposed neurosis back to the author's own (completely made up by me) complexes. Stuff like that. I had a lot of fun with it.
Math was also fun and interesting in a different way, but I didn't often get the full swing of the creative momentum with numbers as I did with letters. Other people can do that, and that's awesome too. :)
@simplersimon I completely agree. I LOVE that the answer is the answer with Math.
@simplersimon @AnnaB @jiltant I wouldn't say that words are easier, just that they're more fun and flexible. They're probably easier chiefly in the sense that they're easier to be creative with. My understanding is that the deeper you get into math the answer isn't necessarily the answer and there's more creative potential. What gets me about this is that kids even just a few years old start to get this and enjoy it.
I always liked that algebra and grammar (in particular sentence structure and conjugations and such) are so similar. Both math and language are symbolic systems.
What's especially fascinating about language is that it's multilayered and multifaceted; even in ordinary conversation (let alone poetry) you have several strands of meaning superimposed and in fact interacting with each other. Even just the visual and auditory elements and the denotative and connotative senses can create enough tension to make the whole fucking thing explode. Seriously, that shit's crazy. And I mean awesome. Also, perspective (background, culture, etc.) is so much more a factor.
Good word play is a little like sex.
@simplersimon @AnnaB @jiltant My kid had some bad English teachers. I don't think I had any that I wasn't able to get a good grade out of or earn the respect of. And when you learn an English instructor's expectations and how to play with them, you're learning not just the material per se, you're learning a person. That "the answer is the answer" is fine, but that "an answer is their answer" is arguably more meaningful. Both are necessary in any case.
@joelmw My college freshman english teacher fell for all sorts of "creative" BS. We had to read Labyrinths and I wrote my paper in a spiral. Not much content and would have been a pain in the ass to read (was a pain in the ass to write it out that way -but less of a pain in the ass than if I had created more content for the book or whatever it was, that I hated) - he was duped and gave me an A on that. Since he fell for the creativity distractor I played that to the hilt. Made that class way less work.
@joelmw Don't get me wrong - I adore the beauty of a well written thought. What I don't like is a teacher telling me what words are supposed to mean to me. Part of what I love about reading is that an author's words can hold different truths for different people, not unlike a painting or a piece of music. I just really dislike having to determine what those words mean to my instructor and then parroting their truth back to them. This makes the whole experience lose its joy for me.
@Kidsandliz Alas, I was usually creating more work for myself. Sigh. I wanted everything I did to be original and undeniably substantive. I didn't learn until later in life to just do what I needed to do and/or game the system.
Actually, to clarify what I said before, I think I was always demonstrably capable of doing the kind of work that each of my instructors wanted, but sometimes on big assignments I would over-complicate things or set the standards too high or procrastinate to the point that I ended up screwing myself over.
@AnnaB I was much more of a sycophant and general people-pleaser as a kid. But in my defense, I often, OFTEN, (maybe usually) took a position contrary either to my instructor or to the established orthodoxy or both, just because that's how I am. The trick--and it is a trick--is to frame that contrariness in such a way as to still meet the requirements and earn the respect.
It's funny, because at this point in my life, I really don't give much of a fuck about fitting into other people's world views. I mean, I do it sometimes and think I still can, but it's too much effort to conform to the Procrustes' Bed of someone else's expectations and limited imagination, because usually it will involve the chopping off of a good bit of both my legs and skull.
I do still have a tendency to please English prof types and other freaks. Except the ones that absolutely demand brevity above all. Again, sometimes, maybe. But fuck those guys.
Of course at work I try to make a point of pleasing my bosses with both written and graphic documents. I do have a tendency to go long with the written, but I eventually bring it down--all by my lonesome if needed. I have a great system worked out with my immediate supervisor, because she usually wants me to start by rambling and including everything; then she decides what she wants to highlight and I (or--her call--we) work on honing it. It feels like she understands my process and the value of beginning with a more comprehensive view and just kind of get it all spread out.
I see the need to communicate and the sometimes necessity and/or value of brevity, but I contend that a big part of our problem as a society is that we over-value brevity.
@AnnaB The other thing I'd say is that I definitely want to understand and, if possible, contain where the other person is coming from. I just inevitably want to add to it.
@joelmw Agreed. I do want to understand the other person's viewpoint. That expands everything - the meaning of the words, my mind, etc. I just really loathed, particularly in Lit classes, being told THE way I was supposed to be thinking about a particular topic. Especially since I am/was often not.
@AnnaB Yeah, I agree with you. It might even be stubborn defiance that drove me to undermine them more subtly and not give them any excuse--aside from my contrary (and obviously superior
) way of thinking. I think it was one of those deals where if I perceived any doubt on their part I was determined to prove that I understood their stupid little thoughts and could contain them. 
Maybe not totally emotionally healthy, but it kept me motivated.
@joelmw @simplersimon @AnnaB @jiltant I dont think one is easier than the other. I think math is more intuitive for some people and words/language come more naturally for others. We're all wired differently. Language is more of an artform, but there is incredible beauty and a lot of room for creativity in math, as well.
For the record (@joelmw!), math can be very fun and flexible. Especially when you get into higher level proofs. Structure often enhances creativity more than it supresses it. There are axioms and absolutes, but infinite ways to put those pieces together. It's like playing with legos. The pieces are what they are, but have limitless potential when you put them together. Well... it's like words.
This statement made me pretty happy, though: "My understanding is that the deeper you get into math the answer isn't necessarily the answer and there's more creative potential." I'm telling myself that I am at least partially responsible for that understanding.
The parallels you (again, @joelmw) draw between math and language are very accurate. The math most people know is essentially the equivalent of spelling and grammar. Creativity and expression build from that foundation. Words and mathematics can be used to describe the world around us and our experiences in it.
Math is "multilayered and multifaceted" comminication. It is a language. You just have to get beyond the "spelling" and "grammar" stages of that language to enjoy those aspects. Most people don't need to become fluent in mathematics, so they never pursue it that far.
@christinewas
I'm gonna forgo any objections just because I love what you said and how you said it even if I might slightly disagree with a few details. I might mostly agree anyway, but I can't tell, because I'm doing that proud dad thing.
You certainly deserve some credit. Though I had some of that feeling and desire for math before you came along. I just ended up being seduced by other forms of thought and expression. I've often wondered what might have been on both sides--if I'd have pursued math (which I almost did) or if you'd pursued English (which you've more than sufficiently demonstrated you easily could have; you're certainly a writer). Your mom and I of course shared the writing thing and we sometimes wondered why the math and not the words were your primary passion--but it wasn't long after that that you showed that you had it under control, despite some awful English teachers and not having done the journalism.
It was probably inevitable that I'd fall mostly into words. And there's always been something more precise and objective and organized (and I mean that as an unambiguous compliment--at least in this case), even if still extremely imaginative and admirably bizarre, about your way of looking at the world. I think I've always had a bit of a squishy world view (not that I'm ashamed of that) and a fondness for the fog and grey spaces.
@christinewas Actually, I think where I might have missed my calling was not in Math, but the Law. Sigh.
@joelmw I think the decision to study math also had a lot to do with how much was out there for me to learn. I felt like I had the basic tools to explore language and literature and the power of words. But there was so much more for me to be introduced to when it came to math. And, without getting a lot of that exposure from my classes, I could not have gotten very far with it. Does that make sense? There are so many fundamentals and basics of mathematics that we don't even begin to explore in K-12. I had mathematical curiosity I didn't know how to pursue in any other way.
@christinewas Yeah, that makes sense. Yaknow, I guess as I think about it, I didn't really see Math that way when I was coming out of high school. I did think of Physics like that, and of course, I thought I'd find something in Philosophy.
And I'm still infatuated with Poetry.
I think that's the nature of love. It's something I started to realize in those last wonderful years with your mother. We speak in terms of commitment and sacrifice, but I think the way that love works is that we're committed and we continue to pursue because we don't lose that sense of fascination and wonder. For me, if ever my love wanes, that's where I find it, in the reawakening of the truth that that other is as yet mostly undiscovered. I think every human is that undiscovered country (and that's my rationale for monogamy--and I think it's biblical, fwiw). I also think that for many of us we find that passion in some or a few or many other forms of knowledge.
If that makes sense.
Was a biochem student, so they were okay with basic freaking algebra. Come on, I did that in fourth grade.
The calculus class I took in high school started to count for college credit two years later. Where did it fall short? There wasn't enough "math history." Teacher said he had to cut a third of actual math he taught to teach about the lives of Newton an Leibniz and a couple others.
When I retook calc in college, I was the only non-math major. Even the math ed majors didn't need it. Of the five of us, three had failed in previous years and were retaking, and the last was supposed to be some math prodigy. And I was the best in the class, both in high school and college. College had three of the classes scheduled for the final so we could party during the actual scheduled time. I finished halfway through the first day. The rest needed to use the scheduled final time and two still failed, one of whom was the prodigy.
In short, I went to school with sucky math majors and owned them. The math professor hated me for it. And yes, I did grab DiffCalc and a couple more, though they were at better schools with better students, so not as fun for the stories. Though I will admit, I haven't used anything higher than basic algebra since college, with a few recreational exceptions.
Highest math I've done is HS Algebra II, and that was a C class... something just never clicked for me...my brain still just locks up sometimes when presented with figures...
now most of my friends were in all the advanced classes, one (who is now a Thoracic surgeon somewhere) could do, I wanna say Integral calculus?, in his head.
Not sure which was higher: Linear Algebra or Differential Equations or Statistics. I took all three.
Also Thermodynamics, Fluid dynamics, and Heat Transfer.
I took Laser Physics just for fun.
@lumpthar I took physics of music just for fun. For my final project a friend borrowed strain gages out of the gravity lab (they were looking for gravitational waves - I see that someone finally found them) and the three of us used them to measure overtones on bell tower bells (rather expensive over kill - luckily we didn't ruin those little buggers).
I got frustrated in physics lab. There was one stupid lab assignment with projectiles and mine were landing all over the place. So I figured out where they were supposed to land, took away all the carbon paper except under where they were suppose to land and shot off enough balls to get the requisite number landing in the right place. LOL. Nope you don't want me in a physics lab doing research for you. Of course the joke was on me later when I ran a science enrichment program for high school students at a linear beam accelerator facility. Physics of amusement park rides was part of the program as well - Bush Gardens has a canned program for that complete with instructions on how to make gravity measuring devises so you spend time on roller coasters measuring the force of gravity while upside down, going around corners, etc.
First semester in college they planned your schedule for you. Gave me Calculus and Finite Math that semester. I was always proficient in math but those classes absolutely fucking killed me. Sure fire way to turn a student off from college.
I took math long enough to know your "buy more to give meh less profit" is flawed.
@MrMark So you say.
I was the math award winner at my high school. Took Calc as a freshman, Differential equations as a soph. Changed majors from engineering to accounting (thanks to physical chemistry) and took two high level stats courses. When I went back to school after 8 years in accounting to study computers, took linear algebra. Calc and differentials were a much higher level of math than linear. Stats was too easy compared to either of them. Never used any of them working with computers, formulas were second year algebra level.
Math is fun.
I was really good at math in high school and took the highest that we had (we didn't have AP or calculus, just trig and pre-calc, back in the day, at least at my school). We had this actuaries' sponsored test that I used to kick ass on. And I saved my grade in Geometry (which had fallen because I just didn't do my homework, because I'm lazy and undisciplined like that) by setting the curve on the final; and yes, this fucked up other people's grades, which--I won't lie, I thought was a little funny, because I'm an asshole like that and it was an honors class and some of those kids were a little snooty.
When I went off to college, I didn't have to take any math. I wanted to, but couldn't fit it in and it just really didn't make any sense for my humanities-focused studies. In retrospect, I wish I'd taken some formal statwistics, just because, well, yaknow, it's a cool tool; I've picked up enough to be dangerous along the way. I do a fair degree of the maths at work (geospatial is a sort of geometry and we've got the budgets and shit like that, which I always get roped into). I kind of think it's important to understand how and why calculations that are done automatically work.
Alas, @christinewas was probably better than me at math by the time she was in the eighth grade (not because I'm stupid, but because she's that smart) and a couple of jobs ago, I had her help me with a formula to determine some kind of coordinate transposition or something or other; she did the math and I translated it into Excel. I remember trying to help her with her math once in junior high or high school and I got the answer, but took a super convoluted way to get to it. She lost patience with me and I think that was the last time she asked me for that kind of help, which she didn't really need anyway. I take winding paths; studying philosophy, theology and literature helped me perfect this gift.
I've forgotten most of the formulas and methods I learned in high school. Now it's mostly about Excel functions and Google searches and if I really get lost, I bug the kid. This is one of the reasons we have kids, right?
@joelmw Why we have kids? Hmm I thought it was hormones. And then later so we'd have someone to fight with about dishes and raking pine needles (that they then earn $3/ bag on craigslist for and then decide to rake half the neighborhood for free because orders were pouring in and in the end clear close to $300 - I paid for all those bags - but still hates me for making her rake our yard for pay plus selling the pine needles) and no you can't have an advance on next month's allowance the first day of this month; so we could wreck our evenings and nights because there was a mattress on the floor in the bedroom because brat child snuck out the window to party and got caught when she was trying to sneak back in like a giant cockroach... There are good reasons why some species eat their young you know (and yes I know DHS and the law both would take a dim view of a dinner of roasted kid - but it can be oh so tempting at times LOL).
@Kidsandliz We're almost to that point at our house. The boy gets to learn how to cut the grass this year.
@Kidsandliz Having raked my share of pine needles as a kid, I'm afraid I might be on the kid's side.
But, yeah, I get you on the rest (even though we didn't have that particular struggle).
I think I got pretty lucky in the offspring department.
Oh, and hormones are definitely part of the equation too. Lotsa parts.
@joelmw
My brother, a Yalie lawyer and an totally wonderful person, used to read his kids assignments and make suggesions if they wished, or were struggling.
So one day he's visiting his oldest, a UVA chem engineering major, they are out for pizza, father/son bonding. And kid asks dad to look over a paper he just finished. The topic of the paper was somewhere between chem eng and diff eq's.
Brother looked at paper, frowned, then laughed, and bought his son another beer. Admitted his days as a friendly critic were done.
Calculus, in High School. 1st period at 7:45am. I slept through the first two 6week periods. Then audited the rest of the course (already had my HS math credits, was taking it just for the AP credit.) Got a 2 on the AP exam, like the rest of the class.
8/10 - would sleep through and audit again.
Took Calc again at uni - but it was some weird almagamation of calculus, stats, and biology. The called it Calculus for the Life Sciences. The course was applied calculus following trends and creating projections in Mathlab and Maple for environments/ecosystems/genetic diversions. Neat course, remember very little of it. Except I hate Mathlab. Maple was OK.
6/10 for retention and disliking Mathlab.
Also took Stats 1 and 2, they were super easy.
9/10 with rice.
@cj0e mathlab or matlab?
@no1 ah shit. Matlab. That piece o poo. Hated it.
I took trig. Never understood it.
Math and I parted back in grade school.
I haven't understood any of it since 5th grade.
My husband was taking calculus as his elective when I met him! Still don't understand that. Endless choices of subjects and he picked math????? Weird.
Aerospace engineering major in college (Go Illini!). Got credit for my first 2 semesters of calculus via AP credit in HS; still had to take 3? 4? more advanced math classes for my degree. These turned out to mostly be a waste of time for my career, but supremely important for my roommate who went into computational fluid dynamics and eventually became a math researcher/professor.
I didn't take that many math courses, but I did end up taking Symbolic Logic and a low-level Discrete Mathematics course (more than the business students, less than the Comp Sci people).
The logic class kind of sucked (although it is really just puzzle solving once you get far enough in), but the other course did leave an impression on me.
One of the coolest parts was sets and cardinality- you learn the sort of mind-blowing fact that infinity isn't the same everywhere, that there are actually larger infinite sets than others, and you can prove this yourself with just the knowledge you learned from the course
Oooh! Oooh! Do I "win"?
BS in Mathematics with an emphasis in pure math. (Changed my major from EE when I realized I was in it for the math.)
I've taken the math classes mentioned here and then some. Topology was one of my more enjoyable/challenging classes that I didn't notice in the above comments. Another I didn't see up there, Complex Variables was... baffling in that they dedicated an entire course to the subject. But, I guess that's what you should expect when you choose pure math over applied math or statistics. The rest were mostly things like Abstract Algebra II or Partial Differential Equations (throw words or numbers onto other course names and study more things).
I could tell you almost nothing about all of those classes, but it comes back pretty quickly.
One of my favorite professors let me sit in on his graduate Knot Theory class (a topology thing), until I realized I was too busy. I'd love to really study Knot Theory someday.
I was recently looking at a master's program in Colorado and realized I had already taken most of the courses and that my classes had probably been much more rigorous. That was a little disheartening. (If I get healthier, realize money is cool, and decide to become an actuary, I might see how they would handle my situation.)
@christinewas
If the program in Colorado is at a "name" school, dont worry about the course listings, those are the same, uni to uni, and the content at a good grad program is not undergrad content. Those profs will hand you the material, lecture a bit, make you prove you know it, and encourage you to take it as far as you can. So will your fellow students, if they're good.
The q is, if you are paying, what's the masters for? Those programs are profit-makers for the uni, if you're not rich and are shelling out, how will you make it pay for itself?
If you're rich and paying, is this how you wanna spend your time? If yes, go to the best program you can get into. The atmosphere is much richer when you are surrounded by people much more skilled than you may be, since they started earlier, and are more immersed.
If you have a grant, that can be great if you can be happy with that life and get the most out of it, and make it pay to better your life in the long run. If it doesnt better your life, you just spent a few years on a wonderful intellectual journey and now have to come back to earth. Can you afford those years? If so, it can be a treasure, esp at a really good school.
Btw, student get to spend far more time/energy "at play in the fields of the Lord", as opposed to drudgery or assigned stuff, and get way better faculty and student interaction, the better the school. Good grad program really matters.
So does $ :(
@f00l I don't have a good reason to pursue an MS, so it is unlikely that I would (especially after all this time). Unless someone else really wanted to pay for it.
To be honest, I wasn't looking at a particularly great school. And I drew as many conclusions from the undergrad program and limited faculty as I did the graduate program. (I briefly looked at another Colorado school this morning and their math programs looked much more solid.
I think I was just... a little bit spoiled at my school. They had professors who were researching and publishing in fields that I found interesting. Which meant they offered learning opportunities that were appealing (like the Knot Theory course). The graduate program (where they started, before beginning to offer undergrad courses) actually seemed interesting. But I had decided, at that point, to take my life in a different direction. I didn't even bother with a senior thesis.
@christinewas
Cool. You seem to have a lot going on, and a bunch of energy to go with. Few get to "follow their bliss" but you may. Hope so. And if you wind up doing something because it pays, suspect you will find a way to turn it into something more.
They keep trying to get me to comeback to do a Masters, but the masters courses are the same as my bs courses with an added paper and discussion period.Plus I only plan to work for another 5 years, so where's the payback. so Meh
@cranky1950 I just started a masters.... it is complete farce. Same material, higher price, waste of time thus far. I am only one class in
@connorbush from what I've seen of the masters programs available near me (at least for math), the courses are actually less rigorous than my undergrad classes. My school had options, variety, and quality that actually made it look like an actual step forward. (The local BS requirements also looked like... well, total BS.)
My econ degree is a BA not a BS. I was able to avoid some of the more arduous math courses. I believe pre-calc was the pinnacle.
@connorbush For whatever reason, this reminds me of the highest grade I ever achieved in any course, ever. I took a financial math course in college to meet a requirement, and the teacher was a brand new, terrified of failure adjunct. She let us take quizzes in groups, discuss and revise homework before turning it in, and gave out absurd amounts of extra credit (maybe all homework was extra credit? memory fuzzy), often potentially nearly 100% worth. My final grade in that class was 183%.
@brhfl
That grade....now that's Math!
I never liked the way I was taught math, which largely made me think I didn't like math. Now that I can explore it on my own with no repercussions, I enjoy it pretty well. And, in school, I enjoyed it in my own way, which largely involved screwing with the relevant teacher but ultimately taught me more important things. Like using a slide rule on my standardized tests (in the late 90s or early 00s) — actually taught (and continues to teach) me a lot about the relationships among numbers, logs, etc. Or like somehow convincing the folks in charge to essentially let me pull an independent study on boolean algebra, which helped me far more than the regular old dull kind ever has.
I saw this thread yesterday, but yesterday was a huge FU day in my life, so put it off till now.
Once upon a time i wanted to be a professional mathematician, research job, PhD, the whole deal. I took it pretty far.
So i have a very nice show-off list on courses and seminars (dont have transcripts handy, just from memory and google, missing quite a bit....)
Differential Equations
Multivariate Calculus
Real Analysis
Complex Analysis
Linear Algebra
Abstract Algebra
Probability
Topology
Algebraic Topology
Number Theory
Fourier Series
Differential Geometry
Algebraic Geometry
Combinatorial Mathematics
Game Theory
Hilbert Spaces
Commutative Algebra
Riemann Surfaces
Lie Groups and Lie Algebras
Logic and Foundations
Galois Representations
Functional Analysis
Knot Theory
Chaos Theory
Stochastic Calculus
Set Theory
Mathematical Logic
None of this involved computers, slide rules, calculators, and after calculus and diff eq, no calculation. Pencil/paper, blackboard/chalk. This has changed: the increasing importance of statistics, big data, mathematical modeling, and computer modeling of symbolic language has transformed the field, i suspect you can no longer get thru any degree program without a lot of machine time.
I remember almost none of the content. The topics i found most fascinating were foundations, logic, topology, algebraic topology.
I thought i wanted to be a PhD mathematician, the way teenagers think they've found a calling when they are 17. And followed this thru college. Only i choose a grad school in Manhattan, and i think the movie and music schedules posted in The New Yorker and The Village Voice called out to me as much as the math. When this happens to a would-be mathematician, it's not usually a good sign, because you need to be pretty intense to get thru the coursework. The other bad thing, intellectually, that happens to a lot of grad students, is that you can get stuck, thru fascination, in a particular area, when your broad mathematical education is not yet sufficiently advanced, and you become so wrapped up in it that you can't be bothered to pay attention to the other material you have yet to master. Which means if you dont pull yourself out of it, you wont finish your degree.
I think most students who do well as math majors in a good undergrad school and do well in the first 2 years of a decent graduate program are perfectly capable of handling the material, doing the work to get PhDs. What gets in the way is burnout, undisciplined fascination, and the increasing importance of the rest of life.
The material is so abstract that you cant give a casual/informal description of what you are doing to anyone outside of other mathematicians, plus some physicists and engineers if the study area is applicable to those disciplines. And later on, when the work is more advanced, you cant even give a casual discription of your work to the mathematician in the next office without taking much time unless your areas of work have a lot of overlap. At the highest levels, even that becomes difficult, unless the other party has time to really absorb your work, as most math is done is done on such incredibly sprecialized topics.
My own perception of math is that calculus and 1st year diff eq are where the math experience starts to change, tho there are early glimpses of what mathematicians do along the way, particularly in high school geometry. But you are just a beginner, in high school and the first year of college. Those (calculus etc) are prep courses for how you will start to think differently as the years pass. I arrived at what i think of as the beginnings of the mathematical experience after diff eq, when i started real analysis and abstract algebra. Not that earlier courses, particularly trig, calc, geometry, set theory, diff eq arent real mathematics - they are, and diff eq in particular is notoriously difficult.
But after a my 1st and 2nd years in college, i looked back on the earlier-studied material with different eyes. Something about the endless practice of definitions, theorems, proofs, examples, counter-examples, was a bit like (in my imagination, anyway) being in an immersive experience in martial-arts - some sort of endless discipline until it's all second nature. (Have no martial arts, have a blown knee.) You start to swim in the water and then learn to breathe the way a fish does.
In spite of the logic, or because of it, it can at times feel a big magical, almost zen. You see (somewhat literally), with your mind. At least i did. Once the problems i dealt with passed beyond what could be resolved thru any form of computation, I would always try to go forward thru a very personal visual imagination - once i had the essential logical elements in my head, to create an symbolic-image-representation of the mathetical environs, and then create a visual symbolic transformation toward a solution, and then try to transform the vision back into mathematical symbolic language, and to see if i could then create a rigorous connection on paper. This failed far more often than it succeeded, but i would try again and again, till i had something.
Different mathematicians work in different ways, i have no idea how common my approach is, tho i have heard of other mathematicians speak of it. If i looked at a publication in a math journal, i would bet that the work was not done in the language that's in the page - it's done in an imaginative state akin to "logical daydreaming". Then you try to make it real and bring it home.
And i burned out, or got close to using up the broad spectrum of my msthematical curiosity. I suspect more than half of grad students, perhaps far more, do that. The work is so very intense and focused and takes such energy, and you get tired of not being able to talk about your work with anyone, you might have kids or other family members to deal with, debt, life, housing....you get curious about normal interests.
Or you live in Manhattan halfway between CBGB's and the Mudd Club, with reperatory cinema and Merce Cunningham and spicy noodles and the Blue Note and Carnegie Hall all around. And i had friends in film, music, dance, holography, journalists, who lived aboard the QE2, who were getting PhDs in something "sane" like economics, friends who were coding, and i didnt want to live and breath only math anymore. And someone with my state of mind at that time is prob a goner for grad school.
I coded for a few years in New York City, then due in part to a domestic situation, wanted out of the city. I've lost touch with almost all my math friends and city friends - didnt put enough time into keeping those connections over the decades. And aside from following own interests, have messed with almost no serious math and only miniscule coding since then. Because math is an enormous and complex structure, and if you dont see the structure, you cant interpret the pieces of it.
But some of the thinking habits stay. Matheticians fall in love with that world, and then most of them, when young adults, want to use their mathematical thinking to resolve problems of relationships, survival, income and prosperity, family, life choices. Particularly relationships. Hmmm. This doesnt go so well. They get over it, laugh at themselves, learn a bit more humility, courtesy, empathy. Most mathematicians are good at admitting when their own reasoning has limits. And they learn to make choices in something resembling the normal way.
Mathematics itself looks more perculiar and perhaps fascinating the more one lives in it. Esp the simple stuff such as logic and simple definitions>theorems>proofs starts to look more and more like an infinitely transforming beast the more one studies it. There's simply so much undiscovered stuff even in the areas that are well-studied (this is provable), let alone the areas where very little is known. And stuff keeps transforming into other stuff in the most unexpected ways. And there keeps being logical space and wiggle room where you thought there was none.
And you can try to applying strictly rigorous methods to real issues posed in normal human languages, which works (imo) poorly, but the results are interesting. And this can impinge into philosophy and other areas (which to my mind use different habits of thinking).
It changes how you think, for life. I dont know how to clarify it to a non-mathematician, but could, i suspect, talk with any mathematician about it. My sense of possible complexity changed completely. My sense of "the space between the words, the echos behind the sentences" changed, the more math i did. Like i became aware of how much possibility of meaning and fact were out there, and how one might tease a little of it out.
And now i'm way off the deep end and beyond earshot in the "incoherence sweepstakes", no doubt. Apologies.
I suspect this mental transformation occurs in the lives of many adults who have studied something using high intellectual energy and rigorous thinking - within other academic disciplines, or out in the real world: the combo of knowledge and practice and repetition and constant challenge changes the brain forever, in ways unforeseeable to those who havent worked that hard with their minds. To me it's a gift to have had the chance.
One math friend (who taught and published for decades in a long, excellent career) said something like this to me: "mathematicians get to see the things and visit the places that are part of why many people drop acid."
All the math prople i knew during those years had done drugs, that era, and tho my friend's point is a bit facile, every one of those math prople would have gotten the sense in which he meant it.
FWIW (me being silly), i think our species is just getting started with math, and during my years, i saw only the tiniest part of it.
@f00l Holy Crap!
Me and math.
"I know my ciphers"
@mfladd
I thought i was the luckiest person ever, for a while....
;)
Byw i make that facial expression, lots of times, every day, over the simplest shit. Math people are not famous for great decision making and common sense. Given many individual exceptions, the lack of stellar rep is for a reason.
@f00l Enjoyable read! Giving @joelmw a run for his money in the verbosity department…
@brhfl
I never get a chance to talk about it, so when that door opens, out-of-control. ;)
@f00l @brhfl That was indeed an enjoyable and worthwhile read--and I'm flattered to be mentioned in comparison (even if only for my verbosity).
@f00l I'm only about half way through this comment, but I'm loving it so much that I just had to pause for a moment to say THIS IS AWESOME. I'm ridiculously tired today and having trouble with... sentences. So I might not end up saying a lot of the things I'm thinking after I read the rest. But... again... I love this.
@f00l I like the way you describe the earlier courses. In geometry, I thought I hated proofs. What I hated was spending so much time on such basic, simple proofs. All of those early classes were often mindnumbingly boring. But the disciplines you need to learn to think mathematically, to conceptualize, comprehend, and then articulate higher mathematics, become second nature through that kind of repetition.
I think the thing that frustrates me most about my love of math is my general inability to articulate the beauty I've seen in it to someone who has not studied math. I can say things about unexpected order or surprising connections. But that doesn't convey much. And then there are all of those beautiful things that I dont even know how to put into words for myself.
It's fun to watch a mathematician get excited about math. I still vividly remember the first time I saw one of my professors flip out over something he was teaching us. I was just a Freshman and it was my first class with that professor. Out of nowhere, he came to life. He left his (unreadable) scribbles on the board and became very animated as he gushed about how beautiful it was and drew connections to topics we wouldn't be covering in that class.
Regarding the process, I can definitely relate to the way you described it. I have found that some of the best descriptions of how I do math (not computations, but the really mathy stuff) have actually been books and articles written about the creative process. I would also say that a startling amount of my mathematical problem solving happened on a subconscious level. I would often be driving, showering, eating, or engaged in some other random task when I would suddenly connect the dots. It happened all the time when I wasn't consciously focusing on the proof or whatever it was that suddenly became clear to me.
I didn't exhaust my mathematical curiosity. I don't think I even came close. Which is probably why I occasionally find myself looking at graduate programs nearby or in places I'd like to live. But, by the time I graduated, there were other things that were just... higher priorities and more important to me. (That "increasing importance of the rest of life" thing you mentioned.) So I went in a different direction. But there were constant moments, in the first few years, that made me long for it. Things like hearing from an old college professor. Having a conversation about math. Those triggers don't happen as often as they used to, but they still happen.
Math definitely changed me. I love the way you described its impact on your understanding of... the true complexity of things and a broadening sense of possibility. So, so true.
It makes me sad to think of mathematics shifting more toward machine time, statistics, and computation. I think the heart of mathematics is on the more abstract end, though that certainly isn't the "math" most people think of. That's where progress happens and our understanding of the world expands. Advances in mathematics enable more accurate models and expanded applications. But you have to get abstract to get there.
Once again, I really enjoyed reading all of that. Thanks for taking the time to post!
@christinewas
Since i'm not a practicing mathematician or math student now, i dont know exactly how the curriculum has change except for sometimes hearing a comment. I'm not sure machine time gets in the way of the stuff that's wildly beautiful and unexpected - it may increase the drudgery, or open doors.
All i did was strictly theorectical pure stuff, in part because i was fascinated by the aesthetics. And in part because that's what my liberal arts college taught. A differential equation may appear beautiful to its mother, but not to me. There is a certain joy in wrestling with them to get a little control. I have enormous respect for the researchers in that area.
But mathematical thinking, as practicing mathematicians experience it, syarts after diff eq. When you talk about the solution and discovery process as being intuitive, that's right on. Only easy delimmas can be solved or reaolves by computation. You gain knowledge suddenly, with fits and spurts and dry spells,
Every mathematician i've spoken with has described the work as being kinda "part drudgery, part the stuff that dreams are made of." An every mathematician i've known had read books on the creative process, and found a sort of mirror therein.
If you wanna keep messing with it....well if i were doing that, if my skills weren't recently honed, i'd do a buncha remedial stuff to get back in the swing. Then i'd try out Coursera, Edx, or similar. I'd try to pick something that doesn't entertwine itself too tightly with the rest of the theorectical structure, because less to keep up with and keep track of. Say number theory or probability, tho i'm decades out of date here, and perhaps wrong about these.
It could be a lot of fun.
I was (perhaps!!) fortunate in my undergrad work, done at a place w no grades, no requirements, didnt even have to take courses if you could come up with an alternative. My 1st term freshman classes contained perhaps 10-20 students. After that, they shrank to 5-10 students, then 2 -5, as we learned to work the system and did everything by custom tutorial. One of my fav profs has pets snakes and brought them to class for us to play with during brainstorming.
The best times were when 2-4 of us grabbed a classroom after hours and just worked all might, feeding ideas to each other. Or when we did the same in a prof's office. It was a very intense place, most students put in 60-80 hours a week, some more, but you were studying exactly what you had chosen to study.
It comes close to me perfect ideal environment.
The downsides: first, that this method unwittingly encouraged the idea of knowledge for self-actualization to the degree that some students faced nasty shocks in their later lives and careers, esp in political or manipulative circumstances, and in dealing with the practicalities of making a living.
Second, that the college no longer exists in the quite the same form. It was a wonderful experiment and it also had to faced the real world. So the school is now part of a state system, tho much is unchanged. It's perhaps not quite as impractical as when a student got 2 terms credit for walking from one ocean to the other, while journalling and making local community contacts. Or perhaps it is. I'm not up on that, my 2 fav profs are no longer living.
Sometimes i wish i'd gone to a normal place, with grades and requirements. Perhaps i would have achieved more, instead of living an eclectic and often foolish life.
And since regret does not re-order the past into a better config, and since i cherish what i was given, i put that away. And apart from family/friends/pets, math had my best, and gave me its best, for many years. I do feel lucky. Like there's this treasure, and most people dont know its there, or get to see it. And i did, i got to live and play and dream there, and thats a gift.
I'm going to reply in this thread, despite only tangentially responding to it, as I suspect only @christinewas, @f00l, and possibly @joelmw will take much of an interest. Or, maybe not, but now I tagged all of you and you're stuck reading this.
Your comment on the inability to articulate the beauty of math resonated with me on several levels, cw. I am the sort of hopeless artistic romantic who constantly finds that struggle in the things that I love. I don't necessarily have that struggle with math, because it's not as important to me, but I definitely understand it.
To me, the beauty or the romance in math is that of a puzzle. You have one outcome, a ton of pieces, and a journey. If someone doesn't understand the magic of math, just tell them it's all a bigger version of Sudoku. A much, much bigger version of sudoku. Or a crossword, but in base 10 (maybe, probably) instead of base 26.
I started programming computers (and calculators - my formative years were on the Commodore 64 and the HP 41C) basically as soon as I could read and understand how to poke buttons. I gave up making a career of this later in life because there's a very clear divide between those who know and are good at syntax, and those who are clever and good at math. The algorithm queens. These sorts of people. And I couldn't hack that. I can knock out an NYT Monday crossword in about 5 minutes, but if it were my job I'd be fighting it all week.
So, to me, numbers are largely a diversion. One of my favorite diversions is Viète's formula. And, assuming I can key it in correctly on whatever calculator happens to be nearest me, it's a great answer to 'why are there calculators everywhere and you paid how much for them!?' It's… beautiful. It's a bunch of 2s, it's (ultimately) a bunch of polygons, and then magically it's pi. Seriously, anyone who is reading this on a Mac or Linux box, go to your terminal and type in
dc -e "12k25si2ddvdsz2/[lz2+vdsz2/*lid1-si2<v]svlvx/p"and watch something resembling pi show up (
dchas no guard digits, so the operating precision and shown precision are the same — error in the last few digits is a given). It's dumb, but it's fun.I don't really know what the point of this ramble is. I know that it's easy to look at these ten characters and only be reminded that our taxes are due in like a week and holy crap that's not a lot of time. To a lot of folks, numbers come into play for… nasty nuisance reasons, mostly. But sometimes, even if you can't convince someone they need an HP 42S in their life, showing them how one number becomes another truly is like a magic trick. I guess that, to me, is the beauty.
@brhfl @f00l @christinewas What I like about this is that ultimately we're talking about passion and beauty and art and the human creative impulse. I completely agree that Math can be the focus and the venue and the muse and goal for human imagination. What pleases me is that the playground of the imagination isn't bound as we conventionally believe it to be--in its domain any more than, well, any other way.
And aside from loving others (not that I in fact consider it distinct from what I'm about to say, as I've implied in a comment above), I'm not sure I think there's anything more fundamentally human and sublime than the joy of discovery and creation that y'all are talking about.
I got as far as third base studying math in high school.
@WTFhqwhgads There are 10 types of people in this world, those who understand base 3, those who don't, and those who realize this joke actually falls horribly flat beyond binary.
@WTFhqwhgads @brhfl The combinations to my locks are engraved on them in base 7.
I suffer from Dyscalculia, I do believe.