/sci/ - Science & Math

Calc 1 is as hard as math gets right? I assume it's like one of those weed out classes. I hear it gets a lot easier after that.

How to do f'(x) using the definition of the derivative?

hello friend,

would you look down on somebody if they wanted to teach math but they only had a masters degree in physics? also, why you choose to lurk /sci/ instead of some other technically literate places on the web.?

>>3903208
Yeah no, not even close. There is a massive difference in doing calc in calc 1 and actually learning proofs and theorems.

What's your research?c

How does it feel when 70% of a class uses the same fallacy to prove something?

>>3903197

What degrees do you hold?

Do you have to take an exam, apart from your degrees, in math in order to teach the subject at a university?

How would you explain topology to a monkey (ie: me)?

what would be the most difficult problem involving the green theorem in the plane with a vector field with a discontinuity point in the region given?

What do you think about the banach tarski paradox? Do you think it shows that the axiom of choice is wrong in some way?

Do you know of any simple proof of Brouwer's Fixed Point Theorem? The one I have is largely horribly un-intuitive...

>>3903215

I've had to answer this one a lot --- first, I like /sci/ because I think that anonymous message boards are a nice place for people to give up their "real" feelings on certain issues. Most important to me are the ones where people ask questions that would otherwise be thought of as "stupid" in class, or what people on here think makes a good professor. I've also taken a few harder problems from here to include in homeworks.

As for "looking down" --- physics is a difficult degree, and there is a large overlap of the subjects now. As for the teaching math part, I'd only look down on you if you did it purely for the money.

>>3903208

Every class after calculus 1 is a ton easier than calculus 1. In particular, you may want to take a master's level PDE class since that's about as easy as things get.

>>3903222

My current research is in an extremely specific branch of algebraic topology. Without giving myself away, I work with structures which are "similar" to CW complexes. For those of you in the "know", you'll know that (X,A) a CW pair is a cofibration, but for other structures we have a natural cofibration that doesn't use the "every map is a cofibration up to homotopy equivalence" thing. The structures that I use are neither inside nor containing CW complexes, but they are just "different."

>>3903226

You have to get through undergrad, then you take usually 3 - 4 qualifying exams, then you take your oral exams, then you write a dissertation and do what is called a Defense of your dissertation; this is usually also oral. After that, you do postdoc work, and there are no more required tests.

What specifically do you teach?

>>3903267
>Every class after calculus 1 is a ton easier than calculus 1. In particular, you may want to take a master's level PDE class since that's about as easy as things get

lol are you trolling?

also are the engineering students the brightest students to take your class? or they just like to think they are?

>>3903279
He's not trolling. Calculus I is really as easy as it gets.

>>3903224

So far, the worst offenders are those who assume something is true, then do a lot of strange calculations, and then state that the things they originally assumed were true are true. For example:

1 = 1, so we have 1*a = 1*a = 1* (a + 0) = 1a * 1(0) = a, so 1*a = a, and plugging in a = 1, we obtain 1 = 1 which proves 1 = 1.

It's kind of upsetting.

>>3903226

Topology. On the plane, we can talk about the distance from one point to another point. But when we only need the idea that these points are "sort of by each other" we talk about the points being in open sets. Continuous maps turn into mappings which "take nearby points to nearby points" in a sense (though, it's actually defined as a pre-image...) and so in topology we care more about "when are these things close?" or "when can we continuously make one thing into another thing?" than "exactly how far away are these things?" or "is there a rigid transform that takes this thing to this thing?" For example, in geometry a circle and a triangle are two different things; in topology, they can be continuously transformed into one-another, so we consider them the same object.

>>3903227

I don't often use Green [or, really, any of the Stokes' theorems. I'm not sure.

>>3903267
>>3903267


they don't make you take 1-2 years of graduate coursework like other Ph.D. programs?


my understanding of Ph.D. is this (after being accepted)

1) take entrance/qualifying exams
2) repeat undergraduate level classes for anything you failed (requiring nothing less than an A in all of these classes)
3) take 1-2 years of graduate level coursework in your core dicipline or related to your specific research
4) all the while TAing and doing research
5) possibly taking cumulative tests at least once in your grad career
6) do your disseration
7) defense

then postdoc, which is just essentially low-paid work in the interim while you find a good job.

theoretically you might only need to do several MONTHS of post-doc if you were offered lucrative job soon after getting your PhD.

you might also do as much as 3 years of Post Doc if you were unlucky or you were working on something cool.

>>3903229

If you don't require the AC, then topology (as an example) becomes extremely boring. In fact, without AC, we cannot use Zorn's lemma (as they are the same) and so we cannot even say that every ring with unity has a maximal ideal. This basically kills off commutative algebra, which kills off algebraic geometry and topology. This madness then spreads around.

Though, there are people (most notoriously see the guy who just wrote about the inconsistency of the arithmetic axioms; it's in a recent post on Baez's blog) who reject it. I require it for my work. Though, it is a bit upsetting.

Though, maybe you should think this way: is this any more upsetting than the fact that there are statements which are true but that we cannot prove? There are many things that are troubling about formal systems, but sometimes we just have to "go with it" and see if it all works out.

>>3903303


I forgot Orals.


and by "cumulative tests," I meant separate from orals.

>>3903279

I don't teach applied classes except lower-level classes; these rarely have engineering students in them. I taught one class in the past which had engineering students in it (it was a complex analysis course) and I felt they were exceptionally rude and full of themselves; but this is, of course, just my opinion. For example, I love the theory of complex analysis, but they all complained to the department head when I put proof-based work on their homework. C'est la vie.

>>3903247

Certainly! In fact, BFPTheorem is a special case of a much more general theorem. Which is a special case of a construction in category theory. Once you prove this construction holds (which is a short proof, once you have built up all of the category theory) then it has BFPTheorem as a corollary. In that sense, it is a one-line proof.

In the "real" sense, I don't have an easy proof for that. It usually requires the calculation (and, ugh, definition) of degrees of maps.

>>3903303

I agree with everything except I have not heard of (5). In my gradwork, and in the two schools I've taught at (one larger, one smaller) we have not had exams like that. It may be different in different places, though.

Months? Maybe if you're amazing or amazingly lucky. My postdoc work was something like two years, but the economy was great and people were looking for math professors. Some of my students from five years ago are still doing postdoc work. A few of the lucky ones have gotten professorships, but as a general rule: don't count on becoming a professor right out of grad school.

>>3903197

whats the best way to learn calc 1? kind of a stupid question but..
my teacher sucks and im having to teach myself / learn from others, tutors etc. but that isnt going very well either

Any idea of how to apply the monte carlo stochastic method to economics?

Is your wife cute?

>>3903337

Could you recommend a text/website where I could read up on that (BFPTheorem)?

>>3903340

There are SO MANY places to learn it, but the BEST WAY to do it is just to get a textbook and do LOTS of questions. Really. There is no better way. There's a book that's called something like, "Calculus Demystified" with questions and answers, but my favorite (student) calculus book has always been Stewart's Calculus.

>>3903348

I'd have to ask someone more applied than myself. In fact, I've had to use programs which use this method (since sometimes I work with complexes which have MANY, MANY faces, and the only really good way to figure things out about them is to do the MC method and randomize) but I'm not sure how to apply it to econ.

>>3903356

Of course! Hatcher's website (google: Hatcher Algebraic Topology) has a FREE algebraic topology book. The theorem you want, I think, is somewhere in Chapter 1. It takes a bit to get up to if you haven't done algebraic topology before, but this is one of the standard Algebraic Topology texts today.

>>3903350

The cutest. Maybe not right now with all these tissues everywhere, but usually.

>>3903307
God damn it I have to keep up with that guy. Thanks.

>>3903369

Cheers! I'll have something to read over the weekend. :)

>>3903267

>Every class after calculus 1 is a ton easier than calculus 1. In particular, you may want to take a master's level PDE class since that's about as easy as things get.

hahahaha Im working on a problem set for PDEs now... just the basic one physics ppl take... spent an hour of lecture today HALF solving of the wave equation on a finite line with dirichlet boundary conditions... Solved up to the point before we include the initial values for u and u_t

hahahaha "easiest course is calc 1" haha good one

Here's a question that I have had for a while.

What approach to learning math is the best for high school students? Do you like the Saxon method, Singapore method, the integrated mathematics method used everywhere except in America pretty much, or the American method of focusing on Algebra exclusively for a course, then geometry, then trig, etc?

Better still, rank them from best to worst in your opinion.

>>3903395

Good! I highly recommend that work, though it might be a bit confusing. For a more "no-nonsenese" approach, there's also May's book (google: May Concise Algebraic Topology) which is also free. But I usually tell my kids to get Hatcher and keep working from Hatcher until they get to something confusing. Then they should ask me. If it's still confusing, read Massey's Algebraic Topology. If it's still confusing, skip it and maybe it'll make sense in the morning.

>>3903419

I have some very strong opinions about this. But my opinions are a little strange. I would rather teach lower-level abstract algebra (minus proofs, perhaps) and topology alongside geometry. I would teach Algebra I but I would greatly restrict algebra II. I also would include Logic and Probability and Statistics.

I'm not sure what all those methods are, but, really, math high school education in this country cannot get much worse.

>>3903337
What books do you recommend for a potential engineering major who might be interested in pure mathematics? I'm currently taking calculus 1. I'm doing the pretty good (have an A). I never ever touched a pure math book. I want to be an engineer for the money but I also would love to be a mathematician for the beauty of math. I know for sure I can graduate as an engineer but pure math intimidates me.

Mathfag doing a Masters here. I always find that I'm extremely forgetful, and I can never really take information from one course to another, unless I'm doing my own research, (which obviously I get super familiar with). Do you ever have the same problems?

Also, I'm doing OR and crypto. Any future for my fields in terms of career?

>>3903454
opps sorry for the sage

>>3903454

Pure mathematics requires a LOT of proof experience. I'd get "how to prove it" just to learn some possible ways to prove potential theorems. For "real pure math", getting an undergraduate Abstract Algebra book would be the best way to go I feel. Fraleigh's Abstract Algebra, in my opinion, is one of the best low-level Algebra books out there. What's better is that you can get an older edition for really, really cheap (for example, I was lucky enough to snag a 6th edition for $2.50.)

>>3903459

As far as your future, crypto is especially useful. I'm not sure what OR is.

If you can "tie a thread together" from what you love to other things, then you can usually remember things better. For example, yes, you can say a module is such-and-such a thing and that they have certain properties and whatever, but if you just think, "vector space but scalars are from a ring" it's SO much easier to remember; you know and love vector spaces already!

Maybe this is not so much a secret, but it is not usually something math professors say aloud: I don't remember 80% of the things I've written in my papers about. We have a joke around the department; one of our professors is especially forgetful --- let's call him Dr. A. The joke goes like this:

Dr. A was working when he came across a problem that looked trivial but, for whatever reason, he could not solve it. He tried for days and days, but the solution eluded him. He finally gave up and searched the literature; he found a number of papers on the topic, but he clicked on one which looked most accessible. Not an hour later, he was able to use the paper to solve the problem. Overjoyed, he began to compose an email to the author to thank him --- only to realize that *he* had written the paper five years earlier.

>>3903488

I'm kinda glad, then. OR is Operations Research. Maybe they call it Management Science in the US? It's about queueing and decision systems. Especially useful for logistics.

what is the usual knowledge of an incoming 1st year grad student?

i basically know undergrad algebra, analysis, complex analysis, topology, along with extensive knowledge of mathematical modeling, numerical analysis and probability, and some independent study on set theory, graph theory and automata theory.

i've taken a bunch of courses related to physical chemistry, since I'm a chem major.

do a lot of incoming students already know grad level analysis and algebra? it seems like a lot of my classmates are currently taking those during their junior or senior year.

>>3903369
>>3903340

alright ill check out those books. thanks man

>>3903505

For math, I assume you mean? There is a good book, "Math You Need for Grad School" or something like that which sort of details the bare bones of what you need to know. It sounds like you're on the right track. Most of my students [being in algebra and topology] have already either had grad algebra or algebraic topology in their undergrad but it's not really been a huge hindrance if they haven't; they simply take it here. Most of the time, even if they HAVE had such courses, they retake them here to solidify their understanding (or to get a good grade?).

It sounds like you ought to be okay, though; check with your advisor as to what you should work on. Usually there is a placement exam which covers a lot of this, though.

OP I am a cocky fag in high school, I have never studied and have always achieved 90+. I grasp mathematics extremely well, especially concepts.

I will be taking math 35 AP next semester which is after introductory calculus. Calculus 2 I assume.

My question is, if I do in fact continue succeeding, should I try for a phd in mathematics? I only enjoy math. I enjoy the theory behind it , is it mainly theory in the higher levels or grinding out formulas?

How much more difficult is the higher level to grasp compared to say Calc 1

Also, do I need to be a good teacher to have use for a phd, I hear you can only teach with a phd in mathematics so I am wondering if my less than helpful personality would be a bad combination.

Thanks in advance

>>3903369
james stewart's early transcendentals?

>>3903435
have you ever read this:

http://www.maa.org/devlin/LockhartsLament.pdf

if so, what's your opinion on it? It's all about math education in america

>>3903534
Not OP
Take a couple of Analysis courses in University then decide on if you want to or can pursue it.

>>3903534

College is going to be a real slap to the face for you, bro.

>prof
>grading exams

TA detected.

>>3903552
Why is that? I don't doubt it and have heard it for many years, but that's what they said about middle school, that's what they said about high school, that's what they said about AP courses. You can see what I'm getting at here, a pattern.

>>3903551
But I am wondering if I can get a career out of it, if I cannot I will have to consider my academia's importance over a career. I do not care for money one bit but I do not wish to be a wage slave for eternity either, can you understand my predicament?

how do I turn a sphere inside out?

>>3903564

>comparing middle school, high school and OMG AP COURSESSSSS to college

I give you two semesters before you fail out.

Are most mathematicians happy when someone finds real life applications in their field, or do they get grumpy that their pure field has been used for applied math?

>>3903569
I don't doubt for a second these are the easiest classes since pre algebra. But are you really so insecure that you must attack me like that? At least give me some reasoning behind it, do you speak from experience?

>>3903569
don't discourage people. give him "intro to proofs" book so he can get a better sense of what's going on

>>3903580
Can I find a mathematics textbook of this caliber at my school's library? I am not swimming in money.

>>3903582
>>3903582
google 'northwestern library' until you find the right link

>>3903587
fuck

nu library

>>3903551
>Analysis
A real analysis course would rape any highschooler, that's not fair.
>>3903534
>formulas
That's more like ACM (Applied computational mathematics).

>>3903521
Hey Prof, sunglasses here. What did I make on that test?

>>3903564
college isn't really that much "harder", you just have assloads more homework. If you're smart and do all your homework, it is still possible to get by without really studying. That said, its not like high school where classes spend a week on a concept that should take a day - you actually make consistent progress.

>>3903534
You most likely have no idea what math is like and deciding on a phd so early on is silly. You should pick up a proof book like some one else suggested. I enjoyed "how to prove it" by daniel vellerman and it has a lot of positive reviews (http://depositfiles.com/files/z3wg2wi6v/29302_0521861241ProveIt.pdf))

And please don't brag about not studying for calculus I (or high school math). It is the easiest course you'll take.

>>3903609
Also, if you truly want to know what "real" math is like, I cannot recommend this book enough. I wish I had it when I was in college.

>>3903578
As a sophomore Math major, I'll tell you that Calc really is a poor way to judge the major. I'm in a standard abstract algebra course, and it's not that much harder than calc for students. It's not like if you got A's in calc. You'll suddenly start getting C's. As long as you work hard, it'll feel similar in that regard. In other words, you'll get smarter as the material gets harder. Whenever you look forward it might seem impossible, but looking back, it always looks easy as shit.

Also it's largely dependent on the school above all else. People who got D's in core calc. at my school got 5's on the BC exam. At other schools, getting a 5 is reason enough to pass out of calculus.

And you see, real math has proofs, which makes things difficult especially if you aren't used to it. Calculus without proofs, (and I don't mean basic delta epsilon) is easy mode. If you don't want proofs but like math do ACM.

>>3903623
oops, forgot the pic

Hey OP, I'm a CS major looking to get into cryptography

What kind of maths am I looking at? General ideas on the height of mathematical knowledge I'll need?

Thanks for the thread

>>3903197
Why are the majority of engineers homosexuals?

If I get a BEng would I be in a good position to purse a mathematics degree? I was sort of forced into Engineering when my passion is really for maths.

My question is what is so great about Stewart's calculus textbooks as opposed to other texts? I often wonder what makes professors pick particular textbooks.

All I want to know is if phd has any job offerings or will I be unemployed indefinitely besides as a teacher. Fuck tenure by the way, have to suck everyone off to get in.

I'd also like to mention, if you think you really are good at calculus or linear algebra, take a problem from Tom Apostles Calculus (vol 1 or 2) and try to solve it without using the internet. pdf's of those books are not that hard to find on the net.

Ultra-stupid question for you...

How do you feel about the "for Dummies" math books?

>>3903684

pdfs of the books aren't, but no solution manuals exist...

Is Apostol good for someone doing the Calculus chain for the first time?

Sorry guys, I had to go get my wife some cough medicine and none of the stores had the kind she likes. The grape kind. Ugh.

>>3903534

To be honest, if you are cocky, there may not be an advisor who really will look forward to working with you. It's nice to be humble in mathematics, especially if you know a lot. Let me also note (to maybe humble you somewhat further) : there are thousands of students who are really, really good at calculus. There are only a few of those who are really, really good at pure mathematics. The ingredients, in my opinion, are: determination, motivation, and general interest. If you have these, then you're all set. I would recommend getting into some pure stuff earlier than later; most mathematics after calculus [at least, pure mathematics] is proof-based. Thus, it would be good to learn some basic proof techniques. I've recommended a book for that above.

>>3903535

Yes.

>>3903546

I think most mathematicians have read this and agree; unfortunately, mathematicians are rarely confrontational, and rarely policy-makers. Hence the problem.

>>3903561

My TA can barely speak english and continues to mark things wrong when they are clearly correct. I spend enough time giving back points on silly things like quizzes and homework --- I do not want 130 kids in my office asking why he took off 4 points for not writing "lim" once and so forth. I grade all my exams; the homework and the quizzes are TA's jobs.

>>3903567

Carefully. The better question is: can I do this for the torus? Think about it.

>>3903609

It is possible to "get by" without studying. I just wanted to emphasize those two words, because that is what separates the boys from the men, so to speak.

>>3903611

Thank you for uploading this; I was scared to, honestly! This is exactly the book I was talking about. I find this is an extremely helpful book, even at the graduate level (for those students who have been allowed to "skimp" on their formal proofs). Even my wife has read it!

>>3903652

There was a crypto person in here before. As far as I know, a good understanding of algorithms (which you should already have; if not "Algorithm Design".) as well as basic number theory will take you far. You may also want basic group theory. The farther you get into Crypto, the more obvious what you need to study will be. Those are the starting points.

>>3903664

I have seen very few engineers go into pure math and stay there; fewer at the grad level. This is not to say it is impossible, nor is it to say that you should not attempt it. Just be careful.

>>3903668

It's not better, per se, it's just that it's EVERYWHERE. It's very polished, solution guides are all over the place, and there are fewer typos than most books. In addition, the amount of information in the book is pretty great; there's even some stuff in there that was new to me when I taught from it! (For example, some of the "projects" at the ends of the chapters.)

>>3903672

I currently do not have tenure at the school I am at now. There are a number of great jobs for phd's in math; basically, you can go into a company and say, "I've got a phd in math." and they'll hire you. Or, at least, they would have 10 years ago. Maybe the economy will rebound. I don't know. Nonetheless, I don't think math is a good field to go into to get a phd if you're "just in it for the money." You do it for the love of the subject, etc, etc.

>>3903685

For people starting out, the for dummies or demystified guides are okay, since they teach the basics and have a number of solved problems. Sometimes texts leave that kind of thing to a minimum.

>>3903697
>>3903684

Apostol's (his real name was Apostolopoulos!) text is not meant to learn from. It is meant more to be a reference, or, at worst, a rehashing of calculus for students who have seen it in high school from a bad teacher, have gone through a lot of mathematics, and would like to solidify their calculus understanding. The problems are not meant for a general audience.

On the other hand, Spivak's Calculus is meant for early math undergraduates (or even ambitious high schoolers!). The problems are, for the most part, very accessible. I would recommend this book if you don't feel challenged enough by high school calculus. As a bonus, the proofs are quite beautiful and explained rather well.

Explain forcing to me (please).

What math courses are best to take if you want to pursue graduate education in computer science.

>>3903850

I'm not so sure about what modern CS people do, but I would imagine graph theory, discrete math, and some number theory would be your best bet.

>>3903844

I am by no means a set theorist (but, in fact, Forcing has become a bit more popular, and I've actually seen it used in a few different, unexpected places!) but I think one of the more popular (quick) introductions to the subject is:

http://arxiv.org/abs/0712.2279

If you have some background in model theory, basic set theory, and some VAGUE idea of what filters might be, then this will be really easy to understand. If not, it's still a pretty good paper. Heck, I can even get through most of it!

>>3903862
thanks!

Formalism, Intuitionism, or Platonism?

So far, my way of studying has not helped me very much at getting better at solving problems. I basically read the book, and before I read the proof of a theorem I try to attempt it, read some of it to see if my work had any resemblance to the proof in the book, and use a pen to correct any logical fallacies I made. The bad part about this is that they always introduce new techniques that I've never seen, so my work isn't very good.

Then I attempt the problems, which are even harder. When I'm stuck on a problem and have no idea what to do, I read the theorems from before, and try to piece them together. This usually doesn't get me very far because, again, I'm not aware of what kind of bad logic I've used, and the hints they give in the book use techniques I would never have thought about.

Is it better to simply skip those problems and move onto new ones for the time being? Even if I move onto a new problem, the bad thing is that I still would be unaware of the technique used to prove the statement in the problem.

>>3903879

Ehhhhh, Plato has always had a special place in my heart. I always think, "What if every math textbook or paper was suddenly destroyed. What would we have? Would the stuff still be there?"

>>3903883

Math is hard. The way I combated that in my undergrad was: talk to your profs, TAs, peers; get different books that cover the same subjects and see what kind of proofs they're doing. Copy the proof, then see if you can explain the proof (if you have a white board, 'pretend' you're giving a lecture on it. I seriously have my students do this in empty rooms.). It really helps.

wait, so what kind of homotopy theory do you do?

>>3903850

Linear Algebra and any other Proof oriented courses would be helpful. Anything to build-up your Logic-Skills.

>>3903904

Ah, I don't *quite* work in homotopy theory. I mean, I do in the sense that "all" algebraic topology is essentially trying to make homotopy theory nice --- but my specific work is (and I will be vague here, I am one of the not-many mathematicians working on this kind of thing; it is not very popular) in proving homotopy lifting and extending properties in certain structures which "mimic" CW complexes in a number of nice ways. If you've got a bit of AT under your belt, I can say this: when do you have a nice cofibration (X,A) when A isn't necessarily a subcomplex (or even subset!) of X? I do not mean here "up to homotopy equivalence", I mean exactly equal to a cofibration. Giving restrictions on X, we can similarly make restrictions of how "nice" A must be. What's more, if we make a new "cover-like" object of i(A) in X which acts sort of like a covering space. With this covering space, it turns out that there are some pretty interesting properties: for example, what about the self-homeomorpisms? Do they extend to A in some nice way? Things like this. The idea is, we don't need something as strict as a CW complex to say nice things about things which "act" like "subcomplexes."

>>3903862
Thanks. I've taken taken all those except number theory and I'm planning to take a course in that this spring.

op, why so secretive? for what it's worth, i have a phd in mathematics; my research was on abstract homotopy theory.

>>3903652

Mathfag here focusing on crypto. Number theory is absolutely essential. You'll probably need to do a fair bit of abstract algebra. It depends on what kind of cryptosystems that you want to work with. I work with lattice-based cryptosystems, and I found that my number theory wasn't as important as statistical knowledge, because of the way it was designed. El-Gamal, RSA and Elliptic Curve all require number theory and group theory.

Interesting story - I was doing an advanced crypto course in IT, which I was extremely nervous about because I'd never done any IT classes before. I found that my grounding in math was far more important than my classmates background in IT was.

I'm currently talking Multivariable Calc, and I'm having a hard time. The concepts seem so abstract, yet while still using the rudimentary basics of calc. I guess I just can't visualize things in n-dimensions =/

Any advice would be greatly appreciated, mathfag.

>>3903965

Ha, well, saying you work on "abstract homotopy theory" is sort of vague too! The particular field I work in would almost immediately give away who I am since it's pretty much just me and four or five very foreign-sounding names. I enjoy the forums, but I would not like being uncovered.

It's strange, though, that it might have been the case that we coauthored a paper, and I would still have no idea who you were!

How hard is stochastic calculus? Looks like it's a bitch.

>>3904055

I did this in my undergrad; it wasn't too bad, but I had already had discrete math. Depends on your teacher, I'd say. I forget the book we used, or I'd recommend it.

Is it easy to detect plagarism? Do you even care since you know that students work together?

thanks for the recommendation of the 'math needed for grad school' book. it's very basic and skims over a lot but it basically neatly organizes all the things i need to review and explain it clearly.

>>3904087

Yes, it's easy to see when kids are cheating. When you teach for a while, you'll figure it out too. I usually don't care for homework or quizzes, since they'll generally bomb the midterms and finals anyway, but if it's a test, then I take action.

For my upper-level students, proofs are very personal things --- if someone copies word for word, I will know and I will not be happy. Especially because there's only usually nine or ten kids in those classes.

I'm interested in a few different subjects, and I was wondering, what made you choose math? I mean, what was that made you realize you wanted to dedicate the rest of your life to this one subject?

Also, in terms of general problem solving, do you think that's something people can really improve and develop over time or are some people just naturally good or bad at it and any improvement won't be really significant?

Currently I'm studying Economics and last Wednesday I turned in papers to change my minor of statistics into another major, which means I'm double majoring in Statistics and Economics.

I'm extremely nervous. I have to take up to Calc II, and right now I'm still in college Algebra......and I've gotten a D and another time I had to withdraw. First time I was lazy, second time my ex gf had to be rushed to the hospital by me, causing me to miss out on a test.

Currently I'm doing "ok" in my class. I feel like I understand the concepts pretty well. I need to take Trigonometry next, then Calc I then II.

Here's the weird thing, when I have to do math involving Statistics....I find it really simple and clear to understand. Why is basic algebra so hard for me then? I've ALWAYS had trouble. Is it a different kind of math? Will I be completely fucked in Trig and Calc I and II? Am I fucked and should I just change my major to Women's studies instead?

How did you get by with your extremely complicated math?

>>3904134

A lot of people think that there is some natural talent in math, but I think this is really not what matters. After all, there are BRILLIANT people working on tragically unimportant problems. I find that there are two types of mathematicians: solvers and askers. The former are amazing at formalism manipulation, and the latter are amazing at intuition and (obviously) asking. Some mathematicians are both.

To take this a step further, I'll use a real life example. I had a few Chinese students (from, in fact, the same undergrad in China!) a few years back at my old uni and they told me they were taught Analysis not as something which is "visual" but as definitions, theorems, and manipulations. They didn't "get" what an Lp space "looked like" because they just knew what it was FORMALLY. On the other hand, I always see (perhaps less formally educated) individuals on this board asking all sorts of interesting questions. I had a student (who is now a professor in his own right) who would come into my office all the time and ask seemingly random questions; some were dumb, but others made me think.

Think about, for example, that Godel Escher Bach guy; he was trained in Physics but left academia and his influence now is probably much greater than if he stayed in his field. Similarly, it is said that Spivak was tired of academia's "publish or perish" mindset so he dropped it and started his own publishing company of the same name.

What was the question? Oh, right. Why did I choose math. I think with math you can feel it. If I ever didn't do math for a while, I'd start craving it. I think that's when you know.

Not to be nosy OP, but how much money do you make?

I am currently a tutor/teacher working with 15 kids or so. I really like it. I'd like to be a professor someday, even if it's only for a couple of years. However, I don't want to live paycheck to paycheck. Not to sound stuck up or anything, but I;m really blessed to be able to currently have a sort of "expensive" life style that I absolutely love, and I'm not sure if I want to give that up.

>>3904143
calm down, jesus, you're making this way harder for yourself

the key to understanding something is not to panic, which is what you're doing right now. take your time, and do it slowly and carefully. don't approach it thinking, "wow, this is impossible!" approach it thinking, "this is hard only because I haven't read it, but I WILL make it through because it's actually easy."

look at a book in a foreign language. it's totally intimidating; the language, once you know it, makes reading it simple.

so how do you get all the time needed to understand a concept a pass homework? be responsible. don't panic. stay calm and allot time for yourself to study, at least 1-2 hours a day if necessary.

also i don't think you have trouble with basic algebra, just with adding/multiplying numbers. since you don't have a good foundation since you were a kid, again, just do it slowly. algebra has no hard concepts...

>>3904032 okay ... i guess i'm a bit confused because, if i remember May correctly, cofibrations must be closed inclusions in Top (and whenever I see a pair (X, A), I mentally replace it by a CW pair anyway) ... in any case, i used to study model categories/axiomatic homotopy theory; now, like everyone else, i'm thinking about equivariant stable homotopy theory.

>>3904161

Hm....out of curiosity, were there any other subjects you were really interested in before you decided to become a math major or just things you're still really interested that you do as a hobby type thing?

>>3904176
Maybe I am making this hard on myself. I feel like my biggest problem is that whenever the professor introduces a new concept, I can only understand that concept when it's related to problems that the teacher has used as examples.

For example, if a teacher shows me a problem, I can do all the problems that are similar to that problem. BUT, if all of a sudden there's an extra square root there, or a fraction of an exponent, all of a sudden my brain freezes, I don't know what to do, I get frustrated, and I just want to punch a baby.

I'm just nervous. Currently my dad pays my tuition, and if I have to drop out cause I couldn't do the math, or if I flunk a class and push my graduation date even farther.....I'd be so ashamed and embarrassed. If I pass all my upper division statistics and math classes, I can graduate next year.

>>3904143
I found Algebra to be the hardest math class I ever took. I got a B in it. I was (pleasantly) shocked to discover that Trigonometry was extremely easy, and most of Calculus (up til the near the end of multivariable) was so intuitive once shown to me that it was almost trivial, although I would have to review a textbook to do random problems now with formulas I don't remember.

I am an extremely visual/intuitive math person, I suffer badly with purely procedural problems and I always make stupid computational errors, which is what most of algebra is. But for something that has "meaning" to me I can almost always catch my errors and do well.

You may be in a similar situation. Take the classes and see. If it's hard for you then maybe not, but you may be surprised to catch a breath of fresh air once you break through the obligatory algebra wall.

>>3904161

Hmmm, hay OPfessor,

I haven't done math since highschool, and it is driving me nuts. It feels like i have forgotten a language or something- but more important.

As a child i was a gifted problem solver and mather.

I want to get into math again, and then go deep.
My question is how to start?

I need to know how and why formulas and equations work, i like to be able to visualize things, see them from above. So knowing formulas and equations and rules is useless to me unless i know the fundamental roots and what's really going on. I don't want so e quadratic formula bs unless i can visualize its curve on a grid.
i shuld mention my primary interest is geometry, i would like to be able to visualize higher dimensional shapes eventually.

How/where should i start?

>>3904201
>>3904201
That really makes me feel better. I'm REALLY hoping that's what it is, that once I get past through this algebra wall the other concepts will be easier for me to understand.
Like I said, Statistics formulas and concepts were simple and easy enough to understand, when most of my friends gasp in shock/horror when I tell them I'm majoring in statistics. I don't know what it is, maybe cause I can actually understand how it's being applied, rather than just "pure concepts"?

I hope I pass this algebra class. How did you end up getting a B?

why is your name alex, op?

>>3904222
Because I am from Russia.

OP, you sound like a huge faggot of a professor, for real.

Just teach your shit and be cool about it. It's not surprising that the kids who were doing engineering got pissed at you for putting in proofs for their math class. Lol @ you trying to force proofs on engineers for no reason. There is enough courseload in the rest of their classes.

That's just a pure example of saying "I like this and you should like it too". You know its not necessary for them to learn proofs if their engineers. Sure, it COULD help them become better thinkers, etc, etc, w/e other ways you want to rationalize it.

Tbh, you sound like a boring ass dude. Just same random ass motherfucker who I would look at irl, and say "wtf does this guy do in his spare time".

And the fact that you're married and not that old just backs that up. Have fun "living the dream" brah.

Just try not to be a faggot to the rest of us who want to have semi exciting lives.

>>3904241
>implying that a complex analysis class with no proofs is worthy of being called a complex analysis class.

>>3904171

At my old job, it was around 80k. At my new job (both were universities, but this one is much smaller) it's about 65k. But you do need to remember: I don't work summers. And, my "official hours" are something like 10 hours a week (three lower-classes, three upper-classes, four office hours). That's one of the job perks.

>>3904143

Maybe Stats is more "real" for you, so it looks better and more reasonable. I'm not sure what to tell you in this case; you should really talk to your advisor or (more useful) some math professors and such. We do talk to students who are in your situation, and we can recommend various things. We can even sign you up for tutors and things if your university has that available. Other than that, I'm not sure. >>3904176 has a good point, though.

>>3904202

Sounds like geometry or topology is where you want to be. Unfortunately, there is no royal road to either. For the latter, you only need to pick up something like Munkres or something, but for the former, I don't know of any good "elementary" geometry text. Maybe someone else here does?

>>3904183

So, you're SOMEWHAT correct here; they can be thought of as inclusions with closed images, but "really" they should be thought of as spaces that satisfy the HEP. It's dangerous (I think!) to think of pairs (X,A) as JUST CW-complexes, because then you get into this trap of JUST using CW-complexes and forgetting that many things are NOT CW-complexes. Also, one should (in my opinion) never work in Top since it is not cartesian closed; instead, if you work in the category of compactly generated spaces.

Let me also note that May's book, while basically the best concise book out there right now, does not really cover adequately what the notion of cofibration and fibration "do" when presented with spaces where the cofibration is not obvious. In particular, he notes that any map is homotopy equivalent to a cofibration --- but what is the homotopy equivalence? How should we think of it? Etc, etc.

>>3904241
lol, look at this kid getting uncontrollably and immaturely mad at a guy who just tried to get his class to understand the material better

proofs are not a death sentence, if you wanted to learn some really basic ones (and I'm betting the ones he put in his class are pretty basic) you can do it. saying "course load in other classes is too much!" works IF it's actually too much, but students aren't going to cry (or most might not) just because someone tried to introduce them to a new way of thinking.

someone who doesn't take their time to understand new ways of problem solving is pathetic and easily defeated. when you're actually out of school and solving new, strange problems, the answers aren't going to be handed and tailored to you. the engineers in the complex variables class wanted to learn complex variables, and most engineers who actually use complex variables need to truly know their concepts; proofs are a good way to learn and thus manipulate them well, instead of just following formulas. there aren't a lot of things you do in school that are 100% mirrored in the real world- the things you do in school are supposed to help you learn the material.

it's obvious from your post that your brain is still stuck in the stage of a stupid, retarded child by jumping to the conclusion that OP is a boring person who doesn't care about anything other than math and doesn't do anything with his life just because he put some proofs on people's tests. boo hoo.

>>3904279


>butthurt
>this guy

Pick 2

OP is still a faggot. Maybe a half faggot because he's from Russia and a mathematician, which is pretty badass. But a faggot nonetheless.

What's your opinion on the influx of Chinese grad students?

I'm going to head off, but thanks for the thread, OP. Hope you keep coming back to /sci/.

If I want to be an engineer, is it important to learn pure math or proofs? I don't plan on being part of academia for the rest of my life. Fuck that shit, I've been in school for over 16 years now and I want to leave as soon as possible.

>>3904302
hey kiddo, everything before high school doesn't really count as "academia" and even high school hardly counts

university is an entirely different ballpark, you may enjoy it if you find the will to work hard within yourself

>>3904260
What made you switch to this new university that required a pay cut?
Besides your "real hours" don't you have to do other things? Like research, conferences, etc? Like I've read that it's extremely exhausting being a professor. Like how some spends countless hours doing research, spending weekends working/looking up things, etc.

>>3904314
Hey faggot, I'm in my third year of college and I wanted to know if learning pure math or proofs is essential to be a good engineer. That was my question, not "What is college like?"

OP, do you enjoy your job? Would you rather be working somewhere else, like in a non-academic setting?

>>3904325
third year of college is a bad time to be deciding if you want to be an engineer or not, especially if you don't even know what kind of math is required

>>3904241

I'm not gonna feed the trolls here, but the class was a master's level complex analysis class in the math department; it has proofs regardless of who takes it. And I don't know who said I was young; I may be "young at heart" but I am probably as old as most of your parents. Maybe a little younger. That's what I like to tell myself, anyway.

>>3904285

I don't know who said I was from Russia (someone emulating my hard-to-emulate tripcode?) but I'm not. I was born in the good old U. S. of A. I haven't even been to Russia before.

>>3904287

Out of the 60 or so Chinese graduate students we've had in our program in the last four years, there were only three who wanted to do pure mathematics, and one who wanted to work with me. He is certainly a hard worker, but he lacks the intuition and "creativity" that some of my other students have --- on the other hand, whenever I need a rigorous argument written up, he's my go-to guy. I have absolutely no problem with them, but we have recently had to institute a "hygiene" and "conversational english" course because there were a number of no-no's going on around the department and there was a significant amount of Chinese-only conversation which we felt excluded many of the other students from working with them and generally just made the department into cliques. We require the Russian, German, Persian, Indian, and French students to speak English --- I'm not so sure why Chinese students were the exception for so long.

>>3904302

The question is: is it REQUIRED? No. Absolutely not. Maybe some of your classes may require a bit, but no. Possibly if you're an EE, but otherwise, probably not.

>>3904331
Welp, my first year was spent taking general education courses(undecided major), and my second year I got into machining technology. Now I want to be an engineer. I'm currently finishing up an associate's degree in machining and taking precal.

Now see my original question.

>>3904350

It's kind of late, but there are a few programs that might allow that. Unless you haven't taken calculus yet. Then you might want to ask your advisor or some math\engineering profs.

Do you have any preference for which courses you teach, OP? I mean, is teaching a lower level class more enjoyable since you know people are probably not as familiar with it, or do you prefer to teach more "seasoned" students in upper level classes?

>>3904370
Late for what?
Allow what?

>>3904381
like I said, third year in college is a little late to be choosing your major, especially one like engineering

>>3904403
he can just do an extra 2 semesters amirite