/sci/ - Science & Math

[mathfag No.3936180]

It's Friday, /sci/, and I'm at my wife's mother's house. So, it's time to ask a math prof things.

[Anonymous No.3936187]

your wifes mom is a math prof? rock on, that's awesome

[Josef crossed the Atlantic !!nUf2NflSAyw No.3936189]

What's your field of interest?

[mathfag No.3936193]

No, my wife's mother is something like 87 years old and worked in a box-processing factory when she was younger. She is a nice woman, though.

[Anonymous No.3936192]

>>3936180

Cool. What is the realistic implication of dividing a number by zero. Most teachers say, "You just can't" but I'm wondering, "Why not?" In reality, I have a pie, and if I divide it by nothing, then nothing happens, the pie still exists.

[Anonymous No.3936194]

Apostol, Stewart, or Larson?

[Anonymous No.3936198]

>>3936192
Not that guy, but in most systems "dividing by zero" doesn't mean anything. You might as well ask what's green divided by Tuesday.

[Anonymous No.3936209]

>>3936198

What's Green divided by Tuesday?

[mathfag No.3936227]

Sorry all, I was getting a strange MySQL error.

[Anonymous No.3936239]

I enjoyed your last thread buddy.

Do you know much about stochastic calculus? I think I'm going to fail this unit, I just can't get my head around these shitty and over complicated notes my prof hands out. Know of any well written texts on the subject?

[Marion Bartoli is my Waifu No.3936240]

What's your Erdos number?

[Anonymous No.3936241]

>>3936192
>>3936192
no, you just didn't divide it, you didn't divide it by nothing

[Anonymous No.3936247]

If a student of yours gets a 100 on the final, do you think they would be worthy of a recommendation letter just for that?

What do you suspect other professors feel on that?

[Anonymous No.3936250]

>>3936180
>>3936180
what is your opinion on adderall/other study drugs? do your students take it? do you think it can make people better at math?

[Anonymous No.3936252]

Russian dicks, sir

[Anonymous No.3936261]

I'm a math/physics double major. I've gone through some shit lately, but I feel like I'm ready to start taking school seriously. For a while know I've been partially aware of the beauty and elegance of mathematics. Enough to spur me to want to study it for the rest of my life. However, I need work with my discipline and motivaiton.

What would you tell a 20 year old college freshman taking a piss-easy calculus I class at community college to do in order to be more involved with math? I took calc I in high school but I like how this class goes into a little more depth. However, it's still pretty easy (since I've done most of it). I want to learn the concepts, the ideas, the schools of thought and different fields. Do I just have to expose myself to the shit out there?

I don't even look post the problems we're assigned. I feel like I should look at all the homework problems and try to do the challenging ones the teacher does not assign, but I just don't (due to time constraints because I procrastinate and still waste away on the computer).

I'm in the middle of changing some habits in my life, and I want academic passion to be one of those changes.

I guess this is just me asking for advice. And ranting as I'm coming down from a 36 hour amphetamine binge.

[Anonymous No.3936262]

I dont think he's coming back

[mathfag No.3936265]

Sorry, guys, I was getting some strange MySQL error for a while.

[mathfag No.3936267]

>>3936189

Algebraic Topology [broadly] and I am currently working a little bit in developmental biology [via a project I'm doing with another professor from my uni; it's more interesting than I thought it would be, really!].

>>3936194
Spivak.

Kidding. For a beginner calculus 1 course, I have always insisted on Stewart for the following reasons: clear exposition (except, possibly, sequences and series), tons of examples, TONS of problems, a number of interesting topics scattered around inside. Other books are fine, but in my opinion nothing touches Stewart.

But once you've done Stewart, Spivak should be your Calculus book of choice.

>>3936198
Speaking slightly more generally, an element m/n is defined as an equivalence class (m,n). You've seen this before. We have things like 2/4 = 1/2, so (2,4) = (1,2). In general, we have the following:

(a,b) ~ (c,d) if and only if there is some element k such that k(ad - bc) = 0. Usually, in the reals, we have k = 1; in this case, this is entirely general [see Field of Fractions]. So suppose we have (a,0) which is division by zero. Then we have our criteria above reduces to

kad = 0

And so there are several choices that allow this to happen. For example, we could let d = 0. We could let a = 0. We could let k = 0. If we let k = 0, then 0 is in our "denominator ring" and everything is equal to itself; we get the trivial field. If we let a = 0, then we have that c/d is equivalent to 0/0 for any c,d. So this is, again, the trivial ring. If we let d = 0, then we have the equality a/0 = b/0 for all a,b. But taking b = 0 gives us what we just mentioned.

Hence, if we allow division by zero, it requires us to work in the trivial field.

[Anonymous No.3936268]

do these make you upset mathfag?

[Anonymous No.3936272]

>>3936194

I wasn't aware Larson was a widely-used elementary calc book. My community college uses it. Now I feel a little better about using it compared to the "University Calculus" text I used when I went (and failed) to university for a year.

[Anonymous No.3936276]

>>3936265

Well if your lying to us and your actually a computer server running mysqladmin. You might be getting hack, bron.

[Anonymous No.3936280]

>>3936272
What was your major and how did you fail?

I never heard of "Univeristy Calculus". Mind telling the author of the book?

[Anonymous No.3936284]

How do you feel about racism threads on /sci/? Should econ threads be banned?

[mathfag No.3936285]

>>3936239

I think you mentioned this in a previous post of mine, because I had to look up exactly what was meant by Stochastic Calculus; I was unable to find anything even remotely readable. A colleague of mine had lecture notes from when he taught something similar [on Brownian Motion], but I got through the first few pages and (honestly) got bored and quit it.

>>3936250
As far as I know, none of my students do any "learning-enhancing" drugs, but I don't know any of them "personally" well enough to know. I know that it's a huge undergraduate deal and there are a number of students who do it. I don't recommend it, but I do see where it is coming from. Back when I was in undergraduate, there was significantly less competition for things and the classes were a bit milder (since we had no internet, we were not expected to know results which were not in an available textbook, etc.). One of my undergraduate students who didn't get into med school [she was a math major] noted to me that grades matter the most for med-school and they wouldn't even care that she took things like abstract algebra and topology --- and this kind of thing breeds all sorts of terrible consequences. Upsetting, really.

[Anonymous No.3936290]

Were you able to make sense of Euler's Identity seconds after the first time you saw it?

[Anonymous No.3936291]

>>3936280

I was (am) a physics major at the time and I failed because of a combination of me never learning decent study habits while in high school, having no self-discipline or self-control, skipping classes and the subsequent depression from shirking my work and choosing to practically lock myself in my dorm room glued to the internet to forget the outside world. I've never had that freedom in my life and I obviously wasn't ready for it. I didn't want to grow up. I'm gradually learning to do so. I'm pretty sure that covers why I fucked up my first college experience. I'm still not completely sure what happened at that point in my life.

Despite all that's happened in my life lately, fucking up university is still my biggest regret.

[Anonymous No.3936293]

What books do you consider vital for all mathematicians, regardless of field?
Do you have a favorite theorem? What is it? (Mine is hilberts 10th problem btw).

What areas of math do you consider vital, regardless of field? As in, you need to know more than most undergrads?

[Anonymous No.3936294]

In your last thread you mentioned that you had a disliking towards engineers because they disliked the proofs you assigned as homework.

Why should they, as engineers, be forced to learn proofs? What benefit does it offer them when they have no interest in becoming mathematicians.

I don't mean to sound antagonistic, I'm curious.

Also, I've heard that math PHD students very rarely do any original research, and most simply review another persons work. Is there any truth to this?
(as pretty much everything has already been done except for the ridiculously challenging and abstract stuff)

[mathfag No.3936295]

>>3936272

Larson and Sallas are two books that a number of unis use because, honestly, they're cheaper than Stewart. We use Steward mainly (at least I think mainly) because I make a big stink about it every year. But I know it costs the school quite a bit more than if they were to use Sallas.

>>3936284
If anything, econ threads should be promoted. Unfortunately, econ and public policy are often tightly knit; this can cause some upsetting and fruitless debating. Often, though, one can go to econ blogs which are, for the most part, apolitical (or, at least, have some posts which are somewhat apolitical ---) and learn some. I personally feel that everyone should learn at least some micro-economics. In fact, Greg Mankiw (who writes the standard textbook on the subject for undergraduates) has a blog which I follow and enjoy.

[Anonymous No.3936306]

>>3936280

Oh yeah, the authors of "University Calculus" are Joel Hass, Maurice D. Weir, and George B. Thomas, Jr. Publisher is Pearson - Addison Wesley.

[Anonymous No.3936305]

>>3936295
funny how you avoid the racist part of the question? you a racist professor?

[Anonymous No.3936316]

>>3936272
If you are taking a course that requires proofs, then you should do the fucking proofs. I study engineering, and honestly there's a shitton of stuff I'll never see or use again, but that doens't mean I have the right not to learn and do them whilst at university.

[mathfag No.3936332]

>>3936290

Euler's identity is something that requires complex analysis to understand and complex manifolds to "see". It may even be more deep than this. So, seeing as how I still don't "get" it entirely (in that the deep correlations between an Exp function and the values of certain nice elements in an extended field are not entirely obvious to me in general) I don't think I got it when I first saw it either.

>>3936293

Find a mathematician who doesn't have space for many books but has been working in the field for a while; you'll notice that they have one or two books per subject. These are usually the ones that are either amazing texts or amazing references; sometimes both. Here are my opinions. Regardless of field, you need "the big three": analysis, topology, algebra.

Analysis: Rudin's Complex.
Algebra: Dummit and Foote's Algebra.
Topology: Munkres, Hatcher.

For reference, Lang's Algebra and Bredon's Algebraic Topology.

Next, a linear algebra book and a calculus text book. I have Strang's Linear Algebra and Spivak's Calculus.

Next, at the very least, you should skim through: Enderton's Logic; Linear Algebra Done Right (AFTER doing Linear Algebra "wrong"); Algorithm Design (the book has Birds making a nest on the front); and Spivak's Calculus on Manifolds.

After this, it's somewhat field-specific, but Differential Geometry / Topology, Lie Algebras and Representation Theory, and Category Theory come up quite a bit in most fields. There are various "okay" books for each of these.

As for vital fields: Algebra, Analysis, Topology. I consider these mandatory for any professor in any field to know. Linear Algebra (if we count this as separate) is also crucial.

[Anonymous No.3936338]

>>3936316

Dude I'm in a calculus I class in my first year of community college. My teacher assigns all odd problems and doesn't have a due date for homework, has no quizzes, and is very laid back. Their highest math course is differential equations. It's easy but not conducive to what I need to learn.

I want to know how I should go about familiarizing myself with the concepts and problems of math I'll need to know and should want to know for my major. I don't just want to go to the classes and follow along, i want more. How do I do it?

[mathfag No.3936346]

>>3936305

I don't usually answer troll-ish questions. I'm obviously not a huge fan of the "are white people better!?!?!" threads or articles that pop up sometimes in newpapers and such. The only thing productive I can see coming from racist or potentially-racist tendencies would be affirmative action change --- and this is something I feel somewhat strongly about, but not for the "race" factor. I dislike having to treat students differently based on if they are an AA student or not; if you do C+ work, you ought to get a C+. Period. I should not have to curve a student up because they are AA.

>>3936293

My favorite "accessible" theorem [that is, one that I learned before specializing] was Liouville's theorem. It seems so mild at first, but you realize that it has HUGE implications. For example, what if you have a complex function where the real part is greater than, say, 1 everywhere on the complex plane? Bam, constant. Insane.

[Anonymous No.3936356]

>>3936332
cool looks like I'm already set for topology.
I'll have to look into the other ones though

[Anonymous No.3936360]

>>3936346
thats it your done. I will find out who you are and I will report for your racist tendencies.

[mathfag No.3936367]

>>3936338

This type of attitude is good to have. What exactly is it you'd like to study? In general, most textbooks are available online, and you may be able to use things like math stackexchange to look up and ask questions based on what you're reading. What I tell some of my more advanced undergrads is: see what the curriculum is at a school you like (yale, harvard, uchicago, penn, caltech) and plot out some stuff to study. Then for each class, look up a syllabus from somewhere where it was taught, and what homework was assigned. Do it as if you were in the class. If solutions are posted, check them; if not, ask a professor if you're stuck (or, if one is not available, ask for help online; tons of resources).

I should warn, though: self-study is ALMOST NEVER considered as a legitimate way to learn mathematics as far as universities are concerned. For example, if you say you have studied complex analysis by yourself, the department will be EXTREMELY SKEPTICAL. Since you are not allowed to take a placement exam before you are accepted, this creates a problem: you can do it, you say you can do it, but no one will believe you.

(It's upsetting, but, to be honest, 99% of the "self-study" cases I've seen fall significantly shorter than what they claim to be able to do. At the very least, be modest about your self-study when talking to other unis.)

[Anonymous No.3936374]

>>3936346
> if you do C+ work, you ought to get a C+. Period. I should not have to curve a student up because they are AA.

Fucking yes.

[mathfag No.3936379]

>>3936346

Let me clarify my claim here: not all of our AA students are minority students; some are just older students who are continuing education or whatnot. My problem is that sometimes the professor is required to have a "normal curve" which curves the class as a whole, and then an "AA curve" which boosts the grade of the AA student artificially. In not-so-rare instances, an AA student who does poorly on the exams and poorly on the homework will receive the same grade as a non-AA student who does mediocre on the exams and well on the homework. This, for me, does not feel fair --- we're taking AA students because they were disadvantaged, and we're helping the "catch up" by giving them a handicap they will not receive in the "real world"? Seems a little backwards.

[mathfag No.3936385]

>>3936356

Note that if you are doing topology, you should have more books than what I just mentioned. I simply listed the books I feel EVERY [pure] mathematician should own.

[Anonymous No.3936388]

>>3936374
hurr you're racist just like me durr I'm so randum xD

>>>/b/

[Anonymous No.3936401]

>>3936367
>>3936367

I honestly have no idea what I'd like to *specifically* study. All I know is I'm double majoring in math/physics and I can recognize (if only a little bit) the role that mathematics plays in our universe (and possibly beyond). I know I want to do something with physics, so why not throw a math degree in there since a lot of the undergrad coursework is similar (I think?).

I know what I could do to supplement my knowledge of mathematics, but the problem I have is with self-discipline and organization. I avoid planning my future, I haven't really given any deep thought as to what I want to do or become. I need a healthy dose of "grow the fuck up" Unfortunatley, they don't offer this online.

[Anonymous No.3936408]

>>3936367
I self studied trig and algebra at 20 years old (fucked up real bad in high school). I placed into Calculus 1 after taking a placement test and now have a 98% after the 2nd midterm. Hoping to get a 100% on the next midterm. I'm the professors favorite student but I will admit that somethings calculus does require a little more explanation from a teacher for me to understand it (theorems and stuff).I plan to self study all of calculus 2 before taking it.

[Anonymous No.3936420]

how much do you get paid as a prof?

do you think you will ever contribute to your field in a tangible way?

[Anonymous No.3936419]

>>3936379


Wow I had no idea this happened.

Huh.

[Anonymous No.3936448]

So...where do you teach?

[mathfag No.3936449]

>>3936420

Not enough. I have been paid from $60k - $85k in my life, depending on where I was. That should give you a good idea of what I make. But remember, this is a 9 month salary.

I've made a few contributions in my field (my extremely specific one). But as far as math in general, very few people can do that. For example, do you know who Francis Macaulay was? Most don't. And yet he made immeasurable contributions to a number of specific areas of mathematics [most notably algebraic geometry]. Therefore, I don't try to think about making huge changes in mathematics --- I just try to do my best and have fun doing it. After all, besides being a love of mine, it is also, in particular, my job.

[mathfag No.3936453]

>>3936401

Sure, this is reasonable. Some note that math is simply the language in which science is done, but this is not entirely accurate; with language, usually, we do not "dive into the depths" to try to find new "truths". Instead, some note that math is a good way to model science which is, in turn, a good way to model the real world. We then have

Math => Science => Real world

and, in turn, the real world give us information about what we should study in science, and science (at times) dictates what kinds of math to focus on, and, hence,

Math <= Science <= Real World.

Some people note that things like, say, 5- and 6-dimensional manifolds will never ever come into play in the real world --- but, in fact, various models of NORMAL phenomena require 5 and 6 dimensions (not necessarily spatial).

As for doing math because it's probably going to share a lot of stuff with physics so "why not", this is an okay way to think, but just remember that your major should be the route to something you love. If you don't love math, or if you are just doing it for physics, then don't spend more time than you need to on it. In my opinion, it's better to have a solid student who studies one thing than to have a mediocre student in two things.

>>3936408

Again, this is not too bad. And the fact that you recognize you need to mature is also good. But this is just the uni part; for the "math" part, you may want to pick a hard problem and try working on it piece by piece. This might motivate things for you --- this is something I do for my students all the time. As far as your self-studying calc 2, I think it's a wonderful idea to go over material before a class. I highly approve.

[Anonymous No.3936466]

A random question maybe, but what book (or other resource) would you recommend for learning the basics of algebraic geometry? I am a physics student, but quite interested in math, and trying to grasp the basics of "basic" interesting math topics. Oh, and do you ever use category theory? I read half of a book about it, and it seems quite cool (even though I cant really see the full usefulness of it).

[Anonymous No.3936469]

Can you explain Cantor and cardinality please

[mathfag No.3936500]

>>3936469

Cantor was a mathematician, cardinality is roughly the size of a set.

>>3936466

For physics, it might require you to do a lot of extra work. Alg Geom in its purest form requires something called Commutative Algebra which, in particular, requires algebra. I think if you want something physic related, Differential Geometry is where it's at. Either way,

Comm Algebra: dummit and foote (the end of the book); atiyah and macdonald (the standard, but it is quite difficult); miles reid (much easier, less standard).

Algebraic Geometry: dummit and foote (the end, as well), miles reid, and Hartshorne (the standard).

Differential Geometry: do Carmo, spivak.

[Anonymous No.3936519]

>>3936500
I am doing physics, of course I have already studied differential geometry (I did in fact read do Carmo as well as Nakahara). Haven't read much algebra though, mostly group theory and representation theory of Lie groups and some such. The amount of math you need to really understand physics nowadays is quite staggering actually, just today I read part of a physics paper talking about Cech cohomology. Thanks for the book tips, by the way.

[Anonymous No.3936528]

>>3936180

I'm having trouble with a basic tensor analysis course, do you have any recommended readings?

[Anonymous No.3936534]

>>3936449
>>3936449
I do, and I don't even study maths. That is, if he's the guy responsible for macaulay brackets used to solve discontinuous loading on beams.

[mathfag No.3936545]

>>3936519

I apologize if I sounded like I was talking down to you; that wasn't how I meant it. Generally when physicists talk about differential geometry, it's because they're doing something like string theory which requires the bare bones of some of the more abstract things. If you've already done differential geometry, then you should have some of the backing for differential topology which is significantly more general and somewhat more interesting. Milnor has the groundbreaking text on this, and Pollock has another text on it which is great.

For algebraic geometry, though, there is no real way around doing the algebra --- after all, that's half of algebraic geometry. Your course of study will look like this:

Dummit and Foote (skim group theory, really work on ring and module theory, do long-exact sequences and all that, and start reading the latter few chapters). At the same time as your module theory learning, you should start Atiyah and start doing the problems in the beginning. When you get to around the middle of Atiyah, you can start algebraic geometry [but, note, it is highly, highly nontrivial. even in the base case, many of the ideas are abstract and difficult]. Also, a "real" power of Algebraic Geometry is the ability to use schemes to your advantage --- thus, Schemes (or some title like this, maybe Introduction to Schemes) by Eisenbud is useful.

[mathfag No.3936549]

>>3936528

Do you mean tensors in the physics sense or the algebra sense? In the physics sense, I believe that there are a number of good texts which introduce the topic --- maybe someone on this thread could recommend one?

[Anonymous No.3936556]

>>3936549

Algebraic sense I suppose. It's a pure math course, we're going to get into applications towards the end. Currently we're reading Lovelock and Rund with some selections from Schutz.

[Anonymous No.3936564]

One of the things I love about math is the fact that math research today could have applications hundreds of years in the future.

[Anonymous No.3936567]

>>3936290

[mathfag No.3936568]

>>3936556

Well, I learned them from Dummit and Foote, but they didn't really make sense until I learned about universal properties. Ah --- I'm not exactly sure about this one. They come up quite frequently, but they're sort of something you just get used to. They're similar to the direct product, but you can sort of "swap things" from each place in the tensor, and the things you can swap are the things in the thing you're tensoring over.

[Anonymous No.3936571]

>>3936528
For learning the basic notion of a tensor and how to manipulate indices etc., Lewis Carrols book on general relativity has a good introduction (and he doesn't skip too much mathematical details, none of this "defined in terms of how components transform" bullshit). That is of course for physicists, so if you are into pure math maybe other books would be better.

[Anonymous No.3936594]

I would like to study statistics.

What makes a good textbook?

Moreover, it seems to me that part of statistics is a philosophy of ontology, of asking the question: "What can I reasonably know?".

Is this a relevant perception? And how do I get into logic? Can statements be treated algebraicly?

[Anonymous No.3936606]

Is infinity a limit or a set?

Does the set of natural numbers include 0?

Is 0 even?

What exactly is "complex infinity"?

What is the most intuitive abstraction of the determinant?

What is your favourite colour?

[Anonymous No.3936604]

>>3936545
Ah, algebraic geometry sounds very difficult when you describe it like that, and I would probably need to work a lot on the algebra. Oh well, maybe I'll look into differential topology instead. So much to learn, so little time...

[Anonymous No.3936614]

>>3936606
The parity of 0 is even. I'm not even OP and I know this, fuck

[mathfag No.3936624]

>>3936294

I missed this question, sorry. And, that's a bit out of context; what happened was the following: I gave a course on complex analysis which was geared primarily towards math undergrads and masters students. Unfortunately (?) a professor in the physics department decided that all of his engineering students should know complex; thus, I got a ton of engineering students and one or two math students. Because the course WAS a math course, there were a great number of proofs. But this made the engineering students whine TO ME about how unfair it was that they had to do proofs.

I don't claim an engineer needs proofs. In fact, I don't think engineers should need to learn proofs. But if you sign up for a class that's all about proofs, don't whine that you have to do proofs. The problem, also, was that at various intervals they actually complained to the department heads, and I was inspected [the department chairs sat in on the class] and was given a stern warning about this kind of thing. The department head *told me not to include proofs on the final exam, because we didn't want to have to have a lot of grade appeals*. This is EXACTLY the same as saying, for example, that integrals and derivatives are useless to lots of people so we should not have to test students on integrals and derivatives in a calculus class.

This is why I hold a slight grudge against engineering students.

[Anonymous No.3936629]

>>3936606
A limit.
This is not universally agreed upon.
Yes.
A point at infinity in the Argand plane.
Whether or not a matrix has an inverse.

[Anonymous No.3936634]

>>3936624

>engineers shouldn't have to know proofs

I would be nice, though, if the people responsible for critical infrastructures knew why shit worked, in case, say, something went wrong.

[Anonymous No.3936638]

>>3936629

>ignores question about favourite colour

I like you.

[mathfag No.3936653]

Also, I'm not sure who told you math phd students don't do original research --- all of my students have done original research (and, in fact, it is required to get your PhD). There are ones which were fairly abstract, but I had one student who did a mild extension to something which was essentially linear algebra. There are many, many unsolved problems, even in relatively "easy" fields.

In addition, sometimes one can "see what happens" if such-and-such is done to some structure. For example, and this is just off the top of my head, what if we give a vector space a "triple product" <x,y,z> where this satisfies something like <a,a,a> = 0 for all a, <a,b,c> = -<b,a,c> for all a,b,c. Is this trivial? Does it have some cool stuff going on? I don't know. But it's something a student could work on and find things out about.

>>3936594

I suppose you could consider statistics like this. I'm not exactly sure if this interpretation makes sense in some settings, but regardless. Every textbook, to me, does stats equally well --- it's like calculus, all of the texts are sort of "okay". I don't know an awesome one, though.

Mathematical logic [which is slightly different from philosophical logic] can be learned from Enderton's book which is, I think, called Mathematical Logic. It's pretty good, but gets heavy near the end.

>>3936606

It's the additional point on a one-point compactification to me; no; yes; it's infinity times i, I would imagine; the determinant is the hypervolume of the parallelepiped which is spanned by the application of the transformation on the standard vectors of euclidean space.

[Anonymous No.3936735]

>>3936653
Regarding your example, there is in fact something called generalized vector cross products which are defined more generally as antisymmetric products of n vectors giving another vector, with the property that (x,y,...,z)=0 if any two vectors are linearly dependent, so it's almost the same as your example. These are quite interesting when defined over vector bundles, and can be used to define instantons and branes (both which are interesting from a physics perspective).

[Anonymous No.3936753]

>>3936653
I am a physics student. I am not allowed to be examined in courses not of my department, but I can still attend math courses. I want to pursue mathematical physics. Can I bridge the gap by studying by myself?

[Anonymous No.3936799]

What do you think of mathematical finance and actuarial science? Should it be part of math or is it more business?

Also, do this ever happen to you? pic related

And I love your threads by the way!

[Anonymous No.3936818]

>>3936799

http://en.wikipedia.org/wiki/Hypnic_jerk

[Anonymous No.3936830]

"In mathematics you don't understand things. You just get used to them." - Von Neumann

Have you ever felt like this before?

[Anonymous No.3936859]

OP: why is linear algebra such a high level math thing, while the two words that make up its name are not :(

[Anonymous No.3936879]

You are a bro for answering these questions. Very thorough.

[Anonymous No.3936883]

>>3936799
http://en.wikipedia.org/wiki/Hypnic_jerk

Tons of people get that.

[Anonymous No.3936889]

>>3936379
>separate affirmative action curve

Dear god how horrible. What state do you teach in?

[Anonymous No.3938159]

>>3936859

Not OP, but Linear Algebra is a lower division course, so it's really not that high level. It's one of the first classes you take as a math major.

[Anonymous No.3938256]

Wow, a legit scibro (or mathbro?). Anyway sir, how do you think should a student study mathematics in a general sense? Should I put put more time studying the concept (which I prefer) or should I do/practice solving problems more?

I hope he's still here.

[Anonymous No.3938385]

What do you think of the lack of applied mathematics in many american math programs. Should there really be math graduates, who have never taken a measure theory based probability theory class or don't understand how the simplex algorithm works?
Some of them don't even know algorithm like the FFT or FEM which most engineers use every day.