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0answers
14 views

Enlightening books giving a guided tour of mathematics, in a style that Gian-Carlo Rota would not mind?

I am currently reading Gian-Carlo Rota's Indiscrete Thoughts. What more can I say apart from "the man can write"? (In other words, you should really read it if you are interested in mathematics.) I ...
2
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0answers
11 views

Cross product of cohomology classes: intuition

Let $X$ and $Y$ be topological spaces and consider cohomology over a ring $R.$ Hatcher (in his standard Algebraic Topology text) defines the cross product of cohomology classes $$H^k(X) \times ...
2
votes
4answers
104 views

What is a good topic for an essay on applications of Calculus 3?

In a class I have, the professor has offered extra credit for 1 page paper on a topic in Calculus 3 that has an application in the real world. I know calculus is used a lot in physics but I do not ...
2
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5answers
112 views

Reference Book on Special Functions

Now I'm studying the topic that uses the special functions frequently, so I find myself in need for some good reference book on the properties and equalities of the special functions. The optimal one ...
11
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11answers
729 views

If there are obvious things, why should we prove them?

Obviously, there are obvious things in mathematics. Why we should prove them? Prove that $\lim\limits_{n\to\infty}\dfrac{1}{n}=0$? Prove that $f(x)=x$ is continuous on $\mathbb{R}$? $\dotsc$ Just ...
3
votes
1answer
50 views

Mathematics or physics at university

I have a strong interest in maths, and I feel that advanced physics is cool too (although I've only studied classical mechanics at high school, which is kind of boring). So I'm not sure about which ...
2
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0answers
24 views

Dependencies of various of areas of maths

Specifically, I want to learn category theory to improve my programming ability in Haskell, but it seems like that would be difficult without a knowledge of abstract algebra, and it seems that a solid ...
1
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0answers
49 views

How exactly does the response “infintely many” answer the question of “how many”?

I admit that the level of this question is roughly about middle school, but this is what the question asks: The ratio of nickels to dimes to quarters is 3:8:1. If all the coins were dimes, the ...
2
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1answer
40 views

What is the optimal strategy for increasing my 'mathematical maturity'? Depth or breadth? Number theory or measure theory?

My apologies for such a general question, but as a 'math enthusiast', I've often wondered what the optimal strategy is to increase my mathematical maturity. Broadly, should I aim to hunker down & ...
0
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1answer
39 views

Preparation for a graduate commutative algebra course based on Eisenbud

I am an undergraduate with two semesters of algebra(groups,rings, Galois theory, etc) under my belt and I am planning on going through Atiyah and MacDonald's book over the summer. Is this sufficient ...
2
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3answers
103 views

Mental Math Tricks [on hold]

What are some interesting mental math tricks that you know? Here's one that I got from my Grandmother who got it from a book: To square a two-digit number (from $26$ to $49$), take the number minus ...
2
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0answers
23 views

Revise high school material

Can you suggest me a comprehensive book to revise high school mathematics (up to besic calculus)? It should be extremely clear and complete and "scientific" (not like most high school books). Thank ...
2
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2answers
37 views

Material for advanced highschooler

I'm a high school student who just finished elementary school.Though since I was into math I started going through advanced math while I was in elementary school and I pretty much finished most of the ...
5
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0answers
52 views

Gap Year Advice-Becoming the Best I can be

I'm an undergraduate studying Mathematics at University of Cambridge. Very recently I had to take an intermit leave due to medical reasons during my second year as an undergraduate. During my time, I ...
3
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3answers
75 views

Things to do before starting math (or physics) at university

What is better to do before starting a math degree? I was thinking that maybe I should do something like: learning latex learning how to use matlab Any other suggestions?
1
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2answers
26 views

Cycloidal coincidence?

For the cycloid $$x=a(t-\sin t)\ ,\quad y=a(1-\cos t)$$ we have, as is easily seen, $$\frac{dx}{dt}=y\ .$$ Does this have any geometrical or physical significance? Or is it just a meaningless ...
2
votes
1answer
43 views

Does memorizing a proof help to provide the intuition behind it?

To be clear, I'm $\bf{\text{not}}$ talking about rote memorization. If I can follow a proof, follow each step on its own, but still have trouble believing that the result is true. I usually try to ...
8
votes
1answer
119 views

Create a Huge Problem

I am wondering if any problems have been designed that test a wide range of mathematical skills. For example, I remember doing the integral $$\int \sqrt{\tan x}\;\mathrm{d}x$$ and being impressed at ...
9
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4answers
337 views

Application of computers in higher mathematics

Currently the main application of computers in mathematics seems to be to compute things, i.e. to solve equations, evaluate integrals, etc. It is at all possible to delegate the thinking of a ...
2
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0answers
48 views

Changing research area in grad school

I'm a PhD student about to close out my third year. My current research area is operator algebras. At the beginning of this semester I completed my qualifying exams (this was accomplished a semester ...
5
votes
4answers
508 views

Topological groups, why need them?

I'm reading through Munkres and Armstrong's books on topology. However, I find topological groups to be really complicated objects! I feel they are twice as hard to deal with then just groups and ...
1
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3answers
30 views

Which discrete mathematics book to read for a software engineer?

I'm a computer science student, but I lack a good mathematics background. So I decided to start working on that. I was searching in the topic and I found that for computer science a good knowledge of ...
0
votes
1answer
32 views

In which course one learns Lie Group&Algebra and to which category of mathematics this subject belongs?

I'm a junior and i have never leanred this subject. I think "Lie Group&Algebra" is really deep and massive theory since the wikipedia page for it is quite long. Nevertheless, i'm not sure ...
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0answers
28 views

What courses require multivariable analysis?

For which undergraduate and introductory graduate mathematics courses is a rigorous course in multivariable analysis an essential prerequisite?
1
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0answers
31 views

Analogy between linear basis and prime factoring

I recall learning that we can define linear systems such that any vector in the system can be represented as a weighted sum of basis vectors, as long as we have 'suitable' definitions for addition and ...
1
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0answers
40 views

Applications of PDEs

I teach an undergrad ODE course. As I have completed basically all the material, I thought it would be nice to give the students a brief introduction to PDEs. At the end of the lecture, I said that ...
4
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1answer
90 views

Forgetting mathematics. Memory problem [duplicate]

I got an A from Game Theory. But after that i forgot almost all the formulas and theorems. What should i do to prevent that? Do you forget math like i do?
0
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0answers
65 views

Choosing between Universities for Mathematics [on hold]

I am trying to advise a younger friend looking into colleges and I was wondering what others would think: Is it better to go for a prestigious university where the focus would be almost exclusively ...
1
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1answer
69 views

Uncertainty of Graduate Mathematics

I will be starting my graduate studies next semester right out of my undergrad and I am uncertain about courses that I am ready to take. The main courses of concern are algebra, analysis and applied ...
0
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0answers
26 views

Proving Maths Skills for MSc Data Science Degree

In September I'll be applying for a Master's degree in Data Science (2015 intake). With the degree I hold (BSc Psychology), I will forfil the entry requirements provided I have a "demonstrable ...
2
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0answers
60 views

Calculus book advice

I'm reading Thomas Calculus now but I don't think it includes Mellin transform or Riemann-Stieltjes integration... Can you recommend an advanced calculus book which includes all of this stuff?
2
votes
0answers
21 views

Pure Math or Stats undegrad for Stats Grad School

Hello I'm currently a first year undergrad double majoring in physics and math. My school offers both a pure math and a statistics concentration and I'm wondering which one would be better for ...
0
votes
0answers
23 views

A nowhere zero point in a linear mapping and Research Resources

Conjecture: If $\mathbb{F}$ is a finite field with at least 4 elements and $A$ is an invertible $n\times n$ matrix with entries in $\mathbb{F}$, then there are column vectors $x,y \in \mathbb{F^n}$ ...
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8answers
6k views

Are there contradictions in math?

Someone told me that math has a lot of contradictions. He said that a lot of things are not well defined. He told me two things that I do not know. $1+2+3+4+...=-1/12$ what is infinity $\infty$? ...
0
votes
2answers
21 views

what are some typical systems of equations generating from practical problems?

I want to know some typical forms of system of equations generating from practical problems in engineering/economics/physics,etc. Some examples or research articles would be good. Specifically, I am ...
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0answers
25 views

Do those red cubes aligned circulary next to MATHEMATICS have any mathematical significance? [migrated]

Or they just look fancy and that's why it was put there ?
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0answers
30 views

The term $rank$ in methematics

Reading wikipedia's disambiguation page about the "rank" word I see many concept of rank of many different matematical object. I only know about the rank of a graded poset and the rank of a set that ...
4
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0answers
74 views

Is it easier to publish in certain areas of mathematics?

I was wondering whether there are areas of mathematics that it is easier to publish in than in others. The reason I'm asking this question is not because I would then want to do research there, but ...
5
votes
1answer
29 views

Surprising constructions in algebraic topology that facilitate one's understanding of underlying theory

I am recently come into the world of algebraic topology and find it a fascinating place with lots of beautiful constructions that challenge one's intuition. Also, understanding these constructions are ...
0
votes
3answers
31 views

Question about variable and constant notation in some properties

I am just starting to think about mathematical notation a lot more and some parts of it do not make as much sense to me as I would like. I am operating under the convention that beginning alphabet ...
0
votes
1answer
43 views

Is there a significance to a matrix having an eigenvector equal to a column vector within a matrix?

Consider matrix $A$: $\begin{bmatrix} 2 & -2\\ 3 & -3\\ \end{bmatrix}$ After little computing, we find the eigenvectors (and their corresponding eigenvalues) to be equal to $E_{\lambda=0}= ...
0
votes
1answer
57 views

Is it bad for a potential grad schooler to take Abstract Algebra and Real Analysis my last year?

I'm taking Abstract Algebra and Real Analysis my last year. I've already taken the following: Calc 1-3 DiffEQ Complex Analysis Operations Research Linear Algebra Mathematics Foundations Theory of ...
2
votes
2answers
69 views

Does attempting numerous questions in Mathematics textbooks actually help?

Specifically for high school/college maths where the textbook contains numerous exercises with similar trivial examples - would attempting all of the questions actually be more beneficial than (lets ...
1
vote
1answer
88 views

Foundations book using category theory?

I'm about to embark on a PhD in mathematical biology. My major is in computer science. I would like to acquire a more rigorous understanding of math, which I am going to need to tackle some research ...
0
votes
0answers
15 views

Help disabling press-to-test [closed]

I've got a TI Nspire CAS (not the newest CX edition) and I accidentally put degrees instead of radians on Press To Test. Now it's stuck in this mode and the information at ...
3
votes
5answers
342 views

Jumping back into Calculus III

At the age of 30 I am going back to school for Electrical Engineering. Because of the way higher education works, all of my previous college coursework is being transferred, which does not allow you ...
3
votes
1answer
46 views

Gain confidence in maths.

I am a maths student and I really want to stand out in maths, to be good at it because I like it. But the transition from high school's computation-based maths to uni's concept-based maths made me ...
0
votes
2answers
54 views

Is 1 rad important?

Of course radians generally come in ratios of π. So is 1 rad important/useful/special? Or, for that matter, is any integer radian measure important? Besides being approximately 57°, I can't seem to ...
8
votes
3answers
634 views

Does writing a bachelor thesis make sense?

I am a math student in my fourth semester. At my university, it is common to write a bachelor-thesis in the end of the bachelor program in almost all subjects while in the math undergraduate program ...
1
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1answer
57 views

How to study analytic number theory?

Should i study many books at the same time? Or should i go one by one? I started with Apostol's book... But for example if i don't understand a proof, i check another book for a different proof of the ...