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2
votes
1answer
54 views

What kind of programming does a mathematician/mathematical engineer need to know?

I was thinking about which program to choose for university studies, and I will probably study an engineering program kind of like mathematical engineering. It is kind of hard to specify a ...
7
votes
5answers
146 views

Composition of Inverse Functions

$f$ and $g$ are inverses of each other when $f(g(x)) = x = g(f(x))$. However, can there be 2 functions where $f(g(x)) = x$ but $g(f(x))$ does not equal to $x$? I feel like there are but I cannot find ...
2
votes
1answer
64 views

resources to get a taste of advanced (graduate) math?

There are a lot of ideas which I'd like to learn more about but that would take years to reach if I follow a traditional path (where "traditional path" means a kind of education where things are ...
1
vote
0answers
17 views

Introductory text on numerical analysis [duplicate]

I was wondering if anyone has a good suggestion for a textbook on numerical analysis. I am an undergraduate with little prior knowledge about topics in numerical analysis since I have never taken a ...
1
vote
3answers
27 views

How likely are extreme observations in a probability distribution?

Given a measurement that follows a probability distribution (for the sake of argument, Gaussian) how likely is it that repeated observations on the distribution are an extreme of low or high? I ...
4
votes
0answers
46 views

The “muscle” behind the fact that ergodic measures are mutually singular

This is really motivated by the soft question at the end, but let me begin with something more circumscribed: Let $(X,\mathcal{B})$ be a measurable space and let $T:X\circlearrowleft$ be a self-map ...
1
vote
1answer
27 views

Exterior derivative cohomology

Let $\Omega^k (U)$ denote the set of differential $k$-forms on an open subset $U\subseteq \mathbb{R}^n$. For each $k\in \mathbb{N}$ the exterior derivative $d_k=d : \Omega^{k-1} (U) \rightarrow ...
3
votes
3answers
56 views

If $1$ was a prime, could it be possible for the prime factorization of any number to go on forever?

If $1$ was a prime, could it be possible for the prime factorization of any number to go on forever? I think this would happen because if you multiply anything by $1$, you get the first factor ...
3
votes
1answer
78 views

Studying for analysis- advice

I find that studying for analysis is unlike other math classes that I've taken. I dedicate a lot of time to studying for it, but it seems like no matter how much time I put into it I am not getting ...
9
votes
2answers
1k views

The Big Book of Proof

Some time ago, I came across an anecdotal story about the "Big Book of Proofs" that God always keeps up in the heaven, which records valid proofs of all theorems in the world. A noted mathematician ...
7
votes
2answers
88 views

How can using a different definition for the integral be useful?

It's often said that the Lebesgue integral is superior to the Riemann integral because it satisfies nicer properties, for instance things like $$\lim_{n\to\infty} \int f_n = \int \lim_{n\to\infty} ...
5
votes
1answer
56 views

Is a thorough study of algorithms useful for a mathematician?

In my university, there is a core course called "basics computer science for mathematicians". The topics covered range from algorithms, to the bases of programming, to theory of computability. The ...
15
votes
9answers
2k views

“Honest” introductory real analysis book

I was asked if I could suggest an "honest" introductory real analysis book, where "honest" means: with every single theorem proved (that is, no "left to the reader" or "you can easily see"); with ...
1
vote
1answer
81 views

In war with exercise, any future for me?

I love theory with theorems, definitions & proofs, but i don't like exercise, I need more context around it. Is there a different way of practicing theory except given exercises, maybe some ...
2
votes
1answer
52 views

How to organize myself around calculus?

Calculus is the biggest topic i have encounter in math. Book that i am using is great, clear as can be, but so many definitions and theorems. I will like to have all most crucial def/thr as ...
2
votes
1answer
46 views

Is this notation for inverse functions bad?

I'm trying to find useful notation for inverse functions that isn't too much in conflict with other notation already in use, but I'm wondering if this notation will come back and bite me in the ...
0
votes
0answers
21 views

Looking for a Real Analysis / Calculus book with theory and proofs

I've encountered before with a certain ebook. It's background is orange. I think it's very popular book, but I couldn't remember it's name. Is somebody familiar with it?
0
votes
1answer
296 views

Is remaining single helpful in mathematical career? [closed]

Even though marriage and children can occasionally be beneficial to one's mathematical research, I think most of the time they are doing more harm than good. For a married (male) mathematician, he may ...
1
vote
0answers
47 views

Is there a general notion of orientability, e.g. for the rationals?

I was discussing orientability with a friend today. To me, orientation is a subtle concept I hardly understand. To get my perspective across, I was trying to come up with spaces which are intuitively ...
8
votes
3answers
379 views

Instructive examples of elegant, clear, rigorous, terse, but “non-dull” mathematical prose

On the "About" page of the Mathgen project one can read: "More seriously, I think this project says something about the very small and stylized subset of English used in mathematical writing. ...
1
vote
0answers
50 views

Differential Geometry for Computer Science

I am looking for a good book or other resources on Differential Geometry for Computer Sciences or more specifically Differential Geometry used in Computer Graphics, Geometric Modelling and Mesh ...
0
votes
1answer
24 views

Verify if symmetric matrices form a subspace

I need to verify if the symmetric matrices form a subspace. But I don't know how to represent a general symmetric matrix. I know that the matrix $A$ is symmetric if $A = A^t$ but I can't write a ...
3
votes
1answer
73 views

Great books on all different types of integration techniques

It's coming up to Christmas so I can ask to have all the books I can't afford from begrudging relatives! I'm really interested (mainly from looking at some of the answers cleo and other fantastic ...
3
votes
1answer
68 views

Can every basic concept of fundamental group be generalized to homotopy group?

I'm taking (undergraduate) algebraic topology this year and I have learned some basic concepts in this subject. I found this subject interesting, but it seems like the usefulness of fundamental groups ...
4
votes
0answers
45 views

Why not differentiable manifolds that are not of class $C^1$

In most, if not all (I cannot say for sure) references on manifolds, we seem to consider $C^k$-manifolds, including the case $k = 0$, which corresponds to topological manifolds. This means that we ...
56
votes
4answers
1k views

“Advice to young mathematicians”

I have been suggested to read the Advice to a Young Mathematician section of the Princeton Companion to Mathematics, the short paper Ten Lessons I wish I had been Taught by Gian-Carlo Rota, and the ...
1
vote
0answers
28 views

Little graham's number, Graham's number and the Graham-conway-number

Sbiis Saibian desbribes on his site in section $3.2.9$ the "little-graham-number" He claims that Graham used this number (much smaller than "Graham's number") in his proof, and Gardner published ...
0
votes
0answers
23 views

Jonathan Bowers' multidimensional arrays

Sbiis Saibian designed a site with large numbers (first hit with the search Sbiis Saibian) In section $4.1$ he describes Bowers' notation, but unfortunately he did not come to the multidimensional ...
0
votes
1answer
23 views

Missing something about second derivative tests

I'm studying second derivative tests, concavity and inflection points in khan academy ...
2
votes
14answers
577 views

Interesting piece of math for high school students? [closed]

I'm giving an hour long lecture to high school math students with a fairly high aptitude in math. I want to present something a little advanced for them (undergrad level) that they have to struggle ...
1
vote
0answers
12 views

Help with finding an optimal bilingual skill-based routing calculation.

First time post, I'm not sure if it is in the correct forum but this seems to be as a good place to try: I was wondering if anyone out there had experience dealing with a similar issue or knew of any ...
38
votes
15answers
1k views

Nobody told me that self teaching could be so damaging…

Even though I've been teaching myself math for a couple of years now I only just started (a month ago) at the university. My experience is rather mixed. For starters, I'd like to mention that I'm 21 ...
3
votes
1answer
59 views

Why is trigonometry important in calculus? [closed]

I need to write short note why trigonometry is important is calculus and engineering mostly for presentation. I am not focusing on on what topic it specifically it appears (because I am guessing the ...
2
votes
0answers
51 views

How to decide which theorems from textbook to prove

I've noticed that theorems in textbooks roughly come in two varieties: those that are worth trying to prove yourself, and those that aren't. I'm not going to try and give criteria for "worth trying" ...
0
votes
1answer
47 views

$\mathbb R^2$ as a plane

What elements allow me to say that $\mathbb R^2$ can be seen simply as a plane (or not if that is the case)? Yes, $\mathbb R^2$ is a vector space (not only with that characteristic) with multiple ...
0
votes
0answers
50 views

Application Question - American universities strong in Differential Geometry?

Can anyone recommend some American universities (except those top 10 ones such as Harvard, Princeton, SUNY and Umichgan etc. ) which have departments with a solid focus on Geometry and Topology, ...
1
vote
0answers
12 views

relationship between Minkowski addition and the trajectory of a numerical controle machine?

This is a very naive question about the Minkowski addition. I hope not to be off-topic. I read in the Wikipedia's article dedicated to it : In numerical control machining, the programming of the ...
3
votes
1answer
50 views

Cut Mobius Band

$$\text{Cut a Mobius band from its center line, and then what do we get?}$$ Someone may find it's not easy to imagine without a paper in hand. However, if we cut a square paper from center line at ...
1
vote
2answers
55 views

Topics for a Ted-Talk-like presentation! (Topology/Non-Euclidean Geometry)

I'm looking for a good topic to base my presentation on (length: 15-20 mins). I'm a freshman mathematics student, and my audience won't be skilled in mathematics beyond high-school maths. I've been ...
3
votes
2answers
70 views

Are there any disadvantages to working in the category of k-spaces as opposed to Top?

Unlike the category Top of topological spaces with continuous maps as the arrows, the full subcategory of compactly generated spaces (k-spaces) is Cartesian closed. It seems like a very nice ...
2
votes
2answers
344 views

Is Physics really a rigorous subject? [closed]

Though I can't give a precise definition of the term rigor (or better to say mathematical rigor) but intuitively in case of mathematics one may note that when we say that 'the proof is rigorous' we ...
8
votes
10answers
350 views

Real analysis book suggestion

I am searching for a real analysis book (instead of Rudin's) which satisfies the following requirements: clear, motivated (but not chatty), clean exposition in definition-theorem-proof style; ...
0
votes
1answer
63 views

How to make a mathematical text more concise

My PhD thesis has 175 pages A4 and I shall provide also a compilation that will summarize the main results on 20 pages A5. My thesis contains algorithms and theorems examining their properties. After ...
1
vote
0answers
38 views

Is there are “sphere” associated to any topological vector space?

If I have a topological vector space that is not locally compact, is it still possible to associate to it some natural "sphere" like object? For locally compact Hausdorff spaces, the my first guess ...
-1
votes
0answers
25 views

To understand mathematics [duplicate]

How do I achieve a good understanding of university level mathematics in order to do research in ? How do I know that the piece of math is understood and that I can go ahead?
0
votes
0answers
44 views

Geometric Meaning of Luna's Slice Theorem

I found the Luna's Slice Theorem very Technical. It will be helpful if someone illustrates the geometry involved in the theorem. Also why this theorem so useful? This is Luna's Slice theorem from a ...
63
votes
8answers
8k views

Will it become impossible to learn math? [closed]

I was thinking about this today and it seems like a good question. Assuming mathematics will keep on expanding, do you think it will ever become impossible for a beginner to learn all the known ...
3
votes
1answer
80 views

Advice for Math Majors -What to do if you come into college with a lot of college credit? [closed]

In high school I was a good maths student and took AP Calculus BC my freshman year and got a 5 and then took Multivariable Calculus, Linear Algebra, Differential Equations, Introduction to ...
2
votes
0answers
16 views

Does this matrix have a name: $x=(x_0, \ldots, x_n)$, $S(x)_{i,j} = x_{i+j \mod(n)}$. Can you help me generalise the idea?

Apologies if this question is vague/unclear (especially the title). Given a vector $x=(x_0, \ldots, x_n)$ define the matrix $S(x)_{i,j} = x_{i+j \mod(n)}$. $$ S(x) = \left( \begin{array}{rrrr} ...
0
votes
0answers
21 views

Physical interpretation of the integral formula for the solution of Laplace equation with Dirichlet/Neumann boundary condition

Suppose we have a bounded domain $D$ with smooth boundary, with $G(x,y)$ being the Green's function for the Poisson equation on $D$, i.e. $G(x,\cdot)=0$ on $\partial D$ and $\Delta_y ...