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0
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0answers
11 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 ...
5
votes
2answers
48 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. This ...
0
votes
0answers
28 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
21 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 ...
2
votes
1answer
36 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 ...
2
votes
1answer
31 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
32 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 ...
10
votes
1answer
102 views

Advice to young mathematicians (see Rota, Tao, and The Princeton Companion to Mathematics)

I was suggested to read the "Advice to a Young Mathematician" section of the Princeton Companion to Mathematics, this short paper by Gian Carlo Rota, and T. Tao's Carrer Advice, and I am amazed by the ...
1
vote
0answers
15 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
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0answers
13 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
0answers
20 views

how to present whether a series of numbers is increasing or decreasing

So I have a series of loan amounts from a customer ordered by date. I would like to calculate whether the customer is increasing or decreasing their loan amount over their history with us. I'm ...
0
votes
1answer
21 views

Missing something about second derivative tests

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

Interesting piece of math for high school students? [on hold]

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
10 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 ...
3
votes
1answer
50 views

Why is trigonometry important in calculus?

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
4answers
318 views

Can an empty set be both torsion and torsion free group?

I was wondering if an empty set can be a torsion group (since the definition of torsion group is that if $x$ is in the set $X$ has a finite order. However, the assumption is false, so the implication ...
2
votes
0answers
45 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
44 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
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0answers
38 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
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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
49 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
51 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
67 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
277 views

Is Physics really a rigorous subject? [on hold]

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 ...
2
votes
4answers
67 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
61 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
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0answers
29 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
24 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
42 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 ...
60
votes
8answers
8k views

Will it become impossible to learn math? [on hold]

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
72 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
14 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
15 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 ...
7
votes
0answers
92 views

Is there really anything wrong with Bourbaki's Set Theory?

Recently I have started reading Bourbaki's Theory of Sets on my own. Regarding one of the explanations of a concept when I went to a Professor of our college, he asked me why I was wasting my time ...
4
votes
2answers
76 views

where to start if you lack basics? [closed]

I've joined this forum for few weeks now and it amazes me that so many people are good at math. For me, I'm more of a history person rather than math person, so I hated math since I was young, not ...
5
votes
0answers
60 views

Apparent Arbitrariness in Mathematics

Something about definitions in mathematics has always interested – confused? - me, I call it “arbitrariness in Mathematics” - it's a bad name, but I don't know a better one. Let me explain: 1st - ...
5
votes
1answer
95 views

understand mathematics [closed]

Please, i need some clarifications and general remarks. I am a grad student in mathematics, once, our teacher give us a simple problem (involving vector spaces) and no one was able to solve it and he ...
3
votes
0answers
103 views

BA vs BS mathematics [on hold]

I am a software developer, I have a bachelor degree in information management. I wanted to do masters in computer science, but I am not eligible due to a lack of mathematical courses (linear algebra, ...
1
vote
0answers
83 views

What is a Toy Model for the mathematician's practice? Definition and examples

Wikipedia says Toy model (physics): "In physics, a toy model is a simplified set of objects and equations relating them so that they can nevertheless be used to understand a mechanism that is also ...
2
votes
0answers
29 views

Prerequisite to study smooth 4-manifolds

I am quite interested in understanding smooth 4-manifolds. What are the necessary prerequisites in order to start my study? Also can you please suggest me some good books from where I can start? ...
-3
votes
0answers
83 views

How did you get so good at math? [closed]

How did you get so good at math?
1
vote
0answers
26 views

Project-Math-Computing

Im an undergraduate student and me and my roomate who is an undergraduate also would like to do a project together. Im on the pure and some aplied math branch and he is on the computing branch.We are ...
2
votes
0answers
90 views
+50

Linear algebra and geometric insight: a rigorous approach to vector spaces, matrices, and linear applications

Could you point out some references (undergraduate level) that give a geometric understanding of vector spaces, matrices, and linear applications? As far as I know, many textbooks start with an ...
4
votes
0answers
53 views

For cardinals, if $\mathfrak{a}\ne\mathfrak{b}$ then $2^\mathfrak{a}\ne 2^\mathfrak{b}$

In the usual ZF (or ZFC) set theory, let $\mathfrak{a}$ and $\mathfrak{b}$ be cardinal numbers. Is it correct that one can neither prove nor disprove the statement: $$\mathfrak{a}\ne\mathfrak{b} ...
2
votes
1answer
46 views

Undergraduate Project Suggestions

A student of mine has expressed interest in doing an independent project next quarter with me. This would not be for credit and it is purely for her own educational stimulation. She wants to study ...
1
vote
1answer
25 views

lim inf and lim sup convergence/divergence

Assume that the following sequences are positive, then the statements: If $\lim \inf a_{n} > 1$, then $\sum_{k = 1}^{\infty} a_{k}$ diverges. If $\lim \sup a_{n} = 0$, then $\sum_{k = 1}^{\infty} ...
2
votes
0answers
53 views

Undergraduate Research Ideas?

I am just finishing off my final exam in my 2nd year of my degree in Mathematics & Applied Mathematics and have quite a long break coming up until I start my final year of undergrad next year. I ...
3
votes
0answers
32 views

Paper accepted in journal, should I remove style file for arXiv preprint? [migrated]

I recently sent a paper to a journal (which I put on arXiv beforehand) which has now been accepted with some corrections. I want to put the corrected version on arXiv. THe corrected version is written ...
2
votes
1answer
79 views

How to prepare myself for an advanced trignonometry exam

I'm gonna have a trigonometry/general algebra exam soon. My teacher has told us about some trignometric proofs, and we defined the $\sin$ and $\cos$ int he right way, doing all formal proofs for the ...
0
votes
0answers
36 views

Reference in other languages

In the reference of many papers there are usually papers/books which are not written in English; some German, some French, some Russian, etc. (I seldom see Chinese or Arabic ones, although there are ...