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2
votes
10answers
358 views

Fascinating limits? (highschool) [closed]

I wonder if there is someone who knows any cool limit who they're are willing to share. I have just started using them in highschool and is interested in learning more.
0
votes
0answers
60 views

How many exercises should I do in Spivak Calculus?

So I'm going through Spivak Calculus 3. Ed. and I'm still on chapter one. It's quite abstract but I'm managing. So far everything is clear but I'll get on the exercises real soon and I don't know if I ...
1
vote
1answer
37 views

Mentally visualizing functions of complex numbers

I've recently been learning about functions of complex numbers (to complex numbers), and I can't quite fit them into my head. When I think about real functions, I tend to mentally visualize them as ...
2
votes
2answers
91 views

Simple & Intuitive Statements that are Difficult to Prove

Looking through the webcomic, I came across one of my favorite comics: (from Saturday Morning Breakfast Cereal) It seems that people have an ongoing interest in results in mathematics that are ...
3
votes
1answer
104 views

Why are mathematicians more interested in elliptic curves than other algebraic curves?

Why are mathematicians more interested in elliptic curves than other algebraic curves? There must be some reason that motivates mathematicians to research elliptic curves specifically.
0
votes
0answers
62 views

Research Papers for undergraduate

I am interested in reading research papers and every time I have come across a paper it seems they are all far too advanced for me. I am an undergraduate currently enrolled in multivariable calc, ...
4
votes
0answers
38 views

Is there a way to figure out the minimum number of participants or maximum number of rounds in my tournament style?

I just finished hosting a Euchre tournament at work that was meant to get people to meet other people in the company. This is the third time I've hosted this type of tournament. The first two times, ...
0
votes
1answer
49 views

Where is the Pinching/Squeeze theorem in Spivak Calculus?

So I got Spivak Calculus 3. Edition. I'm starting it now but I want to know if there is the squeeze theorem clearly explained in the book, as I can't find it in the Appendix(pinching theorem, ...
2
votes
2answers
93 views

Solved Problems in Algebraic Number Theory

I'm not too sure whether this is the right place to ask this (and please correct me if it is not), but I'm currently studying a course in Algebraic Number Theory and would like to be pointed in the ...
3
votes
4answers
128 views

Soft question: Examples where implications derived from mathematical models failed to describe reality

I have always been fascinated by how well conclusions drawn from mathematical models could fit reality, so I wondered if there are any counter examples. In "Gödel, Escher, Bach" I could already find ...
2
votes
3answers
54 views

Software for plotting functions… Any suggestions?

I'm looking for a (hopefully cheap/free) software that could plot functions for academic use. Until this point, I used MATLAB as a primary tool to draw graphs. Although it 'could' plot any functions ...
1
vote
0answers
37 views

Soft question: is there a generalization of compactness satisfying these conditions?

A good intuition about compact topological spaces is that they're spaces that aren't missing any points (not really a huge fan of the "compact = small" intuition, but that's another story). ...
1
vote
2answers
84 views

Why is the $O$ (zero) matrix important?

In reading my linear algebra book I found it quite interesting that they made the following comment: One important property of addition of real numbers is that the number $0$ is the additive ...
3
votes
1answer
59 views

Amusing variations on difficult problems

I'll start with an example of what I mean. Everyone is familiar with Fermat's Last Theorem: $$a^n + b^n ≠ c^n \text{for $n > 2$}$$ A while ago (while reading Gödel, Escher, Bach) I encountered ...
3
votes
0answers
44 views

Good confusion-avoiding notation for gluing toric varieties from fans?

$ \newcommand\R{\mathbb R} \newcommand\C{\mathbb C} \DeclareMathOperator\Cone{Cone} $I'm trying to establish a good notation to avoid confusion when we glue toric varieties from affine pieces. A ...
5
votes
0answers
86 views

Intuition about structures in Galois Theory.

Background Often in mathematics I find we can ask "why" something is true. Of course, this is not a well defined question. However, it usually prompts answers that includes words like ...
0
votes
2answers
34 views

Should I create two distinct proofs? [*Soft question*]

This is a soft question, and if it is of poor quality, just let me know. As a method of improving my proofing abilities, should I make it habit to go about proving something twice. What I mean by ...
2
votes
2answers
315 views

Is my understanding of space correct?

I'm learning more about dimensions in multivariable calc, and have been able to make connections by studying level curves and level surfaces. I've learned that a function of 2 variables is really a 2 ...
0
votes
0answers
17 views

How do we connect our math.stackexchange account to our facebook page??? [migrated]

For instance, I would like to display on my FB page that I have an active account here. Is there some 1-click way of doing that? Has anybody done this? Thanks.
3
votes
3answers
109 views

Most inspirational mathematical books [closed]

I would like to know which books on mathematics (from university texts to divulgative pop-math books) inspired you the most. My choice is Spivak's Calculus, which is, IMHO one of the most ...
8
votes
4answers
766 views

Interesting mathematical problems for 1st year university students

Can you explain some mathematical problems that you find the most interesting (NB: the problem must be accessible to a 1st year university student: that is, a problem for which there is an elegant ...
0
votes
1answer
34 views

Borsuk–Ulam theorem for $n=2$

How one can intuitively prove the following statement: At any moment there is always a pair of antipodal points on the Earth's surface with equal temperatures. What about a rigorous proof?
42
votes
23answers
4k views

“Simple” beautiful math proof

Is there a "simple" mathematical proof that is fully understandable by a 1st year university student that impressed you because it is beautiful?
5
votes
3answers
84 views

Why can mathematicians pick and choose axioms?

Obviously, there need to be some 'self-evident' truths that we can't prove, but on which we base certain theorems; e.g. the axiom of choice lead to the well-ordering theorem (which could well be an ...
10
votes
0answers
258 views

Is this $really$ a categorical approach to $integration$?

Here's an article by Reinhard Börger I found recently whose title and content, prima facie, seem quite exciting to me, given my misadventures lately (like this and this); it's called, "A Categorical ...
1
vote
1answer
63 views

Is it possible to all find trigonometric values without calculator?

Except for 90,0,45,30,60,and other multiples of 5, are trigonometric values calculable without the help of a calculator?
0
votes
0answers
52 views

Understanding reasons for best constant in inequalities

Why, in functional analysis, is so important to calculate best constant in an embedding inequality? Cross-posted to ...
1
vote
3answers
74 views

Elementary linear algebra book

I read and enjoy Spivak calculus book; I was wondering if there is a similar book (in terms of problems, rigor, etc) for elementary linear algebra?
1
vote
2answers
43 views

What should I study to understand knot theory?

I want to ask for some advice :) I am aware that it might be a little early to get interested in specific areas/subareas at his stage, but the theory of knots interests me a lot. I've went ...
1
vote
0answers
34 views

Categorization of Mono, Epis in a Category

Let $C$ be a category. Then the following implications on variants for monos hold: Iso $\implies$ SplitMono $\implies$ RegMono $\implies$ StrongMono $\implies$ ExtMono $\implies$ Mono, And dually ...
1
vote
2answers
121 views

Why do people stick with Riemann-Integration when dealing with differential geometry?

I asked a question yesterday that is, "Is there an introductory differential geometry text using Lebesgue integration?" Then, i got an answer that "since we are dealing with differential geometry we ...
3
votes
4answers
68 views

Can anyone prove for every $a,b \in \mathbb Z^+ < p$ ( $p$ is a prime), $p \nmid ab$?

Can anyone prove for every $a,b \in \mathbb Z^+ < p$ ( $p$ is a prime), $p \nmid ab$? I was trying my best to do the problem but like I don't know where to start or anything!
0
votes
0answers
59 views

Heavy Application of Fermat's Theorem

Show that if p = 4k + 3 is a prime, then the product of all the even integers less than p is congruent modulo p to either 1 or -1. I know now that Fermat's theorem implies that 2^((p-1)/(2)) == 1 or ...
3
votes
1answer
56 views

Why is a perfect group called a perfect group

A group is called perfect if we have $[G,G]=G$. I was wondering in what sense is this group perfect? I've never really done anything much with perfect groups so I don't really know anything about ...
0
votes
0answers
50 views

Is it right to say 1=0,99999999999999..?? Is it agreed by mathematicians? [duplicate]

There is a proof that the numbers 0.999..=1 but i don't like it!I think there are different quantities!!
1
vote
6answers
856 views

Is this a theorem in Number Theory? I can't find this in my textbook

"If $a \equiv b \pmod m$ and $a \equiv b \pmod n$ and $gcd(m,n)=1$, then $a \equiv b \pmod {mn}$ " Is that a true theorem? I can't find it in my textbook!
3
votes
0answers
73 views

Mathematical YouTube channels?

So I'm wondering if anybody knows any good math/science related YouTube channels? As for the math channels, I'm currently subscribed to Numberphile, and that is about it. I know few other channels, ...
0
votes
0answers
51 views

is there an introductory differential geometry text using Lebesgue integration?

Is there an introductory differential geometry text using Lebesgue integration? Every differential geometry text I saw introduces the theory using Riemann integration. (Even Spivak) Would someone ...
-2
votes
1answer
37 views

How do I solve the following Diophantine equation using Congruences?

I'm given: $4x+51y=9$. I am given a hint that when we use $4x=9 \pmod{51}$ we get $x = 15 + 15t$, and also if we use the congruence $51y=9 \pmod 4$ we get $y=3+4s$. They say it's handy to then find ...
0
votes
0answers
13 views

Book suggestion for DImensional Analysis?

Title says it all. I can't find a decent book for an introduction to Dimensional Analysis. I need a book which explains it from the beginning in clear details. I have Dimensional Analysis by ...
1
vote
0answers
46 views

Why is there no universally accepted mathematical definition of turbulence?

Why is there no universally accepted mathematical equation for the definition of turbulent flow?
21
votes
7answers
467 views

“Here's a cool problem”: a collection of short questions with clever solutions

This game will be familiar to many mathematicians, and it is always good fun to play. I am looking to find a list of good questions with short, when-you-see-it solutions. The kind of question one ...
0
votes
2answers
13 views

Helmholtz decomposition - motivation

Our lecturer presented us the Helmholtz decomposition of smooth vector fields. He added a proof, but he didn't provide any single motivation - e.g. where Helmholtz used the decomposition or for which ...
2
votes
1answer
128 views

Is RCA-Rudin one of the worst textbooks? [closed]

Someone told me that "Real and complex analysis - rudin" is actually rated a bad textbook among researchers, since it gives no motivation. Is it true? I agree that this text provides less ...
2
votes
0answers
50 views

Is it generally difficult to memorize 'multivariable calculus' theorems?

There are many weak forms of "Fubini's theorem" with strong hypotheses in elementary calculus texts. However, these strong hypotheses are very unnatural and are thus hard to memorize. Compared to ...
1
vote
1answer
54 views

Is there a way to phrase “there does not exist a universal set” in structural language?

Both ZFC (which is a good example of a material set theory) and ETCS (which is a good example of a structural set theory) prove the sentence "there is no set having maximum cardinality" as an easy ...
0
votes
0answers
23 views

Using Harmonics to find a solution to a boundary value problem

Consider a boundary value problem with two given level sets of phi. One set is in the imaginary plane with center (1,i) and radius 1. This set has level set phi = 0. Another set is in the imaginary ...
1
vote
3answers
140 views

Is it possible to learn abstract algebra no precalculus or calculus?

See above. I am trying to re-teach myself mathematics in a different manner than is formally taught (i.e., set theory, number theory, mathematical logic, abstract algebra, discrete math and then ...
1
vote
1answer
42 views

Is Arizona State University known for their applied mathematics REU/PhD program?

I've been accepeted to ASU's NSF REU program for this summer, but I've also been accepted to Mayo as well for their REU (although not technically sponsored by the NSF). Have you guys heard about ...
8
votes
2answers
423 views

Surprising applications of cohomology

The concept of cohomology is one of the most subtle and powerful in modern mathematics. While its application to topology and integrability is immediate (it was probably how cohomology was born in the ...