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14
votes
5answers
515 views

Reflections on math education

Why is there such a big difference in math education between The Americas and (Europe and Asia) ? except for a few privileged who have the opportunity to access to math much earlier than the ordinary ...
4
votes
5answers
1k views

Math is too hard for me. How can I make it easier?

I am trying to study, and I keep finding that math is hard (any kind), and it doesn't get easier(only harder). I am trying to learn these things all in progression (asynchronously): 1.Math for all ...
0
votes
2answers
42 views

Reverse Polish notation in (abstract) algebra

If I have something like $\phi\circ \psi(x)$ this means first apply $\psi$ and then $\phi$. Going right to left is pretty contrary to my intuition. In computer science some programming languages (and ...
2
votes
2answers
50 views

Does the word 'ten' have a base?

My friends and I had a debate: "Does the word 'ten' have a base?" My Argument: 'ten' is only 10 in base 10 so if i have 10 objects, counting in base 10, when I get to the end of the list, I will ...
0
votes
0answers
31 views

Calculators using Taylor polynomials?

I've always heard that calculators (TI-84's and the like) use Taylor polynomials to approximate trigonometric/exponential/etc functions. Do any of you know this for a fact?
0
votes
1answer
43 views

Fun mathematics exercises [on hold]

I'm looking for fun mathematical exercises to do in my spare time, when I say fun I mean exercises which requires original manipulations and also requires some work, it would also be nice if they gave ...
27
votes
8answers
3k views

How can I learn to “read maths” at a University level?

When I look at math, it's like my mind goes fuzzy. The only way to describe it is in terms of what I can relate it to. You know how when you read, you see the letters and words, but your brain picks ...
32
votes
5answers
2k views

Examples of “Non-Logical Theorems” Proven by Logic

I am still an undergraduate student, and so perhaps I just haven't seen enough of the mathematical world. Question: What are some examples of mathematical logic solving open problem outside of ...
4
votes
0answers
43 views

How to master general topology for analysis?

I started learning topology long ago. I first exposed myself to metric topology in Baby Rudin and Munkres Topology 2nd ed. Part I. Munkres is my most revisited book ever since. The first big ...
0
votes
0answers
14 views

Morphisms of $\mathsf{Meas}$ and Dynamical Systems

The morphisms of a category $\mathsf{Meas}$ whose objects are measure spaces are defined to be equivalence classes of a.e-equal measurable maps that pull back null sets to null sets. Why is pulling ...
6
votes
2answers
862 views

Mathematics celebrities that every mathematician should know? [closed]

As a mathematician, sometimes I meet across very embarrassing questions which were posted by who does not learn of mathematics, for example, my wife and so on. She or he always posted such questions: ...
1
vote
0answers
24 views

Continuous maps vs. open maps [duplicate]

When we study topology, we typically study topological spaces and continuous maps between them. From a categorical perspective, this is "wrong," because continuous maps are not the structure ...
2
votes
1answer
58 views

How to conceptualize unintuitive topology?

I found Project Origami: Activities for Exploring Mathematics in my university's library the other day and quickly FUBAR'd (folded-up beyond all recognition) the couple sheets of paper I had with me ...
2
votes
1answer
40 views

“Almost” Hilbert spaces

This question is a bit (very?) vague. Is there some notion of how "close" a Banach space is to being a Hilbert space? What I have in mind is something like a real or complex valued function on ...
55
votes
4answers
6k views

How do I convince someone that $1+1=2$ may not necessarily be true?

Me and my friend were arguing over this "fact" that we all know and hold dear. However, I do know that $1+1=2$ is an axiom. That is why I beg to differ. Neither of us have the required mathematical ...
-5
votes
0answers
37 views

boy or girl it's on the fathers genes [on hold]

Hi my name is Jacobi Thomas and when I was doing research a while ago I came across a paper called boy or girl it's in the fathers genes. In the paper the scientist talks about the sex of a child ...
7
votes
3answers
125 views

Why are continuous functions the “right” morphisms between topological spaces?

Recently, someone mentioned to me that given a function $f: X \to Y$ there are two natural functions between the powersets $P(X)$ and $P(Y)$. Namely $f: U \subset X \mapsto f(U)$ and $f^{-1}: V ...
4
votes
2answers
50 views

Squaring the Circle

Is squaring the circle possible in any sort of metric at all? It's known that within the Euclidean metric it is impossible, but does there exist some world or space where it is possible? Much like how ...
1
vote
1answer
29 views

Differential Structure of Two Dimensional Manifold

I am a beginner in Differential Topology, and have learnt that Theorem One dimensional differential manifold without boundary is diffeomorphic to $\mathbb R$ or $\mathbb S$. So I am curious ...
1
vote
0answers
60 views
+50

Runge Kutta 8(5,3)

This is actually three small very related questions about Runge Kutta methods. 1) I have programmed a RK 7(8) method also RK 4(5). At the beginning I was assuming that the RK 7(8) uses two ...
14
votes
4answers
234 views

Why are particular combinations of algebraic properties “better” (richer and more pervasive) than others?

I am a second-year graduate student of pure mathematics. Like most graduate students, I have been exposed to many types of algebraic structures, and it seems standard for the major emphasis, if not ...
1
vote
4answers
170 views

Why is the expression $\underbrace{n\cdot n\cdot \ldots n}_{k \text{ times}}$ bad?

For writing a (german) article about the power with natural degree I have the following question: In school one defines the power with natural degree via $$n^k = \underbrace{n\cdot n\cdot \ldots ...
1
vote
0answers
39 views

Can I use theorems that are beyond the scope of my class in my CBSE exams?

I am a student of class $9^{th}$ of a CBSE board school.Tommorow I have my half yearly maths exam.My question is that can I use theorems(such as manelaus theorem,stewart's theorem,ceva's ...
3
votes
1answer
65 views

How important is the “prestige” of your university for undergraduate mathematics?

I go to a university in Canada. It's not really considered a top university (it is one of the best universities in the province but is ranked really low nationally). I study mathematics here and ...
2
votes
0answers
70 views

Igor Pak on priority of results in citation [on hold]

Today I saw Igor Pak's post on his issues with citation of priority http://igorpak.wordpress.com/2014/09/12/how-not-to-reference-papers/ I know this is a very human feeling. How important is ...
146
votes
79answers
13k views

Surprising identities / equations

What are some surprising equations / identities that you have seen, which you would not have expected? This could be complex numbers, trigonometric identities, combinatorial results, algebraic ...
17
votes
4answers
1k views

An equation that generates a beautiful or unique shape for motivating students in mathematics

Could anyone here provide us an equation that generates a beautiful or unique shape when we plot? For example, this is old but gold, I found this equation on internet: $$ \large\color{blue}{ ...
8
votes
4answers
1k views

Should I try to change the way Abstract Algebra is taught at my university? If so, how?

[This (soft) question should be Community Wiki.] Background: A year ago, I did a one-semester long course on Abstract Algebra at my university. When we started, I was excited, because I knew the ...
18
votes
1answer
923 views

Efficient ways to read and learn a new topic

I started reading the book "Topology without tears" by Sidney A Morris and lecture notes on "Elementary Number Theory" by WWL.Chen. To get the maximum out of the book and understand the material ...
1
vote
0answers
59 views

Again with this question. How to learn mathematics [on hold]

So I've been studying mathematics and I am completely sick of being spoon fed with equations and algorithms. I've taken the right step by beginning to learn logic and set theory; having almost ...
17
votes
3answers
1k views

What in Mathematics cannot be described within set theory?

I have begun reading Patrick Suppes' book Axiomatic Set Theory. The first sentence in chapter 1 reads: "Among the many branches of modern mathematics set theory occupies a unique place: with a few ...
6
votes
3answers
362 views

Undergraduate mathematical magazines to improve mathematical knowledge

I'm sorry my ignorance, I don't know very much about mathematical magazines. I'm finishing my master degree in pure mathematics and I'm looking for mathematical magazines which could improve my ...
4
votes
3answers
122 views

Why is differential geometry called differential geometry?

Why is differential geometry called differential geometry? Why it is not called differential and integral geometry? Isn't integration and finding areas as important as differentiation? Is it the case ...
0
votes
1answer
15 views

Soft: Interpretation of a periodic event on circle group

Recently I've been exploring probability measures on topological groups, derived from the (essentially) unique Haar measure defined thereon. I had begun to focus on the example of the circle group ...
16
votes
1answer
467 views

Examples of falsified (or currently open) longstanding conjectures leading to large bodies of incorrect results.

In general, the way that modern mathematical research is conducted isn't the way that many would assume is the ideal method of research. That is, mathematics is not the linear progression of ...
-2
votes
1answer
58 views

Maths as an engineering of functions [on hold]

Sometimes I was thinking why there is not a bigger perspective of maths as a engineering instead of a collection of tools or a way to investigate deeper relations between components. I dont know any ...
9
votes
3answers
268 views

How do you go about formalizing a concept?

I am reading Godel Escher Bach. I love it. In the first few chapters, the author shows what a formal system is and gives examples that eventually lead to a typographical formal system of strings that ...
4
votes
1answer
240 views

What is meant by “folkloric result” in category theory?

I often will see the word "folklore" used in papers on category theory, e.g. in Barr's paper on Isbell Duality, he states a result, which he proves, is "folkloric", on page 512: The following ...
1
vote
1answer
37 views

Book to self-learn probability

I am reading some lecture notes (completed with exercises and competition-like problems) provided by my college professor, but I would like to study probability from a proper book. Can you suggest one ...
2
votes
0answers
16 views

Differential Equation for brownian bridge?

For the brownian motion, we know that probability density of the particle's position at time $ t $, $ \rho(x,t) $ satisfies the diffusion equation pde: $ \partial_t \rho = d \; \partial_x^2 \rho $. Is ...
1
vote
0answers
35 views

Question regarding advanced calculus textbooks

I'd like to start off by mentioning that I'm gonna begin studying Computer Science at the local polytechnic university. As I found out, the study of mathematics stops after two years. Recently I've ...
8
votes
4answers
282 views

What is linearity?

Once someone asked me the question "What is linearity?" in a proficiency exam. I went hot and cold all over. Although, I heard and even used the term linearity many many times, I had not really ...
0
votes
0answers
29 views

Soft question regarding real analysis

I have just started studying ' Principles of mathematical analysis' by Rudin. And I have heard that it is hard to complete . I seriously want to study it and I need some suggestions about how should I ...
0
votes
1answer
24 views

Applications of random walks

I am searching for a clear and interesting exposition of an application of random walks to some physics topics accessible to advanced high school students.
12
votes
3answers
446 views

Mathematical structures

Preamble: My previous education was focused either on classical analysis (which was given in quite old traditions, I guess) or on applied Mathematics. Since I was feeling lack of knowledge in 'modern' ...
3
votes
1answer
57 views

Why Riemannian metrics have to be smooth?

Why do Riemannian metrics have to be smooth? Can you give an example of a smooth curve with a none smooth metric and show me what possibly will go wrong if our metric is not smooth?
1
vote
4answers
34 views

SAT Math problem

In a volleyball league with 4 teams, each team plays exactly 2 games with each other 3 teams in the league. What is the total number of games played in this league? the book says the answer is 12, i ...
0
votes
2answers
59 views

What is global differential geometry?

What is the difference between local and global differential geometry? I cannot find their (exact) definitions. There are some other terms in geometry like "rigid" (e.g. that structure is more rigid ...
3
votes
0answers
145 views

How is $\sqrt{3} * \sqrt{2} = \sqrt{6}$ mathematically possible? [duplicate]

Well, this question is basically a method to point a loophole in Maths which I'm not sure how it is possible... ...
60
votes
19answers
12k views