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6
votes
3answers
203 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 ...
0
votes
1answer
14 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 ...
-2
votes
1answer
46 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 ...
1
vote
1answer
34 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
14 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 ...
4
votes
1answer
231 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
0answers
32 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 ...
0
votes
0answers
25 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
22 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.
7
votes
4answers
275 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 ...
1
vote
4answers
32 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 ...
2
votes
1answer
50 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?
0
votes
2answers
56 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... ...
4
votes
3answers
117 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 ...
1
vote
1answer
99 views

$\sqrt 2+ \sqrt{3} \approx 3.14$ [duplicate]

The square $$\sqrt 2+ \sqrt{3} \approx 3.14$$ Is this a coincidence or is their some mathemtical significance?
1
vote
0answers
15 views

KSE and Shannon entropy

Is there a theoretical connection between Kolmogorov-Sinai and Shannon entropies? What is it?
1
vote
0answers
36 views

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 ...
16
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 ...
0
votes
1answer
45 views

Math Prerequisites for QFT

I am curious about which areas of mathematics one should be comfortable with before learning QFT. I am familiar with the "learn-it-as-you-go" approach often advocated in physics, but would like to ...
0
votes
0answers
75 views

Is really mathematics the mother of all science subjects ? [on hold]

As i was a child i thought because all sciences use maths in it without maths we could never use science . and this is a reason that math have been called mother of all science ! some where i read ...
47
votes
12answers
2k views

I lost my love of math; I'm getting it back. How can I determine if math is actually right for me? [on hold]

This question has been on my mind for a very long time, and I thought I'd finally ask it here. When I was 6, my dad pulled me out of school. The classes were too easy; the professors, too dull. ...
0
votes
1answer
51 views

Pure Mathematics to Actuarial Science.

I did my undergraduate in pure mathematics and recently after a three year break I decided to get a master's degree in Actuarial Science. I am in the second week of classes and I feel completely lost. ...
1
vote
0answers
25 views

Soft Question: What are some elementary motivations of using functional analysis to study probability theory?

Recently i've become curious about the links between functional analysis and probability theory. What are some simple reasons why a functional analytic approach is preferable to a measure theoretic ...
1
vote
0answers
40 views

Geometric algebra and quantum field theory

How does the reformulation of QFT with GA look like? I read that GA can be applied to almost every kind of physics, but QFT is rarely mentioned. Is there a lot of research going on in this direction ...
9
votes
2answers
767 views

Success in maths (soft question)

I would really like to hear from any professional mathematicians who didn't just sail through their university education. If one looks at the pages of many of today's mathematicians, one finds that ...
3
votes
2answers
34 views

Properties and notation of third-order (and higher) partial-derivatives

This question has been bothering me for quite a while and I still haven't found a satisfying answer anywhere on the internet or in any of my books (which may not be that advanced, mind you...). Since ...
5
votes
1answer
88 views

How “big” are the mathematical disciplines?

This question may be difficult to answer, but is it possible to estimate the "size" of the individual mathematical disciplines; measures of size could be number of professionals dealing with it, the ...
0
votes
1answer
52 views

Book for probability theory

I need a good rigorous book to learn probability theory. So far, I've been suggested Gnedenko’s Theory of Probability, Shiyayev’s Probability and Feller’s An Introduction to Probability Theory and ...
4
votes
3answers
83 views

Why do we define modules to be over *abelian* groups?

We define a module to be an abelian group $M$ together with a ring action $R \times M \to M$ that satisfies certain properties. Q: Why do we require that $M$ is abelian? I know that modules ...
-1
votes
0answers
99 views

Is the axiom of choice constructive in the constructible universe?

Even ZF has some non-constructive elements mostly due to contradiction proofs. For example one may be able to construct a sequence of objects some of which have a given property without being able to ...
0
votes
0answers
90 views

How “real” does the mathematician have to be? [closed]

As I am studying mathematics more and more, I have changed my personality. I can't actually go over many things in a way I used to.And as the time passes by it gets harder and harder to lie to myself, ...
0
votes
0answers
13 views

Comparison of Parametric and Polar Equations

Having been introduced to parametric equations, I cannot help but question the similarities between parametrized functions and polar functions. A parametric circle is defined by the following: ...
0
votes
0answers
73 views

The poor relation? Time to reassess?

The idea of functions is one of the most important ideas in mathematics. It rules mathematics: one input gives one output. Although, in game theory one study multi-valued functions: one state of the ...
2
votes
1answer
52 views

Research in Mathematics (Formalities vs. Results)

This question is intended to solve an internal dilemma I have been having lately. I assume that most of those who have gone through the process of mathematical research have, at some point, considered ...
1
vote
2answers
57 views

Books/subjects for proof practice

So I want to practice writing proofs. I've studied general proof-writing but now I want to learn how to apply that to mathematics. From what I understand, the best and most accessible subjects for ...
2
votes
0answers
40 views

Why is the triangle inequality property of a metric space important?

From my understanding, when we use metric spaces, we are trying to measure how "different" certain elements in a metric space are from one another. We all know that a metric space $(S,d)$ satisfies: ...
6
votes
3answers
218 views
+50

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 ...
2
votes
1answer
60 views

Breadth vs. Depth in Maths

As a Maths student (beginning undergraduate), I'm often unable to decide whether to spend my time going in more depth and attempt harder and harder problems (which I do to an extent) or whether I ...
2
votes
1answer
110 views

Unsolved/Least Solved IMO Questions

I recently read this article http://blog.mathfights.com/once-upon-a-time-on-imo/ where the author discusses an IMO problem from 2006 that only about 20 participants out of 600 were able to solve. So ...
1
vote
1answer
96 views

How substantial an advance must be to justify publication in pure mathematics?

In order to publish a paper in pure mathematics, specifically functional analysis, do we really need to come out something which improves a lot of existing work in the field? I ask this because I ...
0
votes
0answers
42 views

Advices on which to choose, uncertainty or certainty?

Currently I am doing my final year project(FYP) on Large-Scale Distributed Storage System, where I apply finite field and coding theory to design new codes which can improve existing codes. I plan to ...
2
votes
0answers
69 views

A Compact Real Analysis book for a graduate student, who is short of time.

I am a Phd student in Computer Science and I want to focus on Machine Learning, especially on statistical methods. My problem is, I always keep hitting the wall when it comes to studying underlying ...
0
votes
1answer
37 views

Reference request: Measure theory and/or manifolds [duplicate]

I have never encountered measure theory or manifolds yet, despite being close to my third year university level. Any texts for either or both of these subjects would be greatly appreciated.
3
votes
0answers
47 views

What is the difference between $\propto$ and $\sim$

Suppose I have two physical quantities, lets name them $a$ and $b$. I wonder what the difference exactly is between $$a\propto b,\tag{1}$$ and $$a \sim b.\tag{2}$$ I know for eq. 1, that it means ...
0
votes
1answer
42 views

Categorising types of Mathematics

What area of Math do the following fall under? 1) Systems of ODEs and Phase planes 2) Laplace Transforms 3) Fourier series 4) PDEs with grad, div, curl, flux
6
votes
4answers
225 views

Why does the definition of the functional limit involve a limit point?

This may be an odd question, and I'm not sure if these type of questions are at all appreciated in the maths community. But given the definition of the functional limit: Let $f: A \to \mathbb{R}$, ...
3
votes
2answers
60 views

Books for inequality proofs

I was wondering: what books for proving inequalities are used in universities when studying mathematics (undergraduate)? I know there are lots of books, but I would like to know which ones are ...
2
votes
0answers
36 views

Which journals may be interested in papers on justification of the use of notation in mathematics

I will have a paper justifying the use of notation in mathematics. The paper shows how symbolic language is necessary in mathematics and related fields. I have no idea about where to submit such ...
1
vote
0answers
43 views

Why are empty measurable spaces and empty topological spaces not desirable?

The definition of a $\sigma$-field $\mathscr{F}$ on a set $X$ (or $\sigma$-ring) requires $\mathscr{F}$ to be a non-empty subset of $\mathscr{P}(X)$. Why is this convention taken? What is the issue ...