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4
votes
0answers
282 views

How much are mathematics driven by applications?

At some point this provocative question came to my mind: Are mathematics mostly driven by applications? I am taking into account some of the comments made to my original question so I want to ...
6
votes
4answers
2k views

What is a great book to read about sequences, sums and products?

I want to learn everything about sequences, sums and products from A - Z. Is there one book that stands out from the rest quality wise? I want to start my research off right!
13
votes
3answers
659 views

Where are the geometric figures in those “advanced geometry” textbooks?

It is me again to bother you. Since my last post I started to look at some seemingly "serious" mathematics for background study. Accidentally I went into a university bookshop and came across some "...
12
votes
1answer
251 views

Studies on lack of mathematical education

I am looking for studies which compare students who did not receive mathematical education beyond basic mthematics and those that learned maths upto introductory calculus, with the assumption that ...
4
votes
2answers
145 views

Any finite set is a null-set

How can we prove that a finite set is a null-set? Maybe would it be easier to prove that the outer measure of a finite set is $0$? any ideas on how to tackle this problem? thanks,
9
votes
3answers
1k views

Is the Riemann Integral good for anything?

Math people: I think it is a good idea to teach beginning calculus students the Riemann Integral (I refer to what calculus books call the "Riemann Integral" and ignore any controversy about whether ...
2
votes
1answer
245 views

4 big ideas in algebra that have rich connections to other fields? [closed]

In his controversial post criticizing high school algebra, Grant Wiggins issued a challenge to his readers: Can you identify 4 big ideas in algebra, ideas that not only provide a powerful set of ...
3
votes
0answers
134 views

What are the Big Theorems in Information Geometry?

I am working on preparing a talk on information geometry to a young finance/applied math audience. Motivating this area is turning out to be a little difficult. What are some big theorems or results ...
3
votes
1answer
113 views

A list of publications by Issai Schur, and Ferdinand Frobenius

I'm interested in works of Frobenius and Schur and I am wondering if there is a list of their publications somewhere that I can go through. I have found some of their works here But it seems like ...
0
votes
1answer
403 views

Competition style mathematics

I'm currently 18 years old and only as of the part year taken a strong interest in maths. I'm working with my school curriculum (UK a-level) and receiving A grades so I am happy with this. However I ...
0
votes
2answers
60 views

Rewriting an equation to include a condition

I have a simple equation: a = b(c/d) but it has a condition: if b > 1, then b = 1 How do I write this condition into the equation?
13
votes
9answers
883 views

Is it possible to alternate the law of mathematics?

I am freelance writer. Recently I have been planning a science fiction - just planning, nothing solid yet - and I was wondering would it be possible for some other universes that have different set of ...
10
votes
5answers
260 views

The use for solving quadradic equations for high school students

I have a little brother who is in high school and he just learnt the quadratic formula for finding roots of second degree polynomials. He asked me what why we learn this and how this could apply to a ...
4
votes
1answer
106 views

Cases where reflexivity is hard to prove

A couple of remarks at Surjections and equivalence relations lead me to wonder: are there any important and/or interesting examples of reflexive relations whose reflexivity is hard to prove? There are ...
14
votes
2answers
2k views

Theorems with the greatest impact on group theory as a whole

In his Contemporary Abstract Algebra text, Gallian asserts that Sylow's Theorem(s) and Lagrange's Theorem are the two most important results in finite group theory. He also provides this quote by G.A....
1
vote
1answer
163 views

What are moments and why do we need them?

I am learning probability and have a question about moment generating functions. So far I've learned how to calculate them and how to find the nth moment of a probability distribution. My question is, ...
8
votes
1answer
406 views

How to write well in analysis (calculus)?

This is kind of a subjective question, I know; often I find myself failing exams and homeworks because of the way i write down proofs. Either I don't know how to start, or somehow the main point of ...
23
votes
7answers
12k views

Teaching a 4 year old maths

Im 18 years old and getting to grips with advanced mathematics (pre-university) and I have a younger brother of 4 years old (quite an age gap). I want to get him interested in learning (and away from ...
3
votes
2answers
6k views

Possible Research Topics for High School

I am a highschool student some experience with Math Olympiads and I will be taking a Scientific Research class next year. I would like to ask for interesting Mathematics topics that I could consider - ...
3
votes
3answers
2k views

Improving basic maths & algebraic manipulation skills

I am currently doing a-levels in the UK (received an A in AS) so doing calculus (differential equations/trig integrals)/linear algebra/mechanics/statistics etc. However I feel that a lot of my basic ...
8
votes
4answers
433 views

Confused about differentiation

I'm new to calculus and have been taught that $\displaystyle \frac{dy}{dx}$ is the rate of change of y with respect to x. Does $\displaystyle \frac{dy}{dx}$ show how much the variable y changes as x ...
8
votes
1answer
516 views

Is the number 8 special in turning a sphere inside out?

So after watching the famous video on youtube How to turn a sphere inside out I noticed that the sphere is deformed into 8 bulges in the process. Is there something special about the number 8 here? ...
9
votes
2answers
247 views

Soft question: Unconventional proofs

I'm not sure if I understood it correctly, but one of my professors told us that one theorem was proved this way: A mathematician assumed the truth of the Riemann hypothesis and was able to prove a ...
3
votes
1answer
57 views

Do I need to prove $f(x)$ is convergent before defining it?

For example, I define $\sin x=\sum_{k=0}^\infty\frac{(-1)^kx^{2k+1}}{(2k+1)!}$, should I show that $\sum_{k=0}^\infty\frac{(-1)^kx^{2k+1}}{(2k+1)!}$ is convergent for all real $x$ first, or I can ...
4
votes
2answers
197 views

Why is “Amenable Group” a pun?

"The original definition, in terms of a finitely additive invariant measure (or mean) on subsets of G, was introduced by John von Neumann in 1929 under the German name "messbar" ("measurable" in ...
-3
votes
1answer
206 views

The Irrationality of 2

I am sorry it is not 'research level'. A quick answer will do. When I attempt using the Square root of 2 method to prove the rationality of Square root of 4 according to how it was done in a book, 2 ...
4
votes
3answers
558 views

Alternative model of Euclidean geometry

I'm planning to teach high-school geometry. As usual, this will be by building from axioms. (The axioms used are AFAICT particular to the book I've been assigned, but they're some combination of ...
1
vote
2answers
4k views

What is a standard precalculus syllabus?

I'm about to start teaching a calculus I class next week and I was wondering what I can expect from my students. I'm a Brit teaching in the US so I am unfamiliar with the system. I am hoping that ...
3
votes
1answer
3k views

What does “rigor” mean in mathematics? [duplicate]

I spend a lot of time on math.se and even though I don't understand many of the questions posed, I try to understand what is being said or atleast wiki something to get some gist of the question and ...
15
votes
1answer
2k views

What kind of matrices are non-diagonalizable?

I'm trying to build an intuitive geometric picture about diagonalization. Let me show what I got so far. Eigenvector of some linear operator signifies a direction in which operator just ''works'' ...
0
votes
2answers
4k views

what is the best book for calculus? [duplicate]

I am looking for the best calculus book to use it to teach myself calculus. I have already had a bit of a search and these are what I have come up so far, But I have no idea which one is truly the ...
6
votes
4answers
1k views

Self-learning Mathematics

My question is very elementary, but I hope that you will endure it. I am currently in a CS Master's program and I notice that my skills in mathematics are lacking. My calculus course was 10 years ago....
3
votes
4answers
221 views

Is math capable of predicting social evolution?

By the way math and statistics are evolving, it seems possible to me that with time, and as the population increases, we are going to be able to create mathematical models that predict social ...
30
votes
5answers
2k views

Level of Rigor in Mathematical Physics

I am a physics/math undergrad and I have recently become familiar with some more rigorous formalisms of mechanics, such as Lagrangian mechanics and Noether's Theorem. However, I've noticed that the ...
7
votes
3answers
3k views

Comparing Hilbert spaces and Banach spaces.

Why do we say Hilbert space is better than Banach space? I know that a Hilbert space has inner product (and so a norm) but Banach space has just norm.
7
votes
1answer
939 views

Quick questions about studying math and physics? [closed]

Just curious about how people usually self study these subjects. 1) Is it the most efficient to read through the chapters, and write down theorems, definitions, and take notes of important parts and ...
20
votes
1answer
727 views

Why did Gauss think the reciprocity law so important in number theory?

Gauss's Disquitiones Arithmeticae centers around the quadratic reciprocity law. It seems that he developed the genus theory of integral binary quadratic forms to find a natural proof of the quadratic ...
7
votes
4answers
485 views

Mere coincidence? (prime factors) [closed]

Whether some things in mathematics are mere coincidences might keep philosophers busy for 100,000 aeons, but maybe when such a coincidence gets exploited then it's not a "mere" coincidence any more. ...
2
votes
2answers
625 views

Question about the mathematics in actuarial studies [closed]

I tried Google but there isn't much information on this and I would really like some insights into actuarial studies, the mathematics involved and how it compars to the mathematics in a bachelor of ...
22
votes
1answer
784 views

Is there any mathematical meaning in this set-theoretical joke?

Recently I heard a joke: If an object exists, mathematicians call it a set and study it. But if an object does not exist, mathematicians call it a proper class and study it anyway. I wonder, ...
4
votes
3answers
263 views

Geometry and Physics

I have to do a presentation on Geometry and Physics. I am asking it here (rather than physics.se) because I have to focus on Geometry More than Physics. The intended audience is Undergraduate Seniors ...
7
votes
3answers
542 views

How was $e$ first calculated?

I understand how $\pi$ is calculated, but I am interested in references that explain when and how the natural exponent $e$ was developed. What mathematical principles are behind the value of $e$?
4
votes
1answer
250 views

Is 4D visualization necessary? [closed]

Is 4D visualization necessary in order to be successful at math (complex analysis for example)?
5
votes
1answer
122 views

Masters in mathematics with bachelors in different subject [closed]

I have a bachelor's degree in electronics engineering, and I'm fairly interested in discrete mathematics, is it possible to study masters in mathematics? If so would it be worth pursing it?
43
votes
11answers
3k views

What if $\pi$ was an algebraic number? (significance of algebraic numbers)

To be honest, I never really understood the importance of algebraic numbers. If we lived in an universe where $\pi$ was algebraic, would there be a palpable difference between that universe and ours? ...
1
vote
0answers
47 views

''Technique manuals'' recommendation

In my studying of generating functions I got hold of this article and I liked it very much. Why? It's concise, does a good job of introducing you to the main ideas and shows a lot of uses of this ...
1
vote
0answers
963 views

What are real life applications of Diophantine equations?

Are there any real life applications of linear Diophantine equations? I am looking for examples which will motivate students.
7
votes
4answers
378 views

How do you retain your ability for contest-like math as you take more and more advanced math courses?

From my limited experience, it seems like many people loose their ability to do contest-like math as they go trough college. For example, before I posted it here I asked a math undergrad student (who ...
3
votes
2answers
265 views

Are there any other interesting functions such as $e^x$ whose derivative and integral are the same?

$e^x$ is interesting, but does anybody know if there are other functions that behave in an interesting way when taking the derivative/integral?
9
votes
2answers
210 views

What is a fiber bundle? (for non-mathematicians)

How can I explain the concept of a fiber bundle to someone with no mathematical background?