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3
votes
1answer
147 views

Is there a 'Mathematics wiki' analogous to 'String theory wiki'?

I came across this site and am wondering if there is a similar page for Mathematics or its sub-areas. Would be very nice if there is one such site which provides 'canonical' references for each sub ...
0
votes
3answers
188 views

Complex book suggestions

I take complex analysis course. And my instructor use -Bak and Newman's complex analysis book, Springer. This book explains complex analysis too rapidly and superficially. Please give me book ...
1
vote
2answers
165 views

Is readability ignored in mathematics? If so, why? [duplicate]

Most of the math equations use single character as variables name and functions name, there are also Greek alphabets as well. This is not acceptable in programming since it is too difficult to ...
0
votes
3answers
492 views

A little confusion about compactness and connectedness

This question may be a bit simple or even naive for some people but it indeed confuses me for a long time. Thank you all if you provide any explanation. I know concepts: compactness means any open ...
2
votes
1answer
144 views

What is a good definition of Hilbert space?

Motivation of my question: in my opinion, in view of the common definition, the statement "$\ell_p$ is a Hilbert space if and only if $p=2$" makes no sense because there is no inner product in the ...
7
votes
1answer
165 views

What fraction of works in mathematics contains mistakes?

In science, mistakes happen: bad experiment design, noisy measurements, incomplete data, expensive experimentations, and other factors. Sometimes theories are wrong because we don't know enough. In ...
7
votes
1answer
432 views

What is the significance of limit points?

When I had my first taste of topology a couple of years ago, our lecturer emphasized the following notions. closed set, closure, closure point open set, interior, interior point Of course, these ...
28
votes
6answers
2k views

Cool mathematics I can show to calculus students.

I am a TA for theoretical linear algebra and calculus course this semester. This is an advanced course for strong freshmen. Every discussion section I am trying to show my students (give them as a ...
8
votes
3answers
762 views

Is there something to the “let $\varepsilon < 0$” joke that I'm missing?

Sorry if this is the wrong place to ask this, but I feel it's a question of vital importance to the future of math education. I hear this listed as a "math joke" all the time and I've never got it. ...
4
votes
5answers
479 views

How to explain infinty to a $3^{rd}$ grader?

In my country in $3^{rd}$ grade in math kids learn the four basic arithmetic operation (addition, subtraction, multiplication and divison) up to $10 000$. My sister this year goes to $3^{rd}$ grade ...
5
votes
2answers
283 views

Dynamical systems and differential equations reviews/surveys?

I would be very glad if someone could point me to modern reviews/surveys on these topics. To be concrete, I'll provide some examples: S. Smale, Differentiable dynamical systems D. V. Anosov, On the ...
4
votes
1answer
429 views

Workshop on Pascal's Triangle for Middle School Students

We're going to hold a three-hour math workshop for some middle school students. It'll about the Pascal's triangle. Well, we can ask the students to find patterns in the triangle, or try to prove some ...
1
vote
1answer
107 views

Shouldn't we refer to an inequality as an 'inequality' instead of an 'equation'?

As far as I'm concerned, an equation is any mathematical statement of the form LHS=RHS, an inequality is any mathematical statement of the form LHS?RHS (where ? is a placeholder for some inequality ...
1
vote
1answer
392 views

Prerequisites of general calculus

I have a unique situation in which I need to know the names of the concepts taught in Pre-Calculus and those taught at the beginning of the school year in Calculus (or just general concepts used in ...
5
votes
6answers
448 views

“$n$ is even iff $n^2$ is even” and other simple statements to teach proof-writing

I am supposed to teach undergraduate students who do not major in mathematics and I would like to give them a short introduction to mathematical reasoning and to the concept of proof. I am looking for ...
0
votes
2answers
46 views

How to introduce cases in a proof.

I am writing a simple proof in regards to a homework problem about a property of stable matching. The content of the proof isn't necessarily what I am asking about as opposed to the presentation of ...
12
votes
2answers
430 views

What was the largest ratio (result size)/(integrand size) you have seen?

Sometimes a definite or indefinite integral of a simple-looking one-liner integrand can give astonishingly huge result. What was the largest ratio of the size of shortest known closed-form result to ...
0
votes
2answers
78 views

Is differential geometry useful for algebra?

Is differential geometry useful for algebra? Or are they not very related? I don't need a complicated answer; I just want to know if it would be useful for learning algebra. Thanks in advance
2
votes
2answers
205 views

transcendental number theory - classification

On Wikipedia one can find that transcendental number theory, or transcendednce theory is a branch of number theory. That confuses me a little since I thought that number theory is concerned with ...
4
votes
1answer
137 views

How to deal with lack of peers?

I am pursuing a B.S in Mathematics(freshman) in a country where people rarely study math for the sake of it and in a new university with good professors. Yet, it is new and I suffer from the lack of ...
7
votes
1answer
3k views

Journals that publish papers quickly [closed]

I have written two papers in Mathematics and want to get them published. Can you suggest some journals that publish quickly? Besides, how can I know if a journal is well-regarded or not? I know there'...
7
votes
2answers
663 views

Coordinate independence of geometrical objects.

I am still trying to get a good grasp on the motivations behind various concepts in Differential Geometry. But I am struggling to come to terms with how certain concepts have this added attribute of ...
2
votes
1answer
123 views

“Generalization” of Gödel's Theorem

One question came to my mind while arguing with a friend about the necessity of Judges in society (I will explain...) In the reasoning, we came across the following argument: "If we put up a good ...
6
votes
5answers
247 views

How would one define a “manifold” object in prose writing?

I have a question that I fear may raise some objection to the fact that it has been posted here, but I cannot think of a more appropriate place to pose it. I am not a mathematician; I'm a historian, ...
10
votes
3answers
865 views

What are some easily-stated recently proven theorems? [closed]

What are some easily-stated relatively recently proven theorems? I don't mean they were necessarily easy to prove, just easy to state. Here are a few examples: The proof of Fermat's Last Theorem ...
5
votes
3answers
177 views

Alternative Creative Proofs that $A_4$ has no subgroups of order 6

Since I've been so immersed in group theory this semester, I have decided to focus on a certain curious fact: $A_4$ has no subgroups of order $6$. While I know how to prove this statement, I am ...
1
vote
3answers
170 views

Rating changes and probability calculations for chess world championship

I have some interesting questions that have to do with the rating changes and calculations for the Anand-Carlsen world championship. Most of this has to do with solving a system of linear equations. ...
7
votes
4answers
2k views

In What order should I Learn math in?

I am a 13 year old boy from Hong Kong, My dad is a math teacher which probably accounts for SOME of my interest in math. I am really interested in math. I self-taught myself (with little help form my ...
0
votes
1answer
80 views

What is the first proof that you've done using induction?

Right now in class I'm learning induction and I'm having a hard time to grasp the concepts of it, especially strong induction which confuses me even further. But out of curiosity, what is the first ...
212
votes
92answers
18k views

Surprising identities / equations [closed]

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 ...
1
vote
1answer
113 views

Is there a way to mathematically describe “surprise”?

Let's say that there are ten people entered into a random drawing, the winner gets some large prize. If I were one of those ten people, and I were to win, then I would be pleasantly surprised. If ...
7
votes
1answer
194 views

Tate's Thesis: Meaning of Local Functional Equation

I am studying the development of Tate's Thesis in Lang's Algebraic Number Theory and have a conceptual question. The setting: Let $k=\mathbb{Q}_p$. Let $\mu$ be the unique Haar measure giving $\mu(\...
11
votes
1answer
899 views

On a joke of Yoneda embedding

I have heard a joke like this: The Yoda embedding, contravariant it is. And a joke concerning "How to put an elephant into a refrigerator", a comment from "Category Theorist" says Isn’t this ...
2
votes
1answer
464 views

Some questions about Fractals and software

Ever since I read this article on math.SE I have been amazed by the wonder of fractals. I have been trying to learn what are fractals and how to write an equation for one, and I am truly confused, I ...
4
votes
1answer
255 views

Motivation and Applications for Toric Varieties

I'm a graduate student of mathematics starting to study algebraic geometry with a focus on toric varieties (along Cox, Little, Schenk). From what I learned so far, I can grasp that toric varieties ...
16
votes
4answers
856 views

Why do we believe the equation $ax+by+c=0$ represents a line?

I'm going for quite a weird question here. As we know, the equation in Cartesian coordinates for a line in 2-dimensional Euclidean geometry is of the form $ax+by+c=0$. I'm wondering why do we "believe"...
12
votes
6answers
1k views

Am I just bad at math? [closed]

I currently pursuing a degree in computer science. When I started back 4 years ago, I took a test to see how I would place into certain subjects. My math scores were absolutely horrible. I started ...
1
vote
1answer
449 views

Continuity Equation

I have a bit of a soft question: The continuity equation in fluid dynamics says that $\frac{\partial p}{\partial t} + div(p\vec{v}) = 0$, where p is the fluid density and v is velocity. From ...
5
votes
3answers
466 views

How to learn mathematics as a beginner

I am a 15 year old mobile app developer. I had a tough time understanding maths when i was little, which have thrown me off balance when i try to study maths or attend a maths class. Things don't ...
0
votes
2answers
61 views

How should I read this $\land$ notation?

I'm studying for SOA Exam C and I was recently introduced to this notation for a minimum $\land$. For example, if there is an limit for how much insurance can be paid out, that limit is $u$ and then ...
2
votes
1answer
644 views

Should I pursue a M.S. in Mathematics or a Ph.D? [closed]

I'm looking forward to any advices, but first of all, here's my story: Right now I'm a freshman in high school. I admit it, I love mathematics! However, I suspect that I have ADHD and I can't ...
3
votes
5answers
190 views

Motivation for Studying Combinatorics (Middle School Version!)

I'm going to teach very elementary combinatorics (limited to basic enumeration) during two weeks to middle school students. At the beginning, I want to demonstrate the importance of counting in real ...
31
votes
2answers
2k views

Word origin / meaning of 'kernel' in linear algebra

It may be the dumbest question ever asked on math.SE, but... Given a real matrix $\mathbf A\in\mathbb R^{m\times n}$, the column space is defined as $$C(\mathbf A) = \{\mathbf A \mathbf x : \...
1
vote
1answer
97 views

Goodstein's theorem

Recently, a friend of mine introduced me to Goodstein's theorem, which I found to be very interesting and mind-blowing. The theorem basically says that every Goodstein sequence (the wikipedia article ...
6
votes
1answer
211 views

Do expressions like $(-1)^{2/3}$ show up naturally in pure or applied math?

Background. Let $x$ denote an arbitrary real number. Then $x^n$ can be defined for each $n \in \mathbb{N}$ as follows: $$x^n = \underbrace{x \times \cdots \times x}_n$$ If $x$ is furthermore non-...
26
votes
1answer
2k views

Why is the continuum hypothesis believed to be false by the majority of modern set theorists?

A quote from Enderton: One might well question whether there is any meaningful sense in which one can say that the continuum hypothesis is either true or false for the "real" sets. Among those set-...
2
votes
0answers
280 views

What is non-linear analysis?

Can anybody tell me what non-linear analysis is? I have no idea. I am not getting wikipedia page, may be because of my bad searching habit. I am seeing a lot of research materials published in ...
1
vote
1answer
520 views

How is algebra and geometry related to calculus?

Probably a too trivial question but here goes: What is the relationship of algebra and geometry with calculus? Are they pre-required knowledge for calculus, is calculus a different type of theory on ...
2
votes
1answer
233 views

Math writing solutions

I will begin to learn in the university next month and I would like to know what is the best way to write math except from handwriting? I am not sure if to use a mathematical software, digital pen or ...
0
votes
1answer
146 views

Combinatorial Game Theory Prerequisites

I am planning to self-study Combinatorial Game Theory. I have gathered some useful references from here. Reference for combinatorial game theory. I plan to make a study about a local combinatorial ...