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1
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0answers
19 views

Why is the powerset axiom more acceptable than the axiom of choice?

The key step in Zermelo's proof of the well ordering theorem is to use $\text{AC}$ to simultaneously choose the next elelment for all possible partial chains in prospective well orderings, but that ...
4
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0answers
17 views

Geometric interpretation of complex path integral

Let's say that we want to make sense of integrating a function $f: \mathbb{C}\rightarrow\mathbb{C}$ over some path $\gamma$. I can imagine two reasonable ways of doing it. First, there's the way ...
3
votes
3answers
617 views

Folland & Functional Analysis

I'm reading Folland's Real Analysis to learn some basic functional analysis. I read through his section Normed Vector Spaces and could make my way through most of the exercises I attempted. I am ...
1
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0answers
24 views

Additional qualifications that would strengthen my profile/CV [on hold]

I apologize if this isn't the right site to ask this question. I am currently doing my Masters in Mathematics, which is a 2 year course (here in India). I was thinking of strengthening my profile by ...
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2answers
151 views
+50

I need help finding a rigorous Pre-calculus textbook

I dislike modern textbooks; their cookie-cutter approach and appearance, over reliance on breaking things down into little boxes, the general spoon-feeding they engender and most of all the poor ...
2
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0answers
64 views

Tool for converting maths writing to $\LaTeX$ [migrated]

I have a dream. I want my maths writing to magically be made into a .tex file so that I can edit it. I want to write my papers, my exams, my lecture notes, ...
3
votes
2answers
290 views

Interesting Problems for NonMath Majors

Sometime in the upcoming future, I will be doing a presentation as a college alumni to a bunch of undergrads from an organization I was in college. I did a dual major in mathematics and computer ...
21
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7answers
2k views

Mathematical literature to lose yourself in

H.M. Edwards in the preface to his book on the Riemann Zeta Function, summarises his philosophy on learning Mathematics: ...I have tried to say to students of mathematics that they should read the ...
4
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1answer
105 views

Ricci flow reference with pictures

I'm going to talk about the singularities of the Ricci flow for a group of physics students on Monday! To create a PowerPoint, I need a text or paper that contains photos and figures to raise the ...
2
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3answers
73 views

“Practical” Claim about Hypothesis Testing of Bernoulli Distribution Parameter

First, let me state the original problem (in my own wording): Describe the decision procedure for testing the hypothesis about the parameter $p$ (success rate) of a Bernoulli distribution. The ...
3
votes
2answers
259 views

Degrees of separation between famous mathematicians

I was recently doing some reading on Wikipedia, and I noticed that if you go far enough though Isaac Newton's notable students' students' students. . . (and so on), eventually one was Augustus De ...
3
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1answer
42 views

How does research in math differ from research in statistics?

I'm at a crossroads where I'm considering switching my major from electrical engineering to math, because quite frankly, I'm just not getting enough math to satisfy my passion from engineering. While ...
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0answers
48 views

Is there a name to this equation: $(y - a|x|^b)^2 + (cx)^2 = d$?

While doing a survey of the various equations that generate the universal love symbol, a heart curve, I find that quite a few fit into this parametrised form: $$(y - a|x|^b)^2 + (cx)^2 = d $$ Where ...
2
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0answers
42 views

Intuitive explanation for $\zeta (2)=\frac{\pi^2}{6}$ [duplicate]

Using $f(x)=x^2$ Fourier' series, the proof for $\zeta (2)=\frac{\pi^2}{6}$ is pretty straight forward. I'm wondering if there is a more intuitive explanation for the equality, one that a layman could ...
68
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6answers
4k views

Is non-standard analysis worth learning?

As a former physics major, I did a lot of (seemingly sloppy) calculus using the notion of infinitesimals. Recently I heard that there is a branch of math called non-standard analysis that provides ...
0
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1answer
52 views

The art of solving exercise problems [on hold]

I do not know whether this question appears to be off topic or not. But I really want to know, how to be well versed in solving exercise problems prescribed at the end of each section. I understand ...
27
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1answer
4k views

Grad school with low undergrad GPA

I'm hoping to apply to grad schools this fall. I think I'm a reasonably good candidate, one aspect aside -- I have around a 2.5 undergraduate GPA in-major and failed several math classes in college. ...
0
votes
2answers
29 views

Splitting a matrix $A \in \mathbb{M}^{n \times n}(\mathbb{C})$by solving $Av = \lambda C v$ for some chosen $C$

If we know a matrix $A \in \mathbb{M}^{n \times n}(\mathbb{C})$ and solve $Av = \lambda v$ where we try to find $\lambda,v$, we can rewrite $A$ in a nice way. What if we choose a matrix $C$ and we ...
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2answers
2k views

Some basic practical applications of Calculus

I am currently studying Calculus on my own for fun. I enjoy different components of math and how they can be used to solve so many problems. Many people, however, think I am crazy because I am ...
4
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0answers
62 views

How inequalities are made

I've been solving a lot of math contest inequality problems last few days and sometimes when I solve the problem I can easily ''see'' the idea behind it's creation (for an example, one clever ...
3
votes
0answers
70 views

What's so special about binomial coefficients that someone decided to organize them in a triangle?

I know that binomial coefficients are related to figurate numbers (which were studied by Greeks a loooong time ago, because of its connections to geometry). I also understand how the Pascal's triangle ...
48
votes
7answers
2k views

Problems that become easier in a more general form.

When solving a problem, we often look at some special cases first, and then try to work our way up to the general case. It would be interesting to see some counterexamples to this mental process, ...
14
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4answers
358 views

Book ref. request: “…starting from a mathematically amorphous problem and combining ideas from sources to produce new mathematics…”

I couldn't find Charles Radin's Miles of Tiles at the local university library or the public library, and cannot afford its Amazon price right now. Thus, while sorely disappointed for the moment, I ...
0
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0answers
38 views

How do I know the impact factor of a certain Journal is true? [on hold]

I am new in publishing, I have never published a paper, and nowaday there are too many online journals. That made me suspicious about their reputation, and it is not easy for me as a beginner in ...
36
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6answers
4k views

What should an amateur do with a proof of an open problem?

Assuming that somebody is not an employee of a university, just a math amateur, and makes a proper proof of some well known open math problem, what should he do with it? Publish on the internet for ...
2
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0answers
47 views

What is combinatorial probability a special case of?

Once I complained to one of my undergrad math professors that I was hopelessly lost when it came to combinatorics and combinatorial probability problems. He remarked, half-jokingly, that combinatorics ...
2
votes
3answers
99 views

Chess and mathematics

I have to choose a research-like project to follow the next year. Because I'm a chess enthusiast, I was thinking of trying to tackle an (open) problem related to chess, and relevant to mathematics. ...
3
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2answers
53 views

Any suggestion on how to justify true/false question in linear algebra exams?

I have hard time bringing words on paper when it comes to true false justification of linear algebra problems. My technique is to use counter example for false and use book theorems for true ones. ...
0
votes
0answers
61 views

The steps to becoming a Pure Mathematician

I'm a college freshmen intending to major in Mathematics. I started college with not so great grades in my calculus courses. However, I realized that to get the grades I just have to practice. I ...
370
votes
43answers
169k views

Visually stunning math concepts which are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain, but are ...
7
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3answers
139 views

Is Adobe Acrobat's icon a special function?

It looks like a function in polar coordinates. Is it a special function ?
5
votes
5answers
249 views

Examples of advancement in mathematics due to war

It's not a lie that, in most sciences, some of their advancement comes from war. A couple examples would be the Haber process in chemistry and none other than the Manhattan Project in both physics and ...
617
votes
25answers
42k views

Can I use my powers for good?

I hesitate to ask this question, but I read a lot of the career advice from mathOverflow and math.stackexchange, and I couldn't find anything similar. Four years after the PhD, I am pretty sure that ...
3
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0answers
47 views

Undergraduate Schools for the Mathematically Inclined

I'm a rising senior and working on generating a list of colleges to apply to, but it seems to me that (with few notable exceptions) my two main criteria are mutually exclusive. Are there any schools ...
0
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1answer
52 views

Dealing with questions with unknown answers

The vast majority of textbook exercises are worded essentially in the format: This assertion is (true/false). Prove this or find a counterexample. This, of course, is not how mathematics is ...
4
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1answer
514 views

Self-studying through an undergraduate math course. Need Tao-like textbooks!

I'm a physics undergraduate student who always enjoyed math, and briefly studied it at a university but for various reasons (laziness, youth) gave up and changed 'majors'. But I always wanted to go ...
2
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0answers
34 views

Equillibrium between Programming and Math Skills? [on hold]

So I enjoy recreationally doing math and programming and am now at a stage where I will be pursuing them in University but I have found myself in a bit of a bind. My programming ability seems to lag ...
1
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1answer
97 views

Too Many Books - Not Enough Time

I am currently a high school student trying to get as far ahead in mathematics as I can. In doing so, I accumulated a good 10 physical math books, and a library of online resources including 2 or 3 ...
3
votes
1answer
68 views

What are the big issues in modern graph theory?

This is inspired by the similar question on modern set theory. I've read through the open problems in graph theory on Wikipedia's list of unsolved problems in mathematics, but what I'm looking for is ...
2
votes
1answer
114 views

Are there any “obviously” true propositions in number theory?

After all efforts spent on wrong proofs of famous number theory conjectures and theorems like Goldbach's or Fermat's last theorem, could one find some simple statements (might be correct ones) whose ...
4
votes
3answers
153 views

What sequence should I study these topics in?

I will shortly list a series of topics that amount to what is essentially the first two years of an undergraduate degree. I'd like to know what is considered best order in which to study these ...
66
votes
9answers
4k views

Math and mental fatigue

Just a soft-question that has been bugging me for a long time: How does one deal with mental fatigue when studying math? I am interested in Mathematics, but when studying say Galois Theory and ...
2
votes
5answers
675 views

Best practice book for calculus

I tried with every inch in me to not ask a question such as this but I just couldn't resist asking this. What is the best Calculus practice book? I tried looking around but couldn't find a ...
12
votes
5answers
3k views

Calculus self taught? Books?

I recently graduated with a degree in bachelor of science with a focus interactive and multimedia design. I had to opportunity to take 1 C++ course and 1 HTML course. I was also only required to take ...
18
votes
1answer
889 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 ...
2
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0answers
148 views

Calculus book advice

I'm reading Thomas Calculus now but I don't think it includes Mellin transform or Riemann-Stieltjes integration... Can you recommend an advanced calculus book which includes all of this stuff?
1
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1answer
17 views

I have been offered year 2 entry for a maths degree but am not sure I want to take it -would love some advice

I am about to start an undergraduate maths degree (MMaths) and am extremely excited about studying maths . I applied for the normal first year entry and was offered an unconditional mid January ...
13
votes
3answers
342 views

Being mathematically critical: how should a student approach statements that appear to be obvious?

Very occasionally, I will read or hear a theorem, and think: isn't that obvious? Not in a contemptuous "I can immediately see how to prove this" way, but rather in a "I would have thought this was ...
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7answers
750 views

A question regarding irrational lengths in reality

I have a square stone slab 1 metre by metre, by the Pythagorean identity the diagonal from one corner to another is given as $\sqrt 2$. However $\sqrt 2$ is an irrational number, could someone ...
12
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2answers
269 views

Why are people more interested in the Riemann hypothesis than Goldbach's conjecture? [closed]

One of my friends, a math professor, told me almost every one of his colleagues (in the math department) had attempted to prove the Riemann hypothesis at some point in their life (maybe secretly). ...