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4
votes
1answer
266 views

Unrivaled math classics that would be of practical benefit to the upcoming generation?

I'm often impressed that top mathematicians in a given field seem to have not only a knowledge of the "state of the art" of their subfield, but also a knowledge of the history of the field and thus ...
4
votes
1answer
207 views

Are Different Areas of Number Theory That Different

I was wondering if number theorists are "number theorists," or eventually resolve themselves into one of the various branches - i.e., algebraic, analytic, etc. Also out of curiosity, I was wondering ...
2
votes
3answers
383 views

Proof that something is undefined?

How can one tell the difference when the result is undefined or math just doesn't know how to provide a value for that particular equation? (the value still exists however) For example, how could one ...
49
votes
9answers
7k views

Does it ever make sense NOT to go to the most prestigious graduate school you can get into?

I'm a senior undergrad at a top-ish(say, top 15) math school. I'm a solid, not stellar, student. This year I'm taking the qualifying exam grad courses in algebra and analysis and have been taken aback ...
1
vote
4answers
398 views

Interesting properties for numbers 1-20? [closed]

I'm sure most of you have heard of the argument that all numbers are interesting: If any uninteresting numbers exist, there must be a "smallest" uninteresting number, which would make it interesting – ...
7
votes
4answers
366 views

Are the computable reals finitary?

In the comment thread of an answer, I said: The computable numbers are based on the intuitionistic continuum, and are not finitary. To which T.. replied: Computable numbers are not based on ...
7
votes
0answers
337 views

The difference between 10 and 9.99999 … (recurring) [duplicate]

Possible Duplicate: Does .99999… = 1? At supper today my daughter was discussing her maths (she's 13) - she had been studying putting decimal numbers into what she called standard ...
12
votes
2answers
1k views

High school mathematical research

I am a grade 12 student. I am interested in number theory and I am looking for topics to research on. Can you suggest some topics in number theory and in general that would make for a good research ...
5
votes
4answers
368 views

Would nonmath students be able to understand this?

For a course, I am required to do a presentation. The topic could either be something mundane, like a career strategy report, or something more interesting, such as a controversial topic, or an ...
11
votes
2answers
631 views

Why do mathematicians care so much about zeta functions?

Why is it that so many people care so much about zeta functions? Why do people write books and books specifically about the theory of Riemann Zeta functions? What is its purpose? Is it just to ...
6
votes
1answer
564 views

Topology needed for differential geometry

I am a physics undergrad, and need to study differential geometry ASAP to supplement my studies on solitons and instantons. How much topology do I need to know? I know some basic concepts reading from ...
18
votes
2answers
1k views

Spotting crankery

Underwood Dudley published a book called mathematical cranks that talks about faux proofs throughout history. While it seems to be mostly for entertainment than anything else, I feel it has become ...
3
votes
2answers
288 views

Number of elements vs cardinality vs size

I have been wondered the definition of cardinality and number of elements. One mathematician told me that one can't said that the cardinality or size of the set $\{1\}$ is one, it should be said that ...
0
votes
1answer
121 views

How useful would it be to have the ability to ask questions and comment on the Arxiv? [closed]

I find these Q&As on philosophy, physics & mathematics very useful. It seems to be a Very Good Idea if some clever dude(s) & dudesses(s) modernised the Arxiv to do this. What are the pros ...
10
votes
4answers
2k views

Math for computer science?

Math for computer science? I'm a computer science major and just completed linear algebra. Many courses are available to take now. Of particular interest: number theory and abstract algebra (Modern ...
2
votes
1answer
366 views

Hard problems in algebraic geometry

People very often say that algebraic geometry is a hard subject and has many challenging problems to solve. I believe the hodge conjecture is the one of the most difficult in the field and you, which ...
3
votes
0answers
86 views

Importance of Poincare's Conjecture [duplicate]

Possible Duplicate: What is the importance of the Poincaré conjecture? It is rather well known that Poincare conjecture was proved by Perelman in 2003 given the amount of coverage it ...
5
votes
1answer
903 views

Research in Mathematics after undergraduate study in Physics?

I am a Physics undergraduate, but over the past year, I have developed more attachment to Mathematics than to Physics. How common is it for a Physics major to go into research in Mathematics and what ...
68
votes
7answers
3k views

A Case Against the “Math Gene”

I'm currently teaching a mathematics course for elementary educators (think of it as math methods, but with less focus on methods and more focus on content). In a student's essay, I encountered the ...
4
votes
5answers
207 views

Are there methods to well order a finite group in a meaningful way?

Can some finite groups be well ordered in a "meaningful" way? I mean, it is clear that we can trivially find a bijection between $\{1,...,n\}$ and a finite group $G$ with $n$ elements, but I am ...
5
votes
1answer
995 views

Knuth's up-arrow notation - Is there practical use for the numbers involved?

From Wikipedia, Knuth's up-arrow notation begins at exponentiation and continues through the hyperoperations: $a \uparrow b = a^b$ $a \uparrow\uparrow b = {\ ^{b}a} = ...
5
votes
6answers
676 views

How to make sure a proof is correct

If you come up with a proof of a mathematical proposition, how do you verify the proof is correct? Put it another way, how do you avoid a wrong proof? I guess there is no definitive answer to this. ...
13
votes
3answers
2k views

Homology and Graph Theory

What is the relationship between homology and graph theory? Can we form simplicial complexes from a graph $G$ and compute their homology groups? Are there any practical results in looking at the ...
3
votes
3answers
568 views

Remembering Taylor series

Could anyone suggest a good way of memorizing Taylor series for common functions? I have tried to remember them but never seem to be able to commit them to permanent memory.
11
votes
1answer
510 views

Journals of math history?

In a related question to this one, in what journals do math historians publish their article in? Brian M. Scott provided a link to Judy Grabiner's, who is a math historian, home page and it seems that ...
13
votes
2answers
727 views

Who is a Math Historian?

In the context of classes, it is very often that discussion on the history of mathematics arises, whether it'd be on who should a lemma be attributed to or a certain event that occurred during the ...
5
votes
0answers
189 views

Convex Hulls vs Shrink Wrap

I was recently explaining to a friend what the convex hull of a set of points is using the analogy of an elastic band around a set of nails hammered into a board. I was about to say that we can ...
2
votes
1answer
213 views

Reverse mathematics in undergraduate program

This might be different from colleges to colleges, but anyway: Is reverse mathematics covered in usual undergraduate math programs? If so, how far is it covered? Just a curious question, as ...
0
votes
2answers
138 views

On Reflexive Banach Spaces

My Functional Analysis lecturer gave me a topic for my assignment, the title is "On Reflexive Banach Spaces". I am a looking for several good references to start my work, that is why I brought this ...
6
votes
2answers
229 views

terminology: what is meant if someone writes “calculus of ..”?

This question might be a little soft as it does not have a definite answer, so I hope I do not break the conventions of this forum by posting it here. I have now come across the term "calculus of ...
3
votes
2answers
177 views

How do you explain paradoxes to non-mathematicians?

For example, how do you explain why the perimeter of this staircase does not converge to $\sqrt2$? Or, why isn't $\sqrt{(-1)(-1)}=\sqrt{-1}\sqrt{-1}$? I would say, the reason is simply because they ...
2
votes
1answer
96 views

Intuition on characters of topological groups

I am coming to the end of a series of lecture notes on representations of $S_n$ and $GL(V)$. Near the end, it attempts to introduce the notion of the "character of a topological group", but doesn't ...
2
votes
3answers
91 views

z-interval and sample size what is a normal sample size

Can a Z-interval be used when the sample size is between 15-30? does the variable play a role? I'm not too sure if it makes a difference. I know it can be used if the population is a normal or large ...
4
votes
1answer
188 views

How to get a more intuitive/and motivated understanding of a solution?

Math is a deductive science, that one starts from basic premises to prove more complicated results. From doing questions and reading solutions (at least at the elementary level eg: Olympiad ...
7
votes
1answer
262 views

How to present a paper?

I am going to present several papers to an audience. I have read through all the papers and have a clear idea about them. But this is the first time I have ever presented papers, and I am guessing ...
11
votes
2answers
756 views

What if your research paper got rejected with few comments given on paper?

I often wonder what if your research paper got rejected? Is it fair enough to resubmit that paper in the same journal? Is there any possibility of publication of that paper in any journal? Thanks
1
vote
1answer
77 views

Good text suggest to abstract algebra and point set topology as well as metric space, or you may consider as introductory to topology

I am going to take courses about those topic. i want some text which is suitable for beginner and with some difficult example or questions.
11
votes
2answers
5k views

How to cite preprints from arXiv?

Obviously when writing a math research paper it is good to cite one's references. However, with the advent of arXiv, oftentimes a paper is only available on arXiv while is awaits the long process of ...
17
votes
6answers
7k views

undergraduate math vs graduate math

It's really a mild, soft question. So far, I am an undergrad student, contemplating on several majors. What will be the major difference if I become a math major and go to a graduate school to study ...
10
votes
7answers
806 views

What is a Number Theorist

I often find myself facing this problem when asked by non-mathematicians about what I do. When the answer, "I'm a mathematician," doesn't suffice and I have to reply that I am a number theorist, I do ...
38
votes
16answers
8k views

Pen, pencils and paper to write math [closed]

The question is inspired by this thread on MO. My father is a mathematician, so I remember seeing very nice pens all around. When I started to do math by myself I've realized how important can be a ...
1
vote
1answer
217 views

Meaning of the Soul Theorem

The Soul Theorem states that in every complete, connected riemannian manifold $M$ with $\mathrm{sec}(M)\geq 0$, there exists compact, totally convex, totally geodesic submanifold $S$ such that $M$ is ...
4
votes
0answers
488 views

Why is unique ergodicity important or interesting?

I have a very simple motivational question: why do we care if a measure-preserving transformation is uniquely ergodic or not? I can appreciate that being ergodic means that a system can't really be ...
9
votes
2answers
580 views

Variety vs. Manifold

In the ambit of differential geometry the aim is to study smooth manifolds. Why the objects studied in algebraic geometry are called algebraic varieties and not for example algebraic manifolds? I am ...
2
votes
2answers
70 views

Isomorphisms that have names (Or: Base-less isomorphisms)

The answer to this question of mine provided me with the fact that every isomorphism $$ \phi: K^{n} \rightarrow V, $$ where $V$ is an arbitrary vector space of finite dimension $n$ over the field ...
-2
votes
1answer
126 views

Fuzzy logical and integer programming

Is there any way of formulating linear/non-linear programming problems in terms of YES, NO, and MAYBE instead of just $0-1$ programming?
0
votes
1answer
206 views

Name of probability distribution

Does this distribution have a name: $f(x) = yx^{y-1}$ for $0 < x<1$ and $y>0$? It looks like an exponential distribution. Or is it a nameless distribution?
3
votes
2answers
173 views

Question on mathematical writing

I am now writing my graduate thesis, it includes some basics mathematical theorems/propositions. I got a trouble in writing, more concretely, I do not know when can I state a mathematical claim as a ...
10
votes
3answers
3k views

Can the Bourbaki series be used profitably by undergraduates?

Can the Bourbaki series be used profitably by undergraduates and high school students?Are we the target audience? I came across the N.Bourbaki texts while surfing the internet(I have not had the ...
5
votes
1answer
305 views

Highest gain mathematical activity

I have this odd dream that online resources like this can serve as a virtual thesis advisor for future mathematicians who are teaching themselves. Here's another question along these lines. You can do ...