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2
votes
3answers
324 views

I would like to buy references in order to review and study mathematics [closed]

I am an ESL learner and most of the time I am able to understand English but In my courses, we don't study mathematics, and I think that it is a mistake or wrong. 1-What are really the best sources ...
11
votes
7answers
859 views

What's the hard part of zero?

A lot of textbooks said it was hard for human to accept zero when it was first introduced. How could it be? It seems to me as natural as positive integer which represent there is no elements at all.
1
vote
2answers
340 views

Largest number that can be written using N characters

I remember reading in RPF's biographical book, "Surely you're joking Mr. Feynman" that he used to have timed contest about writing down the biggest number using standard symbols. Instead of the time ...
12
votes
2answers
1k views

Is everything in mathematics built on add, subtract, multiply and divide?

This is probably a bit of a boring and ridiculously noob question, so apologies in advance, but: Is everything in maths essentially built on adding, subtracting, multiplying and dividing? Are they ...
3
votes
2answers
253 views

Why do our number start over at million, billion, etc

In English (I think this is universal anyway) we use the 1s, 10s, and 100s in a cycle. One, one thousand, one million; twenty two, twenty two thousand, twenty two million; one hundred and forty six, ...
3
votes
5answers
787 views

Preparing for first year CS

I'm in Italian guy almost in my 30. I have a regular job as a programmer. When in school I've never been much interested nor good in math and even at the university I've been studying languages, hence ...
21
votes
5answers
4k views

What are some interpretations of Von Neumann's quote?

John Von Neumann once said to Felix Smith, "Young man, in mathematics you don't understand things. You just get used to them." This was a response to Smith's fear about the method of characteristics. ...
10
votes
5answers
2k views

Common misconceptions about math

YARFMO (Yet another reposting from Mathoverflow) ;-) The more you know about math the more you find conceptions previously thought correct to be false: 1.) math is not as exact as many believe - in ...
10
votes
5answers
686 views

Time in Mathematics

I claim that it is commonly believed that Mathematical objects can be seen as genuinely static, with no "Platonic" time in which they do genuinely evolve. Nevertheless time has its place in ...
7
votes
0answers
313 views

logic lectures on youtube

Currently I am reading Logic an Structure by Dirk van Dalen (2008). As I am missing some basics I try to find related lectures on youtube. I frequently watch MIT, Stanford, and University of ...
5
votes
1answer
261 views

About finding advisors on the internet

The thing is, since I do a job, and work on mathematics in my spare time, I do not have any connection with the academia. Secondly, the internet is the only way I can interact and reach out to other ...
2
votes
4answers
418 views

A question about complex analysis

In complex analysis, we care about the functions of a complex variable. Are such functions just special case of the complex valued function defined in Rudin's Principles of Mathematical Analysis, ...
2
votes
1answer
124 views

What structure is this?

I had hoped that this would be easier. I have power series that I'm using. I want to know what simple structure describes the operations that I'm performing on them. It would be better if I could ...
1
vote
1answer
170 views

Define strange operators

How can I render the connected sum of $n$ topological spaces (or other quite strange topological operations) in a "product-like" manner? What I'm looking for is writing, for example $$ ...
13
votes
3answers
2k views

What are examples of mathematicians who don't take many notes? [closed]

I see people like Terry Tao and others take extensive notes. But is this really necessary? When I do this I feel like I am rewriting a textbook.
24
votes
2answers
7k views

What does closed form solution usually mean?

This is motivated by this question and the fact that I have no access to Timothy Chow's paper What Is a Closed-Form Number? indicated there by Qiaochu Yuan. If an equation $f(x)=0$ has no closed form ...
2
votes
1answer
194 views

Is the above statement true for maths?

In maths, you can use something as simple as statistical analysis to intuit the theory, and in comp-science you can use simulators. Is the above statement true for maths ?
3
votes
1answer
280 views

Inconsistent naming of elliptic integrals

This may be a question whose answer is lost in the mists of time, but why is the elliptical integral of the first kind denoted as $F(\pi/2,m)=K(m)$ when that of the second kind has $E(\pi/2,m)=E(m)$? ...
31
votes
5answers
2k views

Is speed an important quality in a mathematician?

Is solving problems quickly an important trait for a mathematician to have? Is solving textbook/olympiad style problems quickly necessary to succeed in math? To make an analogy, is it better to be a ...
52
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 ...
13
votes
3answers
2k views

What are the prerequisites for learning category theory?

Is category theory worth learning for the sake of learning it? Can it be used in applied mathematics/probability? I am currently perusing Categories for the Working Mathematician by Mac Lane.
38
votes
3answers
1k views

What is your method?

Many young, and not so young, mathematicians struggle with how to spend their time. Perhaps this is due to the 90%-10% rule for mathematical insight: 90 pages of work yield only 10 pages of useful ...
18
votes
4answers
939 views

On the Math Mindset

I am a soon-to-be high school graduate with inclination towards mathematics. I enjoy doing math, and am relatively good at it, but I dislike the way I am being taught. I feel like I am being taught ...
5
votes
7answers
2k views

Best Cities for Mathematical Study

This may sound silly, but... Suppose an aspiring amateur mathematician wanted to plan to move to another city... What are some cities that are home to some of the largest number of the brightest ...
7
votes
2answers
770 views

A Banach Manifold with a Riemannian Metric?

Given an infinite dimensional manifold modeled on a Banach space, what does it mean for it to have a Riemannian metric? Does it necessarily mean that it is actually a Hilbert manifold? My ...
5
votes
2answers
497 views

How to improve number theory related skills?

I know it is a very general question, but i'm not sure how to get started and improve number theory related skills related to ACM ICPC and other programming competitions.Any good way or book ...
18
votes
6answers
840 views

Difficulty in Mathematical Writing

Lots of people (including myself) face lot of problems in tackling Mathematical Problems, which appear as if we can solve it, but then writing out a solution becomes difficult. Let us consider some ...
7
votes
2answers
330 views

A Question on RH relating to Prime Number theorem

Well, in a previous post regarding the explanation of Riemann Hypothesis Matt answered that: The prime number theorem states that the number of primes less than or equal to $x$ is approximately ...
9
votes
2answers
516 views

Automatizing computational skills

"It is a profoundly erroneous truism, repeated by copybooks and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise ...
47
votes
7answers
8k views

Can someone please explain the Riemann Hypothesis to me… in English?

I've read so much about it but none of it makes a lot of sense. Also, what's so unsolvable about it?
58
votes
5answers
8k views

Getting better at proofs

So, I don't like proofs. To me building a proof feels like constructing a steel trap out of arguments to make true what you're trying to assert. Oftentimes the proof in the book is something that I ...
26
votes
5answers
6k views

Kindle as a Tool for Mathematicians?

UPDATED: 1/15/2014 I originally wrote this post in 2010, when I was looking for alternative ways to store and transport papers. I had my laptop, but due to its weight, limited battery life, and the ...
1
vote
2answers
249 views

Gradient flows in metric spaces

What is a good introduction in gradient flows in metric spaces? I know the book Gradient flows: in metric spaces and in the space of probability measures by Luigi Ambrosio, Nicola Gigli and Giuseppe ...
5
votes
2answers
167 views

What is an alternative formulation to a contour integral?

Suppose that a rational generating function is given representing the function $f(x) = \sum_{i=0}^{2n}{c_i x^i}$ where $c_i \in \mathbb{N}$ The goal is to determine if the coefficient in the middle, ...
9
votes
2answers
525 views

How to assess a non-natively english speaking high-schooler's mathematical ability?

I'm a math PhD who has been asked to interview a high school student and determine what he/she is interested in and how strong the student is. Usually I would want them to talk as much as possible ...
14
votes
2answers
2k views

Why is it called Sylvester's Law of Inertia?

By "Sylvester's Law of Inertia," I mean: http://en.wikipedia.org/wiki/Sylvester%27s_law_of_inertia How does the name "Law of Inertia" fit with the statement of the theorem? I guess it's from ...
13
votes
8answers
779 views

Elevator pitch for a (sub)field of maths?

When I first saw the title of this question, I forgot for a moment I was on meta, and thought it was asking about quick, catchy, attractive, informative one-or-two-liner summaries of various fields of ...
16
votes
2answers
1k views

Why can't Cantor sets cover $\mathbb{ R}$?

The Cantor set is uncountable so I expect countably many of them to be able to cover $\mathbb R$, but the set has measure $0$ so countably many of them also has set of measure $0$ and thus can't cover ...
7
votes
4answers
1k views

Theorems in Measure Theory: Fatou's Lemma, Lebesgue DCT, Monotone CT

In measure theory there are three fundamentally related theorems about exchanging limits and integrals: Fatou's lemma, Lebesgue's Dominated Convergence Theorem, and Monotone Convergence Theorem. It is ...
3
votes
6answers
720 views

Are there broad or powerful theorems of rings that do not involve the familiar numerical operations (+) and (*) in some fundamental way?

I am of, and I would like to retain, a mindset that mathematics does not have to have numbers as the central object of interest. With that in mind, I have done a fair amount of self-study on topics in ...
4
votes
2answers
547 views

Hairy Ball theorem and its applications

While searching a question about fibre bundles, which was asked here, i got directed to Vector bundles. I noticed this word "Hairy Ball" which sounded eccentric and made a search at Wikipedia. How ...
15
votes
7answers
1k views

What mathematical questions or areas have philosophical implications outside of mathematics?

Please list both the problem/area and justify why it is important philosophically. This question doesn't cover questions that are only important within the philosophy of mathematics itself.
5
votes
7answers
749 views

Supplementary reading for probability theory studies

Can you advise some good books covering areas which are required for serious probability theory studies (e.g. measure theory, functional analysis)? Preferably this book should have some problem sets ...
2
votes
2answers
579 views

What is the correct way to write product or sum in capital pi or capital sigma notation when you wish to exclude an index?

I have a series of terms $\{t_n : t_n = a_n x_n\}$, and I want to talk about the product of each term except $t_j$. Would any of these be an appropriate way to say that? I like this: $$\prod_{i \ne ...
14
votes
7answers
2k views

Why do statements which appear elementary have complicated proofs?

The motivation for this question is : Rationals of the form $\frac{p}{q}$ where $p,q$ are primes in $[a,b]$ and some other problems in Mathematics which looks as if they are elementary but their ...
10
votes
15answers
13k views

What concepts were most difficult for you to understand in Calculus? [closed]

I'm developing some instructional material for a Calculus 1 class and I wanted to know from experience for yourself, tutoring others, and/or helping people on this site where is the most difficulty in ...
25
votes
11answers
4k views

Vivid examples of vector spaces?

When teaching abstract vector spaces for the first time, it is handy to have some really weird examples at hand, or even some really weird non-examples that may illustrate the concept. For example, a ...
6
votes
3answers
2k views

Group Law for an Elliptic curve

I was reading this book "Rational points on Elliptic curves" by J.Silverman, and J.Tate, 2 prominent figures in Number theory and was very intrigued after reading the first couple of pages. The ...
4
votes
2answers
194 views

Relationship between torsion modules and topology

I was reviewing my class notes and found the following: "The name 'torsion' comes from topology and refers to spaces that are twisted, ex. Möbius band" In our notes we used the following definition ...
7
votes
2answers
551 views

A question on FLT and Taniyama Shimura

Sometime back i watched the documentary of Andrew Wiles proving the Fermat's Last theorem. A truly inspiring video and i still watch it whenever i am in a depressed mood. There are certain ...