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53
votes
8answers
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, ...
3
votes
0answers
53 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 ...
3
votes
2answers
56 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. ...
2
votes
0answers
36 views

Equillibrium between Programming and Math Skills? [closed]

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 ...
0
votes
1answer
63 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 ...
2
votes
1answer
123 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
77 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
124 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 ...
1
vote
1answer
18 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 ...
40
votes
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 ...
0
votes
0answers
11 views

A name for the number system used in versioning software

Software often uses a numbering system where one "digit" increments independently of the others. For instance, the next version of Software 2.9 might be Software 3.0 or Software 2.10 or Software ...
12
votes
2answers
301 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). ...
0
votes
0answers
15 views

Phrases for uniform boundedness and uniform convergence

I have some doubts about using prepositions. I. Let $f_a : \mathbb{R} \to \mathbb{R}$, $f : \mathbb{R} \to \mathbb{R}$. Assume that $f_a (x)$ converges uniformly to $ f (x)$, $x \in [0;1]$, as $a ...
0
votes
0answers
35 views

How do you look for classic/normative/standard books about an established branch of mathematics?

If you want to immerse yourself in a branch of mathematics (e.g. linear algebra and linear optimisation) which is new to you, then you often look for standard books which you can rely on. You could ...
0
votes
2answers
50 views

An ABC soft question about epsilon-delta argument

Someone told me that some textbooks present epsilon-delta argument somewhat misleadingly. For example, consider the simplest one: the convergence of the sequence $(1/n)_{1}^{\infty}$ to $0$. These ...
3
votes
0answers
52 views

Etiquette for proper usage of Greek letters and other notation

I've progressed to the "output" point in my mathematics career and have run into a slightly embarrassing problem while writing a paper. Clearly, certain Greek letters are suitable for some situations ...
0
votes
0answers
22 views

Usage of the phrase “constant parameter”

In general, constants are globally fixed, while parameters are a bit more free. But suppose I wish to use the word "constant" as an adjective to emphasize that a parameter is fixed w.r.t. other ...
1
vote
3answers
152 views

Is tutor essential for success in mathematics? [closed]

Everyone in my Pre-Calc - Calc I class is failing, except the kids who go tutor. They get top percentile ranks in the class. Should I drop maths all together so I don't have to invest in a tutor? I ...
3
votes
0answers
65 views

Is it too late to start studying maths? [closed]

I am 24 years old and I am just beginning to study undergraduate level maths. I have a bachelors and masters in mechanical engineering. Is it too late for me to start studying maths now? I plan to do ...
8
votes
0answers
101 views

Is Category Theory geometric?

In "From a Geometrical Point of View" (http://www.amazon.com/gp/aw/d/1402093837?pc_redir=1407132421&robot_redir=1) Marquis states that category theory is thoroughly geometric. Could someone ...
0
votes
0answers
48 views

Can a Computer Algebra System 'experiment' with expressions?

I have recently been reading about software for symbolic manipulation, and I can see its use as a tool for performing large calculations that would be unfeasible otherwise. Given that these systems ...
5
votes
4answers
210 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 ...
1
vote
0answers
76 views

Why nobel prize is not for mathematicians [closed]

I have heard from many people that nobel prize is not given to mthematicians.Waht is the reason behind this?I also heard that a women rejected the nobel because of some famous mathematician.Is this ...
6
votes
1answer
177 views

How much mathematics should a student of mathematical logic know?

I would like to know what areas of mathematic are directly related to mathematical logic, besides the usual courses on model theory, proof theory and computability. If you suggest only one book on ...
6
votes
7answers
759 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 ...
1
vote
3answers
89 views

What functions are most useful after the ones learned in high school?

I have learnt how to use trig functions, hyperbolic trig functions, exponentials and logs and simple things like polynomials, ellipses, hyperbolas and rational functions but lately when doing calculus ...
3
votes
0answers
65 views

In what order should I study?

I would like to study the basic fundamentals of mathematics from the beginning and move on from there as my understanding of the subject is lacking. In what order should I study? Arithmetic ...
2
votes
1answer
136 views

Math enthusiast wants to learn math

I'm an english major with a vivid interest in mathematics,I've read and enjoyed What Is Mathematics? by Courant and Robbins (does this count as some background?),and I've decided to begin a serious ...
6
votes
1answer
105 views

Why do objects that are farther away look smaller?

What is the reason, mathematical and/or physical, that the further away something is the smaller it looks? We know stars are humungous, but they look like tiny dots in the sky.
1
vote
1answer
39 views

Prerequisites for Hilbert Cohn-Vossen's Geometry and the Imagination?

I've not read this book(not really),but I would like to know how much is assumed by the reader. can I recommend this to the layperson? Also ,any more recent similar books? I already know of Courant ...
1
vote
3answers
222 views

Is there an adjective appropriate for describing mathematical terminology that you feel needs to be phased out? [closed]

Let me firstly apologize; this is more of an English language question, so posting it here is perhaps slightly inappropriate. But I couldn't think of a non-mathematical example, so here we are. ...
1
vote
1answer
69 views

Video/audio lectures on differential topology?

Do there exist decent online video lectures, or even audio lectures, covering differential topology? I'm aware of Milnor's talk, but it is more like exposition and doesn't go very far.
4
votes
3answers
123 views

(translated)Russian mathematics books?

Most russian mathematician(generally) are known to do and teach mathematics in a very original manner,they do in a very intuitive yet rigorous way, with/through wonderful connection to physics. ...
5
votes
1answer
106 views

High school research project ideas

I'm starting my last year of high school, and I will have to do an all year research on a mathematical topic. I'm a really passionate learner and I'm very involved in computer science. I am stuck on ...
5
votes
2answers
53 views

How do I determine if I should submit a sequence of numbers to the OEIS?

When I search a sequence in the OEIS and it's not there, it gives me a message saying "If your sequence is of general interest, please submit it using the form provided and it will (probably) be added ...
1
vote
1answer
185 views

Gilbert Strang's books on calculus and linear algebra?Are they for math majors?

I would to know what are the best resources to use to teach and learn elementary subjects (calculus,linear algebra),I remember when learning calculus, I used Spivak's book which had wonderful ...
5
votes
1answer
173 views

Why do we care about simple groups rather than indecomposable groups?

A first thing that we do to analyze something is "divide and conqur." So it is natural to consider simple groups. In the same way, it appears to be natural to consider indecomposable groups. However, ...
2
votes
2answers
124 views

Three-valued logic as foundation

Isn't it more natural to use Three-valued logic(false-true-unknown) as the foundation of mathematics? It is a better model for natural languages. And it also can model sentences like the lair paradox ...
1
vote
1answer
58 views

Is there anything we can add to the present Euclidean Geometry?

I did not study the detail history of Euclid. As far as I know, the geometry starts from a few postulates and keeps on expanding (through theorems developing) to the present state. Even with these ...
1
vote
1answer
65 views

where can I get math book reviews?

The only two freely available choices are maa.org and zbmath.org ,where can get other mathematical book reviews? any one?
43
votes
7answers
5k views

What is the oldest open problem in geometry?

Geometry is one of the oldest branches of mathematics, and many famous problems have been proposed and solved in its long history. What I would like to know is: What is the oldest open problem in ...
0
votes
1answer
39 views

How do the existence and $L^p$ integrability of weak derivative affect the smoothness of Sobolev functions?

In the definition of Sobolev spaces, let us say the space $W^{1,p}(\Omega)$, where $\Omega$ is an open subset of $\mathbb{R}^n$. What contributes more to the smoothness of a function $f$: 1-The fact ...
6
votes
3answers
136 views

Algorithm for multiplying numbers

Background Today I had to explain to some kid how to multiply numbers with multiple digits in them. Then I recalled, that some other day I answered this question describing one of the numerous ...
4
votes
1answer
86 views

Who are some blind or otherwise disabled mathematicians who have made important contributions to mathematics?

Two prominent mathematicians who were disabled in ways which would have made it difficult to work were Lev Pontryagin and Solomon Lefschetz. Pontryagin was blind as a result of a stove explosion at ...
0
votes
0answers
34 views

Reference: Fields of characteristic p

I am interested in learning more about fields of characteristic $p\neq 0$. Does anyone know of a good reference that covers the basics of this topic and possibly galois theory over fields of prime ...
2
votes
1answer
64 views

Starting with ring theory

Can anyone suggest a book on rings explaining concepts using visual diagrams, similar to the one visual group theory book by Nathan Carter for groups.The problem with me is that after reading that ...
2
votes
2answers
119 views

Set of sequences -roots of unity

Consider $G_n$ as the multiplicative cyclic group given by the $n^{th}$ roots of unity. $$G_n = \left\{ e^{ 2ik\pi/n} \mid 1\leq k \leq n \right\}$$ Now construct a sequence from each $G_n$ by ...
3
votes
0answers
65 views

Attemping Qualifying Exam Problems — and failing

My question is concerning learning strategy. I can solve the majority of the exercises in a typical graduate mathematics textbook like, say, Dummit/Foote's Abstract Algebra. To supplement my education ...
1
vote
0answers
44 views

Most important results from pure math in applied probability?

I'm taking a course next semester at my university on applied probability (with relevance to signal and information theory). Although the nature of probability is mostly problem solving and applying ...
10
votes
3answers
338 views

A question from an engineering undergraduate

My question primarily concerns the necessary transition from an undergraduate program in electrical engineering to graduate program in applied mathematics or pure mathematics. I'm an electrical ...