0
votes
0answers
16 views

Research scopes in Computational Geometry

I have taken a short a course on Computational Geometry and at present I want to do some research works of my own. Can anybody tell me about the research scopes on it? I mean, what are the active ...
5
votes
1answer
73 views

What math have I missed as an Engineeering graduate? [on hold]

To explain, I have a Master's in Engineering from a well known university. We did a wide variety of mathematical topics, vector calc, perturbation methods, numerical methods, linear algebra, discrete ...
0
votes
2answers
120 views

Advice on helping a talented highschool student [on hold]

I've watched an interview of the famous mathematician Pierre Deligne. In it he says that the family had given him 'Set theory' by Bourbaki, which is known for its difficulty, and I happen to know a ...
4
votes
0answers
48 views

Where to post a Calculus review guide?

I created a PDF document (using LaTeX) in which I wrote relevant review materials and Calculus problems for Calculus 1, 2, and 3. Is there an appropriate forum where I could try to post this to ...
0
votes
0answers
30 views

International scholarship for maths [closed]

Do you mathematicians know if there is a scholarship (or something similar) for maths awarded at international level regardless of the country and/or university from which you come?
8
votes
1answer
166 views

How much math is there? [closed]

Among other things I teach high school-level math, and one question that often comes up is: "How long would I have to study math in order to know all of it?" I usually tell them that it's like ...
0
votes
0answers
51 views

Is it necessary to know all the details in proofs of theorems you study in PDE's?

I've been studying PDE from the book by L.Evans for some time now. I came across some statements in the proofs which I couldn't justify. But to complete the exercises I didn't need to know all these ...
1
vote
0answers
36 views

Which Universities in US should I apply to study for a Masters in Statistics?

I've decided that I want to join a masters programme that prepares graduates for industry work as opposed for a phd. At the same time, I also want to really understand the theory behind the ...
2
votes
0answers
60 views

Science Fair project ideas? [closed]

It the summer for me right now, and I'm approaching my junior year. I'm attending a very rigorous high school in Florida in the Math, Science and Engineering program. The program requires that I ...
0
votes
1answer
80 views

The fourth pillar of mathematics? (analysis, algebra, geometry and …) [closed]

Many universities claim that there are three general areas in mathematics: analysis, which deals with continuous aspects of mathematics; algebra, which deals with discrete aspects; and geometry. If ...
7
votes
3answers
731 views

Masters' thesis in group theory [closed]

I would like some ideas on topics in group theory which would be suitable for a masters' thesis. What sort of problems would be suitable for this level? Because it is at masters' level, no original ...
2
votes
1answer
55 views

Rigorous Book on Topology of Surfaces and Simplicial Complexes

In the undergraduate course I am on the topology course covered the basics of point set topogly very well and everything was done, but then moved on to simplicial complexes and surfaces which was very ...
2
votes
1answer
66 views

How do you use reference books?

Reference books at the research levels often does not include any problem or exercise. While you can't read these books like novels(you normally need to work on other sheet of paper), I'm just ...
0
votes
1answer
101 views

Going to math grad school with low GPA [closed]

I am a pure mathematics major and I want to do Ph.D in math, however I want to change to Applied math. I have a low 3.2 < GPA < 3.3 though. I have taken most of Pure math requirements, and ...
2
votes
1answer
91 views

Structured Self-Learning Program for Calculus I & II

I'm interested in a organised program which comprehensively covers the topics of Calculus I and Calculus II. I've recently finished taking my secondary school's university-level Calculus I course, ...
0
votes
0answers
163 views

Math Competitions such as Intel Science Talent Search for High School Freshmen

I am extremely interested in mathematical competitions. I was wondering if there was something like the Intel Science Talent Search, where one can present his/her research, for freshmen in high ...
7
votes
3answers
188 views

Graduate School?

I'm completely clueless on the process, but on track to graduate in two years, so I have a few questions about what I should do. 1) What's the difference between a Master's degree in Mathematics and ...
3
votes
1answer
117 views

How should one go about obtaining “mathematical maturity”?

tl;dr: Is mathematical maturity better obtained by doing hard subjects slightly out of your reach, or by doing more simple subjects to gain experience? The end of the semester is close, and I ...
24
votes
6answers
1k views

Should I understand a theorem's proof before using the theorem?

I find myself embarrassed when using results in books. For example, there are so many results in Sobolev spaces that I think I would not be able to understand all of them. Yes, I could try to ...
9
votes
1answer
139 views

A graph of all of mathematics

In mathematics, one often makes (proves) statements on the basis of: Previously proven statements Axioms I like to think of these dependencies as a directed graph, with edges from the accepted ...
3
votes
2answers
95 views

How many times should students repeat reviews? Frequency of repetitions? [closed]

The usual advice is that a math student has to read or study something "a couple of times" to appreciate it. But is there a narrow range of the optimal number? Any research on this? And what's the ...
1
vote
0answers
76 views

Exam Advice or Tips, specific for Undergraduate Math or Higher [closed]

What are some noteworthy, even rare suggestions for exams in undergraduate math or higher? I'm not interested in general advice that can apply to many different subjects, like ...
1
vote
1answer
81 views

How to remember modular arithmetic and divisibility results?

I tried reviewing the same material $\ge 5$ times, once every 2 weeks or whatnot. Withal, I query intuition like this. But I forget these results quickly or don't remember them 100% perfectly. But ...
3
votes
1answer
142 views

Do the things that you don't know in mathematics frighten you? [closed]

I have zillions of things that I don't know in mathematics. I feel I would never know any of them completely. Especially after this age (26)... and I immediately run away since I am a perfectionist. ...
1
vote
0answers
56 views

Instructive video content for High School kids?

I need some math Youtube channels (or any other visual media, movies maybe...) that I can recommend to High School students, not solely as a method of learning math but more to illustrate the beauty ...
20
votes
4answers
2k views

Is all of mathematics based on logic?

I do not understand the discipline in mathematics that is called "mathematical logic". For me, all of mathematics is based on logic and that is what makes it the exact science. Every theorem or lemma ...
32
votes
10answers
3k views

Becoming Better at Math

How can I become excellent at math? It really interests me but when I fail I become demotivated and begin to give up. EDIT: Could anyone suggest books for someone with a math education that just ...
0
votes
1answer
38 views

Other conditions than necessary and sufficient conditions, $\Rightarrow$, $\Leftrightarrow$?

I know that $$A\Rightarrow B$$ means that $A$ is a necessary condition for $B$ and $B$ is a sufficient condition for $A$. Also, $$A\Leftrightarrow B$$ means that $A$ is necessary and sufficient ...
10
votes
9answers
905 views

A Poster About Prime Numbers [closed]

We're going to design a poster about prime numbers, which will appear in a mathematics magazine for middle school students. The poster should be both visually attractive and mathematically rich. Do ...
50
votes
18answers
5k views

If there are obvious things, why should we prove them?

Obviously, there are obvious things in mathematics. Why we should prove them? Prove that $\lim\limits_{n\to\infty}\dfrac{1}{n}=0$? Prove that $f(x)=x$ is continuous on $\mathbb{R}$? $\dotsc$ Just ...
3
votes
1answer
79 views

Mathematics or physics at university

I have a strong interest in maths, and I feel that advanced physics is cool too (although I've only studied classical mechanics at high school, which is kind of boring). So I'm not sure about which ...
2
votes
0answers
34 views

Revise high school material

Can you suggest me a comprehensive book to revise high school mathematics (up to besic calculus)? It should be extremely clear and complete and "scientific" (not like most high school books). Thank ...
3
votes
3answers
107 views

Things to do before starting math (or physics) at university

What is better to do before starting a math degree? I was thinking that maybe I should do something like: learning latex learning how to use matlab Any other suggestions?
25
votes
3answers
699 views

Create a Huge Problem

I am wondering if any problems have been designed that test a wide range of mathematical skills. For example, I remember doing the integral $$\int \sqrt{\tan x}\;\mathrm{d}x$$ and being impressed at ...
1
vote
3answers
72 views

Which discrete mathematics book to read for a software engineer?

I'm a computer science student, but I lack a good mathematics background. So I decided to start working on that. I was searching in the topic and I found that for computer science a good knowledge of ...
1
vote
0answers
33 views

What courses require multivariable analysis?

For which undergraduate and introductory graduate mathematics courses is a rigorous course in multivariable analysis an essential prerequisite?
23
votes
8answers
6k views

Are there contradictions in math?

Someone told me that math has a lot of contradictions. He said that a lot of things are not well defined. He told me two things that I do not know. $1+2+3+4+...=-1/12$ what is infinity $\infty$? ...
2
votes
1answer
82 views

How to study analytic number theory?

Should i study many books at the same time? Or should i go one by one? I started with Apostol's book... But for example if i don't understand a proof, i check another book for a different proof of the ...
5
votes
1answer
89 views

What's the trick to re-focusing on your math studies?

If you check my history on MSE, you'll see that I was very active about 1/2 a year ago. Right now I'm working and socializing a lot, which is important, but I also have spare time to devote to my ...
3
votes
1answer
102 views

Where to begin my Math journey

I apologize if this is not the correct forum for this, but I felt it appropriate. I want to start getting into more mathematics and learning all I can to step up my programming career. I know plenty ...
2
votes
5answers
338 views

What area of Abstract Algebra do you find most interesting? [closed]

For my Abstract Algebra class, we will be doing small presentations (2 class periods) covering some topic in Abstract Algebra. Thus far, I have studied groups, rings, fields, modules, tensor ...
7
votes
1answer
115 views

why is that most of the books in mathematics don't include answers?

I am currently going through the " Topics in Algebra" By I. N. Herstein. The problems are pretty good. But there are no answers on the back. Same is the case with "Mathematical Analysis" by Rudin. I ...
3
votes
0answers
77 views

Is an undergraduate in engineering sufficient preparation for a masters in mathematics?

I'm a high school student who is considering doing an undergraduate in engineering. However my the long term plan is to pursue math at a higher level. I want to do engineering at undergrad because I ...
78
votes
20answers
13k views

Visually deceptive “proofs” which are mathematically wrong

Related: Visually stunning math concepts which are easy to explain Beside the wonderful examples above, there should also be counterexamples, where visually intuitive demonstrations are actually ...
8
votes
6answers
996 views

Should I do all the exercises in a textbook?

The problem sets that you usually get in a university course is a small fraction of the exercises in your textbook. Which raises a question: do you need to solve all the exercises from your textbook? ...
366
votes
42answers
167k 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 ...
1
vote
3answers
210 views

Is it possible to learn abstract algebra no precalculus or calculus?

See above. I am trying to re-teach myself mathematics in a different manner than is formally taught (i.e., set theory, number theory, mathematical logic, abstract algebra, discrete math and then ...
0
votes
0answers
82 views

Don't feel like I grasp the mathematics I'm supposed to understand

In high school, I used to spend my free time proving the formulas that we were asked to use. I'd prove loads of formulas in Calculus that we never even studied, just because I enjoyed getting to the ...
2
votes
3answers
134 views

University-level books focusing on intuition?

I help some students with difficulties in Mathematics and Physics (especially math, physics, and engineering majors). While in high school they usually don't study, or are not interested, etc., in ...
12
votes
5answers
2k views

Why teach linear algebra before abstract algebra?

Is there a reason why most undergraduate curriculums put linear algebra before abstract algebra? I'm asking this because personally it seems to be much easier to understand the architecture behind ...