Questions asking for advice on various mathematical matters. Be careful that your question is answerable, and also that it is not a polling question (e.g. "What is the best / your favorite way to...").

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2
votes
2answers
122 views

Going Back to Grad School After Being Away from Math

I graduated with a degree in Math-Computer Science(dual degree) from a college in the US in 2012, and have been working in the Software industry ever since. From 2012 to mid 2014 I was a software ...
1
vote
1answer
45 views

Progressive division

Given: L: known length of a line which is to be divided S1: known value represening the starting segment, also maximum segment value SN: known value representing the length of ending segment, also ...
13
votes
5answers
504 views

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
votes
1answer
69 views

Complete list of math topics to study up to college level math?

Aspiring mathematician here. I have always been fascinated by math, physics, and just logic in general. I have noticed that I generally grasp topics and ideas quite quickly, but I am being hindered ...
0
votes
1answer
96 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 ...
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 ...
1
vote
3answers
167 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 ...
1
vote
2answers
51 views

How do you move from just plugging in variables to an equation to actually understanding the equation?

I really can't say I focused on math when in school (didn't focus much ) , but now much later in life, I am trying to learn math. While I can sometime just plug and chug variables into an equation ...
5
votes
4answers
288 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
3answers
45 views

What are the concepts that I need to understand before studying Fourier Analysis?

Background ( Long Story Short ) : For some reasons, I am taking a class in my university that focus on Fourier Analysis Laplace Transform, and Partial Diffiential Equations Problem : I have done ...
6
votes
1answer
242 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 ...
1
vote
2answers
86 views

Sufficient requirements for graduate school in Mathematics?

I am 24 years old, and I will be completing a degree in Computer Science in May 2015. Over the years, I have taken the Calculus series (up to Multivariable Calculus), Intro to Linear Algebra, Intro ...
2
votes
0answers
92 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
3answers
141 views

What is so special about $a*b^{ -1}$ equivalence?

This equivalent is used often in group theory. For example, using this equivalnce you prove Lagranges theroem and also this equivalence gives you the cosets and other things. This equivalence also ...
1
vote
1answer
91 views

A tenth grader's starting point on mathematics

This question primarily concerns the elementary books a Canadian high school student could read and work through to gain further insight into mathematics and be attracted to it. My brother, who has ...
1
vote
1answer
30 views

Is $g$ increasing?

Suppose $f:[a,b]\rightarrow\mathbb{R}$ and define $g:[a,b]\rightarrow\mathbb{R}$ as follows $$ g(x)=\sup\{f(t):a\leq t\leq x\}, $$ with $x\in[a,b]$. Someone told me that $g$ is an increasing ...
10
votes
3answers
414 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 ...
3
votes
1answer
143 views

Actuarial Science or Financial Mathematics?

I’m a second year undergraduate student of Actuarial Science that equally loves finance and pure mathematics. I only knew of Actuarial Science as a career that suited best these two requirements ...
3
votes
2answers
54 views

Favorite Textbooks for introducing a subject?

I'm interested in learning more about number theory, about fractal geometry, and about probability. Anyone have any good recommendations? I've taken calculus and statistics at university if that helps ...
2
votes
1answer
91 views

How to see 4th dimension? [closed]

Anyone has tricks or methods? Great help, thank you. P.S.: Abstractly of course, not actually seeing 4D, which I don't think is possible.
3
votes
1answer
56 views

Re professional mathematicians working on several problems at once. Source needed.

Recently I read a quote from a working mathematician where he pointed out that professionals have to get used to carrying around several unsolved problems at once. Can anyone help me with the source ...
0
votes
0answers
60 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 ...
38
votes
5answers
6k views

What are the work habits of the best mathematicians? [closed]

Of course I would never compare myself to, and don't expect to be, one of the great mathematicians. However, I am curious as to how my work habits, dedication and passion differs from theirs. How ...
7
votes
2answers
327 views

The best balance in studying Mathematics?

I'm a student studying Mathematics at a university level. I've completed Single Variable Calculus, Differential Equations, Multivariable Caculus, Real/Complex Analysis, and Linear Algebra and I've ...
2
votes
4answers
391 views

Should I read about Manifolds or Algebraic Topology?

I really enjoy doing maths and it fills quite a lot of my spare time. I'm starting my first year in the university on october and I probably won't have that much time for independent reading once ...
5
votes
0answers
110 views

Problem solving strategy?

This question has always bothered me, and I've never had a maths coach to guide me along the way and show me what to do next. Nevertheless, I did make top 50 nationally in my national mathematics ...
0
votes
5answers
145 views

Some examples of applications of Game Theory

I'm approaching my junior year of HS now, and I'm looking for a good science fair project to do. I love mathematics, so I decided to a category of mathematics that can help base logical conclusions to ...
2
votes
0answers
180 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 ...
15
votes
5answers
752 views

Understanding mathematical texts

Please could you comment on following: I always wanted to know what mathematicians mean by "understanding a piece of mathematics". For example, I have just finished the second chapter from Rudin's ...
1
vote
1answer
113 views

Math self-study in the holidays

In the upcoming holidays, I have got 6 weeks free to learn some new math (I was thinking of calculus and linear algebra). It's useful for my high school math skills (I don't live in America, so my ...
0
votes
3answers
496 views

I'm forgetting maths.. [closed]

I'm 14, and I'm the Math topper in my grade. But suddenly, I've started loosing confidence, and I've started forgetting maths.. I am looking for a good solution. (If it helps, I'm forgetting a bit of ...
18
votes
11answers
2k views

Gap year to study math

This is a plan in its earliest and thus least concise stage, so either bear with me or don't read the following babble (I bolded some of the important stuff): I am a high school graduate who is about ...
0
votes
0answers
66 views

Complex analysis a good thing to take with algebra?

This is sort of a follow up to a question I asked awhile ago. I'm working out which courses to take my first semester of my second year of university. I've had linear algebra, calculus, and analysis ...
7
votes
3answers
957 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 ...
3
votes
1answer
147 views

Changing streams in PhD

I've a masters degree from a reputed Indian university in pure mathematics, with a specialization in Algebraic Number Theory. However, I'd like to apply for a PhD in computational math/theoretical ...
3
votes
2answers
402 views

What's after undergrad? Advice needed.

I'm currently a rising senior at a small, yet well ranked liberal arts college studying Pure Mathematics. I've taken multiple high level mathematics courses and plan on doing a few more independent ...
0
votes
0answers
131 views

Multivariable calculus and real analysis in one semester. What is the best way to study for such course?

I am in my first year of EECS and planning on taking a lot of maths classes. I have already taken single variable calculus and linear algebra and did well in them and decided to take multivariable ...
6
votes
2answers
181 views

Advice for self-studying Inequalities and Calculus

I'm interested in self-studying the following books over the next year or so: Spivak's Calculus (I'm already in Ch. 5 and it is very slow going) The Cauchy-Schwarz Master Class by J. Michael Steele ...
2
votes
1answer
73 views

Decided to finally jump in

I've finally decided to jump into teaching myself math because I am a junior (soon senior) in high school and have been interested in math for the longest time. I am not sure if this question belongs ...
1
vote
3answers
622 views

Which course is best to take after calculus, linear algebra, and real analysis?

During my first year at university I took our honors versions of multivariable calculus and linear algebra (which was very abstract) as well as an introductory real analysis course focusing on ...
9
votes
3answers
2k views

Is it bad to keep aside Lang's Algebra in graduate school?

Question is as it is stated in title. I will be joining for PhD program in this July 2014. I am interested in working in Algebra/Algebraic Geometry/Algebraic Number Theory. I tried to learn algebra ...
2
votes
3answers
432 views

What languages to learn for maths?

For people with "hands-on" experience in mathematical research, what languages are the most beneficial to learn? I know that many graduate programs require some degree of non-native lingual ...
1
vote
1answer
99 views

Help me with a learning plan!

Now I'm a third-year software-engineering undergraduate and my university doesn't provide proper mathematical basis, so I want to learn all the basic things by myself. Here are subject I'd like to ...
1
vote
2answers
47 views

Use induction to show that $a_{n+1}-a_n=\biggl(-\frac{1}{2} \biggr)^n (a_1-a_0) .$

Let $a_0$ and $a_1$ be distinct real numbers. Define $a_n=\frac{a_{n-1}+a_{n-2}}{2}$ for each positive integer $n\geq 2$. Prove that $$a_{n+1}-a_n=\biggl(-\frac{1}{2} \biggr)^n (a_1-a_0) $$ ...
1
vote
1answer
168 views

Path to Differential Geometry

What do I need to learn to start on the rigorous study of differential geometry? I'm about to start my 3rd undergrad year at school, and have taken Cal 1-3, Linear Algebra, Elementary Number Theory, ...
5
votes
0answers
139 views

Analysis or (abstract) algebra first?

Which one would you recommend? I only know calculus and linear algebra when it comes to university-level mathematics. Is one required to understand the other?
7
votes
1answer
115 views

Follow up to Pinter's abstract algebra

I wanted to learn abstract algebra this summer so I bought Pinter's A book of Abstract Algebra. I was planning on reading it over the course of the summer, but just finished the last problem of its ...
0
votes
2answers
294 views

List of Advanced Math Text Books with answers

Can anybody please recommend a list of Advanced Mathematics Books for physics that can be used for self study. Most importantly they must have answers for odd or even problems. I have a big list of ...
1
vote
1answer
96 views

Book: Functional Calculus

Is there a good book that investigates in detail the various kinds of functional calculus? I'm having now some knowledge about unbounded operators and integration but I would like to understand ...
0
votes
1answer
21 views

About the convergence or divergence?

Whether the following integral converge or diverge by comparison test. \begin{align*} ...