Questions asking for advice on various mathematical matters. Consider adding the tag (soft-question) as well.

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6
votes
1answer
192 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 ...
3
votes
0answers
67 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
134 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
85 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
29 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
353 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
86 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
49 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
84 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
54 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 ...
36
votes
5answers
6k views

How hard should a mathematician work?

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 ...
6
votes
2answers
206 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 ...
5
votes
0answers
92 views

Helping a reluctant 12 year old. [closed]

My 12 year old daughter needs to strengthen her math skills. My strategy up until a year or so ago has been pretty relaxed. I subscribe to the idea that the best motivation for learning is the ...
2
votes
4answers
338 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 ...
4
votes
0answers
90 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
119 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
126 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 ...
14
votes
5answers
716 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 ...
0
votes
0answers
41 views

Master in Mathematics and Computer Science

I have google-d 'master in Mathematics and Computer Science' and the master program does exist. My question is: Would it be favourable to apply for the program? Currently I am a final year ...
1
vote
3answers
421 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
64 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
815 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
130 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
373 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
95 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
147 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 ...
1
vote
3answers
326 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 ...
8
votes
3answers
1k 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
359 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
2answers
45 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
131 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, ...
4
votes
0answers
75 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
94 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
216 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
83 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
19 views

About the convergence or divergence?

Whether the following integral converge or diverge by comparison test. \begin{align*} ...
0
votes
0answers
34 views

General Strategy for solving mathematical problems

Lately I noticed that I am good at solving only those problems, similar to which I have encountered before. I get stuck with problems which ask for new(at least to me) mathematical reasoning. When I ...
4
votes
1answer
182 views

Too “young” for advanced mathematics?

Is it harmful to try to learn an advanced topic that is way beyond your mathematical maturity, even if you're really interested in it? Should I focus only on standard material for undergraduates and ...
0
votes
1answer
57 views

Questions about the field Business Mathematics

What interests should one have to decide to pursue a master's degree in Business Mathematics? Which subjects are related with this field? What career opportunities are there having this master's ...
2
votes
1answer
98 views

Is it worth it? [closed]

I am studying pure mathematics at university, as well as minoring in physics. I am soon to finish to BSc degree, and I am considering continuing on with studying pure mathematics. However, I do have a ...
3
votes
3answers
141 views

Can a mathematician be a multi-discipline expert?

My professor says: If you be a mathematician then you can easily learn any discipline like physics, chemistry, engineering and even medical! Is he right? I am an enthusiast of all scientific ...
3
votes
3answers
49 views

Confusing -Probabilities.!!

Ok so far what i understand is this lets say...Having to draw a card from 52card-deck its probability is of course 1/52.Now the probability to say that i will keep drawing this same card 10 times of ...
3
votes
0answers
166 views

Which is the best transitional mathematics book for self-teaching among the ones listed?

What is Mathematics, An Elementary Approach to Ideas and Methods - Courant Robbins Stewart How to Solve It, A New Aspect of Mathematical Solving - Polya Introductory Mathematics, Algebra and Analysis ...
3
votes
1answer
133 views

How do high-achieving students in math study for their exams?

I'm taking a real analysis course that is a bit more advanced than usual in that it introduces you to the Lebesgue theory and has some deeper concepts in metric spaces. This is an honors and advanced ...
35
votes
9answers
4k views

When to give up on a hard math problem?

I practice olympiad problems from books like Putnam and Beyond. Often I come across a problem that I simply can't solve. After $\sim30$ minutes of deep thinking it feels like I'm ramming my head into ...
17
votes
2answers
428 views

Pure mathematics curriculum for self study with interests in foundational issues

I wonder if I want to make my own pure mathematics curriculum to study along the next 4 or 5 years. What topics should I include? I want it to be like one which an undergraduate student of pure ...
1
vote
2answers
109 views

A unique situation may prevent me from pursuing a science degree. Advice appreciated. [closed]

I'll try to keep this succinct. I'm enrolling in a second degree computer science program at my previous university. I graduated with a double major in Finance and Accounting about a year ago. Here's ...
4
votes
1answer
137 views

What should be in your graduate toolbox?

I've just finished my undergraduate degree at an average uni in the UK. Clearly the content will not be as in depth or rigorous as some of the higher ranked universities. I intend (well, hope!) to ...