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...").

learn more… | top users | synonyms

3
votes
1answer
777 views

Relearn mathematics

I believe that this question is well known, but since I'm not a US resident and do wish to learn math according to the U.S. school syllabus I wish that somebody can help me. At my first eight years ...
21
votes
3answers
1k views

Academic integrity [closed]

This may sound like a childish question and for all its worth, very well may be one as I am only 17, but how do I know who to trust with reviewing or looking at my work? The idea of someone stealing ...
27
votes
8answers
4k views

Math every mathematician should know [closed]

This question is meant as a companion to previously asked questions like Proofs every mathematician should know. More and more I'm beginning to see that there is just too much math to learn. ...
9
votes
1answer
2k views

Choosing a Master Thesis Topic: Logic - Model Theory

I am a first-year graduate student in maths. Around these days, I feel I must decide on which exact part of mathematics I shall go through. Infact, I have narrowed down the suitable options but still ...
2
votes
3answers
1k views

Suggestions on Real, Fourier Analysis textbooks?

I'm new here, and I hope this is within the scope of the website. I'll try to ask few advisory type questions in the future... I'm a college junior, and I was wondering if you guys could offer any ...
182
votes
28answers
23k views

Too old to start math

I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could. This is a question I've been asking myself now for some ...
6
votes
1answer
290 views

Set theorist as a physicist or physicist as a set theorist?

I'm majoring physics, but really interested in mathematics. I liked physics since it was really beautiful to have an analysis on a nature with mathematical tool. However, the more i study, the more ...
23
votes
3answers
1k views

How much time is too much (to put into a single problem)?

As a self-studier, I have no due dates and no time pressure. This is partly a good thing since I do have a life outside of my pursuit of mathematics. However, the lack of pressure is also a bad ...
1
vote
1answer
111 views

prove normality of famlity of analytic functions

I already proved normality for meromorphic functions that omit 3 values. I'm trying now to prove normality of family of analytic functions that omit two values. Is there any way to deduce any one of ...
2
votes
2answers
177 views

Numeric synaesthesia: uses of and advice for learning math.

It turns out that my adolescent son might have numeric synaesthesia-- numbers have specific colors and possibly other distinguishing characteristics for him. He has shown that he can commit long ...
3
votes
3answers
561 views

Should analysis be studied minus point set topology

I have noticed that certain texts like Terry Tao's Analysis I, Bartle and Sherbert's Real analysis as well as Michael Spivak do not use the language of topology in their exposition. A text like ...
2
votes
2answers
499 views

Study Strategy: broad/depth; abstract/intuitive

Research Interest: Chaos, Dynamical System, PDE. Study style: Shallowly Broad: Quickly absorb as many branch as possible [master more 'toolbox'] OR Narrowed Depth: Carefully focus on ...
0
votes
3answers
49 views

Example of no inclusion in set of closures

Let $(X,d)$ be a metric space and $A_j \subseteq X$ for $j = 1,2,...$ . Let $B = \bigcup_{j=1}^\infty A_j$. Find an example for which $\bigcup_{j=1}^\infty \bar{A_j} \neq \bar{B}$. Also, in general ...
9
votes
3answers
14k views

GRE Math Subject Test

I am studying for GRE Math. I am looking for specific tips. What types of questions usually come up? Does anyone know any tricks (e.g. integration tricks) that might be helpful? Which theorems are ...
2
votes
1answer
995 views

How to work faster on the GRE.

I'm fixin' to go to grad school next year, so lately I've been studying for the mathematics subject GRE. What I have heard, from MSE and other places, is that the most important thing is to learn to ...
2
votes
1answer
800 views

Prerequisite for Differential Topology and/or Geometric Topology

What are the prerequisites to learning both or one of the items? Consider that one will have done some of the "core" classes like Differential Geometry, Real Analysis, Abstract Algebra and POint-Set ...
1
vote
2answers
281 views

Need advice. How relearn what Ive forgotten? [closed]

The last time I studied mathematics and algebra was six years ago. I've since forgotten everything except quadratic equations, trigonometric functions and other things at the same level. Now I want to ...
4
votes
3answers
7k views

What is the most effective way of teaching mathematics to my 7 year old kid?

I want to help my kid excel in Math. I can see she has some trouble with additions,subtraction, multiplication and division. Will it help if I let her memorize the multiplication table? or use ...
5
votes
5answers
1k views

Multiplicative inverse of a complex number.

Find the multiplicative inverse of $1+ 3\sqrt{2}$ in the ring $\mathbb{Q}(\sqrt{2})$ and use it to solve the equation $(1+3\sqrt{2})x=1-5\sqrt{2}$. I think that the inverse is the conjugate, so it ...
13
votes
2answers
927 views

Studying mathematics efficiently

I am particularly angry at myself for the last few days. I noticed how inefficiently I work. Here is the general scenario: I decided to study abstract algebra and analysis some days back. I tried ...
4
votes
5answers
1k views

Is it possible to practice mental math too often?

I'm far from a mathematician, but the field I'm trying to break into (management consulting) requires a fair amount of mental arithmetic. I'm okay, but I'm not even close to as good as I need to be in ...
3
votes
1answer
164 views

Lattices inside matrix groups $SL_2(K)$

I am currently a second year undergraduate majoring in math and our university is offering an opportunity for undergraduates to do a project over the summer break. I have spoken to my professor who is ...
1
vote
1answer
208 views

Taking Differential Topology concurrently with Analysis

So I'm trying to finalize my schedule for this semester. I can't decide whether I should enroll in a grad level Differential Topology (Milnor) class or just the undergrad general topology one. The ...
33
votes
7answers
4k views

What are some good math specific study habits?

What are/ were some of your good mathematician's study habits that you found really worked for you? I'm a CS major at a respected school and have a solid GPA... However, I definitely lack when it ...
15
votes
2answers
303 views

How long should I insist?

While studying math, I usually get stuck on some topics, how long should I insist trying to understand it alone? What are the strategies for when this happens?
21
votes
6answers
1k views

What am I losing if I decide to perform all math by computer?

I solve mathematical problems every day, some by hand and some with the computer. I wonder: What will I lose if I start doing the mathematical problems only by computer? I've read this text and the ...
11
votes
3answers
394 views

Module Theory for the Working Student

Question: What level of familiarity and comfort with modules should someone looking to work through Hatcher's Algebraic Topology possess? Motivation: I am taking my first graduate course in ...
79
votes
9answers
8k views

Math and mental fatigue

Just a soft-question that has been bugging me for a long time: How does one deal with mental fatigue when studying math? I am interested in Mathematics, but when studying say Galois Theory and ...
6
votes
4answers
9k views

Math Textbooks for High School

I'm a high school student who is trying to figure out a complete course of self study for each year of high school. Is there a way to self learn grades of math without devoting too much time? For ...
8
votes
4answers
4k views

Advanced Linear Algebra courses in graduate schools

After studying general a linear algebra course, how would an advanced linear algebra course differ from the general course? And would an advanced linear algebra course be taught in graduate schools? ...
3
votes
2answers
438 views

Advice for study plan.

I'm studying math by myself, and now I'm wondering what is the most appropriate for me to study. I think my interest goes to rather pure mathematics than applied math or math for engineers. So far I ...
77
votes
23answers
22k views

Complete course of self-study

I am about $16$ years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study ...
43
votes
3answers
5k views

Motivation and methods for self-study

First, a little background: Beginning with calculus in my first semester of college, I fell in love with mathematics. That was the point at which the concepts became interesting to me, and I started ...
10
votes
1answer
957 views

How to address mistakes in published papers?

I have recently discovered some mistakes in a published maths article. I have contacted the author pointing out politely my concerns, but I got no specific answer, just a "polite" one, that the ...
11
votes
3answers
9k views

I want to start mathematics from scratch. What should I begin with?

I've just finished high school but I don't feel my knowledge of mathematics is good enough. I'd like to start again from scratch, possibly adding a bit (a lot) of problem solving to it. What is the ...
2
votes
0answers
381 views

Schaum's Outlines for self-study

I wish to learn Physics via self-study. I realize that I have a long way to go as far as Mathematics prerequisites: I will need to begin with Precalculus(I took that course many years ago, so I am ...
5
votes
0answers
204 views

Recommendation textbooks on D-module

I am going to take part in a seminar on D-module and applications, the textbooks that will be used are : D-modules, Perverse Sheaves, and Representation Theory, and A Primer of Algebraic D-Modules ...
5
votes
1answer
720 views

How to select an field of study?

As my question implies, I am a young, developing mathematician, with concerns about my future math career. In particular, I'd like to know how to select a future field of study. Through my courses ...
19
votes
5answers
6k views

Graduate school self-doubt (currently an undergraduate)

I don't know if this is the right place for such a question, so please redirect me to a more appropriate place if necessary. My main question is, if you go to a small school, are you doomed to fail ...
51
votes
7answers
2k views

Am I too young to learn more advanced math and get a teacher?

I am still 15 years old, but I am very interested in pure math. I have been teaching myself though books, from the internet and from others for the past year or so. I haven't mastered all the topics ...
14
votes
7answers
2k views

Teaching abstract maths concepts to young children.

I am interested in opinions and, if possible, references for published research, about the pros and cons of teaching abstract maths concepts to young children. My younger brother (five years old) ...
6
votes
2answers
480 views

Recommendations for real analysis

I have completed two courses in real analysis that covered up to chapter 9 in Rudin's Principle of Mathematical Analysis (and one on complex analysis). So if I am interested in continuing on in ...
10
votes
1answer
3k views

Tips and examples for a poster presentation in pure mathematics

I will be presenting a poster in a few weeks but have no experience with them. I've seen and given plenty of talks, read and written papers, but I have never made or even seen a poster in pure ...
19
votes
2answers
2k views

Spotting crankery

Underwood Dudley published a book called mathematical cranks that talks about faux proofs throughout history. While it seems to be mostly for entertainment than anything else, I feel it has become ...
10
votes
4answers
2k views

Math for computer science?

Math for computer science? I'm a computer science major and just completed linear algebra. Many courses are available to take now. Of particular interest: number theory and abstract algebra (Modern ...
49
votes
5answers
2k views

How does one give a mathematical talk?

Sometime tomorrow morning I will be presenting a mathematics talk on something related to commutative algebra. The people present there will probably be two mathematicians (an algebraic geometer and a ...
3
votes
2answers
183 views

Question on mathematical writing

I am now writing my graduate thesis, it includes some basics mathematical theorems/propositions. I got a trouble in writing, more concretely, I do not know when can I state a mathematical claim as a ...
7
votes
1answer
857 views

Independent undergraduate research — what to do?

I hope this question is within the scope of this website. I am currently a rising senior, and need to decide on a topic for my independent undergraduate research/thesis. I was hoping to get some ...
14
votes
8answers
2k views

What math should a programmer know?

I am an application programmer focussing on Line Of Business (LOB) applications. I am from non-mathematics and non-CS background. What mathematics should I learn which help me improve my programming ...
5
votes
2answers
644 views

Math for a high school junior?

I don't find the math taught at my school too challenging so out of personal interest I teach myself other fields of math. I was wondering if you could recommend some areas with a bit more complexity? ...