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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18
votes
7answers
3k views

Mathematics needed in the study of Quantum Physics

As a 12th grade student , I'm currently acquainted with single variable calculus, algebra, and geometry, obviously on a high school level. I tried taking a Quantum Physics course on coursera.com, but ...
72
votes
8answers
8k views

What made you choose your research field?

I was wondering how come modern mathematicians do not seem to discover as many theorems as the older mathematicians seem to have done. Have we reached some kind of saturation limit where all commonly ...
4
votes
3answers
537 views

Independent math learning

I'm an undergraduate math and econ major and I'm planning on graduating relatively soon and I am very limited to the number of math classes I have left (very sad about this fact). So far I have ...
9
votes
6answers
10k 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 ...
32
votes
4answers
6k views

Learning Roadmap for Algebraic Topology

I am now considering about studying algebraic topology. There are a lot of books about it, and I want to choose the most comprehensive book among them. I have a solid background in Abstract Algebra, ...
1
vote
1answer
84 views

Any advice to help visualizing/understanding theorems in Real Analysis?

I am currently taking a real analysis course and sometimes I can't really get the complete meaning/details of certain theorems. For example, one of the statements in the Heine-Borel Theorem saying ...
0
votes
2answers
100 views

Textbook for Mathematical Logic

I am about to take an undergraduate course in Mathematical logic any textbooks to recommend.Want it to be rigorous and not missing things. I am an Math undergraduate. Got still 2 years for my degree. ...
0
votes
0answers
49 views

Comparing the methods of applied mathematics to computer graphics

As an applied mathematician working towards my PhD, I have some personal interest in aspects of computer graphics and procedural animation. Looking up people and reading papers in the field of ...
6
votes
2answers
172 views

suggesting books on Field/galois theory

I have finished courses on group theory and ring theory and linear algebra and abstract algebra(inrroducton with fraleigh's book) im about to take field/galois theory this semester any good book not ...
2
votes
2answers
51 views

How to write this non-linear Epsilon-Delta proof w/ a radical?

The question: Prove that $\lim \limits_{x \to 9} 2+\sqrt{x} = 5$. After reading this link from Milefoot on how to construct a non-linear delta-epsilon proof (second example), this is what I came up ...
5
votes
2answers
314 views

Numerical analysis, differential equations, complex analysis for statistics

I am a student of the Statistics Department. And now I can choose a subject from such list: numerical mathematics (analysis), differential equations, complex analysis, real analysis. Can you please ...
2
votes
1answer
99 views

Can you recommend a mathematical logic textbook that is easy to understand?

I started studying "Introduction to Mathematical Logic, Sixth Edition" by Elliot Mendelson. I tried to not read solutions as long as possible, but most exercises were awfully difficult to me, and the ...
5
votes
1answer
68 views

Important topics to know in Algebra [closed]

I'm trying to prepare for graduate algebra but after looking at Dummit and Foote I realized that there's a lot of material (1000 pages). Which topics do you think a student should study in D&F to ...
463
votes
27answers
110k views

How to study math to really understand it and have a healthy lifestyle with free time?

Here's my problem. I'm studying math and when I really work hard, I think I understand things very good, but that comes at a big cost: in the last few years, I've had practically zero physical ...
2
votes
0answers
463 views

Can I research in complex analysis, PDE and differential geometry without exposure to mathematical physics?

I love mathematics, but physics is far away from my interest. I see that recent mathematics research is strongly connected to mathematical physics which is something doesn't interest me! I love ...
12
votes
4answers
840 views

Visual research problems in geometry

I am considering doing research in mathematics to be my career (and my life) someday. I'm a visually oriented person in general; for example, I prefer chess over cards because when I play chess, I ...
18
votes
3answers
1k views

Understand it or burn [closed]

I have a big problem when I study math,namely when I am stuck on some problem I can't go on and I won't keep studying other material till I haven't solved the problem I've been stuck on. I am ...
2
votes
0answers
50 views

What makes a good mathematical poster? [closed]

During my second year of university I have done some assignments and some papers, but this is my first time I have to make a mathematical poster. What could make my poster stand up. So up to now I ...
1
vote
1answer
65 views

How to find old papers on a particular topic?

When learning mathematics, I think it is better to learn the motivation and the purpose of a particular maths idea. I believe such things are best found in the original paper which proposes the ...
5
votes
2answers
255 views

Learning to understand proofs faster?

There are many books, written by highly decorated academics, which feature proofs that I can hardly comprehend in an acceptable amount of time. Roughly each week, it happens that I find myself having ...
0
votes
1answer
59 views

Schools for Game Theory/Algebraic Geometry [closed]

I am looking into both Game Theory and Algebraic Geometry for graduate study and potentially doing a thesis in. I wanted to know if there are areas of mathematics that rely on both algebraic geometry ...
0
votes
1answer
40 views

Is model theory needed to understand ordinal logic?

By ordinal logic, I mean turing's ordinal logic. I'm going to learn first order logic, elementary set theory, basic computability, and godelian incompleteness as prerequisites for ordinal logic. But, ...
4
votes
0answers
120 views

I have a free summer before university. What should I learn? [closed]

Note: This is a soft question. It may be a bit early to be thinking about this, but I figured I'd ask now and see what responses I get. I'm currently a high school senior, and I quite like pure ...
1
vote
2answers
804 views

A book with simple proof exercises and full answers

I am quite bad at basic proof strategies, and in order to get some practice at this, I'm working through Daniel Solow's How to Read and Do Proofs (third ed.) Unfortunately, I'm having the problem I ...
16
votes
6answers
514 views

Are there any generic thinking approaches for providing mathematical proofs to a given theorem

To produce mathematical proofs for theorems we should have the required knowledge in that area. But even having adequate knowledge, people like me struggle a lot for writing down the proofs for any ...
45
votes
2answers
13k views

What is the proper way to study (more advanced) math?

Here's what happens. I get stuck on some proof or some mathematical construction and I end up staring at the problem for hours, sometimes not making any progress. I do this because sometimes I think ...
12
votes
4answers
228 views

Transitioning to Elementary School teaching and need some advice on bolstering my math skills

I'm an English major trying to make the transition to Elementary School teaching. For as long as I can remember, I've been extremely math-anxious and I've only done the bare-minimum level of Math work ...
23
votes
7answers
10k views

Teaching a 4 year old maths

Im 18 years old and getting to grips with advanced mathematics (pre-university) and I have a younger brother of 4 years old (quite an age gap). I want to get him interested in learning (and away from ...
13
votes
5answers
994 views

I need help finding a rigorous precalculus 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 ...
1
vote
1answer
41 views

How to find out leading research articles in a specific area?

If one needs to find out the leading research articles and most cited or influential research articles in a specific area of mathematics, let's say, fractals, chaos and non-linear dynamics what that ...
11
votes
2answers
1k views

How can I motivate myself to study math every morning? [closed]

I am jobless, so I have relatively plenty of time though life is short. I started studying math and some other things every day because I want to become an artificial intelligence researcher. When ...
5
votes
1answer
89 views

Combinatorics research project [closed]

I am looking for a topic to do an undergraduate research project on in the field of combinatorics. I want the project to relate to computing. Like I mean I want to code a program and test cases .... ...
0
votes
1answer
100 views

need advice to become a mathematician [closed]

I am currently working on my associates with a designation in math, and my overall goal is to get a PhD and become a mathematician. I would like some advice on how to get there and the likelihood of ...
1
vote
0answers
34 views

Number of Magic squares and their applications

A magic square is a square array of numbers consisting of the distinct positive integers $1, 2, ..., n^2$ arranged such that the sum of the $n$ numbers in any horizontal, vertical, or main diagonal ...
2
votes
2answers
101 views

Interesting areas of study in point-set topology

I'm undertaking a little self-study in point-set topology, because my undergraduate course does not have a module in Topology. I have a copy of Topology by James Munkres, but do not have the time to ...
30
votes
26answers
3k views

Gift advice: present for high school graduate interested in math

I am a PhD student in mathematics who recently found out that I will be attending my girlfriend's cousin's high school graduation party. I have never met the cousin, but hear that he is very ...
6
votes
6answers
890 views

I feel like I'm not enjoying Maths, but studying for the sake of exams [closed]

I am currently studying Year 9 Mathematics(perhaps I shouldn't ask middle school related questions here...) I've recently started studying/learning Maths 'seriously'; As in I started having hours of ...
1
vote
0answers
28 views

Information requested regarding variant square brackets

This is a usage question that may or may not be relevant to mathematics. However, as the representative to the Unicode Technical Committee for the STIX project [*], which involved adding mathematical ...
85
votes
10answers
10k views

Math and mental fatigue [closed]

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 ...
8
votes
8answers
5k views

How should I self-study calculus? [duplicate]

So I already took Pre-Calc, and ended up with a B both semesters. I am an incoming senior in high school. My special-ed case manager won't let me take it because she doesn't want to see me panic ...
3
votes
3answers
124 views

mathematical rigore for an engineer! [closed]

I recently bought a used copy of "Mathematical Analysis" by Apostol for \$1.0 and "Probability and Measure Theory" by Robert Ash for \$3.0 (well another \$3.99 for shipping)! When I read the first few ...
3
votes
1answer
97 views

Should I move on to more abstract math? [closed]

I am a junior in high school currently in multivariable calculus (online) and find it kind of boring since it's similar to Calc BC from last year, emphasizing applications of math to, for example, ...
21
votes
2answers
382 views

Is there a profitable way to read mathematical proofs

Mathematical proofs are often presented in a sequential way, i.e., presenting definitions, building lemmas based on these definitions, building further results on these lemmas and finally invoking a ...
2
votes
1answer
93 views

Is the infinitesimal approach good.

I have heard of an infinitesimal approach to calculus. Is it better than the normal approach or is it the other way around.
1
vote
1answer
91 views

How much of mathematical ability is innate? [closed]

Math has always been a source of frustration and anxiety for me, purely because I am so bad at it. I'm in my final year of highschool, and can say now that math is the only class I truly struggle ...
0
votes
1answer
33 views

Advice: applying/getting into number theory and algebra

I am currently a junior in a completely unknown liberal arts college/mathematics department. So far, I have take two courses in Abstract Algebra and group theory, one in linear algebra, currently ...
20
votes
6answers
7k 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 ...
18
votes
5answers
2k views

Bad at computations… but not math?

Very generally, the question I'm trying to ask is: Can someone be a good professional mathematician without being particularly good at (or even being - relatively - bad at) computations? More ...
1
vote
0answers
103 views

Solutions for “What is Mathematics?” by Richard Courant

I am currently reading through Courant's "What is Mathematics?" Most of the time I am not taking the exercises too seriously, given that I am reading this for pleasure, and that often my solutions are ...
0
votes
1answer
48 views

Concepts to learn before learning Stochastic Processes? [closed]

Does the knowledge of Markov chains required before learning Stochastic processes? What are the other concepts that I need to learn before learning stochastic processes?