Questions tagged [learning]
Questions about the process of learning mathematics, both inside and outside a formal environment, including learning strategies, recommendations for learning particular subjects, and studying habits.
603 questions
4 votes
1 answer
202 views
How Can I Truly Understand Mathematics Instead of Just Following Rules?"
I want to ask a somewhat philosophical question. I’m a 10th-grade student currently studying systems of linear equations. I’ve learned to solve both simple and relatively complex equations. However, I’...
- 65
0 votes
0 answers
79 views
Do the algebraic manipulations required in proofs eventually become natural through practice and exercise?
I have been recently reading Walter Rudin's Principles of Mathematical Analysis and (reading the book's proof of the existence and uniqueness of n-th positive roots of positive reals, situated towards ...
- 162
8 votes
5 answers
1k views
Is it valid to learn geometric algebra?
I saw a few people say they recommend to learn geometric algebra. Since I have only finished Apostol's calculus, I do not have ability to evaluate this subject properly. To be honest, I feel it seems ...
- 83
2 votes
1 answer
329 views
How to study algebraic topology? [closed]
I'm graduate student in second semester Since the class uses Hatcher's book, I read it and tried to solve exercises, But it's too hard for me. The reason first is that it's hard to read. I'm reading ...
- 59
2 votes
0 answers
98 views
Are there any good books for studying auxiliary skills or generally useful tools?
By "auxiliary skills," I'm referring to a book like J. Michael Steele's The Cauchy-Schwarz Master Class, which focuses on the specific study of inequalities—something fundamental and useful ...
- 125
1 vote
0 answers
67 views
Some good practice for upper level linear algebra? [closed]
Last semester I took my second course in linear algebra (aptly used Axler's book) and got a good treatment of proof based linear algebra. However I didn't feel like I got very good practice for ...
- 11
0 votes
1 answer
137 views
What are some general guidelines or tips to reading a mathematics textbook? [closed]
I am an undergraduate who started down the math educator path but found pure math to be very intriguing. As I enrolled in higher math courses, I found reading the textbook to be ever more important. ...
4 votes
2 answers
577 views
Roadmap for learning differential geometry
I'm trying to learn differential geometry (or at least, some aspect of it). However, I've come across various textbooks on `this topic', each building up to one major result or the other: Gauss-Bonet (...
- 1,366
14 votes
4 answers
3k views
How can I learn how to solve hard problems like this Example?
Preparing to the Math Olympiad , I found a book and decided to go through it as a summer project. I'm good at math but far from being an Olympian, yet I want to broaden my horizons - problems in this ...
- 143
3 votes
0 answers
124 views
How to restudy functional analysis
I am re-studying functional analysis to prepare for my next year's PDE courses, I've taken it this year but I feel like I am not very good at it. May I ask what is the study routine/strategy for ...
- 663
0 votes
0 answers
139 views
Using A Proof Assistant as a Learning Aid
I don't see that anyone has asked this before, but if I have missed something please let me know. tl;dr - Can you use a proof assistant (like Lean) as a tool to learn math rigorously, and improve ...
- 119
0 votes
0 answers
37 views
What is the optimal time one should spend on a textbook problem before deciding to seek the solution? [duplicate]
I’ve been grappling with a question that I’ve yet to find an answer to. I love solving math problems and I'm going to college this fall for a degree in computer science. Looking long-term, I would ...
- 2,129
3 votes
2 answers
559 views
How can I motivate and deal with speculation?
I am a student of mathematics and have been increasingly feeling doubtful about whether or not I really understand the theory. What I mean by this is highly attributed to the style of textbooks in ...
user1253832
1 vote
0 answers
64 views
Ways to learn mathematics [closed]
I will be graduating with my bachelor's degree in mechanical engineering, in a few months, but I want to pursue master's in mathematics after 2-3 years. To prepare, I am currently doing "Advanced ...
- 37
0 votes
1 answer
125 views
Learning effective [closed]
today I got my midterm test result of Discrete math (It can only raise the grade). I got 63, which is above the average, but still I don't feel comfortable with that. I have 7 courses in the semester, ...
- 217