All Questions
Tagged with self-learning proofs
14
questions
8
votes
5
answers
3k
views
Should I really just "shut up and calculate"? On learning at a good pace without sacrificing rigour
This question is about getting realistic expectations for how a university student actually does and should learn maths. I'm becoming increasingly suspicious that my approach is detrimental, but I don'...
- 478
7
votes
3
answers
770
views
How can I internalize solutions/proofs to theorems and exercises?
In particular, my question is about abstract mathematics such as group theory, analysis, topology, etc. where most textbooks are filled with exercises which require proof, and how to go about ...
3
votes
2
answers
302
views
How to understand the book and the material to the deepest possible level?
I'm a first year mathematics major and I have a problem with my learning process. In my university, I only have books and questions that the university published, so I have to learn the most of the ...
1
vote
1
answer
206
views
Math outside of undergraduate studies and proofs
I read sometimes mathematical works of others outside my undergraduate studies. I think i can not follow the understanding of the proofs of theorems sometimes. What should i do? Should i read other ...
- 159
5
votes
4
answers
2k
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How long would it take someone to master the topics in the book "Book of Proof" by Hammack and similar?
If someone never had any experience with mathematical proofs and had only classes like Calc I-III (which he passed, without paying any attention to the proofs present in the textbooks), how long would ...
- 153
5
votes
4
answers
535
views
Doctorate and examples of difficult solved problems
Okay. My questions are: How do some people do doctorates in mathematics and spend so much time like three to six years trying to answer one or two open problems? How do they have the patience, ...
- 159
2
votes
1
answer
371
views
Solving math problems and learning
Should i solve math problems by writing the answers to papers or notebooks with pencils or should i try solving them in my head at undergraduate studies at university?
Also, sometimes after learning ...
- 159
-3
votes
1
answer
91
views
Abstract math and making proofs
What is abstract math about? I think we can not visualise probably what we read. Or can we? I am talking about the theorems, definitions and proofs in areas of math like Riemannian geometry, ...
- 159
1
vote
2
answers
457
views
Should I do all the proof practice problems in How to Prove It, an intro to proofs book?
Like the title says. I am self studying intro to proofs(How to prove it by velleman) so I can start an introduction to analysis. I am wondering if I should complete all the exercises in the textbook(...
- 71
3
votes
2
answers
621
views
Why are proofs written in flowery language incomprehensible?
Let's take an example in Wu-Ki Tung, Group theory in physics:
Theorem 3.4: Irreducible representations of any abelian group must be of dimension one.
Proof: Let $U(G)$ be an irreducible ...
- 183
2
votes
0
answers
116
views
Strategies for learning proofs
What are the best methods for learning proofs? I'm tasked with learning two dozen proofs about the properties of continuous functions and real numbers in a week well enough to be able to present them. ...
4
votes
2
answers
225
views
If you do not 'read A to Z', then how can you discover the idea? [closed]
The following is from an article in The New Yorker on Y. Zhang and his proof on gaps between primes:
Rutgers University Professor [Henryk] Iwaniec and his friend, John Friedlander, a professor at ...
user155
19
votes
3
answers
2k
views
Is it natural for self-learners to forget most proofs of the theorems they learn?
When I read a theorem and read its proof and fully understand it, am I supposed to know the proof even after a long time or is it natural to forget the it?
I ask this question as I'm a self learner ...
- 291
15
votes
1
answer
2k
views
Proving theorems on one's own: how long should one persist?
I've recently started learning linear algebra on my own. I always try to prove the theorems I encounter by myself, without looking at the book (only to check if my proof is correct), because I found ...
- 253