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-1 votes
1 answer
249 views

Learning, exams, math degree

I have only passed the one fourth of my courses so far, which means like one year of the maths undergraduate studies. I live in a different place from where the university i study at is and try to ...
-2 votes
1 answer
128 views

On doing scientific research [closed]

What I want to ask is: can I use the results of others when doing scientific research, whether it is math, physics or other science, without trying to prove them myself or try to verify them? For ...
5 votes
4 answers
630 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, ...
0 votes
1 answer
127 views

Problem solving and independent scientific research [closed]

Is analogy a way to solve problems when doing research in math and physics? Is it very important?How important is it? Could i do independent scientific research on some open problems perhaps having ...
0 votes
0 answers
106 views

Problem solving approach to learning and psychology

I try to have a problem solving approach to learning math. What i mean by this is if someone sets some questions or problems regarding the material i am reading how should i answer or what questions ...
1 vote
1 answer
211 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 ...
1 vote
2 answers
571 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(...
7 votes
3 answers
2k views

Looking for a HIERARCHY of math subjects

If you were to "map" mathematics onto a tree structure where the top is "Mathematics", and then below it the different branches, then sub-branches, etc. What do you suggest is a good structure, for ...
10 votes
4 answers
10k views

Is it possible to improve logical thinking and problem solving abilities?

I'm from Italy and I'm 13 years old. I'm good in Math and I'm good in languages (I know Italian, English and Russian and I think I'm good at them). I'm a programmer and I know HTML, CSS, JS and Python....
5 votes
2 answers
188 views

Great Worked-out examples books for Mathematics

I'm studying Mathematics in the UK. Back in Italy, where I am from worked-out problems books are very popular in mathematics and they are always recommended or compulsory at university. Going through ...