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14 votes
Accepted

How can I learn how to solve hard problems like this Example?

Technique : rationalization When we are given $A/B$ or $1/B$ , we try to eliminate the Denominator. That will involve "conjugates" , that is , When Denominator is $x+\sqrt{y}$ , we could ...
Prem's user avatar
  • 12.2k
5 votes

How can I learn how to solve hard problems like this Example?

And guess what, these problems are hard for me. Should I spend more time on hard ones before giving up? Should I memorise solutions by heart to get techniques? What could I do if I get stuck? I am ...
preferred_anon's user avatar
4 votes

How can I learn how to solve hard problems like this Example?

Let's start with some tough love: If you gave up after half an hour, you didn't really try. Prem and others have already posted some concrete tips on how this particular problem could be approached, ...
Einar Rødland's user avatar
4 votes

Vladimir Zorich vs Rudin/Pugh/Abbott

This is not an answer to this question but anyone picking up Zorich should understand that at Russian universities, Mathematical Analysis (as the subject is called) is a 4 semester course (the first 4 ...
Sid's user avatar
  • 166
2 votes

How to self taught Linear Algebra correctly?

First, make sure you're comfortable with basic linear algebra computations such as finding determinants, eigenvalues, eigenvectors, and working with quadratic forms. Once you have a solid grasp of ...
Bowei Tang's user avatar
  • 1,543
2 votes

Nonstandard Analysis research project ideas

There are two approaches to non-standard analysis: (1) the "extension" approach and (2) the axiomatic approach. In the "extension" approach, the real numbers are extended to the ...
Mikhail Katz's user avatar
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2 votes

Contemporary Abstract Algebra VS Algebra by Artin

For the Ring Theory part, I would certainly recommend Michael Artin's Algebra chapters. This book is particularly valuable because it provides a swift introduction to some concepts in Algebraic Number ...
dren's theorem's user avatar
1 vote
Accepted

Exponentiation of a linear operator

If $f$ is a function from a space $B$ to itself, then $f^i$ means you apply $f$ i times: $$f^3: B\overset{f}{\rightarrow}B\overset{f}{\rightarrow}B\overset{f}{\rightarrow}B$$ $$f^5: B\overset{f}{\...
Snake707's user avatar
  • 1,090
1 vote

equivalent form of almost sure convergence

You will find more than 60 equivalent forms of Almost Sure Convergence, this note is so great
Chen Deng-Ta's user avatar

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