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Analysis Study Tutorial
Undergraduate and Graduate

Introduction: Analysis is one of the key areas in modern mathematics. They can be classified as the following subjects:

  • Undergruate math analysis, sometimes also called "Principle of Mathematical Analysis", "Advanced calculus", "Introduction to ananlysis" etc. A typical textbook is Walter Rudin's "principle of mathematical analysis". It's usually for 3 quarters or 2 semesters for the whole sequence!

Click the following link to get more lecture notes and practice exam solutions:
Undergruate math analysis lecture notes and practice exam solutions   Solutions to Rudin's textbook: Part-1   Part-2

           

  • Graduate Real analysis, the classic textbook is the red hardcover "Real Analysis" by Royden. It's not an easily-reading textbook! a lot of proof are short, abbreviated. Exercise in each Chapter are classic! Not that easy to finish!

You possibly need to read some other complementary textbooks help you understand the material, one of the good reference book is: Introduction to mathematical analysis. Author: A. Gupta. ISBN, 8185086087. Click the following link to get more lecture notes and practice exam solutions:
Real analysis lecture notes and practice exam solutions   Real analysis Qualify Exams Solutions and Study Notes

         

  • Graduate Functional analysis, the classic textbooks are the following:
Those are tough subjects! Reading those books simply means you are analysis genius! Click following links to get more notes and practice exam solutions:
Functional analysis lecture notes and practice exam solutions   Solutions to Principles of Functional Analysis

           

• Graduate Complex Analysis, the classic textbooks are:
1) "Function Theory of one Complex Variable" by Krantz and Greene.
2) "Complex Analysis" by Lars Ahlfors. Personally I hate this book! How come somebody can write a math book like a novel book? No equations!
Click the following link to get more lecture notes and practice exam solutions:
Graduate-Complex analysis lecture notes and practice exam solutions


• Graduate Harmonic analysis, the classic textbooks are:
1) "Introduction to Harmonic Analysis, 3rd edition" by Y. Katznelson. Click the following link to get more lecture notes and practice exam solutions:
Graduate-Harmonic analysis lecture notes and practice exam solutions


Related Tutorial:
Real Analysis Tutorial   Analysis Home   Undergraduate Analysis
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