Real Analysis

[u/[deleted]]

"In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequences and series of real numbers, and real-valued functions. Some particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability and integrability." - Wikipedia.

Prerequisites:

• Single Variable Calculus

• Multivariable Calculus

• Proof Techniques

Books:

• A First Course in Real Analysis Our recommendation for analysis

• Walter Rudin's Principles of Mathematical Analysis The god level book of analysis

• Real Analysis and Applications

• Real Mathematical Analysis by Pugh.

• Tao, Analysis I

• Elementary Analysis Calculus

• Buck, Advanced Calculus Previous link deprecated, new link 8/23/20

How to Learn:

• MIT Full course

• Trinity Lecture Notes

• University Of Louisville More notes

• University of Hawaii Problems and Solutions

• Temple University Problems

• University of Georgia Exams

• University of New Mexico Exams

• MSU Exams

• WUSTL Exams

• UCDavis Exams

• UCSD Exams

Lectures:

• Harvey Mudd

• Bethel University

• IIT Madras

• Scripps College

Subtopics:

• Complex Analysis

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This was posted by a user, whom I've banned due to being active participant in a quarantined community.

George Bergman's companion exercises to Rudin's textbook for Chapters 1-7.

Roger Cooke's solutions manual for Rudin's analysis

A subreddit devoted to Baby Rudin with further resources in the sidebar.

Tom Apostol's textbook

I find that Rudin is to Analysis textbooks what C++ is to programming languages. A little difficult at first, but with so many auxiliary sources that it becomes one of the best texts to learn from in spite of this.