Portal:Real analysis

Department description
The goal of the department of real analysis is to give rigorous backing to the machinery of calculus and the real number system. By the end of this course, a student should know the real numbers like the back of their hand, and be more than ready to learn the generalizations of topology.

Department news

 * Wednesday, August 23, 2006 - Department founded!

Courses on Real Analysis

 * Introduction to Real Analysis
 * Ordered Sets and Fields
 * Sequences
 * Series
 * Limits

Offsite Courses

 * Analysis 1
 * Analysis 2

Other Resources
Analysis is a highly technical topic and is full of pitfalls and subtle counterexamples. You will need to read and complete the exercises in at least one of the following books in addition to using this site as a supportive community of peers and teachers.

Online Textbooks

 * Real analysis (Work in progress)
 * Mathematical Analysis I
 * Mathematical Analysis II
 * Basic Analysis: Introduction to Real Analysis

Hard-copy Textbooks

 * Lay, Steven R. (2005). Analysis With an Introduction to Proof Pearson Prentice Hall ISBN 0131481010
 * Gelbaum & Olmsted. (2003). Counterexamples in Analysis Dover Publications. ISBN 0486428753
 * Rudin, Walter. (1976). Principles of Mathematical Analysis McGraw-Hill Science/Engineering/Math. ISBN 007054235X

Wikipedia

 * Real analysis

Online courses
Might contain video lectures, course notes, homework, exam question papers and their solutions.

With video

 * 1) Real analysis, Francis Su, Harvey Mudd College, Spring 2010.
 * 2) Analysis Lectures, simpleMath, 2014.

Without video

 * 1) MA541 Real analysis, Bhaba K. Sarma, IIT Guwahati, 2014 – 2015.
 * 2) Analysis I, Oleg Zaboronski, University of Warwick, 2012-2013.
 * 3) Analysis II, Oleg Zaboronski, University of Warwick, 2008-2009.
 * 4) Analysis III, Oleg Zaboronski, University of Warwick, 2015-2016.
 * 5) MATH 6101-090: Foundations of Real Analysis, David C. Royster, University of Kentucky, Fall 2008.
 * 6) MATH 6101-090: Foundations of Real Analysis, David C. Royster, University of Kentucky, Fall 2006.
 * 7) Math 320 Analysis I, Huyi Hu, Michigan State University, Fall 2015.
 * 8) Math 320 Analysis I, Lawrence Roberts, Michigan State University, Spring 2009.
 * 9) Math 421 Analysis II, Richard Siefring, Michigan State University, Spring 2010.
 * 10) Math 140-Analysis, Lei Ni, University of California, San Diego, Winter 2010.
 * 11) Math 4111 Introduction to Analysis, Mohan Kumar, Washington University in St. Louis, Fall 2013.
 * 12) Math 140A Foundations of Real Analysis I, Todd Kemp, University of California, San Diego, Winter 2014.
 * 13) Math 320 (Real Analysis), Santiago Cañez, University of California, San Diego, Winter 2015.
 * 14) Math 401: Introduction to Real Analysis, Aissa Wade, Penn State University, Spring 2009.
 * 15) Math 401: Introduction to Analysis, Aissa Wade, Penn State University, Fall 2005.
 * 16) Math 125A: Real Analysis, John K. Hunter, University of California, Davis campus, Fall 2012.
 * 17) Math 171: Fundamental Concepts of Analysis, K. Soundararajan, Penn State University,  Spring 2010.

Active participants
The histories of Wikiversity pages indicate who the active participants are. If you are an active participant in this department, you can list your name here (this can help small departments grow and the participants communicate better; for large departments a list of active participants is not needed).

Основы математического анализа