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Basic Analysis: Introduction to Real Analysis

(3 reviews)

Jirí Lebl, Oklahoma State University

Pub Date: 2016

Publisher: Independent

Language: English

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Reviewed by Jeromy Sivek, Assistant Professor - NTT, Temple University on 1/15/19

This book gives a very thorough coverage from set-theoretic prerequisites to difficult questions of the more advanced topics that students need for Real Analysis. The proofs are helpfully detailed. The little tricky parts are not skipped or left... read more


Reviewed by Sonmez Sahutoglu, Associate Professor, University of Toledo on 8/22/16

This text covers all the standard material for a senior level undergraduate (or master level) real analysis class. It start with basics set theory and the real numbers. Then it develops supremum and infimum of bounded sets; limit, limsup, liminf... read more


Reviewed by William Newton, Research Scientist, Colorado State University on 1/8/16

The textbook covers everything I would want to cover in a course at this level and some more. A teacher can use this book as the sole text of an introductory analysis class and skip the last two chapters for a slower class. read more


Table of Contents

  • Introduction
  • 1 Real Numbers
  • 2 Sequences and Series
  • 3 Continuous Functions
  • 4 The Derivative
  • 5 The Riemann Integral
  • 6 Sequences of Functions
  • 7 Metric Spaces

About the Book

This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.

About the Contributors


Jirí Lebl, Assistant Professor, Department of Mathematics, Oklahoma State University.