Best reference books of Real Analysis: If you are looking for the best genuine real analysis books, then you are right place. I have over 18 years of experience in Real Analysis which helps me to identify the 10+ best real analysis books. This makes you decide to buy the best book on real analysis even if you are a beginner on this topic. The list contains the following books on real analysis:
1. Introduction to Real Analysis
| Author: S K Mapa |
The reason for keeping “Introduction to Real Analysis” by S K Mapa in the first place is very simple: The book is well-written and easy to understand for students studying analysis. The reader will get a basic understanding about the subject after finishing the book. The book covers a wide range of topics from real analysis:
- Set theory, Real number system, Sets in R
- Real functions, Sequence, Series
- Limits, Continuity, Differentiation
- Functions of bounded variation, Riemann integral
- Improper integrals (beta, gamma functions)
- Sequence of functions, Series of functions, Power series.
The book is highly recommended for self-study and it can be studied parallelly for an undergraduate/graduate-level course on real analysis.
Product Details:
- Publisher : LEVANT BOOKS; Special Edition (1 January 2021)
- Language : English
- Paperback : 666 pages
- ISBN-13 : 978-9388069335
- Customer Reviews: 4.5 out of 5 stars (360 ratings)
2. Principles of Mathematical Analysis
| Author: Walter Rudin |
One of the most well-known Real Analysis books is “Principles of Mathematical Analysis” by Walter Rudin (known as baby Rudin). It helps both undergraduate and first-year graduate students to develop a solid backbone on the topic.
The book begins with a topic on the real number system as a complete ordered field. The theories of convergence, continuity, differentiation, and integration are provided in Chapter 2. Many new and interesting exercises are included in the new edition along with a new section on the gamma function which makes the book very worthy.
Product Details:
- Publisher : MC GRAW HILL INDIA; 3rd edition (January 1, 2013)
- Language : English
- ISBN-13 : 978-1259064784
- Customer Reviews: 4.5 out of 5 stars (682 ratings)
3. Real Analysis: Modern Techniques and Their Applications
| Author: Gerald B. Folland |
Real Analysis by G. B. Folland is a widely used analysis book. Its new edition covers real analysis in greater detail and at a more advanced level than most books on the subject. The book concentrates on measure and integration theory, point set topology, and the fundamentals of functional analysis, covering a number of topics that underlie much of modern analysis. It demonstrates how to apply general ideas and exposes readers to many analytical disciplines, including probability theory, distribution theory, and Fourier analysis.
Students who are interested in dynamic forms will find this revised edition useful because it contains more material. It is a fantastic option for students taking analysis courses at the graduate level because it has a sizable bibliography, multiple exercises, and a review chapter on metric spaces and sets.
Product Details:
- Publisher : Wiley; 2nd edition (May 1, 2007)
- Language : English
- Hardcover : 416 pages
- ISBN-13 : 978-0471317166
- Customer Reviews: 4.5 out of 5 stars (90 ratings)
4. Real Analysis by Royden
| Author: H.L. Royden |
Real analysis by Royden is a very essential book for graduate students and it covers the classical theory of functions of a real variable, measure and integration theory. It also deals with some more important and elementary topics in general topology and normed linear space theory. A general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on analysis is necessary to study this book.
The book is written in a very simple and charming way. The explanations of the topics discussed in the book are very clear and to the point. The reader will have some exposure to real analysis at a reasonably advanced level after reading the book.
Product Details:
- Publisher : Pearson; 4th edition (February 13, 2017)
- Language : English
- Paperback : 528 pages
- ISBN-13 : 978-0134689494
- Customer Reviews: 4.2 out of 5 stars (22 ratings)
5. Introduction to Real Analysis by Bartle-Sherbert
| Author: Robert G. Bartle and Donald R. Sherbert |
Bartle-Sherbert’s book on Real Analysis provides the fundamental concepts and techniques of the subject. It helps students to develop the ability to think rationally and analyze mathematical ideas to extend them to a new level.
The current edition maintains the user-friendly approach with additional examples and expansion on Logical Operations and Set Theory. Many chapters have been revised in this edition; such as introducing point-set topology before discussing continuity, including more details of lim sup and lim inf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, etc.
Product Details:
- Publisher : Wiley; 4th edition (January 18, 2011)
- Language : English
- Hardcover : 416 pages
- ISBN-13 : 978-0471433316
- Customer Reviews: 4.5 out of 5 stars (414 ratings)
6. Counterexamples in Analysis (Dover Books on Mathematics)
| Author: Bernard R. Gelbaum and John M. H. Olmsted |
The book deals with the part of analysis known as “real variables.” The first half of the book describes the various topics of analysis; for example, the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, and many more. The second half discusses functions of two variables, plane sets, area, metric and topological spaces, and function spaces.
The book contains 12 figures. This magical textbook by Bernard R. Gelbaum and John M. H. Olmsted is a great choice for students who are eager to learn real analysis.
Product Details:
- Publisher : Dover Publications; unknown edition (June 4, 2003)
- Language : English
- Paperback : 224 pages
- ISBN-13 : 978-0486428758
- Customer Reviews: 4.7 out of 5 stars (119 ratings)
7. Principles of Real Analysis by S. C. Malik
| Author: S. C. Malik |
The book is a must-buy for postgraduate students of Indian universities to learn real analysis. The book is written very neatly and to the point so that it helps students to understand the subject without tutors.
Product Details:
- Publisher : New Age International Private Limited (January 1, 2022)
- Language : English
- ISBN-13 : 978-8195175536
8. Real Analysis by Carothers
| Author: N. L. Carothers |
Real Analysis by Carothers is mainly focused on advanced undergraduates and beginning graduate students in mathematics and related fields. Readers are required to have a modest background in advanced calculus or real analysis. So it can be a great recommendation for both specialists and non-specialists in the subject. The book covers 3 major topics listed below:
- Metric and normed linear spaces
- Function spaces
- Lebesgue measure and integration on the line
In each chapter, the author gives motivation and an overview of new ideas. The contents are presented with greater details and complete proofs. The book has a great many exercises and suggestions for further study.
Thus, this book is suitable for advanced mathematics and graduate-level engineering students.
Product Details:
- Publisher : Cambridge University Press; 1st edition (August 15, 2000)
- Language : English
- Paperback : 416 pages
- ISBN-13 : 978-0521497565
- Customer Reviews: 4.6 out of 5 stars (80 ratings)
9. A First Course in Mathematical Analysis
| Author: David Alexander Brannan |
One of the hardest maths courses, in the eyes of many students, is mathematical analysis. The author David Alexander Brannan uses a sequential approach (continuity, differentiability, and integration in that order) in this book to make the subject simple to learn.
The textbook contains a large number of diagrams and helpful margin notes to guide students to learn the subject. It has many graded examples and exercises (sometimes with complete solutions). The book is recommended for self-study. One can use this book with a standard university course on real analysis parallelly.
Product Details:
- Publisher : Cambridge University Press; Revised edition (September 4, 2006)
- Language : English
- Paperback : 459 pages
- ISBN-13 : 978-0521684248
- Customer Reviews: 4.3 out of 5 stars (14 ratings)
10. Elements of Real Analysis by Shanti Narayan
| Author: Shanti Narayan |
Elements of real analysis by Shanti Narayan includes the following topics: sets and functions, the real number, limit points of a set, limits and continuity, real functions, infinite series, etc. One of the main features of this book is that it contains the latest question papers from various examinations. The book is very helpful for those who are preparing for competitive exams on Mathematical Sciences.
Product Details:
- Publisher : S Chand & Co Ltd (January 1, 2003)
- Language : English
- Paperback : 312 pages
- ISBN-13 : 978-8121903066
- Customer Reviews: 4.4 out of 5 stars (386 ratings)
11. Basic Real Analysis by Sohrab
| Author: Houshang H. Sohrab |
Basic Real Analysis by Sohrab is a comprehensive and largely self-contained book in the theory of real-valued functions of a real variable. Set theory, real number sequences and series, function limits, the topology of real numbers, and continuity are among the major chapters. Other important topics that are covered here are metric spaces, the derivative, the Reimann integral, and sequences of series of functions.
The chapters on Lebesgue measure and integral are now written neatly and nicely improved. Basic Real Analysis, Second Edition by Sohrab contains expanded chapters, additional problems, and an expansive solutions manual. This book is very useful for senior undergraduates and first-year graduate students.
Product Details:
- Publisher : Birkhäuser; 2nd ed. 2014 edition (November 15, 2014)
- Language : English
- Paperback : 694 pages
- ISBN-13 : 978-1493937141
- Customer Reviews: 5 out of 5 stars (2 ratings)
12. Real and Complex Analysis by Rudin
| Author: Walter Rudin |
The presentation of the topics covered in the Real and Complex Analysis textbook by Rudin is unmatched. This book helps you to prepare for other graduate texts and reading the literature. The book is noteworthy for combining two distinct topics of “complex analysis” and “real analysis” in a single volume. Additionally, it introduces some of the core concepts of functional analysis.
It’s a great choice if you like to gain a fairly advanced level of knowledge in real and complex analysis.
Product Details:
- Publisher : MC GRAW HILL INDIA; 3rd edition (January 1, 1987)
- Language : English
- Paperback : 483 pages
- ISBN-13 : 978-0070619876
- Customer Reviews: 4.4 out of 5 stars (145 ratings)
FAQs
Q: What are the best real analysis books?
Answer: The list of best real analysis books is given as follows:
1. Principles of Mathematical Analysis [by Walter Rudin]
2. Real Analysis: Modern Techniques and Their Applications [Author: Gerald B. Folland]
3. Real Analysis by Royden [Author: H.L. Royden]
4. Introduction to Real Analysis, by Bartle & Sherbert
5. Counterexamples in Analysis (Dover Books on Mathematics) by Bernard R. Gelbaum and John M. H. Olmsted
6. Principles of Real Analysis, by S. C. Malik
7. Real Analysis, by N. L. Carothers
8. A First Course in Mathematical Analysis, [Author: David Alexander Brannan]
9. Elements of Real Analysis [by Shanti Narayan]
10. Basic Real Analysis [by Houshang H. Sohrab]
11. Real and Complex Analysis [by Walter Rudin]
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