Discover the Basics of Real Analysis: A Gentle Introduction

In summary, for a gentle introduction to real analysis, Calculus by Michael Spivak is a highly readable option. However, for a more in-depth exploration of analysis on R and other metric and Hilbert/Banach spaces, Foundations of Mathematical Analysis by Johnsonbaugh and Pfaffenberger is a recommended choice. For those interested in topology, Introduction to Topology by Gamelin and Greene is also a highly recommended option. Another highly recommended book for learning introductory analysis is Understanding Analysis by Stephen Abbott, as suggested in a thread on the subject.
  • #1
ice109
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a gentle intro to real analysis? any suggestions anyone? something very readable?
 
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  • #2
Calculus by Michael Spivak is a very readable introduction to real analysis-- that is, analysis on R.
If you want something which starts with R and moves onto the more general metric space, Hilbert and Banach space setting though, a very readable (Dover) book is Foundations of Mathematical Analysis by Richard Johnsonbaugh and W.E. Pfaffenberger.
You might also appreciate a book on topology if you're looking for something of the latter category-- I'm currently reading through Introduction to Topology by Theodore W. Gamelin and Robert Everist Greene.
Both books were recommended to me in this thread, so you might want to take a look there as well.
 
  • #3
Pughs Real Mathematical Analysis is IMO the best introductory analysis book for learning the subject.
 
  • #4
for anyone else i was recommended understanding analysis by stephen abbott
 

1. What is real analysis?

Real analysis is a branch of mathematics that deals with the properties and behavior of real numbers. It involves studying the properties of real-valued functions, limits, continuity, and differentiation and integration of functions.

2. Why is real analysis important?

Real analysis is important because it provides the foundation for many other areas of mathematics, such as calculus, differential equations, and complex analysis. It also has applications in physics, engineering, and economics.

3. What are the basic concepts in real analysis?

The basic concepts in real analysis include sets, functions, limits, continuity, derivatives, and integrals. These concepts are used to study the properties of real numbers and real-valued functions.

4. What is the difference between real analysis and calculus?

Real analysis is a more rigorous and abstract approach to studying the properties of real numbers and functions, while calculus is more focused on the practical applications of these concepts. Real analysis also covers topics not typically covered in calculus, such as metric spaces and topology.

5. How can I use real analysis in my research or work?

Real analysis can be used in a variety of fields, including physics, engineering, economics, and data analysis. It can help in understanding and modeling real-world phenomena and making predictions based on mathematical principles. It can also be used to prove theorems and solve complex problems.

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