Introduction to Real Analysis (Revised 9th Edition)

DETAILS : 

• Author : S K Mapa
  
• Publisher ‏ : ‎ LEVANT BOOKS
  
• Publication date ‏ : ‎ 11 December 2025
  
• Edition ‏ : ‎ Revised Ninth Edition
  
• Print length ‏ : ‎ 665 pages
  
• ISBN-10 ‏ : ‎ 9391741339
  
• ISBN-13 ‏ : ‎ 978-9391741334
  
• Item Weight ‏ : ‎ 700  g

ABOUT THE BOOK

Introduction to Real Analysis (Revised 9th Edition), authored by the widely esteemed mathematician Prof. S.K. Mapa, is a foundational textbook and an absolute standard for undergraduate mathematics students across India. Published by Levant Books (and historically associated with Sarat Book House), this revised ninth edition has been carefully updated to align with the modern National Education Policy (NEP) framework. The core philosophy of this text is to act as a rigorous, conceptual bridge between computational calculus and abstract mathematical analysis. Prof. Mapa treats real analysis not as a series of arbitrary algorithmic procedures, but as a deeply logical system built from the ground up, requiring absolute semantic precision, strict deductive reasoning, and formal proof construction.

The textbook is structurally organized into a highly disciplined sequence that carefully scales in complexity. It opens with an essential foundation on the properties of Real Numbers, establishing the completeness axiom and the Archimedean property. The early chapters deliver rigorous analyses of the topology of real lines, point set topology, and the exact mechanics of sequences and infinite series. The core narrative then advances into the fundamental pillars of calculus: limits, continuity, uniform continuity, and differentiability, offering a masterclass in the application of Mean Value Theorems. Crucial computational and theoretical chapters focus heavily on the Riemann Theory of Integration, improper integrals, and sequences and series of functions, complete with uniform convergence tests. A defining hallmark of this text is its vast collection of counterexamples, which are strategically placed to dismantle common student misconceptions about limits and continuity.

ABOUT THE AUTHOR

Prof. S.K. Mapa is an elite Indian academician, research scholar, and veteran author who spent decades shaping higher mathematics pedagogy. Renowned for his deep expertise in foundational algebra and mathematical analysis, his classic academic works—including Higher Algebra: Classical and Higher Algebra: Abstract and Linear—have served as standard university literature for generations of mathematics majors.

Prof. Mapa’s pedagogical and authorial style is characterized by remarkable structural logic, clean formal proofs, and an empowering peer-to-peer instructional clarity. Writing as a seasoned mentor who understands exactly where students falter when transitioning from routine calculus to abstract proof-writing, he structures his explanations with unmatched precision. By balancing dense theoretical theorems with an extensive treasury of step-by-step solved problems, his collective literature remains an enduring national benchmark for students preparing for highly competitive examinations like the IIT JAM, CSIR NET, TIFR, and various civil services mathematics options.