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This book provides a structured and intuitive introduction to Elementary Real Analysis, designed in accordance with the National Education Policy (NEP) 2022 syllabus. The book covers fundamental topics- the real number system, sequences and series. Special emphasis is placed on conceptual clarity and problem-solving skills to promote mathematical thinking. Some of the Key Features are :
- Conceptual and Intuitive Learning: Combines rigorous mathematical proofs with clear and intuitive explanations, enabling students to develop both a strong theoretical foundation and practical understanding of the subject.
- Aligned with NEP 2022: The content is designed in accordance with the NEP 2022 curriculum and comprehensively covers the syllabus of Elementary Real Analysis for B.Sc. (Hons.) Mathematics, Elements of Real Analysis offered as a Generic Elective (GE) and the Discipline Specific Course (DSC) for students of B.A. (Programme) and B.Sc. (Physical Sciences).
- Learner-Centric Organization: Structured into concise chapters of approximately 16–17 pages each devoted to a single topic. This modular approach enhances readability, facilitates focused learning and builds students' confidence as they progress through the material.
- Assorted Solved Examples: Every chapter includes a dedicated "Assorted Solved Examples" section featuring a diverse collection of fully worked-out problems that reinforce concepts and strengthen problem-solving skills.
- Comprehensive Practice Exercises: Each chapter offers a rich selection of conceptual, computational, and proof-based questions along with objective-type problems, providing students with ample practice and supporting a variety of assessment methods.
Prof. Ramesh K. Budhraja is a Professor in the Department of Mathematics at Sri Venkateswara College, University of Delhi. With over 41 years of experience in teaching undergraduate Mathematics across diverse courses, he has inspired generations of students through his dedication and excellence in teaching. He earned his Ph.D. in Optimization in 1999 with several publications in reputed national and international journals. In recognition of his outstanding contribution to undergraduate teaching, he received the Distinguished Teacher Award from the University of Delhi in 2009, conferred upon by the then President of India, Dr. A. P. J. Abdul Kalam.
Dr. Nisha Bohra is an Assistant Professor in the Department of Mathematics at Sri Venkateswara College, University of Delhi. An alumna of the college, she has over 13 years of experience teaching undergraduate Mathematics. Her research interests include Geometric Function Theory and Complex Analysis, with several publications in reputed international journals. Passionate about mathematics education, she emphasizes conceptual understanding and intuitive learning, an approach that is reflected throughout this book.
Part I The Real Numbers
1 Prerequisite: Sets and Numbers
2 An Encounter with Real Numbers
3 Absolute Value of a Real Number
4 Bounded Sets: Supremum and Infimum
5 Completeness Property, Archimedean Property and Density Theorem
Part II Infinite Sequences
6 Prerequisite: Functions
7 Sequences
8 Convergent Sequences
9 Non-Convergent Sequences
10 Algebra of Sequences
11 Convergent Sequences: More Properties
12 Monotone Sequences
13 Subsequences and Bolzano-Weierstrass Theorem
14 Cauchy Sequences and Cauchy’s Convergence Criterion
15 Limit Superior and Limit Inferior
Part III Infinite Series
16 Infinite Series and Convergence
17 Necessary Condition and Cauchy’s Criterion for Convergence
18 Positive Term Series and Comparison Tests
19 Cauchy’s Integral Test and Cauchy’s nth Root Test
20 D’Alembert’s Ratio Test and Raabe’s Test
21 Alternating Series: Absolute and Conditional Convergence
Bibliography, Index
