Real Analysis | For B.A./B.Sc. 5th Semester (3rd Year) DSC, All Chhattisgarh State Universities | NEP | Useful for CSIR NET, UGC NET, GATE Mathematics & IIT JAM | Dr. H.K. Pathak

Real Analysis by Dr. H.K. Pathak is the syllabus-exact textbook for B.A./B.Sc. 5th Semester (3rd Year) Discipline Specific Course students across all Chhattisgarh State Universities, built strictly to the New Education Policy curriculum. All four prescribed units are covered in university sequence: contributions and biography of Indian mathematicians (Swami Bharati Krishna Tirth, Madhav, Neelkanth Somayaji, Srinivasa Ramanujan Iyengar) followed by real numbers as an ordered field, least upper bound property, completeness of R, Archimedean property, dense subsets, nested intervals, neighbourhoods, limit points, open/closed/perfect sets; convergence of sequences (bounded and monotonic sequences, limit theorems, monotone convergence theorem, subsequences, Bolzano-Weierstrass theorem, limit superior/inferior, Cauchy sequences and Cauchy's criterion); infinite series (convergence and divergence, comparison test, D'Alembert's ratio test, Cauchy root test, Raabe's test, logarithmic test, Cauchy integral test, alternating series, Leibnitz's test, absolute and conditional convergence, rearrangement, Riemann's theorem); and Riemann integration and improper integrals (Riemann integrability, Darboux theorems, fundamental theorem of integral calculus). Because this is also the core paper tested in CSIR NET, UGC NET, GATE Mathematics (MA) and IIT JAM Mathematics, students preparing for these exams get the same rigorous foundation in one book. Each theorem is proved step by step with solved examples so students can follow the logic, not just memorise results. The author, Dr. H.K. Pathak, is Professor & Head of the School of Studies in Mathematics at Pt. Ravishankar Shukla University, Raipur, with over 3,300 citations on Google Scholar and the Vijnana Parishad of India Distinguished Service Award (2011). Published by Shree Shiksha Sahitya Prakashan, this 406-page paperback First Edition (2026) is built for both the semester exam and future competitive exam preparation.