2.1. History of Mathematics
Reference to contributions of Indian Mathematicians : Aryabhata (476–550 AD), Varahamihira (505–587 AD), Yativṛṣabha ( 6 C-AD), Brahmagupta (598–670 AD) , Bhaskara I (600–680 AD) Shridhara (650–850 AD), Mahavira (9 C-AD), Pavuluri Mallana (11 C-AD ) , Hemachandra (1087–1172 AD) , Bhaskara II (1114–1185 AD), Narayana Pandit (1340–1400 AD), Sangamagrama Madhava (1340- 1425 AD), Parameshvara, (1360–1455 AD), Nilakantha Somayaji, (1444– 1545 AD), Raghunatha Siromani, (1475–1550 AD), Mahendra Suri (14 C-AD), Shankara Variyar (c. 1530) , Jyeshtadeva, (1500–1610), Achyuta Pisharati (1550– 1621), Srinivasa Ramanujan, Harish Chandra, R.C.Bose, Srikhande, P.C.Mahalanobis.
Ancient Indian systems of numbers – KATAPAYDI, Bhuta Sanghtya
Reference: Ancient Indian Mathematics: an overview, S.G. Dani, School of Mathematics, TIFR, Bombay
2.2. Algebra
Galois theory
References: Contemporary Abstract Algebra, Joseph A. Gallian, Fourth edition, Narosa Publishing House, 2011. Topics in Algebra, I. N. Herstein, Second edition, John Wiley and Sons.
2.3. Topology
Review of basic topology, Homotopy
References: Topology, James R Munkres, Prentice Hall (2000). Lecture notes on elementary topology and geometry, I M Singer, J A Thorpe, New York Springer 1967. Elements of Algebraic Topology, James R. Munkres, Addison-Wesley Publishing Company (1984)
2.4.Modern Analysis
Theory of distributions and Fourier Transform
Reference: Functional Analysis, Walter Rudin, McGraw-Hill Education (1973).
2.5. Measure theory
Review of basic measure theory, Radon-Nikodym theorem.
Reference: Real Analysis, Royden, Pearson, 3rd edition (1988).