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
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.
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)
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).