COURSE SUMMARY
Course Title: 
Foundations of Modern Mathematics
Course Code: 
18MAT702
Year Taught: 
2019
Semester: 
1
Degree: 
Doctoral Programs
School: 
School of Arts and Sciences
Campus: 
Kochi

'Foundations of Modern Mathematics' is a course offered in the first semester of M.Phil. in Mathematics program (Full Time/Part Time) offered by School of Arts & Sciences, Kochi.

This course aims to provide a sound philosophical foundation of Modern Mathematics. It would also provide an understanding of the inter-relation between various branches of Mathematics. Applications of Mathematics in various fields including modern technology also to be discussed.

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).