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Mukesh Kumar Nagar

Assistant Professor, Gr-I

Algebraic Combinatorics, Combinatorial Matrix theory, Graph Theory, Linear Algebra
Assistant Professor (PhD IITB)
A-424, Department of Mathematics
BITS Pilani, K.K Bilra Goa Campus
NH-17B, Zuarinagar-403726, Goa, India

Teaching (2024-25)

1. Combinatorial Mathematics (MATH F 421) shared with Prof. T. Singh:

Combinatorics is a fascinating yet extensive subject, making it difficult to classify. The outline of the course MATH F421 is as follows: It begins with basic definitions and motivations through problems involving perfect covers, Latin squares, and magic squares/cubes (SAIM algorithm). Next, the course delves into advanced topics, including the theory of permutations and combinations, counting principles, partition theory, special counting sequences, systems of distinct representatives, combinatorial design, and graph enumeration. For MATH F421, the required textbook is "Introductory Combinatorics" by Richard A. Brualdi, published by Pearson Education (5th Edition, 2020).

2. Mathematics I (MATH F111) shared with Prof. Saranya G. Nair

A course in Multivariate Calculus provides a thorough exploration of calculus principles applied to functions with multiple variables. The topics covered include partial derivatives, multiple integrals, vector calculus, and key theorems such as Stokes' theorem and the divergence theorem. The course focuses on understanding functions of several variables, computing partial derivatives, evaluating multiple integrals over two- or three-dimensional regions, and applying vector calculus concepts to fields like physics and engineering.

3. Mathematics II (MATH F112)

This course offers a robust introduction to Linear Algebra and the captivating theory of complex variable functions. Mastering linear algebra empowers you to effectively solve systems of linear equations and grasp the fundamental properties of linear transformations, both of which are crucial in numerous scientific and engineering disciplines. In parallel, complex analysis unveils the techniques needed to tackle contour integrals that defy conventional evaluation methods. We strongly encourage students to leverage the powerful capabilities of MATLAB to explore and solve the linear algebra challenges presented in the textbook, enhancing both understanding and application in real-world scenarios.