Computational Number Theory and Algebra

ABOUT THE COURSE : Algebra plays an important role in both finding algorithms, and understanding the limitations of computation. This course will focus on some of the fundamental algebraic concepts that arise in computation, and the algebraic algorithms that have applications in real life. The course will cover the problems of fast integer (or polynomial) multiplication (or factoring), fast matrix multiplication, primality testing, computing discrete logarithm, error-correcting codes, lattice- based cryptography, etc. The course intends to introduce both basic concepts and practical applications. INTENDED AUDIENCE : Computer Science & Engineering, Mathematics, Electronics, Physics, & similar disciplines. PREREQUISITES : Preferable (but not necessary)-- Theory of Computation, Algorithms, Algebra Theory of Computation: https://nptel.ac.in/courses/106104148 https://nptel.ac.in/courses/106106242 Fundamental Algorithms:Design and Analysis: https://nptel.ac.in/courses/106105157 Algebra - I: https://nptel.ac.in/courses/111106137 INDUSTRIES SUPPORT : Cryptography, Coding theory, Computer Algebra, Symbolic Computing Software, Cyber Security, Learning Software