Course description: Introduction to Modern Algebra is an elective course for B.Tech(ICT and CS) and M.Tech students. This course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics. Topics include group theory, emphasizing finite groups; ring theory, including ideals and unique factorization in polynomial and Euclidean rings; field theory, including properties and applications of finite fields. 

Course Goals: Upon successful completion of this course, students will be able to effectively write abstract mathematical proofs in a clear and logical manner. Locate and use theorems to solve problems in number theory and theory of polynomials over a field. Also, students will be able to apply modern algebra in other branches of science and technology. 

Prerequisites:  None 

Suggested Textbook/references:  

Topics in algebra, I. N. Herstein, John Wiley and Sons, New York. 

Abstract algebra, David S. Dummit and Richard M. Foote, Wiley. 

Topics in abstract algebra, Sen, Ghosh, Mukhopadhya and Maity, Orient Blackswan Pvt. Ltd. 

Groups and symmetry, M.A. Armstrong, Springer, Undergraduate texts in mathematics.

Grading:  Midsemester exams (20%  each), Final exam (50 %), Tutorials/ Quizzes (10%)