Basic Modern Algebra with Applications

Mahima Ranjan Adhikari, PhD, is a former professor of pure mathematics at the University of Calcutta. His main interest lies is in algebra and topology. He has published a number of papers in several Indian and foreign journals including Proceedings of American Mathematical Society and four textbooks. 11 students have already been awarded PhD degree under his guidance. He is a member of American Mathematical Society and on the editorial board of several Indian and foreign journals. He was the president of the Mathematical Science Section of the 95th Indian Science Congress, 2008. He visited several institutions in India, USA, Japan, France, Greece, Sweden, Switzerland, Italy and many other countries on invitation. He is now the president of the Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC), www.imbic.org/index.html. He is also the principal investigator of an ongoing project, funded by the Government of India. Avishek Adhikari,PhD, is an assistant professor of pure mathematics at the University of Calcutta. He is a recipient of the President of India Medal and Young Scientist Award. He was a post-doctorate fellow at the Research Institute INRIA, Rocquencourt, France. He was a visiting scientist at Indian Statistical Institute, Kolkata, and Linkoping University, Sweden. He visited many institutions in Japan, Sweden, France, England, Switzerland. His main interest lies is in algebra, discrete mathematics, theoretical computer science and their applications. He has published several papers in foreign journals and three textbooks on mathematics. He successfully completed several projects funded by the Government of India, and is a member of the research team from India for a collaborative Indo-Japan (DST-JST) research project. He is a member on editorial board of several journals and secretary (honorary) of the Research Institute IMBIC (www.imbic.org/index.html).                                                                                                                     

Prerequisites: Basics of Set Theory and Integers.- Groups: Introductory Concepts.- Actions of Groups, Topological Groups and semigroups.- Rings: Introductory Concepts.- Ideals of Rings: Introductory concepts.- Factorization in Integral Domains and in Polynomial Rings.- Rings with Chain Conditions.- Vector Spaces.- Modules.- Algebraic Aspects of Number Theory.- Algebraic Numbers.- Introduction to Mathematical Cryptography.- Appendix A: Some Aspects of Semirings.- Appendix B: Category Theory.- Appendix C: A Brief Historical Note.