A Course in Abstract Algebra: Number System, Sets, Groups, Rings, Fields, Integral Domains, Vector Spaces

Dr. Mohammad Ishaq was the first teacher of Abstract Algebra at Lucknow University. He started teaching the subject around 1952. RBM’s Ph.D. supervisor (Padmashri Prof. Dr. R.S. Mishra) introduced teaching of Abstract Algebra, Topology & other contemporary subjects at the UoAllahabad in 1963-64. Then there were hardly few centres of learning these subjects in the Indian sub-continent. RBM recalls U.G.C.-funded Two Summer Workshops on Algebra organized by Prof. R.S. Mishra at UoAllahabad in 1963 & 1964. Two U.S. Professors Jack P. Tull and S.P. Franklin participated there as the subject experts. The first author was also privileged to give a talk on Ring Theory in one of these Workshops. The first edition of the book was very concise covering 4 vital strands: Algebraic Structures, Vector Spaces, Metric Spaces & Topological Spaces. Chapters dealing with Metric Spaces & Topological Spaces are now withdrawn to form a separate book. Rest contents of the previous book are retained in the present edition. It consists of seven chapters: The first one dealing with the basic concepts of Number System is added, while the next one retains the topics of ‘Set Theory’. A new Chapter 3 (on Logic) is added. Topics in algebraic groups are put as Algebraic Structures - I in Chap. 4, and Rings, Fields and Integral domains as Algebraic Structures - II form the subject matter of Chap. 5. The Chap. 4 of the previous edition dealing with the Vector Spaces is retained and is re-numbered as Chap. 6. Proofs of various theorems stated in earlier edition are now supplemented. Tutorial Sheets, Tests and Exam. Papers of various Universities, where the author taught the subject are annexed as Chap. 7. A detailed Bibliography comprising of 15 text-books (including 6 by the first author) is also provided. Appendix 1 presents the additional Mathematical Texts & Research Monographs by him. In the end, an Alphabetical Index of the topics and authors in the literature is also annexed for quick references. The course contents may best suit graduate & postgraduate programmes of any University and can be covered in one semester with 3 credit hours per week.