Lecture on Complete Metric Spaces . Dated 19/11/19.

Course Contents M.Sc. Mathematics 2nd
Course Title:  Algebra II       Course Code:  MATH 301
Credit Hours:  3 + 0
    Groups
    • Definition and examples of groups
    • Abelian group
    • Subgroups lattice, Lagrange’s theorem
    • Relation between groups
    • Cyclic groups
    • Groups and symmetries, Cayley’s theorem
        Complexes in Groups
      • Complexes and coset decomposition of groups
      • Centre of a group
      • Normalizer in a group
      • Centralizer in a group
      • Conjugacy classes and congruence relation in a group
          Normal Subgroups
        • Normal subgroups
        • Proper and improper normal subgroups
        • Factor groups
        • Fundamental theorem of homomorphism
           Sylow Theorems
        • Cauchy’s theorem for Abelian and non-Abelian group
        • Sylow theorems
           Ring Theory
          • Definition and example of rings
          • Special classes of rings
          • Fields
          • Ideals and quotient rings
          • Ring homomorphisms
          • Prime and maximal ideals
          • Field of quotients
          Recommended Books:
          1. Allenby RBJT, Rings, Fields and Groups: An Introduction to Abstract Algebra, 1983, Edward Arnold
          2. J. B. Fraleigh, A First Course in Abstract Algebra, 7th edition, (Addison-Weseley Publishing Co., 2003)
          3. Macdonald ID, The Theory of Groups, 1975, Oxford Clarendon Press, Ma., USA
          4. P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul, Basic Abstract Algebra, (Cambridge University Press, 1986)
          5. Vijay K. Khanna, S K Bhambri, A Course in Abstract Algebra(2nd Revised Edition) Vikas Publishing House PVT LTD.
          6. H. Marshall, The Theory of Groups, (Macmillan, 1967)
          7. Humphreys, J.F.: A Course in Group Theory (Oxford University Press, 2004)
          8. Lederman, W.: Introduction to Group Theory (Cambridge University Press, 1987).
          9. Burton, D.E.: A First Course in Rings and Ideals (Addision Wesley Pub. Co., 1968).