University of Hyderabad Logo School of Mathematics and Statistics University of Hyderabad

Programmes → Foundation course for M.Sc. in Statistics and I.M.Sc. in Mathematical Sciences

← Back to Courses

Basic Algebra

Course Code: FN 135  |  Credits: 3  |  Prerequisite: None

Syllabus Details

  • Unit I:(Set Theory) Finite and infinite sets; countability and uncountability; relations and functions; mathematical induction; partial order relations, posets, chains and anti-chains; Zorn’s lemma; least upper bounds and greatest lower bounds in a poset.
  • Unit II:(Counting Principles) The pigeonhole principle; mathematical induction; the principle of inclusion and exclusion.
  • Unit III:(Introduction to Groups) Semi-groups, groups, subgroups, generators and the evaluation of powers, cosets, Lagrange’s theorem.
  • Unit IV:(More Group Theory) Permutation groups; normal subgroups and quotient groups; group homomorphisms, automorphisms and isomorphisms; the fundamental theorems of group homomorphisms; Cayley’s theorem; group actions and Burnside’s theorem.

Course Learning Objective

  1. Use mathematically correct terminology and notation.
  2. Construct correct direct and indirect proofs.
  3. Use problem-solving strategies such as divide and conquer.
  4. Use counterexamples.
  5. Apply logical reasoning to solve a variety of problems.
  6. Apply combinatorial reasoning appropriate to the discipline.
  1. Gallian, Joseph A. Contemporary Abstract Algebra. 9th ed. Cengage Learning, 2015
  2. Graham, Ronald L., Knuth, Donald E. and Patashnik, Oren. Concrete Mathematics. 2nd ed. Pearson, 2007
  3. Halmos, Paul R. Naive Set Theory. Springer, 1960
  4. Herstein, I. N. Topics in Algebra. 3rd ed. Wiley, 1996
  5. Joshi, K. D. Foundations of Discrete Mathematics. New Age International, 2002
← Back to Courses