UM 205: Introduction to algebraic structures

Credits: 3:1

  1. Set theory: equivalence classes, partitions, posets, axiom of choice/Zorn’s lemma, countable and uncountable sets.
  2. Combinatorics: induction, pigeonhole principle, inclusion-exclusion, Möbius inversion formula, recurrence relations.
  3. Number theory: Divisibility and Euclids algorithm, Pythagorean triples, solving cubics, Infinitude of primes, arithmetic functions, Fun- damental theorem of arithmetic, Congruences, Fermat’s little theorem and Euler’s theorem, ring of integers modulo n, factorisation of poly- nomials, algebraic and transcendental numbers.
  4. Graph theory: Basic definitions, trees, Eulerian tours, matchings, matrices associated to graphs.
  5. Algebra: groups, permutations, group actions, Cayley’s theorem, di- hedral groups, introduction to rings and fields.

Suggested books and references:

  1. L. Childs, A Concrete Introduction to Higher Algebra, 3rd edition, Springer-Verlag.
  2. M. A. Armstrong, Groups and Symmetry, Springer-Verlag.
  3. Miklos Bona, A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory, World Scientific.
  4. D. M. Burton., Elementary Number Theory, McGraw Hill.
  5. Niven, Zuckerman, H. S. and Montgomery, H. L., An Introduction to the Theory of Numbers, 5th edition, Wiley Student Editions.
  6. Fraleigh, G., A First Course in Abstract Algebra, 7th edition, Pearson.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 23 Apr 2021