Syllabus:
Divisibility, prime numbers, Congruences, Fermat's theorem, Chinese remainder theorem,
Groups and subgroups, Lagrange’s theorem, rings, finite fields, polynomial arithmetic, quadratic residues,
discrete logarithms, elliptic curve arithmetic. Fundamental principles of counting, derangements, partitions,
partial order, lattices and Boolean algebra, generating functions, solution of recurrences. Graphs, Euler's
formula, applications of Kuratowski's theorem, graph colouring, chromatic polynomials, weighted trees,
spanning trees, max-flow.
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