Instructor: Dr. Sándor Dobos;

Text:  Hungarian Problem Book III
and printed handouts

Prerequisite: None, but general mathematical experience needed.

Course description: The course provides an introduction to the most important problem-solving techniques typically encountered in undergraduate mathematics. Problems and proofs from different topics of mathematics will help us to understand what makes a proof complete and correct.
The text is the collection of problems of Kürschák Competition which is rightly recognized as the forerunner of all national and international olympiads.

Topics:

Number theory, parity arguments, divisibility, diophantine problems, prime numbers

Algebra, algebraic equations, inequalities, sequences, polynomials, induction

Geometry, geometric construction, geometric inequalities, transformations, trigonometry, combinatorial geometry, inversion, projective geometry

Combinatorics, binomial coefficients, Pascal's triangle, lattice paths and polygons, graphs, recurrence equations, enumeration, permutations, pigeonhole principle