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. Some games make the course colorful, we analyse how to play, how to build strategies.
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, divisors-multiples, diophantine problems, prime numbers, perfect squares

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

Geometry, geometric construction, geometric inequalities, transformations, combinatorial geometry, lattice triangles and polygons

Combinatorics, binomial coefficients, Pascal's triangle, graphs, recurrence equations, enumeration, permutations, pigeonhole principle, sets and subsets

Games, divisor game, two-player games, symmetry and NIM strategies, Grundy numbers

Click here for a set of sample problems so that you have a better understanding of the level of this class.