*Instructor:* ZoltÁn GYENES

*Text: *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. Some games make the course
colorful, we analyse how to play, how to build strategies.

We also discuss some problems of the 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