*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