Instructor: Dr. Attila SALI
Text: The course is based on handouts.
Prerequisite: A course in discrete mathematics (or combinatorics or graph theory) is required. A minimum knowledge of discrete probability and linear algebra is useful for Sections 4 and 5.

Course description: The basic concepts of Hypergraph Theory are introduced. Using this framework, classical and relatively new results are discussed from the theory of finite set systems. The emphasis is on studying several successful proof methods including the Linear Algebra and the Probability methods.

1. BASIC NOTIONS AND EXAMPLES
1.1. Definitions. 1.2. Examples of hypergraphs
2. CHROMATIC NUMBER AND GIRTH
2.1. Chromatic number.
2.2. Graphs from the Hall of Fame.
2.3. How to glue hypergraphs to get graphs?
3. A LOOK AT RAMSEY THEORY.
3.1. Ramsey numbers.
3.2.  Van der Waerden numbers.
3.3.  Tic-tac-toe and Hales-Jewett theorem.

4. COUNTING AND PROBABILITY.
4.1. Proofs by counting.
4.2. Probability method.
4.3. Local Lemma.
4.4. Jokes
5. LINEAR ALGEBRA METHODS.
5.1. The dimension bound.
5.2. Homogeneous linear equations.
5.3. Eigenvalues. SPECIAL OFFERS 1. FRUIT SALAD.
1.1. Distinct representatives of sets.
1.2. Symmetric chain decomposition.
1.3. A property of n sets on n elements.
1.4. A property of n+1 sets on n elements.
1.5. A property of n+2 sets on n elements.
1.6. 3-color-critical hypergraphs.
1.7. Sunflower theorem.
1.8. Sum-free subsets of numbers.