Class materials

All references are taken from the course book:
מתמטיקה בדידה, של ליניאל/פרנס.

Num. Topic Reference Date
1 Introduction, the sum and product principlesChap. 4.1
2 The pigeon-hole principleChap. 4.5
3 Basic counting, choosing k out of n elementsChap. 4.2
4 The binomial coefficientsChap. 4.3
5 Combinatorial identities, Catalan numbersChap. 4.3
6 The multinomial coefficientsChap. 4.7
7 The inclusion-exclusion principleChap. 4.6
8 Applications of the inclusion-exclusion principle: disorders, Euler's functionChap. 4.6
9 Counting via recurrence relationsChap. 4.4
10 Solving linear homogeneous recurrence relationsChap. 6.1
11 More linear recurrencesChap. 6.2
12 Introduction to graph theoryChap. 5
13 Basic properties of graphsChap. 5.1
14 Graph families, treesChap. 5.2
15 Bipartite graphs, planar graphsChap. 5.2
16 Graph coloringChap. 5.5
17 Paths in graphs: Euler tourChap. 5.3
18 Hamiltonian pathsChap. 5.3
19 Extremal graph theory: Ramsey, MantelChap. 5.7
20 Counting treesChap. 5.6
21 Matchings in graphs, Hall's theoremChap. 5.4
22 Introduction to discrete probabilityChap. 8.1
23 Independence, conditional probabilityChap. 8.2
24 Random variables, expectation, distributionsChap. 8.3
25 Variance and tail boundsChap. 8.5,8.7
26 The probabilistic methodChap. 8.8