Course Info

• Instructor: Hamid Zarrabi-Zadeh
• Course Syllabus
• Course Calendar
• Quera Page (Assignments, Announcements)

Lectures

• Counting

  • The Basics of Counting, Permutations and Combinations [Ch6.1,3]
  • Binomial Coefficients, Generalized Permutations and Combinations [Ch6.4-5]
  • Inclusion-Exclusion Principle, Distributing Objects into Bins [Ch8.5-6]

• Logic and Proofs

  • Propositional Logic, Equivalences, Predicates, Quantifiers [Ch1.1-4]
  • Rules of Inference, Methods of Proof [Ch1.6-8]

• Pigeonhole Principle

  • Existence Proofs, Applications of Pigeonhole Principle [Ch6.2]

• Mathematical Induction

  • Induction Steps, Strengthening the Induction Hypothesis [Ch5.1]
  • Strong Induction, Structural Induction, Well-Ordering Principle [Ch5.2-3]

• Sets and Functions

  • Set Operations, Countable and Uncountable Sets [Ch2.1-2]
  • Types of Functions, Schröder-Bernstein Theorem, Cardinality [Ch2.3,5]

• Number Theory

  • Divisibility, Bézout's Lemma, Extented Euclidean Algorithm, Primes [Ch4.1,3]
  • Modular Arithmetic, Fermat's Theorem, Cryptography [Ch4.6]

• Recurrence Relations

  • Applications of Recurrence Relations, Recursive Structures [Ch8.1]
  • Solving Recurrence Relations (Homogeneous and Non-Homogeneous) [Ch8.2]
  • Generating Functions, Application in Counting Problems [Ch8.4]

• Relations and Partial Orderings

  • Properties of Relations, Representation, Closures of Relations [Ch9.1-4]
  • Equivalence Relations, Partially Ordered Sets, Topological Order [Ch9.5-6]
  • Lattices, Boolean Algebra, Properties of Boolean Algebra [Ch12.1-2]

• Graph Theory

  • Special Types of Graphs, Representing Graphs, Graph Isomorphism [Ch10.1-3]
  • Paths and Connectivity, Euler Paths, Euler's Theorem [Ch10.4-5]
  • Hamiltonian Cycles, Dirac's Theorem, Graph Coloring [Ch10.5,8]
  • Planar Graphs, Euler's Formula, Coloring Planar Graphs [Ch10.7]
  • Trees and Forests, Spanning Trees, Minimum Spanning Trees [Ch11.1,4-5]

• Modeling Computations

  • Finite State Machines, Regular Languages, Pumping Lemma [Ch13.3-4]
  • Turing Machines, Decidability, Church-Turing Thesis [Ch13.5]

Textbook

• K. H. Rosen. Discrete Mathematics and Its Applications. 8th edition, McGraw Hill, 2019.

Additional References

• R. P. Grimaldi. Discrete and Combinatorial Mathematics: An Applied Introduction. 5th Edition, Pearson Addison Wesley, 2004.
• A. Engel. Problem-Solving Strategies. Springer, 1998.