Discrete Structure

1. Prove basic set equalities
2. Write arguments using logical notation and determine validity
3. Write and evaluate proofs using mathematical induction
4. Demonstrate understanding of relations and functions
5. Recognize the use of Karnaugh maps
6. Demonstrate different traversal methods for trees and graphs
7. Model problems in Computer Science using graphs and trees
8. Apply counting principles to determine probabilities

13 weeks, about 39 hours in total. Yours will differ.

1. Week 1Module 1: Introduction to Discrete Structures

   • Unit 1: Set Theory · 3 hours

     Read the introduction to mathematical statements and understand statement definitions.. Practice identifying atomic and molecular statements.. Work through examples of logical connectives..

2. Week 2Module 1: Introduction to Discrete Structures

   • Unit 1: Set Theory · 3 hours

     Study set notations and operations on sets.. Solve problems involving union, intersection, and complement of sets.. Practice using Venn diagrams to represent set operations..

3. Week 3Module 1: Introduction to Discrete Structures

   • Unit 2: Proofs and Induction · 3 hours

     Learn basic proof techniques: direct proof, proof by induction, and indirect proofs.. Practice constructing direct proofs for simple mathematical statements.. Understand the initial and inductive steps in proof by induction..

4. Week 4Module 1: Introduction to Discrete Structures

   • Unit 2: Proofs and Induction · 3 hours

     Work through examples of proof by induction, including sums and divisibility.. Understand proof by contrapositive and proof by contradiction.. Solve tutor-marked assignments on proofs and induction..

5. Week 5Module 1: Introduction to Discrete Structures

   • Unit 3: Logic · 3 hours

     Study propositional logic and logical connectives.. Construct truth tables for logical expressions.. Learn about logical equivalence and De Morgan's laws..

6. Week 6Module 1: Introduction to Discrete Structures

   • Unit 3: Logic · 3 hours

     Apply deduction rules to determine the validity of arguments.. Understand first-order logic and its applications.. Solve tutor-marked assignments on logic..

7. Week 7Module 2: Boolean Algebra and Graph Theory

   • Unit 1: Boolean Algebra and Lattices · 3 hours

     Learn about partially ordered sets and lattices.. Distinguish between least upper bound (LUB) and greatest lower bound (GLB).. Understand the properties of lattices..

8. Week 8Module 2: Boolean Algebra and Graph Theory

   • Unit 1: Boolean Algebra and Lattices · 3 hours

     Study Boolean algebra and its axioms.. Understand complemented and distributive lattices.. Solve problems involving Boolean algebra and lattices..

9. Week 9Module 2: Boolean Algebra and Graph Theory

   • Unit 2: Graph Theory · 3 hours

     Learn about vertices, edges, and types of graphs (directed, undirected).. Understand isomorphic graphs and subgraphs.. Study bipartite graphs and their properties..

10. Week 10Module 2: Boolean Algebra and Graph Theory

    • Unit 2: Graph Theory · 3 hours

      Apply the Handshaking Theorem to solve problems.. Learn about Euler paths and circuits.. Study adjacency matrices and their applications..

11. Week 11Module 3: Matrices, Applications to Counting and Discrete Probability

    • Unit 1: Matrices · 3 hours

      Study matrix operations: addition, subtraction, multiplication.. Understand determinants and their properties.. Learn about special matrices: transpose, symmetric, skew-symmetric, singular, non-singular..

12. Week 12Module 3: Matrices, Applications to Counting and Discrete Probability

    • Unit 2: Applications to Counting · 3 hours

      Apply the product and sum rules to solve counting problems.. Understand permutations and combinations.. Learn about combinatorial identities and Pascal's triangle..

13. Week 13Module 3: Matrices, Applications to Counting and Discrete Probability

    • Unit 3: Discrete Probability Generating Function · 3 hours

      Apply the inclusion-exclusion principle and pigeonhole principle.. Understand discrete probability generating functions (PGFs).. Use PGFs to calculate mean, variance, and probabilities..