Logic

• Lesson 01: Propositions. Compound expressions (PDF)
• Lesson 02: Tautologies and Contradictions. Logical Equivalences (PDF)
• Lesson 03: Conditional Statements (PDF)
• Lesson 04: Valid and Invalid Arguments (PDF)
• Lesson 05: Predicate Logic, Quantifiers in Predicate Logic (PDF)
• Lesson 06: Negation of Quantifiers (PDF)
• Lesson 07: Arguments in Predicate Logic (PDF)
• Lesson 08: Proofs (PDF)
• Lesson 09: Mathematical Induction (PDF)

Sets

• Lesson 10: Sets - Basic Definitions, Set Operations (PDF)
• Lesson 11: Set Identities (PDF)
• Lesson 12: Partitions, Cartesian Products, Power Sets (PDF)
• Lesson 13: Boolean Algebra

Relations

• Lesson 14: Relations on Sets (PDF)
• Lesson 15: Operations on Relations (PDF)
• Lesson 16: Properties of Binary Relations (PDF)
• Lesson 17: Equivalence Relations, Partial Orders and Total Orders (PDF)

Functions, Sequences, Recursion, Induction

• Lesson 18: Functions (PDF)
• Lesson 19: Sequences (PDF)
• Lesson 20: Intro to Recursion, Recursion on Numerical Sequences (PDF)

Counting and probability

• Lesson 21: Counting and Probability (PDF)

Graphs and Trees

• Lesson 22: Graphs - Basic Definitions
• Lesson 23: Trees: Basic Definitions. Binary Trees