Module 1: Basic Set Theory
Set Operations
4 Topics
Module 2: Modular Arithmetic, Divisibility, and the Fundamental Theorem of Arithmetic
Module 3: Functions and Relations
Functions Basics
4 Topics
Module 4: Truth Tables and Symbolic Logic
Truth Tables
2 Topics
Conditional Statements
2 Topics
Module 5: Basic Direct Proofs
Basic Direct Proofs
3 Topics
Module 6: Proof Techniques Part 1: Contrapositive and Contradiction
Module 7: Sequences, Sums, and Products
Module 8: Proof Techniques Part 2: (Weak) Induction
Module 9: Recurrence Relations and Recursion
Module 10: Counting Systems (Binary, Hex, Octal, etc.)
Arithmetic in Binary
4 Topics
Module 11: Combinatorics
Module 12: Graph Theory
Paths and Circuits
2 Topics
Module 13: Review
Greatest Common Factors, Least Common Multiples, and Coprimality
In what follows…
We will be discussing some ideas that you may have learned in high school or perhaps earlier, namely that of greatest common divisors and least common multiples. We will also discuss how one can find greatest common divisors and least common multiples using prime factorizations.
Lesson Content
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