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
Prime Numbers and the Fundamental Theorem of Arithmetic
In what follows…
We will be reviewing prime and composite numbers. We have three main goals in the topics that follow. Namely, we will discuss a (relatively) quick way to determine whether a number is prime, develop an algorithm for breaking integers into powers of prime factors, and prove that there are infinitely many prime numbers! Click first topic below to get started.
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