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
Arithmetic in Binary
In What Follows…
Essentially all your life, you’ve been doing arithmetic with “decimal” numbers, indicating that numbers are represented using ten digits, 0 through 9 (“deci-” is a Greek prefix meaning “ten”). It turns out that numbers can be represented using as many digits as one likes! In what follows, we introduce binary numbers, which are numbers represented using only two digits, namely 0 and 1. We also show how one can leverage the arithmetic techniques you learned when you were 5-8 years old to add, subtract, multiply, and divide binary numbers.
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