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
Quantifiers
Recall that when we first introduced statements, we said that a sentence such as
“\(x+1=0\)”
Was NOT a statement. The reason this is not a statement is because statements must evaluate to either true or false, without ambiguity. The truth value of this statement above depends on what \(x\) is. So naturally, if someone just handed you this statement and asserted “this is true,” you might ask something like “True… for some specific \(x\) value? True for every \(x\)-value? What do you mean?” We clear up ambiguities such as these using quantifiers, which add a bit more specificity to the variables in a given sentence.
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