Discrete mathematics /

1. Sets, Subsets, Induction and Recursion. The Pascal Triangle (Application: A Counting Problem).
Induction (Application: The Tower of Hanoi).
Sets, Subsets, and Binary Strings (Application: The Knapsack Problem).
Set Operations (Application: An Error-Correcting Code).
Recursions (Application: Shift Registers).
2. Integers, Remainders, and the Golden Ratio. The Integers (Application: When is Div(n) a Tree?). Lamé's Theorem (Application: Egyptian Fractions).
The Integers Mod n (Application: Public Key Encryption).
3. Functions, Relations, and Counting. Functions and Relations (Application: The Prüfer Correspondence). Counting Rules (Application: Boolean Functions). Three Counting Techniques (Application: Tenth Powers).
4. Graphs. Graphs (Application: The Icosahedron and Dodecahedron). Graph Theory (Application: One-Way Streets). Trees (Application: Structural Induction).
5. Proof Techniques and Logic. Proof Techniques (Application: The Liar Problem). Logic (Application: Logic and the Genetic Code). The Propositional Calculus (Application: Syllogisms).
6. Boolean Algebras, Boolean Functions, and Logic. Boolean Algebras and Functions (Application: Normal Forms in the Propositional Calculus). Boolean Functions and Circuits (Application: Regions in Logic Diagrams). The Predicate Calculus (Application: Proving Program Correctness).
7. Graphs and Relations. Graph Coloring and Matching (Application: Register Allocation). Posets and Lattices (Application: The Kirkman Schoolgirl Problem).
8. Algorithms. Sorting, Searching, and Listing (Application: The Man, Dog, Goat, and Cabbage Problem). Graph Algorithms (Application: Network Flows). The Complexity of an Algorithm (Application: Kruskal's Algorithm and Prim's Algorithm).
9. Combinatorics. Recursions and Their Solution (Application: AVL trees). Probabilities (Application: Network Reliability). Groups and Counting (Application: Rooted Trees).
10. Models of Computation. Languages and Grammars (Application: The Chomsky Heirarchy). Finite State Machines and Turing Machines (Application: DNA Computing). G?del and Turing (Application: The Vanishing).