Programming Foundations: Discrete Mathematics

Introduction

• Welcome
• What you should know
• Using the exercise files

1. Discrete Math Uses

• Basics of discrete mathematics
• Discrete math for programming
• Real-world discrete math
• Abstract discrete math

2. Sets

• Objects as sets
• Set notation
• Set operations
• Power sets
• Sequences and sums
• Recursion
• Cardinality, disjointness, and partitions
• Sets from Cartesian products
• Challenge: Practice with sets
• Solution: Practice with sets

3. Setting Up SML

• Functional programming
• Datatypes
• Characters and strings
• Recursive functions
• Challenge: Learn SML
• Solution: Create new data types

4. Analyzing Data Sequences

• Use SML to create lists
• Perform functions on lists
• Create datatypes that use lists
• Challenge: Model a lunch order
• Solution: Model a lunch order

5. Effective Arguments and Defensible Decisions

• Valid reasoning and inference
• Truth tables
• Identify and evaluate predicates
• Conditional propositions
• Valid arguments
• Rules of inference
• Prove logical equivalence
• Challenge: Write truth tables
• Solution: Write truth tables

6. Proofs Made Easy

• Write a general outline for a proof
• Write subset proofs
• Evaluate conditional proofs
• Understand biconditional proofs
• Prove with mathematical induction
• Challenge: Write a proof
• Solution: Write a proof

7. Advanced Discrete Math Topics

• Visualize data with graph theory
• Network optimization with trees
• Event probability
• Cryptography
• Challenge: Advanced techniques
• Solution: Advanced techniques

Conclusion

• Next steps