Programming Foundations: Discrete Mathematics

Course details

What is discrete math, and how does it apply to programming? Math is an important part of all programming. Discrete mathematics is the study of mathematical structures that are unique (aka discrete). Think integers, graphs, and logical statements—things we use a lot in programming. Discrete math can be used for software design specifications, analysis of algorithms, and other practical applications, but it's really a great tool to develop as a programmer. Put simply, it's a building block for logical thinking.

This course relies on an open-source SML (standard machine language) library to demo the concepts behind discrete math. Peggy Fisher shows you how to manipulate sets of data, write proofs and truth tables, analyze data sequences, and visualize data using graph theory. Challenges at the end of every chapter allow you to test your knowledge. By the end of the course, you should be able to make the leap from theory to using discrete math in practice: saving time and resulting in code that's cleaner and easier to maintain in the long run.

Learning objectives
Real-world discrete math
Objects as sets
Set notation and operations
Standard machine language (SML) setup
Working with data types, strings, and functions in SML
Analyzing data sequences
Writing truth tables
Identifying and evaluating predicates
Validating arguments
Writing proofs: subset, conditional, and biconditional proofs
Visualizing data with graphs
Advanced discrete math techniques

Concepts

0. Introduction

01 - Welcome
02 - What you should know
03 - Using the exercise files

1. Discrete Math Uses

04 - Basics of discrete mathematics
05 - Discrete math for programming
06 - Real-world discrete math
07 - Abstract discrete math

2. Sets

08 - Objects as sets
09 - Set notation
10 - Set operations
11 - Power sets
12 - Sequences and sums
13 - Recursion
14 - Cardinality, disjointness, and partitions
15 - Sets from Cartesian products
16 - Challenge - Practice with sets
17 - Solution - Practice with sets

3. Setting Up SML

18 - Functional programming
19 - Datatypes
20 - Characters and strings
21 - Recursive functions
22 - Challenge - Learn SML
23 - Solution - Create new data types

4. Analyzing Data Sequences

24 - Use SML to create lists
25 - Perform functions on lists
26 - Create datatypes that use lists
27 - Challenge - Model a lunch order
28 - Solution - Model a lunch order

5. Effective Arguments and Defensible Decisions

29 - Valid reasoning and inference
30 - Truth tables
31 - Identify and evaluate predicates
32 - Conditional propositions
33 - Valid arguments
34 - Rules of inference
35 - Prove logical equivalence
36 - Challenge - Write truth tables
37 - Solution - Write truth tables

6. Proofs Made Easy

38 - Write a general outline for a proof
39 - Write subset proofs
40 - Evaluate conditional proofs
41 - Understand biconditional proofs
42 - Prove with mathematical induction
43 - Challenge - Write a proof
44 - Solution - Write a proof

7. Advanced Discrete Math Topics

45 - Visualize data with graph theory
46 - Network optimization with trees
47 - Event probability
48 - Cryptography
49 - Challenge - Advanced techniques
50 - Solution - Advanced techniques

Conclusion

51 - Next steps