2016
Lynda
Peggy Fisher
3:11
English

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.

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

lynda.com/Programming-Foundations-tutorials/Foundations-Programming-Discrete-Mathematics/411376-2.html

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