Programming Discrete Math Concepts for Beginners Course Syllabus

This course bridges discrete mathematics with practical programming, offering beginners a clear pathway to understanding how mathematical concepts form the foundation of algorithms and data structures. Through eight concise modules, you'll explore Boolean algebra, logical expressions, arrays, linear data structures, trees, and algorithmic complexity—all reinforced with hands-on coding challenges and quizzes. The course spans approximately 6 hours total, with bite-sized lessons designed for immediate application across six programming languages. Each module combines theory with real-world implementation, ensuring you build both intuition and practical skills essential for software development and technical interviews.

Module 1: Course Introduction

Estimated time: 0.2 hours

• Foundations of discrete math in programming
• Relationship between math and algorithms
• Connection between variables, expressions, and mathematical principles
• Role of arrays in discrete structures

Module 2: Programming Languages & Boolean Algebra

Estimated time: 0.5 hours

• Logical operators in code
• Truth tables and their programming equivalents
• Short-circuit evaluation
• Grade-threshold and temperature logic problems

Module 3: Logical Expressions & Algorithms

Estimated time: 1 hours

• De Morgan’s Laws in programming
• Control constructs and logical flow
• Implementation of Sieve of Eratosthenes
• Euclid’s GCD algorithm
• Quicksort logic and structure

Module 4: Arrays & Discrete Mathematics

Estimated time: 1 hours

• Array indexing and mathematical patterns
• Sequence analysis in discrete contexts
• Basic combinatorics with arrays
• Prime detection using array operations
• Set-difference operations on arrays

Module 5: Linear Data Structures & OOP

Estimated time: 1 hours

• Class-based design for data structures
• Implementation of stacks and queues
• Linked list construction and methods
• Insertion, deletion, and traversal techniques

Module 6: Trees & Traversals

Estimated time: 1 hours

• Binary tree node structure
• Pre-order, in-order, post-order traversals
• Recursive vs. iterative traversal approaches
• Building traversal functions in code

Module 7: Complexity, Set Operations & Strings

Estimated time: 0.75 hours

• Big-O notation and complexity analysis
• Set-difference algorithms
• String-rearrangement techniques
• String-shuffle coding challenge

Module 8: Review Quizzes & Coding Challenges

Estimated time: 1 hours

• Review of Boolean logic applications
• Algorithm implementation quizzes
• Multi-language coding challenges
• Consolidation of data structure concepts

Prerequisites

• Familiarity with basic programming syntax
• Understanding of variables and control flow
• No prior math expertise required

What You'll Be Able to Do After

• Translate Boolean algebra into working code
• Implement core algorithms like GCD and Quicksort
• Design and manipulate stacks, queues, and linked lists
• Build and traverse binary trees
• Analyze algorithm complexity using Big-O notation