Discrete Math

Algorithms are step-by-step procedures used to solve computational problems and process data. Learners will understand sorting, searching, graph traversal, and how to analyze time and space complexity using Big O notation to write efficient code.

Boolean algebra is the branch of mathematics dealing with variables that have two truth values: true and false. Learners will understand how to simplify logical expressions, design digital logic circuits, and analyze formal mathematical systems.

Combinatorics is the study of finite or countable discrete structures. Learners will understand how to count arrangements, analyze permutations and combinations, use generating functions, and apply graph theory to solve complex optimization and partitioning problems.

Discrete mathematics studies mathematical structures that are countable or distinct rather than continuous. Learners will understand logic, set theory, combinatorics, and graph theory, which form the mathematical foundation of computer science.

Discrete probability deals with random variables that have countable outcomes. Learners will understand how to calculate likelihoods, analyze random events, and apply probability distributions to computer science, combinatorics, and game theory.

Graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. Learners will understand how to analyze network connectivity, find shortest paths, and solve optimization problems.

Mathematical logic explores formal systems of reasoning, propositional calculus, and proof theory. Learners will understand how to construct valid arguments, evaluate truth tables, and apply logical principles to computer programming and hardware design.

Number theory is the study of the properties and relationships of integers. You will understand concepts like prime factorization, divisibility, modular arithmetic, and cryptography, enabling you to solve complex mathematical puzzles and secure digital communications.

Recurrence relations are equations that define sequences recursively using previous terms. Learners will understand how to solve these relations using characteristic equations and generating functions to model algorithmic complexity and population growth.

This topic covers how mathematical objects associate with one another through mappings and ordered pairs. Learners will understand properties like injectivity, surjectivity, and equivalence relations, which are fundamental to algebra and database design.

Set theory is the study of collections of objects, serving as the foundational language of modern mathematics. Learners will understand operations like union and intersection, cardinality, and the axiomatic systems that structure mathematical reasoning.