This course lays the groundwork for understanding the structures that power modern mathematics. We start with the basics of set theory—notation, logic, functions, and operations—and use it as a stepping stone into the world of abstract algebra. From there, we introduce groups, rings, and fields in a way that highlights both intuition and structure. Clear, rigorous, and designed with first-time learners in mind.

This course builds up a key part of the foundation for abstract algebra—relations. We explore equivalence relations, partitions, orderings, and how they help us organize and understand mathematical structures. These ideas connect directly to how we define and work with algebraic systems like groups and rings. Clear, focused, and made for first-time learners stepping into abstract algebra.

This course focuses on mappings—one of the core tools in modern mathematics and abstract algebra. We cover functions, injectivity, surjectivity, bijections, and composition. You'll see how mappings connect sets, preserve structure, and lay the groundwork for understanding homomorphisms in algebraic systems. Straightforward, precise, and built for learners taking their first steps into abstract algebra.

This course introduces binary operations—the basic building blocks of algebraic structures. We explore how operations combine elements of a set, and what it means for them to be associative, commutative, or have an identity or inverse. These ideas form the core of how structures like groups and rings are defined. Clear, hands-on, and designed for anyone beginning their journey into abstract algebra.

This course introduces groups—one of the fundamental structures in abstract algebra. We cover the group axioms, explore classic examples like integers under addition and symmetry groups, and show how groups model structure and transformations in math. Clear, focused, and designed for learners new to abstract algebra.

This course dives into subgroups—key pieces within groups that reveal deeper structure. You’ll learn how to identify subgroups, understand their properties, and see why they matter in the bigger picture of group theory. We’ll also explore examples and criteria that help recognize subgroups quickly. Clear, practical, and perfect for first-time learners ready to explore group structures more deeply.

This course explores homomorphisms—the maps that connect algebraic structures while preserving their operations. You’ll learn what makes a function a homomorphism, see examples between groups and rings, and understand how these mappings reveal similarities and relationships between structures. Clear, focused, and designed for first-time learners ready to deepen their understanding of algebraic connections.

This course introduces rings and fields—two central structures in abstract algebra. You’ll learn how rings extend the idea of groups with two operations, and how fields bring in the familiar arithmetic of fractions and equations. We explore key examples like integers, polynomials, and modular systems. Simple, structured, and made for first-time learners building up their algebra toolkit.

This course brings in elementary number theory as a foundation for abstract algebra. We cover divisibility, prime numbers, greatest common divisors, modular arithmetic, and congruences—all with a focus on the ideas that connect naturally to groups, rings, and fields. Clean, intuitive, and designed for learners building a solid entry point into algebra through number theory.