Concepts in Linear and Abstract Algebra provide a comprehensive understanding of foundational algebraic concepts, from the intricacies of linear systems to the abstract realms of groups, rings, and fields. In Part 1, participants explore Linear Algebra through linear systems, studying their solutions and applications before transitioning into the realm of vector spaces, understanding their properties, subspaces, and dimensions. As Part 1 progresses, participants study linear maps and maps between spaces.  In Part 2, the unit extends what teachers already know about complex numbers, modular arithmetic, functions, polynomials and symmetry to new Abstract Algebraic topics such as groups, equivalent classes, cosets, quotient groups, rings, and fields. These topics are important for their applications in fields such as cryptography, computer science, and physics, and provide the basic skills for further study into Abstract Algebra. Each module relates the topics taught to learning opportunities in upper-level mathematics classes.

 

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