This lecture includes the following topics: Administrative notes; Generalities on groups; Symmetric groups on n letters; A stabilizer subgroup; The subgroups of Z; Cyclic subgroups gen by element.

This lecture includes the following topics: Euclidean domains, PIDs, UFDs. Gauss' lemma. Eisenstein's criterion. Algebraic integers.

This lecture includes the following topics: Euclidean domains, PIDs, UFDs. Gauss' lemma. Eisenstein's criterion. Algebraic integers.

This lecture includes the following topics: Euclidean domains, PIDs, UFDs. Gauss' lemma. Eisenstein's criterion. Algebraic integers.

This lecture includes the following topics: Structure of ring of integers in a quadratic field. Dedekind domains. Ideal class groups.

This lecture includes the following topics: The story so far; Isomorphisms; Homomorphisms; Images.

This lecture includes the following topics: Review, kernels, normality; Examples; Centers and inner autos.

This lecture includes the following topics: Quotient groups, first isomorphism theorem. Abstract fields, abstract vectorspaces. Construction and invariants of vectorspaces.

This lecture includes the following topics: Quotient groups, first isomorphism theorem. Abstract fields, abstract vectorspaces. Construction and invariants of vectorspaces.

This lecture includes the following topics: Quotient groups, first isomorphism theorem. Abstract fields, abstract vectorspaces. Construction and invariants of vectorspaces.

This is a challenging task, suitable for extended work, and reaching into a deep understanding of units. The task requires students to exhibit MP1, Make sense of problems and persevere in solving them. An algebraic solution is possible but complicated; a numerical solution is both simpler and more sophisticated, requiring skilled use of units and quantitative reasoning. Thus the task aligns with either A-CED.1 or N-Q.1, depending on the approach.

HippoCampus is a project of the Monterey Institute for Technology and Education (MITE). The goal of HippoCampus is to provide high-quality, multimedia content on general education subjects to high school and college students free of charge. HippoCampus was designed as part of Open Education Resources (OER), a worldwide effort to improve access to quality education for everyone.

This activity has students explore the patterns that emerge when connecting midpoints of triangles. The activity includes a student worksheet, discussion questions, and an interactive fractal tool.