Algebra: Practice Exam Solutions

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Related lectures (31)

Permutations and Adjacency Log in to Mediaspace to watch this video

Explores permutations preserving adjacency, linear transformations, groups, and sub-groups.

Sylow Subgroups: Group Theory Log in to Mediaspace to watch this video

Explores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.

Torsion and Divisibility: Abelian Groups Log in to Mediaspace to watch this video

Introduces torsion and divisibility concepts in abelian groups to describe their structure.

Finite Abelian Groups & Rings Log in to Mediaspace to watch this video

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.

Sylow Subgroups: Structure and Properties Log in to Mediaspace to watch this video

Explores the properties and structure of Sylow subgroups in group theory, emphasizing a theorem-independent approach.

Quotients in Abelian Groups Log in to Mediaspace to watch this video

Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.

Mathematical Parenthesis on Groups and Lagrange Theorem Log in to Mediaspace to watch this video

Explores cosets in commutative groups, Lagrange theorem, and integer factorization.

Group Homomorphisms: Kernels, Images, and Normal Subgroups Log in to Mediaspace to watch this video

Explores group homomorphisms, kernels, images, and normal subgroups, using the dihedral group D_n as an example.

Groups and Numbers: Mathematical Elements on Groups Log in to Mediaspace to watch this video

Explores fundamental properties of groups and numbers, emphasizing equivalence classes and subgroup concepts.

Polynomials on a Field: Basics and Operations Log in to Mediaspace to watch this video

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Polynomials: Rings and Operations Log in to Mediaspace to watch this video

Covers the basics of polynomials, focusing on rings, operations, and properties.

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