Lectures in course MATH-113: Algebra I - fundamental structures

Covers the basics of formal logic, focusing on logical expressions and mathematical proofs.

Covers the basics of proofs, defining sets, and applications between sets.

Covers logical expressions, sets, elements, and equivalence relations.

Explores equivalence relations, reflexivity, equivalence classes, and constructing new sets based on equivalent elements.

Covers the concept of equivalence relations and how to determine them.

Discusses equivalence relations, partitions, reflexivity, symmetry, transitivity, and set cardinality.

Covers the fundamental theorem of arithmetic, focusing on equivalence and irreducibility of integers.

Covers the definition of a group, properties of symmetries, and group operations.

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

Explores group homomorphisms, Euler's phi function, and group products.

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

Explores homomorphisms, isomorphisms, group properties, and their applications through examples and exercises.

Explores algebraic structures, classes of examples, and properties of cyclic groups.

Explores group operations with cyclic properties and the universal ownership of quotients.

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

Covers the simplified notation for expressing permutations and their applications in mathematics.

Covers the concept of composite of applications and the importance of certain hypotheses in matrix multiplication.

Explores linear projective groups, quaternions, subgroup generation, and normality.

Explores the torus, linear groups, stability properties of matrices, and homomorphisms.

Covers the concepts of groups, products, and homomorphisms, focusing on the hx set and group alternates.