Abstract Algebra - Preliminaries

Learn fundamental proof techniques and mathematical concepts essential for abstract algebra through this comprehensive video lecture covering direct proofs, contrapositive arguments, proof by contradiction, mathematical induction, set relations, equivalence relations, partitions, binary operations, and injective and surjective functions.

Syllabus

Writing Proofs: Direct Proof
Writing Proofs | Direct Proof Example
Writing Proofs | Contrapositive Example 1
Writing Proofs | Contrapositive Example 2
Writing Proofs | Proof by Contradiction Example 1
Writing Proofs | Proof by Contradiction Example 2
Writing Proofs | Principle of Mathematical Induction Example 1
Writing Proofs | Principle of Mathematical Induction Example 1
Abstract Algebra | A relation on a set.
Abstract Algebra | Equivalence Relations
Abstract Algebra | Partitions and Equivalence Relations
Abstract Algebra | Binary Operations
Abstract Algebra | Injective Functions
Abstract Algebra | Surjective Functions