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05 Products sets and mappings
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Classroom Contents
Abstract Algebra
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- 1 01 Introduction
- 2 02 Introduction to sets
- 3 03 Subsets
- 4 04 Our first proof
- 5 05 Products sets and mappings
- 6 06 More about mappings
- 7 08 Exercise problem
- 8 09 Exercise problem
- 9 10 Relations (still with the not-so-exciting-stuff)
- 10 11 Reflexive, symmetric, and transitive properties of relations
- 11 12 Equivalence relations
- 12 13 Equivalence sets
- 13 14 Ordering of sets
- 14 15 Properties of partially ordered sets
- 15 16 You have made it to the first exciting video Operations
- 16 17 Examples of binary operations
- 17 18 Types of binary operations
- 18 19 Defining the types of binary operations
- 19 20 The identity element
- 20 21 The inverse element
- 21 22 Combinations of binary operations
- 22 23 Algebraic system isomorphism
- 23 Definition of a group Lesson 24
- 24 Cancellation law Lesson 25
- 25 Group equation examples Lesson 26
- 26 Groups that commute Lesson 27
- 27 Example problems with inverses Lesson 28
- 28 Integers modulo n
- 29 Groups in abstract algebra examples
- 30 Subgroups abstract algebra
- 31 Cyclic groups and generators
- 32 Symmetric groups
- 33 Homomorphisms in abstract algebra
- 34 Homomorphisms in abstract algebra examples
- 35 Isomorphisms in abstract algebra
- 36 Proof that Cayley table row and column entries are unique and complete
- 37 Cayley theorem proof
- 38 Cosets in abstract algebra
- 39 Cosets and equivalence class proof
- 40 Coset example
- 41 Coset deeper insights
- 42 Normal subgroups
- 43 Cosets generated by elements of cosets
- 44 Lagrange theorem
- 45 Quotient groups
- 46 Quotient group example
- 47 Product groups
- 48 Product group example
- 49 Surjective homomorphisms in abstract algebra
- 50 Kernel of a group homomorphism
- 51 First theorem of isomorphisms
- 52 Group actions in abstract algebra
- 53 Group action proofs in abstract algebra
- 54 Group action examples
- 55 Orbit of a set in abstract algebra
- 56 Stabilizer in abstract algebra
- 57 Example of a stabilizer in abstract algebra
- 58 Orbit stabilizer theorem
- 59 Dihedral groups in abstract algebra
- 60 Dihedral group example
- 61 Center of a group in abstract algebra
- 62 Centralizer of an element in the dihedral group of order 6
- 63 Centralizer of a set in a group
- 64 Normalizer of a set in a group
- 65 Conjugation of a group
- 66 Conjugacy classes of a group
- 67 Class equation of a group
- 68 Cycle types and conjugacy classes of the symmetric group
- 69 Group automorphisms in abstract algebra
- 70 Group automorphism example
- 71 How to use Plotly in a Google Colaboratory notebook
