Unit 2: Structures

• BackSet Theory Axioms [Optional]
• Continue GCDs

2.1 GCDs

• 2.1.1 GCDs & Linear Combinations: Video
• 2.1.2 Euclidean Algorithm: Video
• 2.1.3 Run Euclid Run
• 2.1.4 Pulverizer: Video
• 2.1.5 GCDs I
• 2.1.6 Revisiting Die Hard: Video
• 2.1.7 Prime Factorization: Video
• 2.1.8 Unique Primes
• 2.1.9 Divisors
• 2.1.10 GCDs II

2.2 Congruences

• 2.2.1 Congruence mod n: Video
• 2.2.2 Divisibility and Congruence
• 2.2.3 Inverses mod n: Video
• 2.2.4 Inverses mod n
• 2.2.5 Multiplicative Inverses
• 2.2.6 Inverses With Linear Combinations

2.3 Euler's Theorem

• 2.3.1 Modular Exponentiation Euler's Function: Video
• 2.3.2 Euler's Totient Function
• 2.3.3 The Ring Z: Video
• 2.3.4 The Ring
• 2.3.5 Z mod n
• 2.3.6 Fermat's Little Theorem
• 2.3.7 Euler's Theorem

2.4 RSA Encryption

• 2.4.1 RSA Public Key Encryption: Video
• 2.4.2 RSA Encryption
• 2.4.3 Reducing Factoring To SAT: Video
• 2.4.4 Relative Primality
• 2.4.5 RSA computations

2.5 Digraphs: Walks & Paths

• 2.5.1 Digraphs: Walks & Paths: Video
• 2.5.2 Walks and Paths
• 2.5.3 Digraphs: Connected Vertices: Video
• 2.5.4 Longest Path
• 2.5.5 Adjacency Matrix
• 2.5.6 Counting Paths

2.6 Directed Acyclic Graphs (DAGs) & Scheduling

• 2.6.1 DAGs: Video
• 2.6.2 DAGs
• 2.6.3 Scheduling: Video
• 2.6.4 Scheduling Prerequisites
• 2.6.5 Time versus Processors: Video
• 2.6.6 Processor Time Bounds
• 2.6.7 The Divisibility DAG

2.7 Partial Orders and Equivalence

• 2.7.1 Partial Orders: Video
• 2.7.2 Population Partial Order
• 2.7.3 Representing Partial Orders As Subset Relations: Video
• 2.7.4 Equivalence Relations: Video
• 2.7.5 Relational Properties
• 2.7.6 Properties Of Relations
• 2.7.7 Equivalence Relations & Partial Orders

2.8 Degrees & Isomorphism

• 2.8.1 Degree: Video
• 2.8.2 Counting Degrees & Edges
• 2.8.3 Isomorphism: Video
• 2.8.4 Isomorphism
• 2.8.5 Extreme Graphs
• 2.8.6 Isomorphic Graphs
• 2.8.7 Non-Isomorphic Graphs

2.9 Coloring & Connectivity

• 2.9.1 Coloring: Video
• 2.9.2 Chromatic Number
• 2.9.3 Connectivity: Video
• 2.9.4 k-Connectivity: Video
• 2.9.5 k-Connected [optional]
• 2.9.6 Graph Coloring I
• 2.9.7 Graph Coloring II
• 2.9.8 Connected Components in Integers

2.10 Trees

• 2.10.1 Trees: Video
• 2.10.2 Trees: Many Definitions
• 2.10.3 Tree Coloring: Video
• 2.10.4 2-Colorable Trees
• 2.10.5 Spanning Trees: Video
• 2.10.6 Span all the Graphs!
• 2.10.7 Tree or Not Tree?
• 2.10.8 Leaves
• 2.10.9 Minimum Spanning Trees
• 2.10.10 Graph Algorithm

2.11 Stable Matching

• 2.11.1 Stable Matching: Video
• 2.11.2 Matching Ritual: Video
• 2.11.3 Derived Variables
• 2.11.4 Mating Ritual
• 2.11.5 Optimal Stable Matching: Video
• 2.11.6 Boy Optimal
• 2.11.7 Bipartite Matching: Video
• 2.11.8 Bipartite Equivalence Relation
• 2.11.9 Hall's Theorem: Video
• 2.11.10 Bottleneck
• 2.11.11 Bipartite Graphs
• 2.11.12 Matching
• 2.11.13 Stable Matching Invariants

• BackSet Theory Axioms [Optional]
• Continue GCDs