Math 3325: Transitions to Advanced Mathematics, Spring 2020

Assignments

Videos and Notes

• Cantor's Theorem (11 minutes)
  
• The Continuum Hypothesis, Part 1 (9 minutes)
  
• The Continuum Hypothesis, Part 2 (14 minutes)
  

• Three Important Results About Countable Sets (28 minutes)
  
• Ordering for Cardinality of Sets (14 minutes)
  
• Example 1 for the Cantor-Schroeder-Bernstein Theorem (5 minutes)
  
• Example 2 for the Cantor-Schroeder-Bernstein Theorem (9 minutes)
  
• P(N) has Cardinality c (11 minutes)
  

• An Introduction to Cardinality: Hilbert's Hotel, Part 1 (25 minutes)
  
• An Introduction to Cardinality: Hilbert's Hotel, Part 2 (17 minutes)
  
• Equivalent Sets, Part 1 (21 minutes)
  
• Equivalent Sets, Part 2 (5 minutes)
  
• Definitions and Terms for Cardinalities of Sets (6 minutes)
  
• The Cardinality of an Open Interval, Part 1 (6 minutes)
  
• The Cardinality of an Open Interval, Part 2 (3 minutes)
  

• The Definition of a Function (15 minutes)
  
• When are Functions Equal? (5 minutes)
  
• Functions must be Well-Defined (9 minutes)
  
• Examples of Well-Defined and not Well-Defined Rules of Assignment (11 minutes)
  
• Example of a Hasse Diagram for Division (8 minutes)
  
• Using Hasse Diagrams to Define Partial Orders (5 minutes)
  
• Hasse Diagrams of Totally Ordered Sets (13 minutes)
  
• The concepts of One-to-one (Injective) and Onto (Surjective) for Functions (14 minutes)
  
• Invertibility Theorem (12 minutes)
  
• Inverse Functions are Unique (6 minutes)
  
• Example showing importance of Domains and Codomains (10 minutes)
  
• Example for Finding and Inverse (9 minutes)
  

• Introduction to Order Relations (17 minutes)
  
• The Divides Relation (6 minutes)
  
• Elements in Partially Ordered Sets (8 minutes)
  
• Hasse Diagrams (8 minutes)
  
• Example of a Hasse Diagram for Division (7 minutes)
  
• Using Hasse Diagrams to Define Partial Orders (4 minutes)
  
• Hasse Diagrams of Totally Ordered Sets (3 minutes)
  
• Supremum and Infimum (8 minutes)
  
• Example 1 of Sup and Inf (5 minutes)
  
• Example 2 of Sup and Inf (9 minutes)
  

• Notes on Relations (updated with order relations)
  

• Equivalence Classes (22 minutes)
  
• Partitions (8 minutes)
  
• Equivalence Classes and Partitions - Theorem (Part 1) (12 minutes)
  
• Equivalence Classes and Partitions - Theorem (Part 2) (7 minutes)
  
• Equivalence Classes and Partitions - Theorem (Part 3) (9 minutes)
  

• Introduction to the Online Course (12 minutes)
  
• Relations - Part 1 (5 minutes)
  
• Relations - Part 2 (3 minutes)
  
• Relations - Part 3 (2 minutes)
  
• Relations - Part 4 (13 minutes)
  
• Relations - Part 5 (5 minutes)
  
• Equivalence Relations (20 minutes)
  
• Equivalence Relations - Additional Example (13 minutes)
  

• Notes on Relations