Introduction to Categories

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• Lessons Notes and Presentations
  • Presentation on Logical Operators
  • Notes on Logical  Operators
  • Presentation on Quantifiersr
  • Notes on Quantifers
  • Notes on Negation of Quantiifiers
  • Notes on Nested Quantifiers
• Problem Sets
  • Logical Connectives  Solutions
  • Predicates and Quantifiers
• Assessments and Activities
  • Quiz on Logical Connectives
  • Quiz on Quantifiers V1 V2
  • Lewis Carrol Take Home Test  Solutions

• Lessons and Presentations
  • Presentation on Set Operations
  • Notes on Basic Set Operations
  • Notes on Combinatorics
  • Notes on Power Set and Relations
  • Presentation on Cartesian Products & Axiom of Choice
  • Presentation on Functions
  • Notes on Functions
  • Notes on Countability
• Problem Sets
  • Set Operations
  • Combinatorics and Set Theory
  • Functions
  • Sets and Functions
• Assessments and Activities
  • Quiz on Set Operations  V1 V2
  • Quiz on Power Set and Relations
  • Group Activity on Functions 
  • Quiz on Functions
  • Take Home Quiz on Functions
  • Test on Set Operations
  • Test on Relations and Functions
  • Cumulative Unit Test

• Lessons
  • Notes on Mathematical Induction
  • Notes on Euclidean Algorithm part 1    part 2
  • Notes on Combinatorics
  • Notes on Binary Operations
  • Notes on Groups
  • Notes on Permutation Groups
  • Notes on Dihedral Group (after Dihedral Groups Activity)
  • Notes on Subgroups
  • Notes on Cosets and Theorems
• Problem Sets
  • Classwork Induction 1
  • Classwork Induction 2
  • Combinatorics Homework Solution
  • Dihedral Group Activity and Accompanying Worksheet 
  • Worksheet Mod n  Solutions
  • Groups Homework
• Quizzes and Tests
  • Induction Quiz
  • Euclidean Algorithm Quiz
  • Combinatorics and Induction Quiz
  • Introduction to Groups Quiz
  • Dihedral Group Theory Quiz
  • Mod n Group Theory Quiz

• Lessons
  • Algebraic Categories Notes  with Problems 
  • Algebraic Categories Presentation

* Problem Sets are included with the Lesson Notes

• Lessons
  • Intro to Metric Spaces Notes
  • Metric Space Lecture 1 
  • Metric Space Lecture 2 
  • Metric Space Lecture 3
  • Intro to Topological Spaces Notes
  • Topological Spaces Notes 2
  • Category of Metric Spaces and Topological Spaces
  • Topological Properties 
• Quizzes
  • Metric Spaces Quiz 1
  • Metric Spaces Quiz 2
  • Topological Spaces Reading Quiz
  • Topology Quiz

• Lessons
  • Homotopy - Hatcher Chapter 0
  • Introduction to the Fundamental Group
  • Fundamental Group of Quotient Spaces
  • Fundamental Group Presentation
  • Fundamental Group Lecture pdf
  • Fundamental Group Lecture as notebook file with animation (can 
  • be seen with Smart Notebook Viewer app on Google Playstore)
  • Hatcher Fundamental Group
• Problem Sets and Activities
  • Alphabet Homotopy Activity
  • Fundamental Group by Identification Mapping 

• Lessons
  • Manifold Lecture 1
  • Manifold Lecture 2
  • Manifolds and Covering Spaces
  • Maple File on Parameterizing a Torus
  • Hatcher 1.3 Covering Spaces
  • Covering Spaces and Path Lifting
  • Monodromy Correspondence

• Lessons
  • Categories Lecture
  • Epi and Monomorphisms
  • Universal Objects
  • Product and Coproduct
  • Direct and Inverse Limits
• Problems Sets and Activities
  • Categories Classwork
  • Category Take Home Test   
    • Solutions

What is a Category and Why do we care?