Pre-Analysis & Probability II : Groups, Rings & Fields

Set Theory & Group Theory
Rating: 5.0 out of 5 (1 rating)
700 students
English [Auto]
Additive & Multiplicative Inverses
Idempotence & Boolean Polynomials
Power Sets & Set Operations
Algebraic Structures : Groups, Rings & Fields


  • High school algebra
  • Part I of this course


This course is about algebraic structures. It includes an introduction to identity, inverse and idempotent elements. We'll see that Boolean conjunction and disjunction can be seen as multiplication and addition and investigate possible additive and multiplicative identities and inverses. This is followed by power sets and basic operations on elements of power sets (union, intersection, complement, difference). All concepts are then combined in a discussion of algebraic structures including groups, rings and fields. We end with Boolean rings and describe set algebra as an example Boolean ring. In the review session we complete an example proof from CH1 of W. Rudin's Principles Of Mathematical Analysis using the axioms of a field.

Who this course is for:

  • Those planning to study probability and/or mathematical analysis

Course content

3 sections • 12 lectures • 1h 58m total length
  • Introduction


AP Ruymgaart
Arnold Ruymgaart
  • 4.8 Instructor Rating
  • 15 Reviews
  • 1,593 Students
  • 2 Courses

My passion for applied math and data science stems from my study of computational chemistry. Although I don't believe you need a degree to learn any subject I did complete a PhD at UT Austin. Our research group studied biophysics with statistical mechanics and molecular dynamics simulations. My graduate studies included completing all math course requirements for a MS in applied mathematics qualifying me to teach both math and chemistry at university level. I have 4 years of university teaching experience. After graduating I did a postdoctoral fellowship in a robotics group in the computer science department at UNM. I decided to go into industry and I am currently a senior data scientist at a Fortune 15 company