Pure Mathematics for Beginners - Lesson 3 - Abstract Algebra
3.8 (2 ratings)
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Pure Mathematics for Beginners - Lesson 3 - Abstract Algebra

Semigroups, Monoids, and Groups
3.8 (2 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
17 students enrolled
Created by Steve Warner
Last updated 12/2018
English
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Current price: $13.99 Original price: $19.99 Discount: 30% off
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This course includes
  • 1 hour on-demand video
  • 1 downloadable resource
  • Full lifetime access
  • Access on mobile and TV
  • Certificate of Completion
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What you'll learn
  • Abstract Algebra
Requirements
  • The content in this lesson is mostly self-contained. It does use a bit of notation that was developed in Lesson 2.
Description

Pure Mathematics for Beginners consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra.

Lesson 3 from this series introduces a few basic algebraic structures. In this lesson we will learn about binary operations, associativity, commutativity, identity elements, invertible elements. We will also look at examples of semigroups, monoids, and groups.

The content in this lesson is mostly self-contained. It does use a bit of notation that was developed in Lesson 2. Specifically, it will be helpful to understand set-builder notation, the membership relation, and the subset relation.

Who this course is for:
  • College students taking an introductory course in higher mathematics
  • Students who want to begin learning theoretical mathematics
  • Students who want to increase their level of mathematical maturity
Course content
Expand all 5 lectures 48:16
+ Lesson 3 - Abstract Algebra
4 lectures 38:18
Semigroups and Associativity
14:38

This is the end of Lesson 3. After completing this part, you should be ready to attempt the problems from the attached problem set.

Monoids and Identity
04:24
Groups and Inverses
08:53
+ Preliminaries from Lesson 2 - Set Theory
1 lecture 09:58

This part of Lesson 2 is included as a review. Some of the notation from this lesson is used in Lesson 3. You can watch this video if you are having trouble understanding any of the symbols used in the previous videos.

Sets and Subsets - Describing Sets
09:58