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Mathematics

When numbers form groups...

Abstract Algebra 01 - The Introduction of Groups

December 25, 2020

This is the first post of the Introduction to Abstract Algebra series, and we will start with groups. In this very first post, we will introduce the basic concepts in group theory, starting from mappings, equivalent relations, partitions, and extending to groups and homomorphisms. We will also encounter the first important theorem, the Lagrange's theorem.

Abstract Algebra 02 - The Isomorphism Theorems

January 01, 2021

This is the second post of the Introduction to Abstract Algebra series. In the first post, we introduce the basic concepts of groups. In this post, we will introduce four isomorphism theorems. But first of all, we need to define normal groups.

Abstract Algebra 03 - Group Actions

January 04, 2021

This is the third post of the Introduction to Abstract Algebra series. In this post, we will introduce group actions, which give rise to the Cayley's Theorem and the class equation.

Abstract Algebra 04 - The Sylow Theorems

January 09, 2021

This is the fourth post of the Introduction to Abstract Algebra series. In the first three posts, we are acquainted with the fundamental concepts and techniques in group theory. In this post, we will introduce the Sylow theorems.


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