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Isomorphisms and a proof of Cayley's Theorem

We discuss the definition of a group isomorphism, some examples of isomorphisms, and we construct an in-depth proof of Cayley's theorem.

March 12, 2013 | Read the full article

Programming Language Translation Issues

In this article, we learn about the process of translating programming languages. Topics covered include program-subprogram structure, BNF grammers, finite-state automata, and recursive descent parsing.

February 27, 2013 | Read the full article

Programming Language Design Issues

We begin studying programming language design and implementations by examining the history of programming languages, the role of programming languages, and the details on programming environments.

February 14, 2013 | Read the full article

Finite groups and subgroups - part 2

In continuing the discussion of finite groups and subgroups, we look at the two-step subgroup test and more examples of groups.

January 28, 2013 | Read the full article

Finite groups and subgroups - part 1

We continue our discussion of groups by learning about subgroups, the order of a group, subgroup tests, and more properties of groups.

January 26, 2013 | Read the full article

Introduction to groups

Introduction to group theory. Includes definitions related to groups, examples of groups, theorems of basic proof properties along with proofs of the theorems.

January 16, 2013 | Read the full article

Abstract algebra preliminaries

A refresher on basic definitions and theorems needed to begin studying abstract algebra. Items of interest include computing gcd, the division algorithm, and modular arithmetic.

January 13, 2013 | Read the full article

Division in number theory - part 1

We begin our descent into introductory Number Theory material with the help of the book "Elementary Number Theory" by Gareth A. Jones and J. Mary Jones. The first topic is divisibility. This post discusses the division algorithm and the definition of "divides".

January 04, 2013 | Read the full article

Proving the sum of two odd numbers is even

A simple proof that the sum of two odd numbers is even.

December 30, 2012 | Read the full article

Proving the sum of two even numbers is even

A simple proof of the equally simple claim that the sum of two even numbers is also even.

December 30, 2012 | Read the full article

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