This week, our Resource List of the Week concentrates on Algebra. Before starting, let’s give a definition to this topic.
What is Algebra?
According to the Merriam-Webster, algebra consists of
“a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic”.
To better understand the topic, we recommend you read the following titles and resources.
1. Algebra – Flanders, H. and Price, J.J.
This book presents the essentials of algebra with extensive examples. Firstly, the title put emphasis on practical skills, problem-solving, and computational techniques. Secondly, it covers topics ranging from equations and inequalities to functions and graphs, from polynomial and rational functions to exponentials and logarithms. Also, the book considers trigonometric functions and complex numbers. Finally, the text counts eight chapters, discussing the fundamentals of algebra along with explaining topics with illustrations and providing a wide set of exercises.
2. Introduction To Commutative Algebra, Student Economy Edition – Atiyah, M.
The main aim of this text is providing a rapid introduction to algebra. To those students who have already attended a first elementary course in general algebra.
The title is mainly focused on central topics but it doesn’t cover a large area such as field theory. Finally, following the modern trend, more emphasis is put on modules and localization.
3. Category Theory and Applications – Grandis, M.
This text covers most of mathematics, theoretical computer science and parts of theoretical physics. Firstly, it considers and combines different branches leading to a deeper understanding of their roots. Secondly, it covers its basic tools, like universal properties, limits, adjoint functors and monads. This book is a useful resource for students and researchers of these fields and can be used as a text for the first course in category theory.
4. Computational Algebra – Fischer, K.G.
The book is based on the fifth Mid-Atlantic Algebra Conference held recently at George Mason University, Fairfax, Virginia. It focuses on both the practical and theoretical aspects of computational algebra. Furthermore, it demonstrates specific computer packages, including the use of CREP to study the representation of theory for finite dimensional algebras and Axiom to analyse algebras of finite rank.
5. Abstract Algebra – Menini, C. and Van Oystaeyen, F.
This text covers subject matter generally taught over the course of two or three years and provides a self-contained presentation of detailed definitions and exercises. It also includes a representation of finite groups that avoid the use of semisimple ring theory and explains sets, maps, posets and lattices.
The title is a reliable resource that Firstly, it has been field-tested through advanced use in the ERASMUS educational project in Europe.
Study.com offers a wide range of resources around the different areas of algebra including example papers and exams.
Khan Academy is a non-profit educational organization founded in 2008 by Salman Khan with the aim of delivering a set of online tools for students. The site covers topics such as the foundations of algebra and its equations
This video from “Anywhere Math” explores expressions in Algebra in a simple and basic way.