# Rings, Fields, and Vector Spaces

## An Introduction to Abstract Algebra via Geometric Constructibility

• B. A. Sethuraman
Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xiii
2. B. A. Sethuraman
Pages 1-7
3. B. A. Sethuraman
Pages 9-28
4. B. A. Sethuraman
Pages 29-62
5. B. A. Sethuraman
Pages 63-95
6. B. A. Sethuraman
Pages 97-117
7. B. A. Sethuraman
Pages 119-154
8. B. A. Sethuraman
Pages 155-168
9. B. A. Sethuraman
Pages 169-184
10. Back Matter
Pages 185-191

### Introduction

This book is an attempt to communicate to undergraduate math­ ematics majors my enjoyment of abstract algebra. It grew out of a course offered at California State University, Northridge, in our teacher preparation program, titled Foundations of Algebra, that was intended to provide an advanced perspective on high-school mathe­ matics. When I first prepared to teach this course, I needed to select a set of topics to cover. The material that I selected would clearly have to have some bearing on school-level mathematics, but at the same time would have to be substantial enough for a university-level course. It would have to be something that would give the students a perspective into abstract mathematics, a feel for the conceptual elegance and grand simplifications brought about by the study of structure. It would have to be of a kind that would enable the stu­ dents to develop their creative powers and their reasoning abilities. And of course, it would all have to fit into a sixteen-week semester. The choice to me was clear: we should study constructibility. The mathematics that leads to the proof of the nontrisectibility of an arbitrary angle is beautiful, it is accessible, and it is worthwhile. Every teacher of mathematics would profit from knowing it. Now that I had decided on the topic, I had to decide on how to develop it. All the students in my course had taken an earlier course . .

### Keywords

Abstract algebra Microsoft Access Vector space algebra boundary element method construction field mathematics polynomial proof set time university

#### Authors and affiliations

• B. A. Sethuraman
• 1
1. 1.Department of MathematicsCalifornia State University NorthridgeNorthridgeUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-2700-5
• Copyright Information Springer-Verlag New York 1997
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4757-2702-9
• Online ISBN 978-1-4757-2700-5
• Series Print ISSN 0172-6056
• Buy this book on publisher's site