A History of Abstract Algebra

by Israel Kleiner

This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.

Genres: Mathematics, History

184 pages, Paperback

First published January 1, 2007

Reviews

[Victor · Rating 3 out of 5]

Un buen libro que muestra la historia del álgebra abstracta. Aunque no tengo mucha idea de estos temas, tan sólo álgebra lineal y básicas nociones de teoría de grupos, el libro es interesante porque muestra realmente como es el desarrollo de las ideas matemáticas, que casi siempre suelen nacer de un revoltijo de ideas inconexas, parciales, con la idea de solucionar problemas muy concretos, y luego con el paso de los años (a veces cientos) y trabajo de los distintos matemáticos se pone un poco de orden, se generalizan las ideas, se da cohesión, se limpia la teoría y se da luz a una nueva rama de las matemáticas con numerosas aplicaciones, muchas más de las que en principio se hubiera imaginado cuando se concivió por primera vez.

[Justin · Rating 4 out of 5]

This was a helpful book for me. I teach an abstract algebra course every fall, and thought I understood its development fairly well, but this text showed me I was only familiar with one strand of the story. I was well aware of the Galois side of the history, but hadn’t thought much about the way groups were used in number theory ended up merging with the groups/fields of Galois theory. Also: I always understood that Noether was an important figure in the early 20th century, but this book made me realize that I didn’t really understand why. On the downside, at one point the author lists the 3 greatest mathematicians of history, and leaves out Euler. So that’s why this only gets 4 stars.

[Dave · Rating 2 out of 5]

Rapidly became too technical for me.

[Aryan Prasad · Rating 2 out of 5]

It is a History of Abstract (as well as) Algebra written for teachers, complete with instructions on how to plan a History focused course of Abstract Algebra. The book is in very dry and academic language, pop maths book Unknown Quantity: A Real and Imaginary History of Algebra is a good supplement to read alongside this.