Concepts of Modern Mathematics is a 1975 book by mathematician and science popularizer Ian Stewart

Ian Stewart (mathematician)

Ian Nicholas Stewart FRS is a professor of mathematics at the University of Warwick, England, and a widely known popular-science and science-fiction writer. He is the first recipient of the , awarded jointly by the LMS and the IMA for his work on promoting mathematics.-Biography:Stewart was born...

 about recent developments in mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

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The book arose out of an extramural

Extramural

Extramural means to study outside, but under the aegis of, a university or other institution. Extramural studies are taken by the student away from the physical campus, and are often used for those unable to attend classes....

 class that Ian Stewart taught at the University of Warwick

University of Warwick

The University of Warwick is a public research university located in Coventry, United Kingdom...

 about "New math

New math

New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s. The name is commonly given to a set of teaching practices introduced in the U.S...

" (called "Modern mathematics" in the UK). In the 1995 Dover

Dover Publications

Dover Publications is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche. It publishes primarily reissues, books no longer published by their original publishers. These are often, but not always, books in the public domain. The original published editions may be...

 edition Stewart wrote that the aim of the class was:

to explain why the underlying abstract point of view had gained currency among research mathematicians, and to examine how it opened up entirely new realms of mathematical thought.

The book is aimed at non-mathematicians. However, there are frequent equations and diagrams and the level of presentation is more technical than some of Stewart's other popular books such as Flatterland

Flatterland

Flatterland is a 2001 book by mathematician and science popularizer Ian Stewart about non-Euclidean geometry. It was written as a sequel to Flatland, an 1884 novel that discussed different dimensions.-Plot summary:Almost 100 years after A...

. Topics covered include Analytic Geometry

Analytic geometry

Analytic geometry, or analytical geometry has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties...

, Set Theory

Set theory

Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

, Abstract Algebra

Abstract algebra

Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...

, Group Theory

Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...

, Topology

Topology

Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

 and Probability

Probability

Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

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ISBN 0-14-021849-1, ISBN 0-486-28424-7