This lively, stimulating account of non-Euclidean geometry by a noted mathematician covers matrices, determinants, group theory, and many other related topics, with an emphasis on the subject's novel, striking aspects. 1955 edition.

## Prelude to Mathematics

## A Mathematical Prelude to the Philosophy of Mathematics

This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.

## Mathematics with Understanding

Mathematics with Understanding, Book 1 provides a guide for teaching primary mathematics. This book consists of nine main topics–aims of a modern approach; language of sets; relations and sorting; recording of number and use of different bases; open sentences, number facts and pictorial representation; natural numbers and addition; subtraction; multiplication; and division. In these topics, this text specifically discusses the union and intersection of two sets, Cardinal number of a set, and recording by means of a mapping. The collection of data, fundamental operations for natural numbers, and subtraction algorithm are also deliberated. This compilation likewise covers the Cartesian product of two sets and properties of division. This publication is recommended for math teachers intending to acquire a deeper understanding of the structure behind many mathematical ideas and processes.

## Math is Precise, Period, vs. Math is Precise, Strings Attached

*Reflections of a Math Teacher on Teaching Mathematics*

## Ball of Confusion

*Puzzles, Problems and Perplexing Posers*

## History of Analytic Geometry

Specifically designed as an integrated survey of the development of analytic geometry, this classic study takes a unique approach to the history of ideas. The author, a distinguished historian of mathematics, presents a detailed view of not only the concepts themselves, but also the ways in which they extended the work of each generation, from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850. Appropriate as an undergraduate text, this history is accessible to any mathematically inclined reader. 1956 edition. Analytical bibliography. Index.

## Mathematical Economics

*Prelude to the Neoclassical Model*

## Mathematics in the Primary School

*A Sense of Progression*