Mathematics is a wonderfully austere science, but it also has a very human side. It is embedded in a colorful history filled with extraordinary personalities, deep philosophical debates, and breath-taking advances in knowledge. This book offers a brief but penetrating synopsis of that history. This book includes many detailed explanations of important mathematical procedures actually used by famous mathematicians. This gives the reader an opportunity to learn the history and philosophy of mathematics by way of problem solving. For example, there is a careful treatment of topics such as unit fractions, perfect numbers, linear Diophantine equations, Euclidean construction, Euclidean proofs, the circle area formula, the Pell equation, cubic equations, log table construction, the four-square theorem, quaternions, and Cantor's set theory. Several important philosophical topics such as infinity and Platonism, are pursued throughout the text. This book is written as an undergraduate textbook, but it is intended for anyone who wants to understand how mathematics grows out of, and nourishes, the total human experience.

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