Connected Mathematics

Master the content from Paper 1 (Pure Mathematics 1) of Cambridge International A-Level Maths

Getting certified to teach high school mathematics typically requires completing a course in real analysis. Yet most teachers point out real analysis content bears little resemblance to secondary mathematics and report it does not influence their teaching in any significant way. This textbook is our attempt to change the narrative.

During the last few decades historians of science have shown a growing interest in science as a cultural activity and have regarded science more and more as part of the gene­ ral developments that have occurred in society. This trend has been less evident arnong historians of mathematics, who traditionally concentrate primarily on tracing the develop­ ment of mathematical knowledge itself. To some degree this restriction is connected with the special role of mathematics compared with the other sciences; mathematics typifies the most objective, most coercive type of knowledge, and there­ fore seems to be least affected by social influences. Nevertheless, biography, institutional history and his­ tory of national developments have long been elements in the historiography of mathematics.

Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story.

This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come.