The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models.

This book provides a rich account of major mathematical milestones, from the geometry of the Greeks through Newton’s calculus, and on to the laws of probability, symbolic logic, and the fourth dimension.

The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries.

This book is an introductory real analysis textbook, presented through the lens of history. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context.

Euclid was a Greek mathematician, often referred to as the "Father of Geometry". His Elements is one of the most influential works in the history of mathematics, serving as the main textbook until the late 19th or early 20th century.

This open access book provides an overview of Felix Klein's ideas. It discusses the meaning, importance and the legacy of Klein's ideas today and in the future, within an international, global context.

This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics.

Today neuroscientists peer into game players brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks.

This book is the famous essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible.

This work examines the main directions of research conducted on the history of mathematics education. Mathematics education practices and tools and the preparation of mathematics teachers, from a historical perspective.

A course introducing the idea of mathematical discovery, especially to students who may not be particularly enthused about mathematics as yet, in which the students could actually participate in the discovery of mathematics.

In 1900, David Hilbert asked whether each locally euclidean Topological Group admits a Lie group structure. This book should give the reader an overview of topological group theory as it developed over the last 115 years, as well as current research.

The book begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet.

Twentieth-century developments in logic and mathematics have led many people to view Euclid's proofs as inherently informal, especially due to the use of diagrams in proofs. It introduces a diagrammatic computer proof system, based on this formal system.

Computers have rapidly become so pervasive in mathematics that future generations may look back to this day as a golden dawn. The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.

This is an enjoyable book with suggested uses ranging from a text for a undergraduate Honors Mathematics Seminar to a coffee table book. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics.

The book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist. It promotes the art and the skills of developing logical proofs.

In short, this is a survival manual for the professional mathematician. A successful mathematical career involves doing good mathematics, to be sure, but also requires a wide range of skills that are not normally taught in graduate school.