REVOLUTIONS IN MATHEMATICS

Revolutions in Mathematics charts the origins and development of key mathematical concepts that have laid the foundation for the advanced technological world we enjoy today. This is a journey through thousands of years of human discovery, effort, and struggle. Behind the simple elegance of everyday mathematics lies a long, winding path filled with false starts, questionable beliefs, rivalries, and persistence in the face of sickness, despair, and doubt. This book brings those human stories to life, showing how determination and sacrifice shaped the mathematical breakthroughs we now take for granted. At the same time, it offers a clear, accessible understanding of the ideas themselves — designed for the general reader, not the specialist. By blending history with insight, Revolutions in Mathematics hopes to not only deepen appreciation for the role of mathematics in our world, but also spark curiosity to explore further into mathematics, science, and technology.

Professor Arthur Kramer began his primary academic life in the New York City borough of Brooklyn, NY and then spent the bulk of his time in Manhattan at Stuyvesant High School, Cooper Union Engineering School, Columbia University and New York University earning a PhD in Mathematics. Having worked as an engineer for a couple of years, he then honed his teaching skills for a short time at a high school, before going on to teach Mathematics at New York University. Soon after, he began a life-long career at New York City College of Technology of the City University of New York, teaching a variety of mathematics courses, with a specialty in the history and culture of mathematics, as well as courses in the Physics, Electrical Engineering and Computer Engineering departments. During this time, he spent several years as an Adjunct Professor of Mathematics at the New School for Social Research.

While early on he was interested in mathematical research and published several articles, soon a calling in mathematics education became paramount, resulting in educational grants and programs at New York City College of Technology. In particular, he developed a curriculum for a program called "Access for Women," which held weekend sessions for high school girls where they did basic experiments in various engineering disciplines, hoping to motivate them to enter one of these fields.

Professor Kramer has published four textbooks in technical mathematics, his latest being Mathematics for Electricity and Electronics, and continues to teach in the Electrical Engineering department at his college.

Alfred S Posamentier is currently a Distinguished Lecturer at New York City College of Technology of the City University of New York. Previously, he was the Executive Director for Internationalization and Sponsored Programs at Long Island University, New York. This was preceded by a five-year period where he was Dean of the School of Education and tenured Professor of Mathematics Education at Mercy University, New York. He is now also Professor Emeritus of Mathematics Education at the City College of the City University of New York, and former Dean of the School of Education, where he was tenured for 40 years. Dr Posamentier is the author and co-author of more than 90 mathematics books for teachers, secondary and elementary school students, as well as the general readership, and is a frequent commentator in newspapers and journals on topics related to education.