Maxima And Minima: How Extremes Can Explain Mathematics Concepts And Facilitate Problem Solving (Problem Solving in Mathematics and Beyond) - Softcover

Humenberger, Hans; Posamentier, Alfred S

Softcover

ISBN 10: 9819824826 ISBN 13: 9789819824823

Publisher: WSPC, 2026

Synopsis

This book explores the versatile concept of maxima and minima — extremes and optimal values — across a broad spectrum of mathematics. Far from being limited to calculus, the concept of extremes is applicable to nearly every field of mathematics, including geometry, arithmetic, algebra, and stochastics, offering powerful tools for problem solving. The first part of the book introduces a wide range of applications of the method of extremes, showing how it can be used to tackle problems both in everyday life and in mathematical contexts. The second, larger part focuses on solving extreme value problems without relying on derivatives, instead building reasoning and proof from first principles. Here, special emphasis is placed on geometry, where questions of optimality often reveal surprising insights about shapes and figures. By approaching mathematics through the lens of extremes, readers will gain a deeper understanding of core concepts and discover fresh ways to enrich both learning and teaching.

About this title

About the Authors

Hans Humenberger has been a Professor of Mathematics at the University of Vienna, Austria, since 2005. Previously, he was Associate Professor at the University of Dortmund (Germany). His interests lie in teaching mathematics as a process (not a ready product), applications of mathematics and problem solving. On the latter topic he teaches a seminar every year. Since 2007 he has been the editor of an Austrian school mathematics textbook series for grades 5–8 and has initiated a program for grade 5–8 students at the university to enhance their experience with problem solving. He has edited and written several books in German, and has written many contributions in English for several journals.

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.

Edition details

• Publisher: WSPC
• Publication date: 2026
• Language: English
• ISBN 10: 9819824826
• ISBN 13: 9789819824823
• Binding: Paperback
• Number of pages: 320