1st Edition
Mathematical Reasoning Patterns, Problems, Conjectures, and Proofs
1. What Is Mathematics? 2. Counting. 3. Numbers. 4. Deduction and Abstraction. 5. Proofs. 6. Informal Reasoning. 7. Representations. 8. Infinity. 9. Infinitesimals. 10. Predilections. 11. Esthetics in Mathematics. 12. The Usefulness of Mathematics. 13. Foundations. 14. Preschool Development. 15. Math in Schools. 16. Math Problem Solving. 17. Final Thoughts.
Biography
Raymond S. Nickerson, retired senior vice president of Bolt Beranek and Newman Inc. and research professor at Tufts University, is a fellow of the American Association for the Advancement of Science, the American Psychological Association, the Association for Psychological Science, the Human Factors and Ergonomics Society, and the Society of Experimental Psychologists. He is the founding editor of The Journal of Experimental Psychology: Applied, the founding and series editor of Reviews of Human Factors and Ergonomics, an annual publication of the Human Factors and Ergonomics Society, and the author of several books, including Aspects of Rationality: Reflections on What it Means to be Rational and Whether We Are (Psychology Press, 2008).
"Few authors who are not mathematicians have the understanding and sympathy for the subject and its practitioners that is shown in this book, whose author is an experimental psychologist and former VP of Bolt Beranek and Newman Inc. He surveys the nature, joys, usefulness, foundations, and teaching of mathematics, in its manifestations of pattern-finding, problem-solving, conjecture-making, and proof-devising. He concludes, "the supreme reason for acquiring some competence in mathematics is the door it opens to an immensely attractive and rewarding workspace—or playground—for the mind." This is a great book for nonmathematicians, one that a mathematician can praise." - Paul Campbell, Beloit College, USA
"Nickerson is a reliable and enthusiastic guide through a many-layered forest of ideas, leading us at each turn to a new appreciation of its topography – the box canyons and precipices and monumental vistas – of this very human adventure. His excellent references mark trailheads for those who would venture farther." - Peter Killeen, Ph.D., Arizona State University, USA
"A wide-ranging and insightful account of the nature of mathematics (its origins, utility, beauty) as well as of cognition and reasoning in general. This book is a welcome antidote to the notion that math is primarily a matter of computation." - John A. Paulos, Ph.D., Temple University, USA
