Advanced Mathematical Thinking

This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. It is

Books about Advanced Mathematical Thinking

Books about Structural understanding in advanced mathematical thinking

First Published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

In this paper the notion of "procept" (in the sense of Gray & Tall, 1994) is extended to advanced mathematics by considering mathematical proof as "formal procept". The statement of a theorem as a symbol may theoretically evoke the proof deduction as a process that may contain sequential procedures and

Бестселер The New York Times, який рекомендує прочитати співзасновник компанії Microsoft Білл Ґейтс.

What mathematics is entailed in knowing to act in a moment? Is tacit, rhetorical knowledge significant in mathematics education? What is the role of intuitive models in understanding, learning and teaching mathematics? Are there differences between elementary and advanced mathematical thinking? Why can't students prove? What are the characteristics of

Here is a unique book that reduces the time & frustration involved in learning virtually every college-level undergraduate mathematics course & is as appropriate for freshman as it is for seniors. Standard textbooks teach specific subject matter, but this book explains for the first time the underlying thinking processes used

Provides a smooth and pleasant transition from first-year calculus to upper-level mathematics courses in real analysis, abstract algebra and number theory Most universities require students majoring in mathematics to take a “transition to higher math” course that introduces mathematical proofs and more rigorous thinking. Such courses help students be prepared

Besides giving readers the techniques for solving polynomial equations and congruences, An Introduction to Mathematical Thinking provides preparation for understanding more advanced topics in Linear and Modern Algebra, as well as Calculus. This book introduces proofs and mathematical thinking while teaching basic algebraic skills involving number systems, including the integers