(eBook PDF) The Tools of Mathematical Reasoning

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product details:

• ISBN-10 ‏ : ‎ 1470428997
• ISBN-13 ‏ : ‎ 978-1470428990
• Author:  Tamara J. Lakins 

This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.

table of contents:

Part I: Introduction. L.D. English, Analogies, Metaphors, and Images: Vehicles for Mathematical Reasoning.

Part II: Cognitive Foundations for a Mind-Based Mathematics. G. Lakoff, R.E. Núñez, The Metaphorical Structure of Mathematics: Sketching Out Cognitive Foundations for a Mind-Based Mathematics.

Part III: Mathematical Reasoning: Analogies. R.B. Davis, C.A. Maher, How Students Think: The Role of Representations. P.A. Alexander, C.S. White, M. Daugherty, Analogical Reasoning and Early Mathematics Learning. B. Gholson, D. Smither, A. Buhrman, M.K. Duncan, K.A. Pierce, Children’s Development of Analogical Problem-Solving Skill. L.D. English, Children’s Reasoning Processes in Classifying and Solving Computational Word Problems. M. Bassok, Two Types of Reliance on Correlations Between Content and Structure in Reasoning About Word Problems. M.J. Rattermann, Commentary: Mathematical Reasoning and Analogy.

Part IV: Mathematical Reasoning: Metaphors, Metonymies, and Images. N.C. Presmeg, Reasoning With Metaphors and Metonymies in Mathematics Learning. G.H. Wheatley, Reasoning With Images in Mathematical Activity. N.C. Presmeg, Generalization Using Imagery in Mathematics. D.H. Clements, J. Sarama, Children’s Mathematical Reasoning With the Turtle Programming Metaphor. A. Sfard, Commentary: On Metaphorical Roots of Conceptual Growth.

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