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Foundations of Mathematical Reasoning

Foundations of Mathematical Reasoning
Author: Dana Center
Publisher: Pearson
Total Pages:
Release: 2015-07-20
Genre:
ISBN: 9780134192499
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NOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, and registrations are not transferable. To register for and use Pearson's MyLab & Mastering products, you may also need a Course ID, which your instructor will provide. Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for Pearson's MyLab & Mastering products may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. "This course is ideal for accelerating students as an alternative to the traditional developmental math sequence and preparing them for a college-level statistics, liberal arts math, or STEM-prep course." "MyMathLab for Foundations for Mathematical Reasoning" is the first in a series of MyMathLab courses built to support the New Mathways Project developed by the Charles A. Dana Center. The New Mathways Project embodies the Dana Center s vision for a systemic approach to improving student success and completion through implementation of processes, strategies, and structures built around three mathematics pathways and a supporting student success course. "Foundations for Mathematical Reasoning" is the common starting point for all three mathematics pathways and is designed to build the mathematical skills and understanding necessaryfor success in a quantitative literacy, statistics, or algebra course. "

Mathematical Reasoning

Mathematical Reasoning
Author: Lyn D. English
Publisher: Routledge
Total Pages: 393
Release: 2013-04-03
Genre: Education
ISBN: 1136491074
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How we reason with mathematical ideas continues to be a fascinating and challenging topic of research--particularly with the rapid and diverse developments in the field of cognitive science that have taken place in recent years. Because it draws on multiple disciplines, including psychology, philosophy, computer science, linguistics, and anthropology, cognitive science provides rich scope for addressing issues that are at the core of mathematical learning. Drawing upon the interdisciplinary nature of cognitive science, this book presents a broadened perspective on mathematics and mathematical reasoning. It represents a move away from the traditional notion of reasoning as "abstract" and "disembodied", to the contemporary view that it is "embodied" and "imaginative." From this perspective, mathematical reasoning involves reasoning with structures that emerge from our bodily experiences as we interact with the environment; these structures extend beyond finitary propositional representations. Mathematical reasoning is imaginative in the sense that it utilizes a number of powerful, illuminating devices that structure these concrete experiences and transform them into models for abstract thought. These "thinking tools"--analogy, metaphor, metonymy, and imagery--play an important role in mathematical reasoning, as the chapters in this book demonstrate, yet their potential for enhancing learning in the domain has received little recognition. This book is an attempt to fill this void. Drawing upon backgrounds in mathematics education, educational psychology, philosophy, linguistics, and cognitive science, the chapter authors provide a rich and comprehensive analysis of mathematical reasoning. New and exciting perspectives are presented on the nature of mathematics (e.g., "mind-based mathematics"), on the array of powerful cognitive tools for reasoning (e.g., "analogy and metaphor"), and on the different ways these tools can facilitate mathematical reasoning. Examples are drawn from the reasoning of the preschool child to that of the adult learner.

The Tools of Mathematical Reasoning

The Tools of Mathematical Reasoning
Author: Tamara J. Lakins
Publisher: American Mathematical Soc.
Total Pages: 233
Release: 2016-09-08
Genre: Mathematics
ISBN: 1470428997
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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.

Foundations of Logic and Mathematics

Foundations of Logic and Mathematics
Author: Yves Nievergelt
Publisher: Springer Science & Business Media
Total Pages: 425
Release: 2012-12-06
Genre: Mathematics
ISBN: 146120125X
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This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.

Practical Foundations of Mathematics

Practical Foundations of Mathematics
Author: Paul Taylor
Publisher: Cambridge University Press
Total Pages: 590
Release: 1999-05-13
Genre: Mathematics
ISBN: 9780521631075
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This book is about the basis of mathematical reasoning both in pure mathematics itself (particularly algebra and topology) and in computer science (how and what it means to prove correctness of programs). It contains original material and original developments of standard material, so it is also for professional researchers, but as it deliberately transcends disciplinary boundaries and challenges many established attitudes to the foundations of mathematics, the reader is expected to be open minded about these things.

Mathematical Reasoning

Mathematical Reasoning
Author: Theodore A. Sundstrom
Publisher: Prentice Hall
Total Pages: 0
Release: 2007
Genre: Logic, Symbolic and mathematical
ISBN: 9780131877184
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Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom

An Introduction to Mathematical Reasoning

An Introduction to Mathematical Reasoning
Author: Peter J. Eccles
Publisher: Cambridge University Press
Total Pages: 364
Release: 2013-06-26
Genre: Mathematics
ISBN: 1139632566
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This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

Algebraic Foundations of Many-Valued Reasoning

Algebraic Foundations of Many-Valued Reasoning
Author: R.L. Cignoli
Publisher: Springer Science & Business Media
Total Pages: 238
Release: 2013-03-09
Genre: Mathematics
ISBN: 9401594805
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This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as a simple proof of the completeness theorem and of the equivalence between Chang's MV algebras and Abelian lattice-ordered groups with unit - a necessary prerequisite for the incorporation of a genuine addition operation into fuzzy logic. Readers interested in fuzzy control are provided with a rich deductive system in which one can define fuzzy partitions, just as Boolean partitions can be defined and computed in classical logic. Detailed bibliographic remarks at the end of each chapter and an extensive bibliography lead the reader on to further specialised topics.

The Logical Foundations of Mathematics

The Logical Foundations of Mathematics
Author: William S. Hatcher
Publisher: Elsevier
Total Pages: 331
Release: 2014-05-09
Genre: Mathematics
ISBN: 1483189635
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The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems. The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory. Comprised of eight chapters, this book begins with an introduction to first-order logic. In particular, two complete systems of axioms and rules for the first-order predicate calculus are given, one for efficiency in proving metatheorems, and the other, in a "natural deduction" style, for presenting detailed formal proofs. A somewhat novel feature of this framework is a full semantic and syntactic treatment of variable-binding term operators as primitive symbols of logic. Subsequent chapters focus on the origin of modern foundational studies; Gottlob Frege's formal system intended to serve as a foundation for mathematics and its paradoxes; the theory of types; and the Zermelo-Fraenkel set theory. David Hilbert's program and Kurt Gödel's incompleteness theorems are also examined, along with the foundational systems of W. V. Quine and the relevance of categorical algebra for foundations. This monograph will be of interest to students, teachers, practitioners, and researchers in mathematics.

Introduction to Mathematical Thinking

Introduction to Mathematical Thinking
Author: Keith J. Devlin
Publisher:
Total Pages: 0
Release: 2012
Genre: Mathematics
ISBN: 9780615653631
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"Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.