An Introduction To Mathematical Reasoning
Download An Introduction To Mathematical Reasoning full books in PDF, epub, and Kindle. Read online free An Introduction To Mathematical Reasoning ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads.
Author |
: Peter J. Eccles |
Publisher |
: Cambridge University Press |
Total Pages |
: 364 |
Release |
: 2013-06-26 |
ISBN-10 |
: 9781139632560 |
ISBN-13 |
: 1139632566 |
Rating |
: 4/5 (60 Downloads) |
Synopsis An Introduction to Mathematical Reasoning by : Peter J. Eccles
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.
Author |
: Keith J. Devlin |
Publisher |
: |
Total Pages |
: 0 |
Release |
: 2012 |
ISBN-10 |
: 0615653634 |
ISBN-13 |
: 9780615653631 |
Rating |
: 4/5 (34 Downloads) |
Synopsis Introduction to Mathematical Thinking by : Keith J. Devlin
"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.
Author |
: Theodore A. Sundstrom |
Publisher |
: Prentice Hall |
Total Pages |
: 0 |
Release |
: 2007 |
ISBN-10 |
: 0131877186 |
ISBN-13 |
: 9780131877184 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Mathematical Reasoning by : Theodore A. Sundstrom
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
Author |
: V. M. Bradis |
Publisher |
: Courier Dover Publications |
Total Pages |
: 225 |
Release |
: 2016-10-28 |
ISBN-10 |
: 9780486816579 |
ISBN-13 |
: 0486816575 |
Rating |
: 4/5 (79 Downloads) |
Synopsis Lapses in Mathematical Reasoning by : V. M. Bradis
Unique, effective system for teaching mathematical reasoning leads students toward clearly false conclusions. Students then analyze problems to correct the errors. Covers arithmetic, algebra, geometry, trigonometry, and approximate computations. 1963 edition.
Author |
: Raymond Nickerson |
Publisher |
: Taylor & Francis |
Total Pages |
: 597 |
Release |
: 2011-02-25 |
ISBN-10 |
: 9781136945397 |
ISBN-13 |
: 1136945393 |
Rating |
: 4/5 (97 Downloads) |
Synopsis Mathematical Reasoning by : Raymond Nickerson
The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.
Author |
: Lyn D. English |
Publisher |
: Routledge |
Total Pages |
: 407 |
Release |
: 2013-04-03 |
ISBN-10 |
: 9781136491146 |
ISBN-13 |
: 1136491147 |
Rating |
: 4/5 (46 Downloads) |
Synopsis Mathematical Reasoning by : Lyn D. English
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.
Author |
: Tamara J. Lakins |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 233 |
Release |
: 2016-09-08 |
ISBN-10 |
: 9781470428990 |
ISBN-13 |
: 1470428997 |
Rating |
: 4/5 (90 Downloads) |
Synopsis The Tools of Mathematical Reasoning by : 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.
Author |
: William J. Gilbert |
Publisher |
: Pearson |
Total Pages |
: 0 |
Release |
: 2005 |
ISBN-10 |
: 0131848682 |
ISBN-13 |
: 9780131848689 |
Rating |
: 4/5 (82 Downloads) |
Synopsis An Introduction to Mathematical Thinking by : William J. Gilbert
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 and complex numbers. Ample questions at the end of each chapter provide opportunities for learning and practice; the Exercises are routine applications of the material in the chapter, while the Problems require more ingenuity, ranging from easy to nearly impossible. Topics covered in this comprehensive introduction range from logic and proofs, integers and diophantine equations, congruences, induction and binomial theorem, rational and real numbers, and functions and bijections to cryptography, complex numbers, and polynomial equations. With its comprehensive appendices, this book is an excellent desk reference for mathematicians and those involved in computer science.
Author |
: Susanna S. Epp |
Publisher |
: |
Total Pages |
: 0 |
Release |
: 2011 |
ISBN-10 |
: OCLC:1301967373 |
ISBN-13 |
: |
Rating |
: 4/5 (73 Downloads) |
Synopsis Discrete Mathematics by : Susanna S. Epp
Author |
: Larry Gerstein |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 355 |
Release |
: 2013-11-21 |
ISBN-10 |
: 9781468467086 |
ISBN-13 |
: 1468467085 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Introduction · to Mathematical Structures and · Proofs by : Larry Gerstein
This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the rudiments of logic, set theory, equivalence relations, and other basic mathematical raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried the students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a nontrivial level if they are to achieve the sophisticated blend of knowledge, disci pline, and creativity that we call "mathematical maturity. " I don't believe that "theorem-proving" can be taught any more than "question-answering" can be taught. Nevertheless, I have found that it is possible to guide stu dents gently into the process of mathematical proof in such a way that they become comfortable with the experience and begin asking them selves questions that will lead them in the right direction.