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Author : Douglas K. Brumbaugh,Linda Brumbaugh
Publisher : Unknown
Page : 240 pages
File Size : 52,8 Mb
Release : 2011-01-18
Category : Mathematics
ISBN : 0894558862
Author : Peter J. Eccles
Publisher : Cambridge University Press
Page : 366 pages
File Size : 54,9 Mb
Release : 1997-12-11
Category : Mathematics
ISBN : 0521597188
The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. 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 : Linda Brumbaugh,Douglas K. Brumbaugh
Publisher : Unknown
Page : 235 pages
File Size : 44,8 Mb
Release : 2005
Category : Education
ISBN : 089455882X
Author : Theodore A. Sundstrom
Publisher : Prentice Hall
Page : 0 pages
File Size : 42,9 Mb
Release : 2007
Category : Logic, Symbolic and mathematical
ISBN : 0131877186
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 : Doug Brumbaugh,Linda Brumbaugh
Publisher : Unknown
Page : 264 pages
File Size : 54,6 Mb
Release : 2008-03-11
Category : Electronic
ISBN : 1601441827
Author : Linda Brumbaugh,Douglas K. Brumbaugh
Publisher : Unknown
Page : 48 pages
File Size : 51,5 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 1601441975
Author : Gregory Michaelson
Publisher : Springer Nature
Page : 173 pages
File Size : 40,5 Mb
Release : 2021-11-20
Category : Computers
ISBN : 9783030778798
This collection of essays examines the key achievements and likely developments in the area of automated reasoning. In keeping with the group ethos, Automated Reasoning is interpreted liberally, spanning underpinning theory, tools for reasoning, argumentation, explanation, computational creativity, and pedagogy. Wider applications including secure and trustworthy software, and health care and emergency management. The book starts with a technically oriented history of the Edinburgh Automated Reasoning Group, written by Alan Bundy, which is followed by chapters from leading researchers associated with the group. Mathematical Reasoning: The History and Impact of the DReaM Group will attract considerable interest from researchers and practitioners of Automated Reasoning, including postgraduates. It should also be of interest to those researching the history of AI.
Author : Tamara J. Lakins
Publisher : American Mathematical Soc.
Page : 217 pages
File Size : 49,8 Mb
Release : 2016-09-08
Category : General -- Instructional exposition (textbooks, tutorial papers, etc.)
ISBN : 9781470428990
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 : Lyn D. English
Publisher : Routledge
Page : 393 pages
File Size : 53,6 Mb
Release : 2013-04-03
Category : Education
ISBN : 9781136491078
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 : Carolyn Anderson
Publisher : Unknown
Page : 448 pages
File Size : 44,5 Mb
Release : 2013-06-27
Category : Electronic
ISBN : 1601443145
Author : Alina Galvão Spinillo,Síntria Labres Lautert,Rute Elizabete de Souza Rosa Borba
Publisher : Springer Nature
Page : 324 pages
File Size : 46,8 Mb
Release : 2021-05-24
Category : Education
ISBN : 9783030696573
This book adopts an interdisciplinary approach to investigate the development of mathematical reasoning in both children and adults and to show how understanding the learner’s cognitive processes can help teachers develop better strategies to teach mathematics. This contributed volume departs from the interdisciplinary field of psychology of mathematics education and brings together contributions by researchers from different fields and disciplines, such as cognitive psychology, neuroscience and mathematics education. The chapters are presented in the light of the three instances that permeate the entire book: the learner, the teacher, and the teaching and learning process. Some of the chapters analyse the didactic challenges that teachers face in the classroom, such as how to interpret students' reasoning, the use of digital technologies, and their knowledge about mathematics. Other chapters examine students' opinions about mathematics, and others analyse the ways in which students solve situations that involve basic and complex mathematical concepts. The approaches adopted in the description and interpretation of the data obtained in the studies documented in this book point out the limits, the development, and the possibilities of students' thinking, and present didactic and cognitive perspectives to the learning scenarios in different school settings. Mathematical Reasoning of Children and Adults: Teaching and Learning from an Interdisciplinary Perspective will be a valuable resource for both mathematics teachers and researchers studying the development of mathematical reasoning in different fields, such as mathematics education, educational psychology, cognitive psychology, and developmental psychology.
Author : Carlo Cellucci,Donald Gillies
Publisher : College Publications
Page : 252 pages
File Size : 52,5 Mb
Release : 2005
Category : Mathematics
ISBN : UOM:39015063202694
This volume is a collection of papers on philosophy of mathematics which deal with a series of questions quite different from those which occupied the minds of the proponents of the three classic schools: logicism, formalism, and intuitionism. The questions of the volume are not to do with justification in the traditional sense, but with a variety of other topics. Some are concerned with discovery and the growth of mathematics. How does the semantics of mathematics change as the subject develops? What heuristics are involved in mathematical discovery, and do such heuristics constitute a logic of mathematical discovery? What new problems have been introduced by the development of mathematics since the 1930s? Other questions are concerned with the applications of mathematics both to physics and to the new field of computer science. Then there is the new question of whether the axiomatic method is really so essential to mathematics as is often supposed, and the question, which goes back to Wittgenstein, of the sense in which mathematical proofs are compelling. Taking these questions together they give part of an emerging agenda which is likely to carry philosophy of mathematics forward into the twenty first century.
Author : George Polya
Publisher : Lushena Books
Page : 0 pages
File Size : 50,6 Mb
Release : 2023-02-08
Category : Computers
ISBN : 1639235663
This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics". This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can be given, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but no proved until much later. In the same way, solutions to problems can be guessed, and a god guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser."-From the Dust Jacket.
Author : Carolyn Anderson
Publisher : Unknown
Page : 448 pages
File Size : 44,9 Mb
Release : 2011-09-28
Category : Critical thinking
ISBN : 1601442661
Author : Linda Brumbaugh,Douglas K. Brumbaugh
Publisher : Unknown
Page : 48 pages
File Size : 42,8 Mb
Release : 2011-12-19
Category : Analogy
ISBN : 1601441967