πŸ“’ Author : Sergiy Klymchuk
πŸ“’ Publisher : MAA
πŸ“’ Release Date : 2010
πŸ“’ Pages : 101
πŸ“’ ISBN : 9780883857656
πŸ“’ Available Language : English, Spanish, And French
πŸ“’ Category : Mathematics

SYNOPSIS : Originally published: New Zealand: Maths Press, 2004.


πŸ“’ Author : John Mason
πŸ“’ Publisher :
πŸ“’ Release Date : 2009
πŸ“’ Pages : 98
πŸ“’ ISBN : 1848163592
πŸ“’ Available Language : English, Spanish, And French
πŸ“’ Category : Mathematics

SYNOPSIS : This book makes accessible to calculus students in high school, college and university a range of counter-examples to β€œconjectures” that many students erroneously make. In addition, it urges readers to construct their own examples by tinkering with the ones shown here in order to enrich the example spaces to which they have access, and to deepen their appreciation of conspectus and conditions applying to theorems.


πŸ“’ Author : Andrei Bourchtein
πŸ“’ Publisher : CRC Press
πŸ“’ Release Date : 2014-09-09
πŸ“’ Pages : 362
πŸ“’ ISBN : 9781482246674
πŸ“’ Available Language : English, Spanish, And French
πŸ“’ Category : Mathematics

SYNOPSIS : This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. The book encourages students to think critically and analytically, and helps to reveal common errors in many examples. In this book, the authors present an overview of important concepts and results in calculus and real analysis by considering false statements, which may appear to be true at first glance. The book covers topics concerning the functions of real variables, starting with elementary properties, moving to limits and continuity, and then to differentiation and integration. The first part of the book describes single-variable functions, while the second part covers the functions of two variables. The many examples presented throughout the book typically start at a very basic level and become more complex during the development of exposition. At the end of each chapter, supplementary exercises of different levels of complexity are provided, the most difficult of them with a hint to the solution. This book is intended for students who are interested in developing a deeper understanding of the topics of calculus. The gathered counterexamples may also be used by calculus instructors in their classes.


πŸ“’ Author : Sergiy Klymchuk
πŸ“’ Publisher : MAA
πŸ“’ Release Date : 2013
πŸ“’ Pages : 98
πŸ“’ ISBN : 9780883857816
πŸ“’ Available Language : English, Spanish, And French
πŸ“’ Category : Mathematics

SYNOPSIS : Paradoxes and Sophisms in Calculus offers a delightful supplementary resource to enhance the study of single variable calculus. By the word paradox the authors mean a surprising, unexpected, counter-intuitive statement that looks invalid, but in fact is true. The word sophism describes intentionally invalid reasoning that looks formally correct, but in fact contains a subtle mistake or flaw. In other words, a sophism is a false proof of an incorrect statement. A collection of over fifty paradoxes and sophisms showcases the subtleties of this subject and leads students to contemplate the underlying concepts. A number of the examples treat historically significant issues that arose in the development of calculus, while others more naturally challenge readers to understand common misconceptions. Sophisms and paradoxes from the areas of functions, limits, derivatives, integrals, sequences, and series are explored. The book could be useful for high school teachers and university faculty as a teaching resource; high school and college students as a learning resource; and a professional development resource for calculus instructors.


πŸ“’ Author : Bernard R. Gelbaum
πŸ“’ Publisher : Courier Corporation
πŸ“’ Release Date : 2012-07-12
πŸ“’ Pages : 224
πŸ“’ ISBN : 9780486134918
πŸ“’ Available Language : English, Spanish, And French
πŸ“’ Category : Mathematics

SYNOPSIS : These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.


πŸ“’ Author : Andrei Bourchtein
πŸ“’ Publisher : John Wiley & Sons
πŸ“’ Release Date : 2017-01-17
πŸ“’ Pages : 272
πŸ“’ ISBN : 9781119303404
πŸ“’ Available Language : English, Spanish, And French
πŸ“’ Category : Mathematics

SYNOPSIS : A comprehensive and thorough analysis of concepts and results on uniform convergence Counterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals presents counterexamples to false statements typically found within the study of mathematical analysis and calculus, all of which are related to uniform convergence. The book includes the convergence of sequences, series and families of functions, and proper and improper integrals depending on a parameter. The exposition is restricted to the main definitions and theorems in order to explore different versions (wrong and correct) of the fundamental concepts and results. The goal of the book is threefold. First, the authors provide a brief survey and discussion of principal results of the theory of uniform convergence in real analysis. Second, the book aims to help readers master the presented concepts and theorems, which are traditionally challenging and are sources of misunderstanding and confusion. Finally, this book illustrates how important mathematical tools such as counterexamples can be used in different situations. The features of the book include: An overview of important concepts and theorems on uniform convergence Well-organized coverage of the majority of the topics on uniform convergence studied in analysis courses An original approach to the analysis of important results on uniform convergence based\ on counterexamples Additional exercises at varying levels of complexity for each topic covered in the book A supplementary Instructor’s Solutions Manual containing complete solutions to all exercises, which is available via a companion website Counterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals is an appropriate reference and/or supplementary reading for upper-undergraduate and graduate-level courses in mathematical analysis and advanced calculus for students majoring in mathematics, engineering, and other sciences. The book is also a valuable resource for instructors teaching mathematical analysis and calculus. ANDREI BOURCHTEIN, PhD, is Professor in the Department of Mathematics at Pelotas State University in Brazil. The author of more than 100 referred articles and five books, his research interests include numerical analysis, computational fluid dynamics, numerical weather prediction, and real analysis. Dr. Andrei Bourchtein received his PhD in Mathematics and Physics from the Hydrometeorological Center of Russia. LUDMILA BOURCHTEIN, PhD, is Senior Research Scientist at the Institute of Physics and Mathematics at Pelotas State University in Brazil. The author of more than 80 referred articles and three books, her research interests include real and complex analysis, conformal mappings, and numerical analysis. Dr. Ludmila Bourchtein received her PhD in Mathematics from Saint Petersburg State University in Russia.


πŸ“’ Author : Chris Sangwin
πŸ“’ Publisher : OUP Oxford
πŸ“’ Release Date : 2013-05-02
πŸ“’ Pages : 200
πŸ“’ ISBN : 9780191635861
πŸ“’ Available Language : English, Spanish, And French
πŸ“’ Category : Mathematics

SYNOPSIS : Assessment is a key driver in mathematics education. This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to establish the mathematical properties of expressions provided by students in response to questions. In order to automate such assessment, the relevant criteria must be encoded and, in articulating precisely the desired criteria, the teacher needs to think very carefully about the goals of the task. Hence CAA acts as a vehicle to examine assessment and mathematics education in detail and from a fresh perspective. One example is how it is natural for busy teachers to set only those questions that can be marked by hand in a straightforward way, even though the constraints of paper-based formats restrict what they do and why. There are other kinds of questions, such as those with non-unique correct answers, or where assessing the properties requires the marker themselves to undertake a significant computation. It is simply not sensible for a person to set these to large groups of students when marking by hand. However, such questions have their place and value in provoking thought and learning. This book, aimed at teachers in both schools and universities, explores how, in certain cases, different question types can be automatically assessed. Case studies of existing systems have been included to illustrate this in a concrete and practical way.


πŸ“’ Author : Louis Brand
πŸ“’ Publisher : Courier Corporation
πŸ“’ Release Date : 2013-10-10
πŸ“’ Pages : 608
πŸ“’ ISBN : 9780486157993
πŸ“’ Available Language : English, Spanish, And French
πŸ“’ Category : Mathematics

SYNOPSIS : A course in analysis that focuses on the functions of a real variable, this text introduces the basic concepts in their simplest setting and illustrates its teachings with numerous examples, theorems, and proofs. 1955 edition.


πŸ“’ Author : Robert E. Gompf
πŸ“’ Publisher : American Mathematical Soc.
πŸ“’ Release Date : 1999
πŸ“’ Pages : 558
πŸ“’ ISBN : 9780821809945
πŸ“’ Available Language : English, Spanish, And French
πŸ“’ Category : Mathematics

SYNOPSIS : Since the early 1980s, there has been an explosive growth in 4-manifold theory, particularly due to the influx of interest and ideas from gauge theory and algebraic geometry. This book offers an exposition of the subject from the topological point of view. It bridges the gap to other disciplines and presents classical but important topological techniques that have not previously appeared in the literature. Part I of the text presents the basics of the theory at the second-year graduate level and offers an overview of current research. Part II is devoted to an exposition of Kirby calculus, or handlebody theory on 4-manifolds. It is both elementary and comprehensive. Part III offers in-depth treatments of a broad range of topics from current 4-manifold research. Topics include branched coverings and the geography of complex surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces. The authors present many important applications. The text is supplemented with over 300 illustrations and numerous exercises, with solutions given in the book. I greatly recommend this wonderful book to any researcher in 4-manifold topology for the novel ideas, techniques, constructions, and computations on the topic, presented in a very fascinating way. I think really that every student, mathematician, and researcher interested in 4-manifold topology, should own a copy of this beautiful book. --Zentralblatt MATH This book gives an excellent introduction into the theory of 4-manifolds and can be strongly recommended to beginners in this field ... carefully and clearly written; the authors have evidently paid great attention to the presentation of the material ... contains many really pretty and interesting examples and a great number of exercises; the final chapter is then devoted to solutions of some of these ... this type of presentation makes the subject more attractive and its study easier. --European Mathematical Society Newsletter


πŸ“’ Author : Stephen Cole Kleene
πŸ“’ Publisher : Courier Corporation
πŸ“’ Release Date : 2013-04-22
πŸ“’ Pages : 416
πŸ“’ ISBN : 9780486317076
πŸ“’ Available Language : English, Spanish, And French
πŸ“’ Category : Mathematics

SYNOPSIS : Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including GΓΆdel's completeness theorem, Gentzen's theorem, more.