Author: Stephen Abbott
Publisher: Springer Science & Business Media
ISBN: 0387215069
Category : Mathematics
Languages : en
Pages : 269
Get Book
Book Description
This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.
Author: Stephen Abbott
Publisher: KBookstore
ISBN: 1441928669
Category : Mathematics
Languages : en
Pages : 160
Get Book
Book Description
This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.
Author: Stephen Abbott
Publisher: Springer Science & Business Media
ISBN: 9780387950600
Category : Mathematics
Languages : en
Pages : 284
Get Book
Book Description
This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.
Author: Paul Zorn
Publisher: CRC Press
ISBN: 1315315076
Category : Mathematics
Languages : en
Pages : 336
Get Book
Book Description
Understanding Real Analysis, Second Edition offers substantial coverage of foundational material and expands on the ideas of elementary calculus to develop a better understanding of crucial mathematical ideas. The text meets students at their current level and helps them develop a foundation in real analysis. The author brings definitions, proofs, examples and other mathematical tools together to show how they work to create unified theory. These helps students grasp the linguistic conventions of mathematics early in the text. The text allows the instructor to pace the course for students of different mathematical backgrounds. Key Features: Meets and aligns with various student backgrounds Pays explicit attention to basic formalities and technical language Contains varied problems and exercises Drives the narrative through questions
Author: Nicholas H. Wasserman
Publisher: Springer Nature
ISBN: 3030891984
Category : Education
Languages : en
Pages : 226
Get Book
Book Description
Getting certified to teach high school mathematics typically requires completing a course in real analysis. Yet most teachers point out real analysis content bears little resemblance to secondary mathematics and report it does not influence their teaching in any significant way. This textbook is our attempt to change the narrative. It is our belief that analysis can be a meaningful part of a teacher's mathematical education and preparation for teaching. This book is a companion text. It is intended to be a supplemental resource, used in conjunction with a more traditional real analysis book. The textbook is based on our efforts to identify ways that studying real analysis can provide future teachers with genuine opportunities to think about teaching secondary mathematics. It focuses on how mathematical ideas are connected to the practice of teaching secondary mathematics–and not just the content of secondary mathematics itself. Discussions around pedagogy are premised on the belief that the way mathematicians do mathematics can be useful for how we think about teaching mathematics. The book uses particular situations in teaching to make explicit ways that the content of real analysis might be important for teaching secondary mathematics, and how mathematical practices prevalent in the study of real analysis can be incorporated as practices for teaching. This textbook will be of particular interest to mathematics instructors–and mathematics teacher educators–thinking about how the mathematics of real analysis might be applicable to secondary teaching, as well as to any prospective (or current) teacher who has wondered about what the purpose of taking such courses could be.
Author: David Bressoud
Publisher: American Mathematical Society
ISBN: 1470469049
Category : Mathematics
Languages : en
Pages : 339
Get Book
Book Description
In this second edition of the MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on Infinite Summations, Differentiability and Continuity, and Convergence of Infinite Series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created. The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early 19th century. It follows Cauchy's attempts to establish a firm foundation for calculus and considers his failures as well as his successes. It culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof.
Author: Kenneth A. Ross
Publisher: CUP Archive
ISBN:
Category : Mathematics
Languages : en
Pages : 192
Get Book
Book Description
Author: Charles Chapman Pugh
Publisher: Springer Science & Business Media
ISBN: 0387216847
Category : Mathematics
Languages : en
Pages : 445
Get Book
Book Description
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.
Author: Ho-Won Jeong
Publisher: SAGE
ISBN: 1849206406
Category : Political Science
Languages : en
Pages : 282
Get Book
Book Description
′...effectively fills a long-standing void and will no doubt be hailed as a much-needed new addition to the literature... This text very much exemplifies the strength of Ho-Won Jeong as a theorist and one of the more prolific writers in the larger peace and conflict studies field... the final three chapters on ′De-escalation Dynamics′ (which includes a brief section on third party intervention), on ′Conciliation Strategies,′ and especially the one on ′Ending Conflict,′ which provides a range of outcomes beyond the usual focus on third party intervention (read mediation) epitomizes the value of this new text′ - Journal of Peace Research ′...an awesome tour d′horizon of modern war, violence, and confrontation within and between nations. Illustrating via just about every conflict in every corner of the world, the author invokes an endless array of insights and interpretations, ranging from the micro to the macro, beautifully written in a seamless sequence of closely linked and discursive essays.′ - Professor J. David Singer, University of Michigan ′Ho-Won Jeong has written an illuminatinbg analysis of the dynamics of conflict. He lays out the tools we have to analyze conflict in a literate and comprehensive way. A valuable book for anyone interested in a more comprehensive understanding of conflict, its sources, and its deescalation and termination′ - Janice Gross Stein, Belzberg Professor of Conflict Management, Director, Munk Centre for International Studies, University of Toronto ′Jeong has successfully combined behavioral and structural analysis of the dynamics of social conflict. This volume covers the multiple dimensions - escalation, entrapment, de-escalation, termination, and resolution - both of violent and non-violent confrontation between adversaries, as well as the utility and limitations of external intervention. For students of the social sciences, it should serve as an excellent introduction to the complex realities of social conflict.′ - Milton Esman, John S. Knight Professor of International Studies, Emeritus, Cornell University By examining the dynamic forces which shape and re-shape major conflicts, this timely book provides students with the knowledge base needed to successfully study conflict sources, processes and transformations. Broad in focus, it addresses the multiple social, political and psychological features central to understanding conflict situations and behaviour. A range of both recent and historical examples (including the Arab-Israeli conflict, the ′War on Terrorism′, the Cold War, and the civil wars in Sudan, former Yugoslavia and Sri Lanka) are discussed, illustrating the application of concepts and theories essential to the analysis of inter-group, inter-state and intra-state conflict and conflict resolution in a wider context. Understanding Conflict and Conflict Analysis is key reading for students of international relations, peace and conflict studies, conflict resolution, international security and international law.
Author: Robert Bruhl
Publisher: SAGE Publications
ISBN: 1506317375
Category : Social Science
Languages : en
Pages : 320
Get Book
Book Description
Understanding Statistical Analysis and Modeling is a text for graduate and advanced undergraduate students in the social, behavioral, or managerial sciences seeking to understand the logic of statistical analysis. Robert Bruhl covers all the basic methods of descriptive and inferential statistics in an accessible manner by way of asking and answering research questions. Concepts are discussed in the context of a specific research project and the book includes probability theory as the basis for understanding statistical inference. Instructions on using SPSS® are included so that readers focus on interpreting statistical analysis rather than calculations. Tables are used, rather than formulas, to describe the various calculations involved with statistical analysis and the exercises in the book are intended to encourage students to formulate and execute their own empirical investigations.
