Book Description
Concerned with the logical foundations of number systems from integers to complex numbers.
Author : Keith Hirst
Publisher : Butterworth-Heinemann
Page : 213 pages
File Size : 48,10 MB
Release : 1994-12-08
Category : Mathematics
ISBN : 0340610433
Concerned with the logical foundations of number systems from integers to complex numbers.
Author : Konrad Knopp
Publisher :
Page : 596 pages
File Size : 49,78 MB
Release : 1928
Category : Series, Infinite
ISBN :
Trans from the 2nd German ed , pub 1923.
Author : Daniel D. Bonar
Publisher : American Mathematical Soc.
Page : 278 pages
File Size : 37,8 MB
Release : 2018-12-12
Category : Mathematics
ISBN : 1470447827
This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series.
Author : Konrad Knopp
Publisher : Courier Corporation
Page : 212 pages
File Size : 31,53 MB
Release : 2012-09-14
Category : Mathematics
ISBN : 0486152049
Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.
Author : Herbert S. Wilf
Publisher : Elsevier
Page : 193 pages
File Size : 17,16 MB
Release : 2014-05-10
Category : Mathematics
ISBN : 1483276635
Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.
Author : Bharath Sriraman
Publisher : IAP
Page : 502 pages
File Size : 42,47 MB
Release : 2009-06-01
Category : Mathematics
ISBN : 1607522187
The word "critical" in the title of this collection has three meanings, all of which are relevant. One meaning, as applied to a situation or problem, is "at a point of crisis". A second meaning is "expressing adverse or disapproving comments or judgments". A third is related to the verb "to critique", meaning "to analyze the merits and faults of". The authors contributing to this book pose challenging questions, from multiple perspectives, about the roles of mathematics in society and the implications for education. Traditional reasons for teaching mathematics include: preparing a new generation of mathematics researchers and a cadre of technically competent users of mathematics; training students to think logically; and because mathematics is as much part of cultural heritage as literature or music. These reasons remain valid, though open to critique, but a deeper analysis is required that recognizes the roles of mathematics in framing many aspects of contemporary society, that will connect mathematics education to the lived experiences of students, their communities, and society in general, and that acknowledges the global ethical responsibilities of mathematicians and mathematics educators. The book is organized in four sections (1) Mathematics education: For what and why? (2) Globalization and cultural diversity, (3) Mathematics, education, and society and (4) Social justice in, and through, mathematics education The chapters address fundamental issues such as the relevance of school mathematics in people's lives; creating a sense of agency for the field of mathematics education, and redefining the relationship between mathematics as discipline, mathematics as school subject and mathematics as part of people's lives.
Author : Walter G. Kelley
Publisher : Academic Press
Page : 418 pages
File Size : 23,35 MB
Release : 2001
Category : Mathematics
ISBN : 9780124033306
Difference Equations, Second Edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics. Phase plane analysis for systems of two linear equations Use of equations of variation to approximate solutions Fundamental matrices and Floquet theory for periodic systems LaSalle invariance theorem Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory Appendix on the use of Mathematica for analyzing difference equaitons Exponential generating functions Many new examples and exercises
Author : Kristine K. Fowler
Publisher : CRC Press
Page : 412 pages
File Size : 34,85 MB
Release : 2004-05-25
Category : Language Arts & Disciplines
ISBN : 9780824750350
This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.
Author : James M Hyslop
Publisher : Courier Corporation
Page : 146 pages
File Size : 45,19 MB
Release : 2012-05-11
Category : Mathematics
ISBN : 0486154858
This concise text focuses on the convergence of real series. Topics include functions and limits, real sequences and series, series of non-negative terms, general series, series of functions, the multiplication of series, more. 1959 edition.
Author : Cornel Ioan Vălean
Publisher : Springer
Page : 572 pages
File Size : 26,94 MB
Release : 2019-05-10
Category : Mathematics
ISBN : 3030024628
This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series.