Series: Universitext
2008, Approx. 410 p. 300 illus., Softcover
ISBN: 978-0-387-78240-9
Due: July 2008
About this textbook
Many unique topics are covered, such as fractals and cycloids
Author uses a non-traditional approach (he defines a right angle by using the Pythagorean theorem)
This is a book on Euclidean geometry that covers the standard material in a completely new way, while also introducing a number of new topics that would be suitable as a junior-senior level undergraduate textbook. The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry while at the same time giving the student tools that will be useful in other courses.
Table of contents
Preface.- Plane Geometry.- Transformations.- Symmetry.- Curves.- Solid Geometry.- Appendix.- References.- Index.
2008, Approx. 430 p. 3 illus., Hardcover
ISBN: 978-0-387-77765-8
Due: July 2008
About this book
In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated gRamanujan's lost notebook.h Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. The "lost notebook" contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work. Mathematicians are probably several decades away from a complete understanding of those functions. More than half of the material in the book is on q- series, including mock theta functions; the remaining part deals with theta function identities, modular equations, incomplete elliptic integrals of the first kind and other integrals of theta functions, Eisenstein series, particular values of theta functions, the Rogers- Ramanujan continued fraction, other q-continued fractions, other integrals, and parts of Hecke's theory of modular forms.
Table of contents
Preface.- Introduction.- The Heine transformation.- The Sears-thomae transformation.- Bilateral series.- Well-poised series.- Bailey's lemma and theta expansions.- Partial theta functions.- Special identities.- Theta function identities.- Ramanujan's cubic analogue of the classical ramanujan-weber class invariants.- Miscellaneous results on elliptic functions and theta functions.- Formulas for the power series cofficients of certain quotients of eisenstein series.- Two letters on eisenstein series written from matlock house.- Eisenstein series and modular equations.- Series representable in terms of eisenstein series.- Eisenstein series and approximations to p.- Miscellaneous results on eisenstein series.- Location guide.- Provenance.- References.- Index.-
2008, CXLII, 6 p. 33 illus., Dustjacket
ISBN: 978-0-387-78129-7
Due: July 2008
About this book
Chance continues to govern our lives in the 21st Century. From the genes we inherit and the environment into which we are born, to the lottery ticket we buy at the local store, much of life is a gamble. In business, education, travel, health, and marriage, we take chances in the hope of obtaining something better. Chance colors our lives with uncertainty, and so it is important to examine it and try to understand about how it operates in a number of different circumstances. Such understanding becomes simpler if we take some time to learn a little about probability, since probability is the natural language of uncertainty.
This second edition of Chance Rules again recounts the story of chance through history and the various ways it impacts on our lives. Here you can read about the earliest gamblers who thought that the fall of the dice was controlled by the gods, as well as the modern geneticist and quantum theory researcher trying to integrate aspects of probability into their chosen speciality. Example included in the first addition such as the infamous Monty Hall problem, tossing coins, coincidences, horse racing, birthdays and babies remain, often with an expanded discussion, in this edition. Additional material in the second edition includes, a probabilistic explanation of why things were better when you were younger, consideration of whether you can use probability to prove the existence of God, how long you may have to wait to win the lottery, some court room dramas, predicting the future, and how evolution scores over creationism. Chance Rules lets you learn about probability without complex mathematics.
Table of contents
A brief history of chance - What are the chances? assigning probabilities - Choice and chance: permutations and combinations - Tossing coins and having babies - Rolling dice - Gambling for fun: lotteries and football pools - Serious gambling: roulette, cards and horse racing - Balls, birthdays and coincidences - Conditional probability and the Reverend Thomas Bayes - Puzzling probabilities - Taking risks - Statistics, statisticians and medicine - Alternative therapies: panaceas or placebos.
Series: Science Networks. Historical Studies , Vol. 36
2008, Approx. 350 p., Hardcover
ISBN: 978-3-7643-8744-0
Due: July 2008
About this book
Japanese mathematics, known also under the name of wasan, experienced a remarkable development between the seventeenth and nineteenth centuries. Wasan took its roots from the Chinese tradition of mathematics and shared its language and its categories of problems, but gave it a new impetus, transforming the Chinese algebraic method of the "heavenly element" into a powerful tool with a much wider scope. All domains of mathematical research were revisited in the light of this new algebra.
This book focuses on the first period of the development of wasan. It offers a survey of the earliest manuals for learning the use of the abacus published in the seventeenth century, notably the famous Jinkoki, which counted among the bestsellers of the Tokugawa period. The works of the two greatest mathematicians of this period, Seki Takakazu and Takebe Katahiro, and the way they transformed the face of mathematics, are examined in detail, with particular emphasis on the historical context, the relations between these two mathematicians and the political leaders of the epoch, and the role that mathematics played in this rapidly rising society.
Table of contents
From the contents: The Jinkoki (1627) by Yoshida Mitsuyoshi.- The Jugairoku (1639) by Imamura Tomoaki.- The Sanso (1663) by Muramatsu Shigekiyo.- The Treatise of Ancient and Modern Mathematics (1671) by Yoshida Mitsuyoshi.- Seki Takakazu (?-1708) and his epoch.- Seki Takakazu's works on techniques of problem-solving.- The career of Takebe Katahiro as advisor of the shogun.- Takebe's works in trigonometry.
Originally published by Hemisphere Publishing Company, 1987. ISBN: 978-0891165736.
2009, XX, 700 p. 330 illus., 70 in color., Hardcover
ISBN: 978-0-387-48806-6
Due: October 2008
About this atlas
Modernized and upgraded edition of a valuable reference work first published in 1987
Uses the language of mathematics that is common to all branches of science and engineering
Print volume includes the inclusion of innovative software--Equator, the Atlas Function Calculator. This software obviates the need for tables or programming to find numerical values (once installed onto your Windows XP based PC, this unique function calculator instantly generates precise function values on demand)
This second edition of An Atlas of Functions provides comprehensive information on several hundred functions or function families, of interest to all those scientists, engineers and mathematicians who are concerned with the quantitative aspects of their field. Beginning with simple integer-valued functions, the book progresses to polynomials, exponential, trigonometric, Bessel, and hypergeometric functions, as well as many more. The 65 chapters are arranged roughly in order of increasing complexity, mathematical sophistication being kept to a minimum while utility is stressed throughout. In addition to providing definitions and simple properties for every function, each chapter catalogs more complex interrelationships as well as the derivatives, integrals, Laplace transforms and other characteristics of the function. Numerous color figures in 2 or 3 dimensions depict their shape and qualitative features and flesh out the readerfs familiarity with the functions. In many instances, the chapter concludes with a concise exposition on a topic in applied mathematics associated with the particular function or function family.
Features that make the Atlas an invaluable reference tool, yet simple to use, include:
full coverage of those functions?elementary and "specialh?that meet everyday needs
a standardized chapter format, making it easy to locate needed information on such aspects as: nomenclature, general behavior, definitions, intrarelationships, expansions, approximations, limits, and response to operations of the calculus
extensive cross-referencing and comprehensive indexing, with useful appendices
the inclusion of Equator obviates the need for tables or programming to find numerical values
the inclusion of innovative software--Equator, the Atlas Function Calculator--on a CD with the print book obviating the need for tables or programming to find numerical values (once installed onto your Windows XP based PC, this unique function calculator instantly generates precise function values on demand)
the inclusion of new material dealing with interesting applications of many of the function families, building upon the favorable responses to similar material in the first edition.