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Features fresh approaches and broad coverage of topics especially suitable for high school and the first two years of college. The volumes in this series are an excellent source of enrichment material for teachers and students. Good mathematical reading. The books in this series are paperbound.

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41 results in Anneli Lax New Mathematical Library

Page 1 of 3

The Riemann Hypothesis
  • Roland van der Veen, Jan van de Craats
  • Published by:
    Mathematical Association of America
    Published online:
    26 May 2017
    Print publication:
    01 March 2016
  • The Riemann hypothesis concerns the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 ...Ubiquitous and fundamental in mathematics as they are, it is important and interesting to know as much as possible about these numbers. Simple questions would be: how are the prime numbers distributed among the positive integers? What is the number of prime numbers of 100 digits? Of 1,000 digits? These questions were the starting point of a groundbreaking paper by Bernhard Riemann written in 1859. As an aside in his article, Riemann formulated his now famous hypothesis that so far no one has come close to proving: All nontrivial zeroes of the zeta function lie on the critical line.

    Hidden behind this at first mysterious phrase lies a whole mathematical universe of prime numbers, infinite sequences, infinite products, and complex functions. The present book is a first exploration of this fascinating, unknown world. It originated from an online course for mathematically talented secondary school students organized by the authors of this book at the University of Amsterdam. Its aim was to bring the students into contact with challenging university level mathematics and show them what the Riemann Hypothesis is all about and why it is such an important problem in mathematics.

When Life is Linear
  • From Computer Graphics to Bracketology
  • Tim Chartier
  • Published by:
    Mathematical Association of America
    Published online:
    05 December 2015
    Print publication:
    15 January 2015
  • "Tim Chartier has written the perfect supplement to a linear algebra course. Every major topic is driven by applications, such as computer graphics, cryptography, webpage ranking, sports ranking and data mining. Anyone reading this book will have a clear understanding of the power and scope of linear algebra." Arthur Benjamin, Harvey Mudd College "Not only is it true that "Life Is Linear," as Tim Chartier asserts, but through his engaging style and modern, enticing applications he brings linear algebra to life. This small volume will be a popular read by math fans of all ages and of all backgrounds. Finally we have a little book that focuses on the utility and power of the theorems of linear algebra and makes that exploration joyful." Edward B. Burger, President and Professor, Southwestern University "I'm often asked which areas of mathematics should students study. I always say linear algebra. However, typical linear algebra texts I've seen either have very few applications, or the applications are contrived and not very relevant to students. Chartier's text is a refreshing change as it is driven by real-world applications that are inspiring and familiar to his audience. From Google searches and image processing to sports rankings and (my favorite) computer graphics."Tony DeRose, Pixar Animation Studios From simulating complex phenomenon on supercomputers to storing the coordinates needed in modern 3D printing, data is a huge and growing part of our world. A major tool to manipulate and study this data is linear algebra. When Life is Linear introduces concepts of matrix algebra with an emphasis on application, particularly in the fields of computer graphics and data mining. Readers will learn to make an image transparent, compress an image and rotate a 3D wireframe model. In data mining, readers will use linear algebra to read zip codes on envelopes and encrypt sensitive information. Chartier details methods behind web search, utilized by such companies as Google, and algorithms for sports ranking which have been applied to creating brackets for March Madness and predict outcomes in FIFA World Cup soccer. The book can serve as its own resource or to supplement a course on linear algebra.

Elementary Cryptanalysis
  • A Mathematical Approach
  • 2nd edition
  • Abraham Sinkov
  • Revised by Todd Feil
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 July 2009
  • Originally published in the New Mathematical Library almost half a century ago, this charming book explains how to solve cryptograms based on elementary mathematical principles, starting with the Caesar cipher and building up to progressively more sophisticated substitution methods. Todd Feil has updated the book for the technological age by adding two new chapters covering RSA public-key cryptography, one-time pads, and pseudo-random-number generators. Exercises are given throughout the text that will help the reader understand the concepts and practice the techniques presented. Software to ease the drudgery of making the necessary calculations is made available. The book assumes minimal mathematical prerequisites and therefore explains from scratch such concepts as summation notation, matrix multiplication, and modular arithmetic. Even the mathematically sophisticated reader, however, will find some of the exercises challenging. (Answers to the exercises appear in an appendix.)

Geometric Transformations IV
  • Circular Transformations
  • Circular Transformations
  • I. M. Yaglom
  • Translated by Abe Shenitzer
  • Published by:
    Mathematical Association of America
    Published online:
    26 October 2011
    Print publication:
    30 June 2009
  • The familiar plane geometry of high school - figures composed of lines and circles - takes on a new life when viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries. This book is the concluding Part IV of Geometric Transformations, but it can be studied independently of Parts I, II, and III, which appeared in this series as Volumes 8, 21, and 24. Part I treats the geometry of rigid motions of the plane (isometries); Part II treats the geometry of shape-preserving transformations of the plane (similarities); Part III treats the geometry of transformations of the plane that map lines to lines (affine and projective transformations) and introduces the Klein model of non-Euclidean geometry. The present Part IV develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The notion of inversion, or reflection in a circle, is the key tool employed. Applications include ruler-and-compass constructions and the Poincaré model of hyperbolic geometry. The straightforward, direct presentation assumes only some background in high-school geometry and trigonometry. Numerous exercises lead the reader to a mastery of the methods and concepts. The second half of the book contains detailed solutions of all the problems.

Mathematical Miniatures
  • Svetoslav Savchev, Titu Andreescu
  • Published by:
    Mathematical Association of America
    Published online:
    26 October 2011
    Print publication:
    03 January 2003
  • Mathematical Miniatures is a problem collection of arresting mathematical insight and ingenuity. The authors brought together materials from mathematical competitions, books, research papers, discussions, and their own work. Such mathematical substance went far beyond the purposes of a traditional problem-solving book. The most attractive results refused to fit into the schemes of an instruction manual meant to exemplify typical problem solving techniques. A broader interpretation of these problems had to be identified, and this book is the fruit of that effort. Savchev and Andreescu detach certain statements or groups of related statements into independent sections. Treating these gems separately, in self-contained essays, emphasizes the source of their natural charm---connections with genuine mathematical experience. The essays are of impressive diversity, enlivened by fresh and original ideas. They involve concepts not only useful but also beautiful and nonstandard, with lots of esthetic appeal. The book is thus not so much a mathematical toolchest: it is an anthology of mathematical verse.

Hungarian Problem Book III
  • Based on the Eötvös Competitions 1929-1943
  • Edited and translated by Andy Liu
  • Published by:
    Mathematical Association of America
    Published online:
    05 February 2012
    Print publication:
    15 January 2001
  • The Eötvös Mathematics Competition is the oldest high school mathematics competition in the world, with a tradition dating back to 1894. In 1963, the first two of the Hungarian problem books were published in the New Mathematical Library by the MAA. This book is continuation of those volumes, taking the competition up through 1943. In the Hungarian Problem Book III, forty-five problems in all are presented in six chapters. Problems are classified into five groups: combinatorics, number theory, algebra, and geometry (in two parts). Multiple solutions are presented along with background material providing generalizations and remarks about the problems. This book is intended for beginners, although the experienced student will find much here. Beginners are encouraged to work the problems in each section and then to compare their results against the solutions presented in the book. They will find much material in each section to aid them in improving their problem-solving techniques.

The Contest Problem Book VI
  • American High School Mathematics Examinations 1989-1994
  • Edited by Howard Dorwart, Thomas R. Berger
  • Compiled by Leo J. Schneider
  • Published by:
    Mathematical Association of America
    Published online:
    05 December 2011
    Print publication:
    01 June 2000
  • Contest Problem Book VI chronicles the high school competitions sponsored by the Mathematical Association of America. It contains 180 challenging problems from the six years of the American High School Mathematics Examination [AHSME], 1989 through 1994, as well as a selection of other problems. Many problem solving techniques for problems in this book show alternative approaches that appear in print for the first time. Some aspects of mathematical problem solving unique to competitions is discussed. Useful tools are selected from important areas of high school mathematics. A Problems Index classified the 180 problems in the book into subject areas: Algebra (with 65 subclasses), Complex Numbers (with 11 subclasses), Discrete Mathematics (with 20 subclasses), Geometry (with 43 subclasses), Number Theory (with 24 subclasses), Statistics (with 5 subclasses), and Trigonometry (with 12 subclasses). Many subclasses have sub-subclasses, some with over a dozen. The Pigeon Hole Principle proves that some problems must appear in more than one class. That, in fact, is the case! Outstanding problems combine elementary techniques from diverse areas of mathematics, occasionally three or more. You will find many of them here.

The Geometry of Numbers
  • C. D. Olds, Anneli Lax, Giuliana P. Davidoff
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 January 2000
  • The Geometry of Numbers presents a self-contained introduction to the geometry of numbers, beginning with easily understood questions about lattice-points on lines, circles, and inside simple polygons in the plane. Little mathematical expertise is required beyond an acquaintance with those objects and with some basic results in geometry. The reader moves gradually to theorems of Minkowski and others who succeeded him. On the way, he or she will see how this powerful approach gives improved approximations to irrational numbers by rationals, simplifies arguments on ways of representing integers as sums of squares, and provides a natural tool for attacking problems involving dense packings of spheres. An appendix by Peter Lax gives a lovely geometric proof of the fact that the Gaussian integers form a Euclidean domain, characterizing the Gaussian primes, and proving that unique factorization holds there. In the process, he provides yet another glimpse into the power of a geometric approach to number theoretic problems.

Episodes from the Early History of Mathematics
  • Asger Aaboe
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 January 1998
  • Among other things, Aaboe shows us how the Babylonians did calculations, how Euclid proved that there are infinitely many primes, how Ptolemy constructed a trigonometric table in his Almagest, and how Archimedes trisected the angle. Some of the topics may be familiar to the reader, while others will seem surprising or be new.

The Contest Problem Book V
  • American High School Mathematics Examinations and American Invitational Mathematics Examinations 1983-1988
  • Compiled by George Berzsenyi, Stephen B. Maurer
  • Published by:
    Mathematical Association of America
    Published online:
    05 December 2011
    Print publication:
    01 June 1997
  • Over the years perhaps the most popular of the MAA problem books have been the high school contest books, covering the yearly American High Mathematics Examinations (AHSME) that began in 1950, co-sponsored from the start by the MAA. Book V also includes the first six years of the American Invitational Mathematics Examination (AIME) which was developed as an intermediate step between the AHSME and the USA Mathematical Olympiad (USAMO). The AIME has a unique answer format-all answers are integers between 0 and 999. The editors of this volume, George Berzsenyi and Stephen B. Maurer, were respectively the chair of the AIME and the AHSME during this period. In addition to a thorough index, they have added much material not included in Contest Books I-IV: a comprehensive guide to other problem materials world wide, additional solutions, dropped problems, statistical information, and information on test development and history. This is a must volume for avid fans of elementary problems, young and old.

Over and Over Again
  • Gengzhe Chang, Thomas W. Sederberg
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1997
  • Suitable as supplemental reading in courses in differential and integral calculus, numerical analysis, approximation theory and computer-aided geometric design. Relations of mathematical objects to each other are expressed by transformations. The repeated application of a transformation over and over again, i.e., its iteration leads to solution of equations, as in Newton's method for finding roots, or Picard's method for solving differential equations. This book studies a treasure trove of iterations, in number theory, analysis and geometry, and applied them to various problems, many of them taken from international and national Mathematical Olympiad competitions. Among topics treated are classical and not so classical inequalities, Sharkovskii's theorem, interpolation, Bernstein polynomials, BŽzier curves and surfaces, and splines. Most of the book requires only high school mathematics; the last part requires elementary calculus. This book would be an excellent supplement to courses in calculus, differential equations,, numerical analysis, approximation theory and computer-aided geometric design.

Episodes in Nineteenth and Twentieth Century Euclidean Geometry
  • Ross Honsberger
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 January 1995
  • Euclidean geometry was worked out by Euclid and his predecessors more than 2300 years ago and is studied today mostly as a background to other branches of mathematics. In fact, however, as Professor Honsberger masterfully demonstrates, geometry in the style of Euclid is still alive and well. Mathematicians have again been studying the properties of geometric figures from a synthetic point of view and have discovered many new and unexpected results which Euclid himself never found. And since all of us have studied Euclidean geometry, at least the ancient version, this book is easily accessible. Exercises with their solutions are included in the book.

Groups and Their Graphs
  • Israel Grossman, Wilhelm Magnus
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 January 1992
  • The abstract nature of group theory makes its exposition, at an elementary level, difficult. The authors of the present volume have overcome this obstacle by leading the reader slowly from the concrete to the abstract, from the simple to the complex, employing effectively graphs or Cayley diagrams to hlep the student visualize some of the structural properties of groups. Among the concrete examples of groups, the authors include groups of congruence motions and groups of permutations. A conscientious reader will acquire a good intuitive grasp of this pwerful subject.

Graphs and Their Uses
  • Oystein Ore
  • Revised by Robin J. Wilson
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1990
  • In 1963 Oystein Ore wrote this classic volume, which was published in the New Mathematical Library Series. This elegant book has provided students and teachers with an excellent introduction to the field of graph theory for close to thirty years. Robin Wilson's revision adds strength to the book by updating the terminology and notation, bringing them in line with contemporary usage. Wilson has added new material on interval graphs, the traveling salesman problem, bracing frameworks, shortest route problems, and coloring maps on surfaces. Most of the diagrams in the book have been redrawn.

Riddles of the Sphinx
  • Martin Gardner
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1987
  • This material was drawn from Gardner's column in Issac Asimov's Science Fiction Magazine. His riddles presented here incorporate the responses of his initial readers, along with additions suggested by the editors of this series. In this book, Gardner draws us from questions to answers, always presenting us with new riddles-some as yet unanswered. Solving these riddles is not simply a matter of logic and calculation, though these play a role. Luck and inspiration are factors as well, so beginners and experts alike may profitably exercise their wits on Gardner's problems, whose subjects range from geometry to word play to questions relating to physics and geology. We guarantee that you will solve some of these riddles, be stumped by others and be amused by almost all of the stories and setting that Gardner has devised to raise these as yet unanswered. Only Gardner could fit so many diverse and tantalizing problems into one book.

International Mathematical Olympiads 1978-1985
  • And Forty Supplementary Problems
  • Compiled by Murray S. Klamkin
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1986
  • This title is the sequel to NML27 International Mathematical Olympiads, 1959–1977. International Mathematical Olympiads 1978–1985 is a compilation of 116 problems of arresting ingenuity given to high school students competing in the International Mathematical Olympiads. All are accessible to secondary school students. The alternative solutions are particularly interesting because they show that there are many ways to solve a problem.

The Role of Mathematics in Science
  • M. M. Schiffer, Leon Bowden
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1984
  • The Role of Mathematics in Science aims to illustrate the many ways in which mathematical methods have helped discovery in science. It is aimed at a group of readers who are interested in mathematics beyond the level of high school. The authors occasionally use some calculus and more intricate arguments. The book should appeal to college students and general readers with some background in mathematics. The authors state that, 'If we succeed in giving an impression of the beauty and power of mathematical reasoning in science, the purpose of our work will have been achieved.' This book includes the laws of levers and inclined planes, the laws of exponential versus limited population growth, ray optics, and relativity.

The Contest Problem Book IV
  • Annual High School Examinations 1973-1982
  • Compiled by Ralph A. Artino, Anthony M. Gaglione, Niel Shell
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1982
  • The Annual High School Mathematics Examination (AHSME) began as a local contest in New York City in 1950. By 1960, 150,000 students throughout the United States and Canada took the AHSME. The 1982 Examination was administered to 418,000 participants in the United States and Canada and to 20,000 students in various countries of other continents. In the United States and Canada, one use of AHSME is to select approximately one hundred participants in the U.S.A. Mathematical Olympiad, and the Olympiads are used in the selection of a student team to represent the United States in the International Mathematical Olympiad. Since the difficulty of problems appearing in the AHSME varies over a wide range, they are a valuable teaching aid for all high school students interested in mathematics.

International Mathematical Olympiads 1959-1977
  • Compiled by Samuel L. Greitzer
  • Published by:
    Mathematical Association of America
    Published online:
    05 February 2012
    Print publication:
    01 June 1978
  • Every year 100 of the most mathematically talented high school students in the country compete in the USA Mathematical Olympiad (USAMO). The USAMO is the third stage of a three-tiered mathematical competition for high school students in the United States and Canada that begins with the AHSME taken by over 400,000 students, continues with the American Invitational Mathematics Exam involving 2,000 students, and culminates with the 100-contestant USAMO. Winners of the USAMO go on to compete in the International Mathematical Olympiad. Compilation of 116 problems of arresting ingenuity given to high school students competing in the International Mathematical Olympiads. All are accessible to secondary school students. The alternative solutions are particularly interesting because they show that there are many ways to solve a problem.

Mathematical Methods in Science
  • George Pólya
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 January 1977
  • If you have ever wondered how the laws of nature were worked out mathematically, this is the book for you. Above all, it captures some of Pólya's excitement and vision.

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