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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.

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.

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 I
  • Annual High School Mathematics Examinations 1950-1960
  • Compiled by Charles T. Salkind
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1961
  • The annual high school contests have been sponsored since 1950 by the Mathematical Association of America and the Society of Actuaries, and more recently by Mu Alpha Theta (1965), the National Council of Teachers of Mathematics (1967) and the Casulty Actuarial Society (1971). Problems from the contests during the periods 1950-1960 are published in Volume 5 of the New Mathematical Library, and those for 1966-1972 are published in Volume 25. This volume contains those for the period 1961-1965. The questions were compiled by C.T. Salkind, Chairman of the Committee on High School Contests during the period, who also prepared the solutions for the contest problems. Professor Salkind died in 1968. In preparing this and the other Contest Problem Books, the editors of the NML have expanded these solutions with added alternative solutions.

The Contest Problem Book II
  • Annual High School Contests 1961-1965
  • Compiled by Charles T. Salkind
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1966
  • The annual high school contests have been sponsored since 1950 by the Mathematical Association of America and the Society of Actuaries, and later by Mu Alpha Theta (1965), the National Council of Teachers of Mathematics (1967) and the Casulty Actuarial Society (1971). Problems from the contests during the periods 1950-1960 are published in Volume 5 of the New Mathematical Library, and those for 1966-1972 are published in Volume 25. This volume contains those for the period 1961-1965. The questions were compiled by C.T. Salkind, Chairman of the Committee on High School Contests during the period, who also prepared the solutions for the contest problems. Professor Salkind died in 1968. In preparing this and the other Contest Problem Books, the editors of the NML have expanded these solutions with added alternative solutions.

The Contest Problem Book III
  • Annual High School Contests 1966-1972
  • Compiled by Charles T. Salkind, James M. Earl
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 January 1973
  • The annual high school contests have been sponsored since 1950 by the Mathematical Association of America and the Society of Actuaries, and later by Mu Alpha Theta (1965), the National Council of Teachers of Mathematics (1967) and the Casulty Actuarial Society (1971). Problems from the contests during the period 1950-1960 are published in Volume 5 of the New Mathematical Library, and those for the 1961-1965 are published in Volume 17. The New Mathematical Library will continue to publish these contest problems from time-to-time; the present volume contains those from the period 1966-1972. The questions were compiled by Professor C.T. Salkind until his death, and since 1968 by Professor J.M. Earl,. In preparing this and the earlier Contest Problem Books the editors of the NML have expanded these solutions and added alternative solutions.

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 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.

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.

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.

The Lore of Large Numbers
  • Philip J. Davis
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 July 1961
  • Large numbers have always been a source of wonder and many questions are raised about them. 'What comes after billions?' or 'How do the relative sizes of an atom and a man compare to the relative sizes of a man and the sun?' The author has answered some of these questions by explaining the arithmetic and the uses of large numbers in a way which introduces the reader to the horizons of modern mathematics. Using large num bers as a unifying theme and employing only the simplest materials, the author provides the reader with an understanding for numbers, their magnitude, and their growth. The reader is introduced to exponents, computation, number theory, and to the rapidity of growth of sequences. Several historical passages reveal mathematics as a living thing that grows and changes with the generations. Tables listing interesting and useful numbers in the physical universe are appended.

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.

Geometric Inequalities
  • Nicholas D. Kazarinoff
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1961
  • Anybody who liked their first geometry course (and some who did not) will enjoy the simply stated geometric problems about maximum and minimum lengths and areas in this book. Many of these already fascinated the Greeks, for example, the problem of enclosing the largest possible area by a fence of given length, and some were solved long ago; but others remain unsolved even today. Some of the solutions of the problems posed in this book, for example the problem of inscribing a triangle of smallest perimeter into a given triangle, were supplied by world famous mathematicians, other by high school students.

What is Calculus About?
  • W. W. Sawyer
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 January 1962
  • This book gives students the big picture of calculus. It should be read by prospective and current calculus students and by their teachers. Even someone who has completely mastered the technical side of the subject can benefit from being reminded of the essentially simple ideas and the calculational needs that led mathematicians to develop the rather complex machinery of calculus. Sawyer deals with it all, from what background a student needs to begin, to the study of speed and acceleration, to graphing (slope and curvature), to areas, volumes, and the integral.

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.

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.

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.

Numbers
  • Rational and Irrational
  • Ivan Niven
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1961
  • A superb development that starts with the natural numbers and carries the reader through the rationals and their decimal representations to algebraic numbers and then to the real numbers. Along the way, you will see characterizations of the rationals and of certain special (Liouville) transcendental numbers. This material is basic to all of algebra and analysis. Professor Niven's book may be read with profit by interested high school students as well as by college students and others who want to know more about the basic aspects of pure mathematics.

An Introduction to Inequalities
  • Edwin Beckenbach, Richard Bellman
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1961
  • Most people, when they think of mathematics, think first of numbers and equations-the number (x)=that number (y). But professional mathematicians, in dealing with quantities that can be ordered according to their size, often are more interested in unequal magnitudes that are equal. This book provides an introduction to the fascinating world of inequalities beginning with a systematic discussion of the relation 'greater than' and the meaning of 'absolute values' of numbers, and ending with descriptions of some unusual geometries. In the course of the book, the reader will encounter some of the more famous inequalities in mathematics. Starting with the basic order properties of real numbers, this book carries the reader through the classical inequalities of Cauchy, Minkowsky and Hörder with many variants and applications. The concluding chapter points the way to other metrics in the plane and the interrelations between geometry (convexity) and algebra (inequalities).

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