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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 2 of 3

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.

Continued Fractions
  • C. D. Olds
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 January 1963
  • Continued fractions were studied by the great mathematicians of the seventeenth and eighteenth centuries and are a subject of active investigation today. Fractions of this form provide much insight into many mathematical problems — particularly into the nature of numbers — and the theory of continued fractions is a powerful tool in number theory and other mathematical disciplines. The author of this book presents an easy-going discussion of simple continued fractions, beginning with an account of how rational fractions can be expanded into continued fractions. Gradually the reader is introduced to such topics as the application of continued fractions to the solution of Diophantine equations, and the expansion of irrational numbers into infinite continued fractions.

Ingenuity In Mathematics
  • Ross Honsberger
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 January 1970
  • Sit with this book for half to three-quarters of an hour and you will have mastered an elegant and pleasing bit of mathematics. Nineteen independent essays on topics including number theory, geometry, combinatorics, logic, and probability. The nineteen essays contained in this volume are independent of one another; they represent many different aspects of mathematical thinking. Standard high school courses in algebra and geometry furnish a sufficient basis for understanding each essay. The Topics treated in this volume include number theory, geometry, combinatorics, logic, probability; and the methods used often involve an interaction of these various disciplines. Some essays are easy to read, others are more challenging; some exercises are routine, others led the reader deeper into the subject.

Invitation to Number Theory
  • Øystein Øre
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1967
  • Number theory has been instrumental in introducing many of the most distinguished mathematicians, past and present, to the charms and mysteries of mathematical research. The purpose of this simple little guide will have been achieved if it should lead some of its readers to appreciate why the properties of numbers can be so fascinating. It would be better still if it would induce you to try to find some number relations of your own; new curiosities devised by young people turn up every year. In any case, you will become familiar with some of the special mathematical concepts and methods used in number theory and will be prepared to embark upon the study of the more advanced books in its rich literature.

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.)

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.

From Pythagoras to Einstein
  • K. O. Friedrichs
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1965
  • The main thread running through this somewhat unorthodox approach to the special theory of relativity is the Pythagorean theorem. It appears in its most elementary geometric form in the very beginning of this monograph. Then it reappears in algebraic garb, it is further modified and finally reinterpreted to play the role of one of the main characters in the special theory of relativity. The first four chapters are easily accessible to high school sophomores or juniors. The remaining part of the book may be a little difficult for students who never studied physics, although the author actually employs only the notion of impact and presupposes no background in physics. With the aid of the vector geometry introduced earlier, he leads the reader from the impact conservation laws to the famous formula e=mc^2.

First Concepts of Topology

Mathematics of Choice
  • Or How to Count without Counting
  • Ivan Niven
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 June 1965
  • Counting lies at the heart of much mathematics, and Niven's subtitle is — How to count without counting. This is the whole art of combinatorics: permutations, combinations, binomial coefficients, the inclusion-exclusion principle, combinatorial probability, partitions of numbers, generating polynomials, the pigeonhole principle, and much more.

Geometry Revisited
  • H.S.M. Coxeter, Samuel L. Greitzer
  • Published by:
    Mathematical Association of America
    Published online:
    05 January 2012
    Print publication:
    01 March 1967
  • Among the many beautiful and nontrivial theorems in geometry found here are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.

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.

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.

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 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.

Hungarian Problem Book I
  • Based on the Eötvös Competitions 1898-1905
  • Translated by Elvira Rapaport
  • Published by:
    Mathematical Association of America
    Published online:
    05 December 2011
    Print publication:
    15 January 1963
  • The Eötvös Contests in elementary mathematics have been open to Hungarian students in their last year of high school ever since 1894. They are famous for the simplicity of the concepts employed, the mathematical depth reached, and the diversity of elementary mathematical fields touched. But perhaps their most remarkable feature is the influence that they, together with a mathematics journal for students, seem to have had on the young people of that small country. Among the winners of the first eleven contests (i.e., those contained in the present volume) many turned into scientists of international fame; e.g., L. Fejér, T. von Kármán, D. Kónig, M. Riesz. Among the winners of the next twenty contests (i.e., those contained in volume 12) are G. Szegró, T. Radó, E. Teller; all three are well known in the United States, where they now reside. This translation of the Eötvös Contests Problems from 1894–1928 is based on the revised Hungarian edition of J. Kürschák's original compilation. Kürschák combined his excellence in mathematics with his interest in education when he supplied the elegant solutions and illuminating explanations.

Geometric Transformations III
  • Affine and Projective Transformations
  • I. M. Yaglom
  • Translated by Abe Shenitzer
  • Published by:
    Mathematical Association of America
    Published online:
    26 October 2011
    Print publication:
    03 January 1973
  • This book is the sequel to Geometric Transformations I and II, volumes 8 and 21 in this series, but can be studies independently. It is devoted to the treatment of affine and projective transformations of the plane these transformations include the congruencies and similarities investigated in the previous volumes. The simple text and the many problems are designed mainly to show how the principles of affine and projective geometry may be used to furnish relatively simple solutions of large classes of problems in elementary geometry, including some straight edge construction problems. In the Supplement, the reader is introduced to hyperbolic geometry. The latter part of the book consists of detailed solutions of the problems posed throughout the text.

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.

Geometric Transformations II
  • Similarities
  • I. M. Yaglom
  • Translated by Allen Shields
  • Published by:
    Mathematical Association of America
    Published online:
    26 October 2011
    Print publication:
    30 June 1968
  • This book is the sequel to Geometric Transformation I which appeared in this series in 1962. Part 1 treats length-preserving transformation (called isometries), this volume treats shape-preserving transformations (called similarities); and Part III treats affine and protective transformations. These classes of transformation play a fundamental role in the group-theoretic approach to geometry. As in the previous volume, the treatment is direct and simple. The introduction of each new idea is supplemented by problems whose solutions employ the idea just presented, and whose detailed solutions are given in the second half of the book.

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.

Hungarian Problem Book II
  • Based on the Eötvös Competitions 1906-1928
  • Translated by Elvira Rapaport
  • Published by:
    Mathematical Association of America
    Published online:
    26 October 2011
    Print publication:
    15 June 1963
  • The Eötvös Contests in elementary mathematics have been open to Hungarian students in their last year of high school ever since 1894. They are famous for the simplicity of the concepts employed, the mathematical depth reached, and the diversity of elementary mathematical fields touched. But perhaps their most remarkable feature is the influence that they, together with a mathematics journal for students, seem to have had on the young people of that small country. Among the winners of the first eleven contests (i.e., those contained in volume 11) many turned into scientists of international fame; e.g., L. Fejér, T. von Kármán, D. Kónig, M. Riesz. Among the winners of the next twenty contests (i.e., those contained in this volume) are G. Szegró, T. Radó, E. Teller; all three are well known in the United States, where they now reside. This translation of the Eötvös Contests Problems from 1894–1928 is based on the revised Hungarian edition of J. Kürschák's original compilation. Kürschák combined his excellence in mathematics with his interest in education when he supplied the elegant solutions and illuminating explanations.

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