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Classic biography of Gauss, updated with new introduction, bibliography and new material.
An introduction to the basic mathematical techniques involved in cryptanalysis.
The derivative and the integral are the fundamental notions of calculus. Though there is essentially only one derivative, there is a variety of integrals, developed over the years for a variety of purposes, and this book describes them. No other single source treats all of the integrals of Cauchy, Riemann, Riemann-Stieltjes, Lebesgue, Lebesgue-Steiltjes, Henstock-Kurzweil, Weiner, and Feynman.
A concise investigation into the connections between tiling space problems and algebraic ideas, suitable for undergraduates.
A guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from.
A classic advanced textbook, containing a cross-section of ideas, techniques and results that give the reader an unparalleled introductory overview of the subject. The author gives an integrated presentation of overall theory and its applications in, for example, the study of groups of matrices, and group representations.
A book describing how visualization techniques can be used in understanding and teaching mathematics.
This book contains key topics that form the foundations for high-school mathematics.
Resources for teachers of mathematics to enrich their courses with environmental issues.
Dealing with various aspects of Euclidean geometry, this work begins with the broken-chord theorem, attributed to Archimedes by Islamic mathematicians, and goes on to discuss various properties of circles, triangles, and quadrilaterals.
Uses popular literature and philosophy to bring the mechanics of motion to life.
Demonstration of the use of simple counting arguments to describe number patterns; numerous hints and references.
This book traces a remarkable path of mathematical connections through seemingly disparate topics.
A collection of 90 short elementary gems from algebra, geometry, combinatorics, and Number Theory.
A collection of 40 monthly columns from MAA Online about the work of the 18th-century Swiss mathematician Leonhard Euler.
Celebrating the 300th birthday of Leonhard Euler - collected articles address aspects of Euler's life and work.
Martin Gardner's aha! Gotcha and aha! Insight combined: 144 wonderful puzzles from the reigning king of recreational mathematics.
In the second edition of this MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on infinite summations, differentiability and continuity, and convergence of infinite series have been reorganized to make it easier to identify the key ideas.
Challenging problems in maths plus solutions to those featured in the earlier Olympiad book.
An examination of the evolution of one of the cornerstones of modern mathematics.
Problems illustrating important mathematical techniques with solutions and accompanying essays.
A collection of stories and anecdotes about mathematics and mathematicians.
This book looks carefully at Archimedes' fundamental advances in the fields of geometry, mechanics, and hydrostatics.
A commonsense approach to numerical algorithms for the solution of equations.
One of the principles of mathematical growth is that the relabelling process often suggests a new generation of problems. Means become ends; the medium rapidly becomes the message. This book is not wholly self-contained. Readers will find that they should be familiar with the elementary portions of linear algebra and of the theory of functions of a complex variable.
Illustrates how simple observations can be made the starting point of rich and fruitful theories and how the same theme recurs in seemingly unrelated disciplines. Mark Kac conveyed his infectious enthusiasm for mathematics and its applications in his lectures, papers, and books. Two of his papers won Chauvenet awards for expository excellence.
Covers the story of trigonometry. This is a swift overview, but it is complete in the context of the content discussed in beginning and advanced high-school courses. The purpose of these notes is to supplement and put into perspective the material of any course on the subject.
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