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This book is intended to provide students with the appropriate mathematical tools and problem-solving experience to successfully compete in high-level problem solving competitions. In each section, the authors attempt to "fill in" the appropriate background and then provide the student with a variety of worked examples and exercises to help bridge the gap between what he or she may already know and what is required for high-level competitions. Answers or sketches of the solutions are given for all exercises. The book makes an attempt to introduce each area "gently" assuming little in the way of prior background - and teach the appropriate techniques, rather than simply providing a compilation of high-level problems.
(source: Nielsen Book Data)

Delves into the world of ideas, explores the spell mathematics casts on our lives, and helps you discover mathematics where you least expect it. Be spellbound by the mathematical designs found in nature. Learn how knots may untie the mysteries of life. Be mesmerized by the computer revolution. Discover how the hidden forces of mathematics -hold architectural structures together -connect your telephone calls -help airplanes get off the ground - solve the mysteries of the living cell. See how some artists use a mathematical palette in their works and how many writers draw upon the wealth of its ideas. Experience all this in The Magic of Mathematics.
(source: Nielsen Book Data)

• The Measure and the Goal of a Life.- Family Background and Upbringing.- School and Education.- In Tune with the Times.- Professor in Christiania.- Professor in Leipzig.- At the End of the Road.- Appendices.
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Sophus Lie (1842-1899) is without doubt one of Norway's greatest scientific talents. His mathematical works have made him famous around the world no less than Niels Henrik Abel. The terms Lie groups and Lie algebra are today part of the standard mathematical vocabulary. In his comprehensive biography the author Arild Stubhaug let us come close to both the person Sophus Lie and his time. We follow him through childhood at the vicarage in Nordfjordeid, his growing up in Moss, school and studying in Christiania, travelling in Europe and his contacts with the leading mathematicians of his time. The academic and scientific career brought Lie from Christiania to Leipzig as professor, before the attempt to call him back to Norway, when she stood on the threshhold to national sovereignty, was successful.
(source: Nielsen Book Data)

• Introduction Fourteen case studies: Changing sections Emily's test Fundamental problems part I Making the Grade (College algebra version/Calculus I version/Multivariable calculus version) Making waves Order out of chaos Pairing up The quicksand of problem four Salad days Seeking points Study habits Studying the exam (College algebra questions/Calculus II questions/Multivariable calculus questions) There's something about Ted part I What were they thinking? Supporting materials for faculty: Developing effective mathematics teaching assistants using case studies: An introduction for faculty Using case studies in a TA-development program Types of cases Summaries of cases How these cases were created Changing sections, teaching guide Emily's test, teaching guide Fundamental problems part II (Fundamental problems, teaching guide) Making the grade, teaching guide Making waves part II (Making waves, teaching guide) Order out of chaos, teaching guide Pairing up, teaching guide The quicksand of problem four, teaching guide Salad days, teaching guide Seeking points, teaching guide Study habits, teaching guide Studying the exam, teaching guide (College algebra version/Calculus II version/Multivariable calculus version) There's something about Ted Part II/There's something about Ted, teaching guide What were they thinking?, teaching guide.
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Progress in mathematics frequently occurs first by studying particular examples and then by generalizing the patterns that have been observed into far-reaching theorems. Similarly, in teaching mathematics one often employs examples to motivate a general principle or to illustrate its use. This volume uses the same idea in the context of learning how to teach: By analyzing particular teaching situations, one can develop broadly applicable teaching skills useful for the professional mathematician. These teaching situations are the Case Studies of the title. Just as a good mathematician seeks both to understand the details of a particular problem and to put it in a broader context, the examples presented here are chosen to offer a serious set of detailed teaching issues and to afford analysis from a broad perspective. Each case raises a variety of pedagogical and communication issues that may be explored either individually or in a group facilitated by a faculty member. Teaching notes for such a facilitator are included for each Case in the Faculty Edition. The methodology of Case Studies is widely used in areas such as business and law. The consideration of the mathematics cases presented here will help readers to develop teaching skills for their own classrooms.
(source: Nielsen Book Data)

• I Induction II Combinatorics III Geometric Transformations IVInequalities V Sets, Equations, and Polynomials VI Graphs VII ThePigeonhole Principle VIII The Quaternions IX The Derivative X TheFoundations of Analysis.
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This book aims at introducing the reader possessing some high school mathematics, to both the higher and the more fundamental developments of the basic themes of elementary mathematics. To this end most chapters begin with a series of elementary problems, behind whose diverting formulation more advanced mathematical ideas lie hidden. These are then made explicit and further developments explored, thereby deepening and broadening the reader's understanding of mathematics -- enabling him or her to see mathematics as a hologram. The book arose from a course for potential high school teachers of mathematics taught for several years at St. Petersburg University, and nearly every chapter ends with an interesting commentary on the relevance of its subject matter to the actual classroom setting. However it can be recommended to a much wider readership, including university--level mathematics majors; even the professional mathematician will derive much pleasurable instruction from reading it.
(source: Nielsen Book Data)

• v. 1. Logic, sets, and numbers. 2 v. --
• v. 2. A critical approach to elementary analysis. 2 v.

International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research.

• Preface.- The Expanding Universe of Numbers.- Divisibility.- More on Divisibility.- Continued Fractions and their Uses.- Hadamard's Determinant Problem.- Hensel's P-Adic Numbers.- Notations.- Axioms.- Index.
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• The Arithmetic of Quadratic Forms.- The Geometry of Numbers.- The Number of Prime Numbers.- A Character Study.- Uniform Distribution and Ergodic Theory.- Elliptic Functions.- Connections with Number Theory.- Notations.- Axioms.- Index.
• (source: Nielsen Book Data)

Undergraduate courses in mathematics are commonly of two types. On the one hand are courses in subjects - such as linear algebra or real analysis - with which it is considered that every student of mathematics should be acquainted. On the other hand are courses given by lecturers in their own areas of specialization, which are intended to serve as a preparation for research. But after taking courses of only these two types, students might not perceive the sometimes surprising interrelationships and analogies between different branches of mathematics, and students who do not go on to become professional mathematicians might never gain a clear understanding of the nature and extent of mathematics. The two-volume "Number Theory: An Introduction to Mathematics" attempts to provide such an understanding of the nature and extent of mathematics. It is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A, which should be accessible to a first-year undergraduate, deals with elementary number theory. Part B is more advanced than the first and should give the reader some idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches, we may obtain a broad picture.
(source: Nielsen Book Data)

• Pre-viewing the rainbow
• Invisible origins and ancient traditions
• A quiet millennium: from the early Middle Ages into the European Renaissance
• The age of trigonometry: Europe, 1540-1660
• The calculus and its consequences, 1660-1750
• Analysis and mechanics at centre stage, 1750-1800
• Institutions and the profession after the French Revolution
• Mathematical analysis and geometries, 1800-1860
• The expanding world of algebras, 1800-1860
• Mechanics and mathematical physics, 1800-1860
• International mathematics, but the rise of Germany
• The rise of set theory: mathematical analysis, 1860-1900
• Algebras and geometries: their relations and axioms, 1860-1900
• An era of stability: mechanics, 1860-1900
• An era of media: mathematical physics, 1860-1900
• The new century, to the Great War and beyond
• Re-viewing the rainbow.