Offers a basic introduction to the types of problems that illustrate the earliest forms of algebra. This book presents some significant steps in solving equations and, wherever applicable, to link these developments to the extension of the number system. It analyzes various examples of problems, with their typical solution methods.
Explores the mathematical ideas involved in creating and analyzing maps. This book presents the famous problem of mapping the earth. Through the visual context of maps and mapmaking, it shows students how contemporary mathematics can help them to understand and explain the world.
Contains 20 essays, each dealing with a separate mathematical topic. This book contains topics that range from mathematical statements with interesting proofs, to simple and effective methods of problem-solving, to interesting properties of polynomials, to exceptional points of the triangle.
An investigation of interrelationships between mathematics and music. It reviews the background concepts in each subject as they are encountered and explores the common foundations of the two subjects. It brings together musical and mathematical notions, such as scales and modular arithmetic, and timbre and harmonic analysis.
Contains articles published from 1970 to 1990 in the Russian journal, ""Kvant"". This collection represents the Russian tradition of expository mathematical writing. It is designed to be used by students and teachers who love mathematics and want to study its various aspects, thus deepening and expanding the school curriculum.
Crisscross, zigzag, bowtie, devil, angel, or star: which are the longest, the shortest, the strongest, and the weakest lacings? This book presents the mathematics of shoelaces which is a mix of combinatorics and elementary calculus.
Includes discussion of smoothness, differentiability, and analyticity, the idea of local coordinates and coordinate transformation, and a detailed explanation of the Whitney imbedding theorem (both in weak and in strong form). This book describes the notion of the area of a figure on the plane and the volume of a solid body in space.
Presents the Russian tradition of expository mathematical writing. Suitable for students and teachers who want to study its various aspects, this book includes topics in number theory. It treats diverse aspects of analysis and algebra.
The mathematical theory of games gained widespread recognition when it was applied to the theoretical study of economics by von Neumann and Morgenstern in Theory of Games and Economic Behavior in the 1940s. This book presents proofs for both von Neumann's Minimax Theorem and the existence of the Nash Equilibrium in the $2 \times 2$ case.
Deals with the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, this book moves to less trivial results, both classical and contemporary. It demonstrates the advantage of purely geometric methods of studying conics.
A cipher is a scheme for creating coded messages for the secure exchange of information. This book develops various encryption schemes, and also introduces the reader to number theory. It places the study of integers and their properties in the context of cryptology.
Leads readers to discover some real mathematics. This book is suitable for a one-semester course at the beginning undergraduate level.
Offers an account of Indian work in diophantine equations during the 6th through 12th centuries and Italian work on solutions of cubic and biquadratic equations from the 11th through 16th centuries. The volume traces the historical development of algebra and the theory of equations from ancient times to the beginning of modern algebra.
Includes a treatment of exponential, logarithmic, and trigonometric functions, progressions, and induction method, as well as an extensive introduction to differential and integral calculus.
Suitable for both students and teachers who love mathematics and want to study its various branches beyond the limits of school curriculum. This book contains vast theoretical and problem material in main areas of what authors consider to be 'extracurricular mathematics'.
Leads readers to discover some real mathematics. This book is suitable for a one-semester course at the beginning undergraduate level.
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