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Algebra
This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted...
Functions and Graphs
This text demonstrates the fundamentals of graph theory. The first part employs simple functions to analyze basics; second half deals with linear functions, quadratic trinomials, linear fractional functions, power functions, rational functions. 1969 edition.
Discriminants, Resultants, and Multidimensional Determinants
"This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of the authors. The book nicely complements these original papers with many examples illustrating both old and new results of the theory."—Mathematical Reviews
The Method of Coordinates
Two-part treatment begins with discussions of coordinates of points on a line, coordinates of points in a plane, and coordinates of points in space. Part two examines geometry as an aid to calculation and peculiarities of four-dimensional space. Abundance of ingenious problems — includes solutions, answers, and hints. 1967 edition.
Lectures on Linear Algebra
Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector.
Calculus of Variations
Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.
Geometry
This text is the fifth and final in the series of educational books written by Israel Gelfand with his colleagues for high school students. These books cover the basics of mathematics in a clear and simple format – the style Gelfand was known for internationally. Gelfand prepared these materials so as to be suitable for independent studies, thus allowing students to learn and practice the material at their own pace without a class. Geometry takes a different approach to presenting basic geometry for high-school students and others new to the subject. Rather than following the traditional axiomatic method that emphasizes formulae and logical deduction, it focuses on geometric constructions....
Trigonometry
In a sense, trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles, or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions, and of the so-called transcendental functions, which cannot be described using finite algebraic processes. It also has many applications to physics, astronomy, and other branches of science. It is a very old subject. Many of the geometric results that we now state in trigonometric terms were given a purely geometric exposition by Euclid. Ptolemy, an early astronomer, began to go beyond ...
Rule Makers, Rule Breakers
A celebrated social psychologist offers a radical new perspective on cultural differences that reveals why some countries, cultures, and individuals take rules more seriously and how following the rules influences the way we think and act. In Rule Makers, Rule Breakers, Michele Gelfand, “an engaging writer with intellectual range” (The New York Times Book Review), takes us on an epic journey through human cultures, offering a startling new view of the world and ourselves. With a mix of brilliantly conceived studies and surprising on-the-ground discoveries, she shows that much of the diversity in the way we think and act derives from a key difference—how tightly or loosely we adhere to ...
Positional Decision Making in Chess
Positional Decision Making in Chess offers a rare look into the mind of a top grandmaster. In his efforts to explain his way of thinking, Boris Gelfand focuses on such topics as the squeeze, space advantage, the transformation of pawn structures and the transformation of advantages. Based on examples from his own games and those of his hero, Akiba Rubinstein, Gelfand explains how he thinks during the game.
