Kiselev's Elements of Algebra and Analysis, Part Two: The Classic Russian Mathematics Textbook — First Complete English Translation (Russian Math Classics — English Editions)

For more than seventy years, A. P. Kiselev's mathematics textbooks were used in Russian and Soviet schools. More than 80 million schoolchildren are estimated to have learned mathematics from his pages. The tradition they created shaped the mathematical education of generations of mathematicians, scientists, and engineers. Now, for the first time, Elements of Algebra and Analysis, Part Two is available in a complete English translation. Andrei Petrovich Kiselev (1852–1940) was a Russian mathematician, teacher, and textbook author. A graduate of St Petersburg University who studied under P. L. Chebyshev, he chose school teaching and textbook writing as his life's work. His achievement was to bring serious mathematics into the classroom without making it superficial: definitions, examples, geometric constructions, calculations, and proofs are arranged so that each idea prepares the next. This volume is Part Two of Elements of Algebra and Analysis, It continues the numbering begun in Part One and develops the transition from algebra and geometry into analysis. It is a distinct work from Kiselev's separate "Elementary Algebra." WHAT THIS VOLUME COVERS The theory of limits. Definitions and properties of limits, with applications to elementary geometry. Derivative functions. Slopes of straight lines and curves; the derivative; increasing and decreasing functions; maxima and minima; concavity and convexity; velocity and acceleration; cubic functions; and the function y = a/x. Analytic geometry. The straight line, the circle and the ellipse, the hyperbola, and the parabola. The antiderivative. Areas, the antiderivative function, applications, and volumes. Additions. Polynomial divisibility, systems of linear equations, polynomial square roots, nested radicals, inequalities, complex numbers, and algebraic and binomial equations. Problems and exercises. A concluding section that lets the reader work through the ideas in Kiselev's own sequence. WHAT MAKES KISELEV VALUABLE TODAY Modern textbooks often separate algebra, geometry, calculus, and applications into different subjects. Kiselev connects them. Algebra supplies the language, geometry supplies the picture, and limits show how finite calculations lead to analysis. Results are not merely formulas to memorize: the definitions and reasoning that make them work are developed in order, with examples and proofs throughout. The result is demanding but unusually clear — a rigorous bridge from secondary mathematics to university-level analysis. This is a faithful English edition of the Russian text. It preserves Kiselev's mathematical content, exposition order, numbered articles (§§307–420), examples, exercises, cross-references, formulas, and source-derived figures. The typography, figure captions, and notation have been prepared for contemporary English readers, while the historical mathematical structure remains visible. IDEAL FOR: students preparing for calculus or real analysis, homeschool and classical-curriculum families, teachers and tutors, readers rebuilding their mathematical foundations, and anyone interested in the history of Russian mathematical education. Part of Kiselev's Mathematics (English Editions) from Northern Star Academic Press. Read it with Elements of Algebra and Analysis, Part One to follow Kiselev's complete progression from algebra to analysis. Translated by Valery Manokhin, PhD, MBA, CQF (Royal Holloway, University of London). Part of *Russian Math Classics — English Editions*. Translated by Valery Manokhin, PhD (Royal Holloway, University of London). Published by Northern Star Academic Press. Full catalogue at russianmathbooks.com.