BooksAlgebra
Algebra books
Kiselev’s algebra courses, the other classic Russian algebra textbooks, and the problem books written to go with them.
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Algebra books: 16 books
Kiselev's Elementary Algebra
by A. P. Kiselev
US grades 7–11 · UK Years 8–12
The single-volume algebra course, covering in one book essentially what Algebra Part I and Part II cover between them. Concepts arrive in a deliberate order, rules are tied to the operations that justify them, and proof is treated as part of elementary education rather than an ornament. Keeps hand extraction of cube roots, indeterminate multipliers and compound interest; omits the functions-and-graphs material of the two-part course.
Bugaev's Algebra
by N. V. Bugaev
US grades 8–12 · UK Years 9–13
The algebra course by N. V. Bugaev, later president of the Moscow Mathematical Society, in first faithful English translation from the original Russian edition. Fifteen chapters and 160 numbered sections lead from worked examples to general rules: fundamental concepts and operations, the greatest common divisor and least common multiple, algebraic fractions, equations of the first degree, powers and roots with imaginary quantities, quadratic equations, inequalities, indeterminate equations, continued fractions, ratio and proportion, progressions, logarithms with compound interest, and ordered selections with Newton's binomial. Supplements add a short history of algebra, irrational equations and simultaneous equations of the second degree. More than 400 numbered review questions close the book.
Malinin and Burenin's Algebra
by A. F. Malinin & K. P. Burenin
US grades 8–12 · UK Years 9–13
The algebra course and its problem collection in one volume, in first faithful English translation from the original Russian edition. An Introduction and sixteen chapters, 429 numbered articles, run from positive and negative numbers and the operations on algebraic expressions through equations of the first degree in one and several unknowns; powers and roots, with the square and cube roots of numbers and the square root of polynomials; quadratic equations, imaginary expressions and the trinomial of the second degree; inequalities; indeterminate equations; proportions; arithmetic and geometric progressions; logarithms; combinations and Newton’s binomial; continued fractions; the method of limits; and series. Problem sets follow the articles throughout — more than 3,300 numbered problems, 620 of them in a closing chapter of miscellaneous problems — and 2,698 answers are printed at the back.
Rashevsky's Elementary Algebra
by K. N. Rashevsky
US grades 8–11 · UK Years 9–12
A complete course in school algebra, taught with the graph as a working instrument, in first faithful English translation from the original Russian edition. An Introduction and nineteen chapters, 308 numbered articles, run from the use of letters and signed numbers through operations on expressions, factoring, algebraic fractions, negative exponents and proportions; equations of the first degree in one and several unknowns and their investigation; functions of the first degree and their graphs; powers and roots, square roots of numbers, irrational numbers and expressions, and the generalized concept of a power; the quadratic equation, functions of the second degree and the graphical solution of quadratics; imaginary numbers and their representation on the plane; irrational and higher-degree equations and systems of the second degree; progressions; logarithms with the use of tables, exponential equations and compound interest; and groupings, Newton’s binomial and a short historical sketch of algebra. Forty-nine figures carry the graphical method from the first chapter on. Six short exercise sets are included, without answers.
Barsukov's Algebra
by A. N. Barsukov
US grades 8–10 · UK Years 9–11
The Soviet school's standard algebra textbook — ten editions, roughly ten million copies. The first complete, faithful English translation of Barsukov's course, prepared from the original Russian and typeset to modern standards with source-exact section numbering. Twelve chapters, 130 numbered sections: from algebraic expressions and rational numbers through factoring, algebraic fractions, coordinates and graphs, systems of equations, the square root worked digit-by-digit, quadratic equations, and functions and graphs. Includes a full chapter on the slide rule — a subject once central to technical education, almost never found in a modern Western algebra text.
Davidov's Algebra
by A. Yu. Davidov
US grades 8–12 · UK Years 9–13
The algebra course written by the founding president of the Moscow Mathematical Society, in first faithful English translation from the original Russian edition. Five divisions and 478 numbered articles run from algebraic signs and the fundamental operations through polynomials, the greatest common divisor, algebraic and continued fractions, ratio and proportion; equations of the first degree in one, two and several unknowns; powers and roots, irrational and incommensurable quantities, Newton’s binomial, quadratic equations and their investigation, imaginary quantities and equations of the third and fourth degree; indeterminate analysis; and progressions, series, logarithms and compound interest. Full solutions to the problems are included.
Fuss's Algebra
by N. I. Fuss
US grades 8–12 · UK Years 9–13
The algebra course Euler's assistant wrote for the schools of the Russian Empire, in first complete English translation. Four divisions, 59 chapters and 570 numbered sections. Simple quantities: the four operations, common and decimal fractions, squares and square roots, irrational and imaginary numbers, cubes and cube roots, powers with fractional exponents, logarithms and the use of logarithmic tables. Compound quantities: the four operations, the resolution of fractions into infinite series, powers and roots of polynomials, the permutation of letters on which the binomial rule rests, and the expansion of irrational and negative powers into series. Equations of the first degree in one and several unknowns, indeterminate problems, equations of the second, third and fourth degree, and their approximate solution. Ratios, proportions, arithmetic and geometric progressions, and compound interest. Seventy questions are solved in full in the text; there are no exercise sets.
Kiselev's Algebra II
by A. P. Kiselev
US grades 9–12 · UK Years 10–13
12 chapters plus Supplements, 187 sections. Functions, quadratic systems, inequalities, logarithms, progressions, complex numbers, the binomial theorem, and continued fractions.
Kiselev's Elements of Algebra & Analysis I
by A. P. Kiselev
US grades 8–11 · UK Years 9–12
Part One builds a connected foundation: algebraic notation and operations, signed numbers, identities, equations and inequalities, polynomials, fractions, ratio and proportion, functions, coordinates and graphs, powers, roots and irrational numbers, progressions, logarithms with four-figure tables, compound interest and the binomial theorem. A distinct work from the 1888 Elementary Algebra.
Kiselev's Elements of Algebra & Analysis II
by A. P. Kiselev
US grades 11–12 · UK Years 12–13
Part Two carries the numbering of Part One forward into analysis: the theory of limits and its applications to elementary geometry, derivative functions, slopes of straight lines and curves, increasing and decreasing functions, and maxima and minima.
Kiselev's Algebra I
by A. P. Kiselev
US grades 7–9 · UK Years 8–10
6 chapters, 126 sections, 239 exercises. From relative numbers and polynomials through first-degree equations, powers, roots, and quadratics.
Shaposhnikov & Valtsov, Part I
by N. A. Shaposhnikov & N. K. Valtsov
US grades 7–10 · UK Years 8–11
2,228 classical algebra exercises with answers, in the first complete English translation. First published 1887–1890 and reissued in more than 50 editions, this is the problem collection that trained generations of Russian students alongside Kiselev. 9 chapters, sequenced from elementary operations through quadratic equations, with an answer key covering more than 1,300 entries.
Shaposhnikov & Valtsov, Part II
by N. A. Shaposhnikov & N. K. Valtsov
US grades 9–12 · UK Years 10–13
1,531 classical algebra problems with answers, in the first complete English translation. Part II continues the sequence begun in Part I, carrying the student through the advanced topics of the classical Russian algebra course — the problem collection that trained generations of students alongside Kiselev.
Kiselev's Algebra Problems
by A. P. Kiselev
US grades 7–11 · UK Years 8–12
The companion problem collection to Kiselev's Algebra. Hundreds of carefully sequenced problems and exercises that mirror the chapter structure of Algebra Part I and Part II — the same problem set Russian students worked through alongside Kiselev's algebra textbooks for over a century.
Lebedintsev's Algebra Problems, Part I
by K. F. Lebedintsev
US grades 7–9 · UK Years 8–10
A graded collection of 1,637 problems for the first course in algebra, in first faithful English translation from the original Russian edition. Five divisions and sixty numbered sections lead from general formulas built out of arithmetic problems, coefficients, exponents and roots; through negative numbers, zero and coordinates on a line; the operations on integral and fractional expressions, factoring, the greatest common divisor and least common multiple, and zero and negative exponents; equations and inequalities of the first degree, proportions, and systems in two and three unknowns, with long runs of word problems from trade, travel, work and physics; to points and straight lines on the coordinate plane, functions of the first order and their graphs, and graphs of uniform change. No answers are printed: the author held that a pupil should check his own work.
Math Circle Problems
by I. I. Bazhenov, A. G. Poroshkin, A. Yu. Timofeev & V. D. Yakovlev
US grades 6–10 · UK Years 7–11
A problem book for school mathematics circles, in first faithful English translation from the original Russian edition: 271 problems with hints, answers and worked solutions. The first part teaches the methods one at a time — logic problems, pouring and weighing, Euler circles, the Dirichlet (pigeonhole) principle, the extremal principle, invariants and semi-invariants, colouring, games, division with remainder, primes, Diophantine equations, graphs and combinatorics. The second is a collection for independent and olympiad practice. 85 figures.