Books
The complete collection of faithful translations of the Russian classics. From basic arithmetic through advanced algebra, geometry, trigonometry, and calculus.
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Kiselev's Systematic Arithmetic
by A. P. Kiselev
US grades 5–8 · UK Years 6–9
Kiselev's definitive systematic arithmetic — the expanded companion to his classic arithmetic textbook. 207 pages, 264 numbered articles across seven divisions: whole numbers; concrete (denominate) numbers and the metric system; divisibility, primes, and factorisation; common fractions; decimal fractions with limits and repeating decimals; ratio and proportion; and a full course of word problems on proportional quantities. Includes elementary treatments most textbooks leave out — Euclid's proof of the infinitude of primes and the concept of a limit used to prove that 0.999… equals 1.
Vereshchagin's Arithmetic Problems
by I. P. Vereshchagin
US grades 4–8 · UK Years 5–9
The largest arithmetic problem collection of imperial Russia — 3,238 problems with the complete answer key, in English for the first time. Approved by the Ministry of Public Education for the Empire's secondary schools and teachers' seminaries, and separately for the girls' gymnasia of the Empress Maria department, it ran to eighteen editions. Three Parts and fifty-seven sections cover whole numbers and compound named numbers; divisibility; common and decimal fractions; the metric system; ratio and proportion; and the commercial rules — the rule of three, percentage, interest, discount, partnership and alligation. Vereshchagin insisted his data be real, so the problems run on railway timetables, the heights of Elbrus and Everest, the assay of the new silver ruble, and Eratosthenes measuring the earth between Syene and Alexandria. Translated from the seventh edition of 1891, with source-exact problem numbering.
Berezanskaya's Arithmetic Problems
by E. S. Berezanskaya
US grades 4–7 · UK Years 5–8
The iconic companion to Kiselev's Arithmetic — the problem collection Russian classrooms used side-by-side with Kiselev for over 70 years. 2,354 problems across eight chapters in the canonical order: numeration; the four operations on whole numbers; divisibility; common fractions; decimal fractions; ratio and proportion; percentages; and a concluding chapter of mixed problems drawing on everything before. Oral drills, written exercises, and word problems of real substance, sequenced from easy to demanding. The first complete, faithful English translation, with source-exact problem numbering.
Kiselev's Arithmetic
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The foundational arithmetic textbook used in Russian schools for over a century, in complete English translation. 6 parts, 214 sections. Whole numbers through proportional quantities, with mathematical proofs for every operation. Paperback, hardcover and Kindle on Amazon; the digital edition is read online in Gumroad; there is no file to download.
Malinin & Burenin Problems
by A. Malinin & K. Burenin
US grades 5–8 · UK Years 6–9
3,807 problems with a complete answer key — the problem collection that accompanies Malinin and Burenin's arithmetic textbook, and the exercises Imperial Russian students worked through alongside the theory. First complete English translation from the original Russian edition.
Egorov's Arithmetic Problems
by F. I. Egorov
US grades 3–5 · UK Years 4–6
A graded problem book for the whole course of arithmetic in whole numbers, in first faithful English translation from the original Russian edition: 1,600 problems, with answers to 1,245 of them. It begins with numeration to a thousand, a million and beyond and with the meaning of the four operations, then works through written addition, subtraction, multiplication and division of multi-digit numbers, with its own sections on how a sum, difference, product and quotient change when their components change. Compound denominate numbers run alongside at every stage, followed by problems on time and on square and cubic measures, and a final set on all operations.
Malinin & Burenin
by A. Malinin & K. Burenin
US grades 5–8 · UK Years 6–9
A complete English translation of Malinin and Burenin's Imperial Russian arithmetic textbook. 11 chapters, 301 sections. Covers numeration, operations on whole numbers, divisibility, fractions, ratios, proportions, percentage, interest, and Diophantine problems.
Rashevsky's Arithmetic
by K. N. Rashevsky
US grades 5–8 · UK Years 6–9
A complete course in arithmetic in nine sections, in first faithful English translation from the original Russian edition. The four operations on whole numbers with the written methods set out in full; named and metric quantities; areas and volumes worked from drawings; tests for divisibility, primes, greatest common divisor and least common multiple; common and decimal fractions, including repeating decimals; ratio, proportion and proportional division; percentage and mixing problems; and plans, diagrams and graphs. Long divisions and column multiplications are printed digit under digit, so the reasoning stays visible on the page.
Malinin's Mental Calculation
by A. F. Malinin
US grades 2–7 · UK Years 3–8
First faithful English translation from the original Russian edition. 1,963 problems arranged from short numerical exercises to demanding multi-step work with fractions, money, weights, measures, and proportions. Preserves Malinin's original numbering and five-part progression.
Perelman's Entertaining Arithmetic
by Ya. I. Perelman
US grades 4+ · UK Year 5+
The classic of Russian popular mathematics. Puzzles, riddles, and curiosities that make arithmetic genuinely entertaining.
Rachinsky Solutions
by Valery Manokhin
US grades 4–8 · UK Years 5–9
The essential companion to Rachinsky's 1001 Problems — every problem solved, every error corrected. Step-by-step arithmetic reasoning for all 1,001 problems in the 1899 collection, with 12 errata corrections to misprints in the original answer key (problems #188, #410, #454, #468, #519, #563, #705, #779, #796, #836, #889, #892 — independently verified). Includes a complete conversion table for pre-revolutionary Russian units (puds, funts, zolotniks, sazhens, arshins, vershoks, desyatinas, chetveriks). 257 pages, professionally typeset. Solutions organised by problem number to match the companion problem book exactly.
Berman's Calculation Techniques
by G. N. Berman
US grades 6–10 · UK Years 7–11
Three parts covering mental calculation, written calculation, and approximate calculation — the practical arithmetic skills the Russian school tradition treated as foundational. A short, dense book on how to compute well without a calculator.
Rachinsky's 1001 Problems
by S. A. Rachinsky
US grades 4–8 · UK Years 5–9
1,001 carefully selected problems from the village schoolteacher whose students were depicted in Bogdanov-Belsky's famous 1895 painting "Mental Arithmetic."
Amenitsky's Arithmetic Games
by N. N. Amenitsky
US grades 4+ · UK Year 5+
Four mathematical games — the racing game, guessing numbers, the Tower of Lucas and the game with a needle — that turn place value, doubling, parity and a first experiment in probability into play, in first faithful English translation from the original Russian edition. A short 31-page reading edition with four illustrations, for curious students, teachers and readers of recreational mathematics. No prerequisites beyond arithmetic.
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.
Kiselev's Elementary Geometry
by A. P. Kiselev
US grades 8–11 · UK Years 8–13
The complete geometry course — five books of plane geometry and three of solid geometry — in one English volume. Definitions are precise, theorems are proved, constructions are justified, and each idea is prepared by the one before it. 380 pages and 450 figures.
Rashevsky's Geometry
by K. N. Rashevsky
US grades 8–11 · UK Years 9–12
A complete school course in plane and solid geometry in one volume, in first faithful English translation from the original Russian edition. Two parts, thirty chapters and 406 numbered articles. The planimetry runs from the straight line, polygons and the circle through the three cases of equality of triangles, parallel lines, parallelograms and trapezoids and construction problems; the method of loci, parallel translation and rotation; ratio and common measure, angles in a circle, proportional segments, similarity and homothety; the basic trigonometric functions of the right triangle; regular polygons, areas, the concept of a limit, the circumference and area of the circle, and algebra applied to geometry. The stereometry covers the position of a plane, perpendicular and parallel lines and planes, dihedral and polyhedral angles, polyhedra and their volumes, the cylinder, cone and sphere, incommensurable quantities, and closes with practical work: making a plan and levelling. 338 figures and 367 exercises in ten graded sets.
Kiselev's Planimetry
by A. P. Kiselev
US grades 8–10 · UK Years 8–11
The first complete English translation of Kiselev's proof-based Euclidean geometry. 269 sections across 6 chapters: basic concepts, triangles, circles, similarity, regular polygons, and areas. Digital edition, paperback and hardcover.
Rybkin's Planimetry Problems
by N. A. Rybkin
US grades 8–11 · UK Years 9–12
The companion problem collection to Kiselev's classical Russian geometry — now in English for the first time. Rybkin's Planimetry Problems is the set Russian students worked through alongside Kiselev's geometry textbook for over a century. Kiselev gives the definitions, theorems, and proofs; Rybkin gives the problems that turn those proofs into geometric intuition. 970 problems across 16 sections, organised chapter-by-chapter to mirror Kiselev's Planimetry — from preliminary concepts and lines through triangles, quadrilaterals, similar figures, the circle, regular polygons, and the measurement of areas. Worked solutions for the harder problems, hints for the rest.
Delone: Geometry Problems
by B. N. Delone, O. K. Zhitomirsky & A. I. Fetisov
US grades 10–12 + · UK Years 11–13
85 problems with full solutions, from three mathematicians who wrote for students who wanted to be stretched. Construction, loci, congruence, similarity, areas and geometry in space — with each solution showing how to analyse a construction, carry it out, prove it correct and establish when it exists. Includes the Simson line, homothety, regular polyhedra, and the common part of a cube and a rotated copy of itself. 75 figures.
Kiselev's Stereometry
by A. P. Kiselev
US grades 9–11 · UK Years 10–13
Kiselev's three-dimensional geometry text — the first complete English translation. Polyhedra, the five Platonic solids, cylinders, cones, the ball, and Cavalieri's principle.
Kvasnikova's Stereometry Problems
by Z. Ya. Kvasnikova, A. I. Pospelov, E. N. Yermolayeva & N. M. Kalitkin
US grades 10–12 · UK Years 11–13
A graded problem book for the whole of solid geometry, in first faithful English translation from the original Russian edition: 838 problems in 33 sections, numbered in one run from first to last, with an answer section. It begins with the axioms of stereometry and the relative position of lines and planes, then works through parallel and orthogonal projection, dihedral and polyhedral angles, prisms, pyramids and truncated pyramids, the regular polyhedra, cylinders, cones and truncated cones, the sphere, solids of revolution, inscribed and circumscribed spheres, and a closing mixed section. Five sets of practical exercises call for measurement and models. 54 figures.
Aleksandrov's Geometric Problems
by I. I. Aleksandrov
US grades 10–12 + · UK Years 11–13
A course in geometric construction organised by the idea that solves the problem, not by topic: direct constructions, geometric loci, similarity, symmetry, parallel translation, inversion, rotation and algebraic methods. Every problem is treated through analysis, construction, proof and discussion.
Fuss's Geometry
by N. I. Fuss
US grades 8–12 · UK Years 9–13
The geometry of Fuss's course of pure mathematics, the volume that follows his Algebra, in first complete English translation. Two parts, twelve chapters and 460 numbered sections. Planimetry: definitions and axioms; straight lines, angles and the sides of rectilinear figures; the circle and the figures inscribed in it and circumscribed about it; proportional lines and similar figures; the comparison and measurement of figures; the transformation and division of figures. Stereometry: the position of planes and of lines drawn outside them; the surface, comparison and volume of solids; and the five regular solids. 107 theorems with their proofs, 61 construction problems with their solutions and 158 corollaries. All 230 figures are reproduced on the nine engraved plates.
Perelman's Geometry
by Ya. I. Perelman
US grades 7–10 · UK Years 8–11
A practical course in plane and solid geometry for self-study, carried as far as the trigonometry of the right triangle, in first faithful English translation from the original Russian edition. Nine chapters: the straight line and the circle, with scales, circumferential speed, belts and gear wheels; angles and parallel lines, with the protractor; the triangle, its construction and the tests for equality; polygons and the parallelogram, with the vernier and slide calipers; chords, tangents, conjugation and the ellipse; similarity, Pythagoras’ rule and the square root; tangent, cotangent, sine and cosine, with their tables; areas, from the rectangle to the circle, the ellipse and irregular figures; and the surfaces, volumes and weights of solids. The main text rests on about forty theorems; 458 problems, about half the book, carry the rest, with solutions or answers to 423 of them. 230 figures.
Rybkin's Stereometry Problems
by N. Rybkin
US grades 10–12 · UK Years 11–13
The problem set Russian students worked through alongside Kiselev's geometry. 730 problems across 25 sections: perpendiculars and oblique lines to a plane, parallel lines and planes, dihedral and polyhedral angles, regular polyhedra, prisms, pyramids and frustums, cylinders, cones and the sphere, volumes and surface areas. Original numbering and all 46 figures retained.
Davidov's Geometry
by A. Yu. Davidov
US grades 8–11 · UK Years 9–12
The geometry course written by the founding president of the Moscow Mathematical Society, in first faithful English translation from the original Russian edition. Two parts, thirteen chapters and 305 numbered sections. The planimetry treats straight lines and angles; figures, the equality of triangles, perpendicular and oblique lines; parallel lines, parallelograms and trapezoids; similarity and the ratio of lines; the circle — chords and tangents, the measurement of angles, proportional lines, inscribed and circumscribed polygons, the relative position of two circles, the four remarkable points of a triangle, reciprocal points and polars; regular polygons; the measurement of areas, with the surveying of a plan; and the circumference and area of the circle by limits. The stereometry covers lines and planes in space; dihedral, polyhedral and trihedral angles; prisms, pyramids, symmetric and regular polyhedra; volumes; the cylinder, cone and sphere, the spherical triangle, and the conic sections. 344 figures and 256 problems, with solutions to all of them. A digital edition, read online in Gumroad Reader.
Raykovsky: Foundations of Geometry
by Stepan Raykovsky
US grades 9–12 · UK Years 10–13
A systematic course in plane and solid geometry, never before published in English. Definitions, axioms and postulates first; then 310 numbered articles building from the straight line to the sphere, each proposition proved and each construction carried out in full. Four divisions: straight lines in a plane, the line and the circle, measurement of plane figures, and the geometry of solids. All 157 figures reproduced from the five engraved plates.
Geometry Through Problems
by S. I. Shokhor-Trotsky
US grades 6–10 · UK Years 7–11
A complete school course in plane and solid geometry, written for the teacher and built from graded problems rather than ready-made theorems, in first faithful English translation from the original Russian edition. It opens with the author’s essay “To the Attention of the Teacher” on teaching by expedient problems, then runs in six chapters and eighteen numbered sections: the straight line, the angle and the arc; triangles, parallel lines and polygons, the length of the circumference and construction problems; areas of rectilinear figures and of the circle; the lateral surfaces of cylinders and cones and the surface of the sphere; lines and planes in space, dihedral and polyhedral angles, and projections of figures and solids onto a plane; and the volumes of prisms, cylinders, pyramids, cones and the sphere. 439 numbered problems with 251 lettered sub-problems, each with the teacher’s notes on how the class works it, answers given in the text, 398 drawings, the author’s alphabetical index and a selection of reviews. The numbers missing from the sequence belong to the companion pupils’ book, as the author explains.
Davidov's Trigonometry
by A. Yu. Davidov
US grades 10–12 + · UK Years 10–13
Plane and spherical trigonometry in one course, by the founding president of the Moscow Mathematical Society, in first complete English translation. Three parts and 97 numbered sections. Goniometry builds the trigonometric lines from geometric construction, follows them through the whole circle, and treats the addition, multiplication and division of arcs and the construction and use of trigonometric tables, Lalande’s and the seven-digit tables among them. Plane trigonometry solves right and oblique triangles and applies them to measurement: inaccessible distances and heights. Spherical trigonometry derives the fundamental formulas, Delambre’s formulas and Napier’s analogies, solves right and oblique spherical triangles and finds the area of a spherical triangle. A seven-part Supplement takes up inverse trigonometric functions, De Moivre’s formula, the roots of xᵐ = 1, regular polygons, the cubic equation solved by trigonometric lines, and the expansion of the functions into series. Sixty figures, and 265 problems, 212 of them answered in the key at the back.
Derzhavin's Trigonometry
by S. S. Derzhavin
US grades 10–12 · UK Years 10–13
A complete classical course in plane trigonometry, in first complete English translation. Eight divisions and 86 numbered sections run from the function concept and radian measure through the trigonometric functions traced quadrant by quadrant, the addition and reduction formulas, the construction and use of logarithmic tables, the solution of oblique triangles by the laws of sines and cosines and by Mollweide’s formulas, measurement in the field and triangulation, the computation of π, and trigonometric equations. Sixty-eight figures and Tables I–V.
Vereshchagin's Plane Trigonometry
by I. P. Vereshchagin
US grades 10–12 · UK Years 11–13
A classical Russian problem book in plane trigonometry, in English for the first time. Questions and problems organised to carry a student from the definitions of the trigonometric functions through identities, equations, and the solution of triangles — the problem-solving companion to a classical trigonometry course.
Anoshchenko's Trigonometry
by P. M. Anoshchenko
US grades 10–12 · UK Years 10–13
The 1905 secondary-school course in plane trigonometry, in first faithful English translation from the original Russian edition. Three parts: goniometry builds the measurement of angles and the trigonometric quantities from first principles across twelve chapters; rectilinear trigonometry proper solves the right triangle and then the oblique triangle, and closes with a full chapter on field triangulation; supplementary articles take up trigonometric equations, inverse trigonometric quantities, and maxima and minima. Sixty-three figures on eight plates.
Rybkin's Plane Trigonometry
by N. A. Rybkin
US grades 10–12 · UK Years 10–13
A complete course in plane trigonometry, in first faithful English translation from the original Russian edition. Eleven chapters and 126 numbered sections in three divisions. Goniometry builds the six trigonometric functions from lines in the circle, first for the acute angle and then through the full revolution: reduction formulas, negative angles and periodicity, graphs of the functions, inverse circular functions, the sum and difference, double-angle and half-angle formulas, reduction to logarithmic form and the auxiliary angle, and a chapter of trigonometric equations that shows how roots are lost. The second division explains how trigonometric tables are constructed and how four- and five-place tables are used. The third solves right and oblique triangles, each case worked with natural values and again with logarithms, and closes with measurement in the field: inaccessible distances, heights and triangulation. Fifty-four figures and a summary of the basic formulas.
Rybkin's Trigonometry Problems
by N. A. Rybkin
US grades 10–12 · UK Years 10–13
A problem book in trigonometry by the author of the planimetry and stereometry problem collections, in first faithful English translation from the original Russian edition. 1,009 numbered problems in 24 sections and two parts, with an answer key at the back. Part One works through trigonometry itself: the measurement of arcs and angles and radian measure, the variation of the functions, the relations between the functions of one angle, tables of natural values, right and oblique triangles, reduction formulas, the addition theorem, multiple and half arguments, sums turned into products and the auxiliary angle, logarithmic computation, trigonometric equations and inverse circular functions. Part Two applies trigonometry to geometry: plane figures, lines and planes, dihedral and polyhedral angles, the area of a projection, prisms and pyramids, cylinders and cones, volumes, the sphere and solids of revolution. Forty-five figures and a table of natural values.
Rashevsky's Trigonometry
by K. N. Rashevsky
US grades 10–12 · UK Years 10–13
A faithful English edition of the classical Russian trigonometry textbook. A complete course in plane trigonometry — the trigonometric functions, radian measure and the unit circle, identities, equations, and the solution of triangles — built the way the Russian school tradition built it: define, prove, apply.
Schiff's Trigonometry Problems
by V. I. Schiff
US grades 10–12 · UK Years 10–13
A problem book in plane trigonometry by Vera Schiff, who taught mathematics at the Bestuzhev Courses in St Petersburg for thirty-five years, in first faithful English translation from the original Russian edition. 389 numbered problems, with 306 further lettered parts, in ten sections: angles in degrees and radians; the sines and cosines of the simplest angles and the simplest equations; tangent, cotangent, secant and cosecant, with the proof of identities; sums and differences, double, triple and half angles, and sums turned into products; inverse trigonometric functions; the relations between the sides of a triangle and the functions of its angles; logarithmic tables; trigonometric equations; the solution of triangles, including the solids swept out by a triangle turning about an axis; and mixed problems. Answers and worked solutions are given for 209 of the problems.
Fuss's Pure Mathematics, Part III
by N. I. Fuss
US grades 11–12 and university · UK Years 12–13 and undergraduate
The third part of Fuss's course of pure mathematics, after the Algebra and the Geometry, in first faithful English translation from the original Russian edition. Four divisions, 32 chapters and 480 numbered sections. The application of algebra to geometry: geometric questions solved by equations of the first to the fourth degree. Plane trigonometry: the trigonometric lines and their properties, the solution of triangles, questions of practical geometry, further formulas, and the solution of cubic equations by trigonometry. Conic sections: the sections of a cone, curved lines in general, the circle, the ellipse, the parabola and the hyperbola. The foundations of the differential and integral calculus: differentials of algebraic and transcendental functions, tangents, points of inflection, greatest and least quantities, integrals, the length and quadrature of curves, the surfaces and volumes of solids of revolution, and the inverse method of tangents. 219 questions are worked with full solutions; the 157 figures are reproduced on twelve engraved plates.
Markov: Probabilities
by Andrei A. Markov
US grades 12 and university · UK Year 13 and university
The foundational 1900 work on probability theory by the mathematician who gave us Markov chains. A modern annotated English translation.
Fikhtengol'ts' Analysis, Vol. I
by G. M. Fikhtengol'ts
US grades University 1–2 · UK Undergraduate 1–2
The university course in mathematical analysis by the founder of the Leningrad school of the theory of functions, in first faithful English translation from the original Russian edition. Fourteen chapters run from the real numbers through functions, limits and the number e, continuity, the derivative and the differential, the mean-value theorems and Taylor's formula, the study of functions by their derivatives, functions of several variables and their differentiation and extrema, the indefinite and the definite integral, geometric and mechanical applications, curvature, and a historical survey of the origins of analysis from its prehistory to Newton and Leibniz. 390 pages with an alphabetical index.
Gunter & Kuzmin
by N. M. Gunter & R. O. Kuzmin
US grades University 1–4 · UK Undergraduate
The standard Russian problem collection for higher mathematics — the book used across Soviet technical universities. 814 pages spanning mathematical analysis, differential and integral calculus, series, differential equations, and probability theory, in the first complete English translation. Also published as two separate volumes, Part I and Part II, for readers who want half the book at a time.
Gunter & Kuzmin, Part I
by N. M. Gunter & R. O. Kuzmin
US grades University 1–2 · UK Undergraduate
The first half of the standard Russian problem book for higher mathematics, as a volume on its own: analytic geometry in the plane and in space, differential calculus and its applications including differential geometry, higher algebra, and indefinite and definite integration. 448 pages.
Gunter & Kuzmin, Part II
by N. M. Gunter & R. O. Kuzmin
US grades University 2–4 · UK Undergraduate 2–3
The second half completes the collection: multiple, curvilinear and surface integrals, field and potential theory, ordinary and partial differential equations, improper integrals and special functions, series and Fourier series, approximate computation, functions of a complex variable, mathematical physics, the calculus of variations and probability. 379 pages.
Demidovich's Analysis Problems
by B. P. Demidovich
US grades University 1–2 · UK Undergraduate 1–2
Demidovich's university problem book in mathematical analysis, in first faithful English translation from the original Russian edition. Two parts, eight chapters and 82 numbered sections hold 4,683 numbered problems, each section opening with a short summary of theory: real numbers, sequences, limits and continuity, O-notation, uniform continuity and functional equations; the differential calculus of one variable, from the theorems of Rolle, Lagrange and Cauchy to curvature and evolutes; indefinite and definite integrals with their geometric and physical applications; numerical, functional, power and Fourier series, infinite products and Stirling's formula; the differential calculus of several variables; integrals depending on a parameter, Euler's integrals and the Fourier integral formula; and double, triple, many-fold, line and surface integrals, through the formulas of Green, Stokes and Ostrogradsky to the elements of field theory. Answers, with hints, are at the back. Fourteen figures.
Kiselev's Calculus
by A. P. Kiselev
US grades 11–12 · UK Years 12–13
The first complete English translation of Kiselev's calculus — the final volume in his school course. Single-variable differential and integral calculus, proof-based, with classical applications to mechanics and physics. The bridge from Algebra II into the analysis tradition that produced Markov's probability theory.
Fikhtengol'ts' Analysis, Vol. II
by G. M. Fikhtengol'ts
US grades University 1–2 · UK Undergraduate 1–2
The second volume of the university course in mathematical analysis by the founder of the Leningrad school of the theory of functions, in a faithful new English edition. Ten chapters continue directly from Volume I: numerical series and infinite products; sequences and series of functions, power series and approximate computation; improper integrals and integrals depending on a parameter, with the Eulerian integrals; implicit functions and functional determinants; line, double, surface and triple integrals, the formulas of Green, Ostrogradsky and Stokes, and the elements of field theory; Fourier series and the Fourier integral. A concluding sketch points towards differential equations, the calculus of variations, complex and real analysis and functional analysis. 192 numbered articles (Nos. 234–425), 88 figures, 412 pages with an alphabetical index.
Yushkevich: Mathematics in Russia
by A. P. Yushkevich
US grades University and adult · UK Undergraduate and adult
A. P. Yushkevich’s history of mathematics in Russia from its beginnings to 1917, in first faithful English translation from the original Russian edition. Four parts and 26 chapters: numeration, metrology and the arithmetic and geometric manuscripts of old Rus’; Magnitsky’s Arithmetic and the schools of Peter the First; the Petersburg Academy of Sciences, with five chapters on Euler — infinite series, his trilogy on analysis, differential equations and the calculus of variations — and one on his students and successors, Fuss among them; Lobachevsky and the discovery of non-Euclidean geometry; Ostrogradsky and Bunyakovsky; Chebyshev and the Petersburg school, with chapters on number theory, probability theory, the approximation of functions, differential equations, series, analytic functions, geometry and algebra; and the rise of the Moscow school of function theory under Egorov and Luzin. The school textbooks of Kiselev, Davidov, and Malinin and Burenin appear in their place. Fifty numbered figures with portraits and facsimiles, and a name index. 673 pages.
Demidovich's Analysis Problems for Engineers
by B. P. Demidovich (editor)
US grades University 1–2 · UK Undergraduate 1–2
The problem collection in mathematical analysis written for engineering colleges by ten authors under the editorship of B. P. Demidovich, in faithful English translation from the original Russian edition. Ten chapters and 102 numbered sections hold 3,199 numbered problems, each section opening with a summary of theory and worked examples: functions, limits and continuity; differentiation and its geometrical and mechanical applications; extrema, asymptotes and curve sketching; the indefinite and the definite integral, with areas, volumes, centres of gravity and physical problems; functions of several variables, through directional derivatives, envelopes and the curvature and torsion of space curves; multiple, line and surface integrals and the elements of field theory; number, functional, Taylor and Fourier series; a full chapter of 404 problems on differential equations; and a chapter of approximate calculations — interpolation, real roots of equations, numerical integration of functions and of differential equations. Answers follow, with hints and, for the problems marked with two asterisks, solutions. 107 numbered figures and six appendix tables.
International editions
Kiselev's Arithmetic translated from the Russian original into 12 further languages.
算术 (简体中文)
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The complete Simplified Chinese edition of Kiselev's Arithmetic, translated from the Russian original. Whole numbers, divisibility, measurement, fractions, ratio and proportion — every rule derived, not asserted.
Aritmética (Português)
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The complete Brazilian Portuguese edition of Kiselev's Arithmetic, translated from the Russian original. Whole numbers, divisibility, measurement, fractions, ratio and proportion — every rule derived, not asserted.
Aritmetik (Dansk)
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The complete Danish edition of Kiselev's Arithmetic, translated from the Russian original. Whole numbers, divisibility, measurement, fractions, ratio and proportion — every rule derived, not asserted.
Aritmetica (Italiano)
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The complete Italian edition of Kiselev's Arithmetic, translated from the Russian original. Whole numbers, divisibility, measurement, fractions, ratio and proportion — every rule derived, not asserted.
算術 (日本語)
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The complete Japanese edition of Kiselev's Arithmetic, translated from the Russian original. Whole numbers, divisibility, measurement, fractions, ratio and proportion — every rule derived, not asserted.
산술 (한국어)
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The complete Korean edition of Kiselev's Arithmetic, translated from the Russian original. Whole numbers, divisibility, measurement, fractions, ratio and proportion — every rule derived, not asserted.
Arytmetyka (Polski)
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The complete Polish edition of Kiselev's Arithmetic, translated from the Russian original. Whole numbers, divisibility, measurement, fractions, ratio and proportion — every rule derived, not asserted.
Aritmética (Español)
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The complete Spanish edition of Kiselev's Arithmetic, translated from the Russian original. Whole numbers, divisibility, measurement, fractions, ratio and proportion — every rule derived, not asserted.
Aritmetik (Svenska)
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The complete Swedish edition of Kiselev's Arithmetic, translated from the Russian original. Whole numbers, divisibility, measurement, fractions, ratio and proportion — every rule derived, not asserted.
Aritmetik (Türkçe)
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The complete Turkish edition of Kiselev's Arithmetic, translated from the Russian original. Whole numbers, divisibility, measurement, fractions, ratio and proportion — every rule derived, not asserted.
Arithmétique (Français)
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The complete French edition of Kiselev's Arithmetic, translated from the Russian original. Whole numbers, divisibility, measurement, fractions, ratio and proportion — every rule derived, not asserted.
Arithmetik (Deutsch)
by A. P. Kiselev
US grades 4–7 · UK Years 5–8
The complete German edition of Kiselev's Arithmetic, translated from the Russian original. Whole numbers, divisibility, measurement, fractions, ratio and proportion — every rule derived, not asserted.