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[MATHEMATICS] Sammerbalt of two works on Finite Differences

Item #2719

1. Tikhomandritskiy M.A. Kurs teorii konechnykh raznostey [i.e. Course on the Theory of Finite Differences ] / [By] M. Tikhomandritsky, Ordinary Professor at Kharkov University. Kharkov: D.N. Poluekhtov, 1890. 288 p.
2. Markov, A. A. (Senior). Ischisleniye konechnykh raznostey [i.e. Calculus of Finite Differences]. In 2 Parts. Saint Petersburg: Printing House of the Imperial Academy of Sciences, 1889–1891. Part 1: Interpolation. 1889. [4], 122 p. Part 2: Finite Difference Equations and Summation. 1891. [4], 124 p. 23,5x16 cm.

Contemporary half-leather. Gilt lettering on the spine with authors’ names and the common title of the sammerbalt. Raised bands. Endpapers with floral ornament. Minor foxing of the first few leaves of the first work. Spine lacks a piece from the top. Otherwise in very good condition.

Two rare mathematical works in Russian.

Matvey Alexandrovich Tikhomandritsky (1844, Kyiv –1921, Yalta) was a Ukrainian mathematician, Doctor of Pure Mathematics, and Distinguished Professor of Mathematics at Kharkov University. In February 1883, he was elected Associate Professor at Kharkov University; he was confirmed in this position on April 12 and began delivering lectures in August. In the spring of 1884, he was sent abroad on an academic assignment (to Leipzig, Berlin, and Paris). From Paris, he submitted his dissertation, *The Inversion of Hyperelliptic Integrals*; on November 24, 1885, he was awarded the degree of Doctor of Pure Mathematics, and on December 31, he was confirmed as Extraordinary Professor. Beginning in the autumn of 1885, he also began lecturing on integral and differential calculus at the Kharkov Practical Technological Institute. Effective July 1, 1888, he was confirmed as Ordinary Professor in the Department of Pure Mathematics at Kharkov University. He delivered 16 lecture courses, the majority of which were subsequently published. A textbook on probability theory authored by M. A. Tikhomandritsky was recognized by the St. Petersburg Academy of Sciences with the V. Ya. Bunyakovsky Prize. Matvei A. Tikhomandritsky’s scholarly work reflects a sustained engagement with advanced areas of 19th-and early 20th-century mathematics, particularly within analysis and geometry. His early research focused on hypergeometric series and the theory of elliptic and hyperelliptic functions, including the use of theta functions and the inversion of integrals. Over time, he expanded his investigations to encompass Abelian integrals, trigonometric and elliptic function expansions, and the study of algebraic curves, including their singular points and curvature. Alongside his research contributions, Tikhomandritsky was deeply involved in mathematical pedagogy. He produced a number of comprehensive university-level textbooks and courses, covering higher algebra, finite differences, differential and integral calculus, analytic and differential geometry, including work adapted from contemporary European scholarship. His later writings also demonstrate an interest in the institutional and historical development of mathematics, as seen in his account of the first century of the Faculty of Physics and Mathematics at Kharkov University. Andrey Andreyevich Markov (1856–1922) was a Russian mathematician and academician who made significant contributions to probability theory, mathematical analysis, and number theory. Andrei A. Markov’s scientific work spans several major areas of mathematics, with his most influential contributions lying in probability theory. He is best known for introducing what are now called Markov processes—stochastic systems in which the future state depends only on the present state and not on the preceding history. Although initially regarded as highly abstract, this concept has since become foundational to modern probability theory and the broader study of stochastic processes. Markov also significantly advanced classical results such as the law of large numbers and the central limit theorem, extending them to dependent sequences, thereby deepening and generalizing earlier work. A substantial portion of his research was devoted to mathematical analysis, where he investigated topics such as continued fractions, finite difference calculus, interpolation theory, extremal problems in functional spaces, the moment problem, orthogonal polynomials, quadrature formulas, differential equations, and approximation theory. Building on the work of his teacher, Pafnuty Chebyshev, Markov contributed to the development of the theory of moments and extremal methods in analysis, producing results that remain influential. Although smaller in number, his works in number theory are also of lasting importance. His early research focused on binary quadratic forms and the problem of arithmetic minima, later extending these investigations to higherdimensional forms. These studies, connected to the work of Korkin and Zolotarev, had a notable impact on the subsequent development of number theory. Taken together, Markov’s oeuvre reflects a mathematician of broad scope, whose work not only advanced several core areas of pure mathematics but also laid essential groundwork for modern probabilistic and analytical methods. In public life, Markov is known for his protracted conflict with the Russian Orthodox Church: in 1901, he wrote a letter opposing the excommunication of Leo Tolstoy, and in 1912, he was himself excommunicated for the following public statements: "I perceive no essential difference between icons and relics, on the one hand, and idols—which are, of course, not gods themselves but merely their images—on the other; nor do I sympathize with any religions that, like Orthodoxy, are upheld by fire and sword and themselves serve as instruments thereof."

Two paper copies (Brown, Stanford) of the first Tikhomandritsky found in the Worldcat and no copies of the Markov work.

Price: $2,500.00