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The Logical Structure of Mathematics: An Overview of Mathematical Concepts book cover

1st Edition

The Logical Structure of Mathematics An Overview of Mathematical Concepts

By Simon Serovajsky Copyright 2027
552 Pages 219 B/W Illustrations
by Chapman & Hall

552 Pages 219 B/W Illustrations
by Chapman & Hall

The Logical Structure of Mathematics is devoted to the presentation of the logical structure of mathematics from its foundations to its main standard areas and sections. It is intended to give an idea of mathematics as a uniform, integral system of knowledge, where different areas and concepts are intertwined with multilateral connections. The book is conceived as a brief mathematical... Read more

Part 1: Languages  Part 2: Sets  Part 3: Numbers  Part 4: Objects  4A. Ordered Objects  4B. Algebraic Objects  4C. Topological Objects  Part 5: Theories  5A. Applications of Linear Algebra and Geometry  5B. Topological Algebra and Functional Analysis  5C. Calculus  5D. Algebraic Geometry and Algebraic Topology  Part 6: Categories

Biography

Simon Serovajsky. Professor of Mathematics of al-Farabi Kazakh National University, Almaty, Kazakhstan.
Research Interests. Optimal Control Theory, Partial Differential Equations, Nonlinear Functional Analysis, Mathematical and Computational Modeling, History and Philosophy of Mathematics, Foundations of Mathematics. Scientific Achievements. Definition of the extended operator derivative. Extended differentiability of the solution for the nonlinear infinite dimensional systems with respect to parameter without its Gateaux differentiability. Necessary conditions of optimality for nonlinear infinite dimensional control systems. Definition of the weakened approximate solution of optimal control problems. Definition of the sequential model of systems. Sequential extension of optimal control problems. Mathematical modeling of problems in medicine and epidemiology.

General Books:
1. Counterexamples in the Optimal Control Theory. – Brill Academic Press. Netherlands, Utrecht, Boston, 2004. – 176 p.; Berlin, Boston, De Gruyter, 2011 (reprint).
2. Optimization and Differentiation. – Chapman and Hall / CRC Press. Taylor and Francis group, London, 2017. – 517 p.
3. Sequential models of the Mathematical Physics. – Boca Raton, London, New York, CRC Press, Taylor and Francis Group, 2019.– 266 p.
4. History of Mathematics. Evolutions of mathematical ideas. Part 1. Number Theory. Geometry. Topology. – Moscow, URSS, 2019. – 224 p.; Moscow, URSS, 2021 (reprint); Moscow, URSS, 2022 (reprint).
5. History of Mathematics. Evolutions of mathematical ideas. Part 2. Algebra. Analysis. Differential Equations. Extremum Theory. – Moscow, URSS, 2019. – 368 p.; Moscow, URSS, 2021 (reprint); Moscow, URSS, 2022 (reprint).
6. History of Mathematics. Evolutions of mathematical ideas. Part 3. Computational Mathematics. Probability Theory. Computer Science. Mathematical Logic. – Moscow, URSS, 2019. – 240 p.; Moscow, URSS, 2021 (reprint); Moscow, URSS, 2022 (reprint).
7. Architecture of Mathematics. – Boca Raton, London, New York, Chapman and Hall/CRC Press. – 2020. – 394 p. 
8. Mathematical Modelling. – Boca Raton, London, New York, CRC Press. Taylor and Francis Group, 2022. – 441 p.
9. Optimization. 100 Examples. – New York, Chapman and Hall/CRC, 2024. – 556 p.

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