Abstract
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 encyclopedia but presents the necessary information about the main sections of mathematics and the most important mathematical concepts not in alphabetical order, but in their logical sequence. All the concepts and statements considered are illustrated by numerous examples. Due to the breadth of the material covered and the emphasis on identifying interdisciplinary connections, the book can help mathematicians expand the scope of their scientific interests and draw new ideas from related mathematical areas. Due to the thorough explanation of the meaning of newly introduced concepts, the presence of rich illustrative material, and the absence of cumbersome technical calculations, the book can help young researchers and students navigate the boundless ocean of mathematical ideas. Features • Brief introduction to the main sections of mathematics from the most fundamental ones such as algebra, topology, and analysis to more specialized ones such as differential equations, probability theory, calculus of variations, and differential and algebraic geometry • Comprehensive treatment of the basic concepts of mathematics in their logical interconnection • Significant portion of the material is included in appendices to parts and chapters, which allows the book to be used by readers with different levels of preparation and interests • Includes numerous illustrations and examples • Requires minimal mathematical prerequisites • Extensive subject index makes the book easy to use as a reference book