Documents in Technical Books
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The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs.
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Requiring only high school algebra as mathematical background, the book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, and a discussion of The Seven Bridges of Konigsberg.
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This book walks the reader through the classic parts of Combinatorics and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate.
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An emerging field of Discrete Differential Geometry (DDG) aims at the development of discrete equivalents of notions and methods of classical differential geometry. No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.
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Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory.
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Assuming little mathematical background, this short introduction to Category Theory is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time. Suitable for independent study or as a course book, it gives extensive explanations of the key concepts along with hundreds of examples and exercises.