“…This graduate-level text also addresses a broader interdisciplinary audience, keeping the mathematical level essentially uniform throughout the book, and involving only basic elements from calculus, algebra, geometry and systems theory. .…”
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“…Essential for undergraduate students, PhD students, and instructors, the problems in this book vary in difficulty and cover most of the obligatory courses given at the undergraduate level, including calculus, algebra, geometry, discrete mathematics, measure theory, complex analysis, differential equations, and probability theory. …”
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“…The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. …”
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“…They provide an insight into the foundations of each of the main branches of mathematics--algebra, geometry, number. theory, analysis, logic and set theory--with narratives to show how they are linked. …”
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“…In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available.…”
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“…The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. …”
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“…This volume, dedicated to the memory of the great American mathematician Bertram Kostant (May 24, 1928 – February 2, 2017), is a collection of 19 invited papers by leading mathematicians working in Lie theory, representation theory, algebra, geometry, and mathematical physics. Kostant’s fundamental work in all of these areas has provided deep new insights and connections, and has created new fields of research. …”
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“…Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. …”
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“…Mathematical areas explored include combinatorics, logic, graph theory, linear algebra, geometry, topology, computer science, operations research, probability, game theory, and music theory. …”
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“…It differs from the traditional exposition in two major ways: on the one hand in its closer relation to natural-science applications (primarily to physics and mechanics) and on the other hand in a greater-than-usual use of the ideas and methods of modern mathematics, that is, algebra, geometry, and topology. The course is unusually rich in ideas and shows clearly the power of the ideas and methods of modern mathematics in the study of particular problems. …”
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