Gröbner bases in commutative algebra
by Ene, Viviana, Herzog, Jürgen
fromGraduate studies in mathematics
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Type: Book
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Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal…
This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to represe…
Although Évariste Galois was only 20 years old when he died, shot in a mysterious early-morning duel in 1832, his ideas, when they were published 14 years later, changed the course of algebra. He invented what is now called Galois Theory, the modern form of what was classically …
3-manifold groups
by Aschenbrenner, Matthias, Friedl, Stefan, Wilton, Henry
fromEMS series of lectures in mathematics
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Type: Book
The field of 3-manifold topology has made great strides forward since 1982, when Thurston articulated his influential list of questions. Primary among these is Perelman's proof of the Geometrization Conjecture, but other highlights include the Tameness Theorem of Agol and Calega…
Stimulating collection of over 300 unusual problems involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms and more. Problems range from easy to difficult. Detailed solutions, as well as brief answers, for all problems are pro…
The study of derived categories is a subject that attracts increasingly many young mathematicians from various fields of mathematics, including abstract algebra, algebraic geometry, representation theory and mathematical physics. The concept of the derived category of sheaves wa…
"As it says on the front cover this book is an introduction to Category Theory. It gives the basic definitions, goes through the various associated gadgetry such as functors, natural transformations, limits and colimits, and then explains adjunctions. This material could be deve…
An exciting approach to the history and mathematics of number theory ". . . the author's style is totally lucid and very easy to read . . .the result is indeed a wonderful story." {u2013} Mathematical Reviews Written in a unique and accessible style for readers of varied mathema…
Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Later…
Discover New Methods for Dealing with High-Dimensional Data A sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generaliz…
Primality testing for beginners
by Waldecker, Rebecca, Rempe-Gillen, Lasse
fromStudent mathematical library
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Type: Book
This book is about the theory and practice of integer factorization presented in a historic perspective. It describes about twenty algorithms for factoring and a dozen other number theory algorithms that support the factoring algorithms. Most algorithms are described both in wor…