Lecture Notes in Mathematics Computational Synthetic Geometry Vol. 1355 by Jurgen Bokowski, B. Strurmfels, Bernd Sturmfels, Constantin Niculescu, Lars-Erik Persson Paperback, 168 Pages, Published 1989 by Springer-Verlag ISBN-13: 978-0-387-50478-0, ISBN: 0-387-50478-8 "This book can be used for a one-semester graduate course on Convex Functions and Applications, and also as a valuable reference and source of inspiration for researchers working with convexity."
Algebraic Statistics for Computational Biology(Updated) by Lior Pachter, Bernd Sturmfels Hardcover, 420 Pages, Published 2005 by Cambridge University Press ISBN-13: 978-0-521-85700-0, ISBN: 0-521-85700-7 "The quantitative analysis of biological sequence data is based on methods from statistics coupled with efficient algorithms from computer science. Algebra provides a framework for unifying many of the seemingly disparate techniques used by computational biologists. This book offers an introduction to this mathematical framework and describes tools from computational algebra for designing new algorithms for exact, accurate results. These ..."
Grobner Bases and Convex Polytopes(1st Edition) (University Lecture Series, No. 8) by Bernd Sturmfels Paperback, 162 Pages, Published 1995 by American Mathematical Society ISBN-13: 978-0-8218-0487-2, ISBN: 0-8218-0487-1 "This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centres around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Gröbner bases is reflected by the ..."
Combinatorial Commutative Algebra (Graduate Texts in Mathematics) by Ezra Miller, Bernd Sturmfels Paperback, 420 Pages, Published 2005 by Springer ISBN-13: 978-0-387-23707-7, ISBN: 0-387-23707-0 "Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals a ..."
Combinatorial Commutative Algebra (Graduate Texts in Mathematics) by Ezra Miller, Bernd Sturmfels Hardcover, 420 Pages, Published 2004 by Springer ISBN-13: 978-0-387-22356-8, ISBN: 0-387-22356-8 "Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals a ..."
Solving Systems of Polynomial Equations (CBMS Regional Conference Series in Mathematics) by Bernd Sturmfels Paperback, 152 Pages, Published 2002 by American Mathematical Society ISBN-13: 978-0-8218-3251-6, ISBN: 0-8218-3251-4 "A classic problem in mathematics is solving systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely used across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, statistics, and numerous other areas. This book furnishes a bridge across mathematical disciplines and exposes many facets of systems of polynomial equations. I ..."
EOM(2nd Edition) 46 Oriented Matroids 2ed (Encyclopedia of Mathematics and its Applications) by Neil White, Michel Las Vergnas, Bernd Sturmfels, Gunter M. Ziegler, Anders Björner, Glnter M. Ziegler, Michel Las, Anders Bjã Rner, Anders Bjoerner Paperback, 564 Pages, Published 2000 by Cambridge University Press ISBN-13: 978-0-521-77750-6, ISBN: 0-521-77750-X "Oriented matroids are a very natural mathematical concept which presents itself in many different guises and which has connections and applications to many different areas. These include discrete and computational geometry, combinatorics, convexity, topology, algebraic geometry, operations research, computer science and theoretical chemistry. This is the second edition of the first comprehensive, accessible account of the subject. It is ..."
Introduction to Tropical Geometry (Paperback) by Diane Maclagan, Bernd Sturmfels Paperback, 363 Pages, Published 2021 by American Mathematical Society, United States ISBN-13: 978-1-4704-6856-9, ISBN: 1-4704-6856-5 "The following theorem was stated in the early 1990s in an unpublished manuscript by Mikhail Kapranov . A proof appeared in [ EKL06 ] . It establishes the link between classical hypersurfaces over a field K and tropical hypersurfaces in ..."
Invitation to Nonlinear Algebra by Mateusz Michałek, Bernd Sturmfels 226 Pages, Published 2021 by American Mathematical Soc. ISBN-13: 978-1-4704-6551-3, ISBN: 1-4704-6551-5 "Mateusz Michałek, Bernd Sturmfels. Invitation to Nonlinear Algebra Mateusz
Michałek Bernd Sturmfels Invitation to Nonlinear Algebra Invitation to Nonlinear
Algebra Mateusz Michałek. GRADUATE STUDIES IN MATHEMATICS 211 Cover."
Invitation to Nonlinear Algebra by Mateusz Michałek, Bernd Sturmfels 226 Pages, Published 2021 by American Mathematical Society ISBN-13: 978-1-4704-5367-1, ISBN: 1-4704-5367-3 "Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject."
Combinatorial Algebraic Geometry Selected Papers From the 2016 Apprenticeship Program by Gregory G. Smith, Bernd Sturmfels 390 Pages, Published 2017 by Springer ISBN-13: 978-1-4939-7486-3, ISBN: 1-4939-7486-6 "Proposition 6.4 We have .S=/an D San=an as topological spaces. Proof First, we
prove the equality of sets .S=/an D San=an. Consider x 2 .S=/an and its image .x/
2 S=. If U D Spec.A/ is an affine neighbourhood of the point .x/, then the point x
corresponds to a semi-norm jjx on A and .x/ corresponds to the prime ideal px D ff
2 A W jfj x D 0g; see [5, Remark 1.2.2]. We denote by H .x/ the fibres consists
completion San x of D multip ..."
Geometric Combinatorics by Ezra Miller, Victor Reiner, Bernd Sturmfels 691 Pages, Published by American Mathematical Soc. ISBN-13: 978-0-8218-8695-3, ISBN: 0-8218-8695-9 "After treating 3-polytopes in the first lecture and the /-vector shapes of very high-
dimensional polytopes in the second one, we will start to analyze the case of 4-
dimensional polytopes in detail. Thus the third lecture will explain a surprisingly
simple construction for 2-simple 2-simplicial 4-polytopes, which have symmetric f-
vectors. Lecture four sketches the geometry of the cone of /-vectors for 4-
polytopes, and thus identifi ..."
Oriented Matroids (Encyclopedia of Mathematics and its Applications) by Michel Las Vergnas, Bernd Sturmfels, Neil White, Anders Björner, Günter M. Ziegler, Anders Bjã Rner, G|Nter M., Anders Bjoerner Hardcover, 528 Pages, Published 1993 by Cambridge University Press ISBN-13: 978-0-521-41836-2, ISBN: 0-521-41836-4 "Oriented matroids are a very natural mathematical concept which presents itself in many different guises, and which has connections and applications to many different areas. These include discrete and computational geometry, combinatorics, convexity, topology, algebraic geometry, operations research, computer science and theoretical chemistry. This is the first comprehensive and accessible account of the subject. This book is intended f ..."
Algorithms in Invariant Theory (Texts and Monographs in Symbolic Computation) by Bernd Sturmfels Paperback, 300 Pages, Published 1993 by Springer Verlag ISBN-13: 978-0-387-82445-1, ISBN: 0-387-82445-6 "J. Kung and G.-C. Rota, in their 1984 paper, write: "Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics." The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is t ..."
Applied Geometry and Discrete Mathematics The Victor Klee Festschrift by Peter Gritzmann, Bernd Sturmfels, Victor Klee 608 Pages, Published 1991 by American Mathematical Soc. ISBN-13: 978-0-8218-7083-9, ISBN: 0-8218-7083-1 "The Victor Klee Festschrift Peter Gritzmann, Bernd Sturmfels, Victor Klee. For
completeness we give the proof of Lemma 2. Proof. Let K = conv((c, , \z\ + \z") , ... ,
(Cn , \zn + J<£)) , *' = conv((c,,z', ),..., (c„, 2^)), K = conv((c,, z,),... , (c„, zn)). The
sets K , K' , K" have the same orthogonal projection C = conv(c, , ... , cj on H. If x
E C, let (x, "x) and (x,x') denote the upper and lower points in K' , and similarly let ..."
Groebner Deformations of Hypergeometric Differential Equations, Algorithms and Computation in Mathematics, Volume 6 by Mutsumi Saito, Bernd Sturmfels, Nobuki Takayama Hardcover, 272 Pages, Published 2000 by Springer ISBN-13: 978-3-540-66065-1, ISBN: 3-540-66065-8 "In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Grobner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Grobner deformations of left ideals in the Weyl algebra are the algebraic analogue to classical perturbation techniques. The algorithmic method ..."
Computations in Algebraic Geometry with Macaulay 2 by Daniel R. Grayson, Bernd Sturmfels, Professor David Eisenbud, Michael Stillman, David Eisenbud, David Eisenbud And, Mike Stillman Hardcover, 345 Pages, Published 2001 by Springer ISBN-13: 978-3-540-42230-3, ISBN: 3-540-42230-7 "Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re cently developed algorithms have made theoretical aspects of the subject accessible to a broad range of mathematicians and scientists. The algorith mic approach to the subject has two principal aims: developing ..."
Lectures on Algebraic Statistics (Oberwolfach Seminars) by Mathias Drton, Seth Sullivant, Bernd Sturmfels Paperback, 180 Pages, Published 2008 by Birkhauser Basel ISBN-13: 978-3-7643-8904-8, ISBN: 3-7643-8904-4 "How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems usi ..."
