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Books on the topic 'Toric algebra'

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Published: 4 June 2021

Last updated: 4 February 2022

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1

1975-, Panov Taras E., ed. Toric topology. Providence, Rhode Island: American Mathematical Society, 2015.

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2

B, Little John, and Schenck Henry K. 1963-, eds. Toric varieties. Providence, R.I: American Mathematical Society, 2011.

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3

William, Fulton. Introduction to toric varieties. Princeton, N.J: Princeton University Press, 1993.

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4

Jorge, Donoso Pacheco, ed. Tomic testimonios. [Santiago, Chile]: Centro Latinoamericano Simón Bolivar, 1988.

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5

Dimer models and Calabi-Yau algebras. Providence, R.I: American Mathematical Society, 2012.

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6

1962-, Sturmfels Bernd, ed. Introduction to tropical geometry. Providence, Rhode Island: American Mathematical Society, 2015.

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7

P, Banks Stephen. Clifford algebras, nonlinear dynamical systems and isochronous tori. Sheffield: University of Sheffield, Dept. of Automatic Control and Systems Engineering, 1997.

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8

Oda, Tadao. Convex bodies and algebraic geometry: An introduction to the theory of toric varieties. Berlin: Springer-Verlag, 1988.

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9

Musson, Ian M. Invariants under tori of rings of differential operators and related topics. Providence, R.I: American Mathematical Society, 1998.

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10

Ewald, Günter. Combinatorial convexity and algebraic geometry. New York: Springer, 1996.

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11

Oda, T. Convex bodies and algebraic geometry: An introduction to the theory of toric varieties : with 42 figures. Berlin: Springer-Verlag, 1987.

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12

Shevchenko, Alesya. Numerical methods. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/996207.

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The textbook describes the basics of numerical methods for solving problems of mathematical analysis, linear algebra and ordinary differential equations. Considerable attention is paid to the issues of algorithmization of methods. It can be used when performing laboratory, course, final qualification and research works. Each topic contains a theoretical justification and a large number of examples of solving practical problems using the Maple mathematical package. Meets the requirements of the federal state educational standards of higher education of the latest generation. It is intended for students, postgraduates, university teachers, as well as for engineers and researchers who use numerical methods to solve applied problems.

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13

Maillot, Vincent. Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables. [Paris, France]: Société mathématique de France, 2000.

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14

Stanford Symposium on Algebraic Topology: Applications and New Directions (2012 : Stanford, Calif.), ed. Algebraic topology: Applications and new directions : Stanford Symposium on Algebraic Topology: Applications and New Directions, July 23--27, 2012, Stanford University, Stanford, CA. Providence, Rhode Island: American Mathematical Society, 2014.

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15

Tatsuoka, Maurice M. Multivariate analysis: Techniques for educational and psychological research. 2nd ed. New York: Macmillan, 1988.

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16

Real solutions to equations from geometry. Providence, R.I: American Mathematical Society, 2011.

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17

1957-, Gurvits Leonid, and Banff International Research Station for Mathematics Innovation & Discovery, eds. Randomization, relaxation, and complexity in polynomial equation solving: Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, February 28--March 5, 2010, Banff, Ontario [i.e. Alberta], Canada. Providence, R.I: American Mathematical Society, 2011.

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18

M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Linked Tori, II. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0006.

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This chapter proves several more results about weak isomorphisms between Moufang sets arising from quadratic forms and involutory sets. It first fixes a non-trivial anisotropic quadratic space Λ‎ = (K, L, q) before considering two proper anisotropic pseudo-quadratic spaces. It then describes a quaternion division algebra and its standard involution, a second quaternion division algebra and its standard involution, and an involutory set with a quaternion division algebra and its standard involution. It concludes with one more small observation regarding a pointed anisotropic quadratic space and shows that there is a unique multiplication on L that turns L into an integral domain with a multiplicative identity.

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19

M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Linked Tori, I. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0005.

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This chapter investigates the consequences of the assumption that one Moufang set is weakly isomorphic to another. It first introduces some well-known facts about involutions which are assembled in a few lemmas, including those dealing with an involutory set, a biquaternion division algebra, and a quaternion division algebra with a standard involution. It then presents a notation for a non-trivial anisotropic quadratic space and another for an involutory set are presented, along with assumptions for a pointed anisotropic quadratic space and the standard involution of a quaternion. It also makes a number of propositions regarding the standard involution of a quaternion and a biquaternion. Results about weak isomorphisms between Moufang sets arising from involutory sets are given.

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20

Fulton, William. Introduction to Toric Varieties. (AM-131), Volume 131. Princeton University Press, 2016.

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21

Geometrie D'Arakelov Des Varietes Toriques Et Fibres En Droites Integrables. Societe Mathematique De France, 2000.

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22

Mann, Peter. Near-Equilibrium Oscillations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0012.

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In this chapter, the theory of near-equilibrium oscillations is developed and normal mode analysis is performed. This topic requires a little bit of linear algebra when dealing with matrices, as well as an understanding of differential equations. The chapter explores small perturbations (small nudges or tiny shifts) to a stable equilibrium point in configuration space and introduces the characteristic equation. Interdisciplinary examples are then investigated, including a surface science example in which the bond frequencies of surface adsorbates are calculated, an example in which the motion of atoms in a triatomic molecule is examined and an example in which the molecular physics of atomic force microscopy is analysed. The properties of the eigenvalue problem for small oscillations are also investigated.

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23

Petersen, Wesley, and Peter Arbenz. Introduction to Parallel Computing. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198515760.001.0001.

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In the last few years, courses on parallel computation have been developed and offered in many institutions in the UK, Europe and US as a recognition of the growing significance of this topic in mathematics and computer science. There is a clear need for texts that meet the needs of students and lecturers and this book, based on the author's lecture at ETH Zurich is an ideal practical student guide to scientific computing on parallel computers working up from a hardware instruction level, to shared memory machines and finally to distributed memory machines. Aimed at advanced undergraduate and graduate students in applied mathematics, computer science and engineering, subjects covered include linear algebra, fast Fourier transform, and Monte-Carlo simulations, including examples in C and in some cases Fortran. This book is also ideal for practitioners and programmers.

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24

Little, Max A. Machine Learning for Signal Processing. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198714934.001.0001.

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Digital signal processing (DSP) is one of the ‘foundational’ engineering topics of the modern world, without which technologies such the mobile phone, television, CD and MP3 players, WiFi and radar, would not be possible. A relative newcomer by comparison, statistical machine learning is the theoretical backbone of exciting technologies such as automatic techniques for car registration plate recognition, speech recognition, stock market prediction, defect detection on assembly lines, robot guidance and autonomous car navigation. Statistical machine learning exploits the analogy between intelligent information processing in biological brains and sophisticated statistical modelling and inference. DSP and statistical machine learning are of such wide importance to the knowledge economy that both have undergone rapid changes and seen radical improvements in scope and applicability. Both make use of key topics in applied mathematics such as probability and statistics, algebra, calculus, graphs and networks. Intimate formal links between the two subjects exist and because of this many overlaps exist between the two subjects that can be exploited to produce new DSP tools of surprising utility, highly suited to the contemporary world of pervasive digital sensors and high-powered and yet cheap, computing hardware. This book gives a solid mathematical foundation to, and details the key concepts and algorithms in, this important topic.

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25

Algebraic And Combinatorial Aspects Of Tropical Geometry Ciem Workshop On Tropical Geometry December 1216 2011 International Center For Mathematical Meetings Castro Urdiales Spain. American Mathematical Society, 2013.

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