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Abstraction and infinity

Mancosu, Paolo, author

Oxford : Oxford University Press, c2016

The mathematical practice of definitions by abstraction from Euclid to Frege (and beyond) -- The logical and philosophical reflection on definitions by abstraction: from Frege to the Peano school and Russell -- Measuring the size of infinite collections of natural numbers: was Cantor's theory of infinite number inevitable? -- In good company? On Hume's Principle and the assignment of numbers to infinite concepts.

Paolo Mancosu provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. An example of this is Hume's Principle, which introduces the concept of number by stating that two concepts have the same number if and only if the objects falling under each one of them can be put in one-one correspondence. This principle is at the core of neo-logicism. In the first two chapters of the book, Mancosu provides a historical analysis of the mathematical uses and foundational discussion of definitions by abstraction up to Frege, Peano, and Russell. Chapter one shows that abstraction principles were quite widespread in the mathematical practice that preceded Frege's discussion of them and the second chapter provides the first contextual analysis of Frege's discussion of abstraction principles in section 64 of the Grundlagen. In the second part of the book, Mancosu discusses a novel approach to measuring the size of infinite sets known as the theory of numerosities and shows how this new development leads to deep mathematical, historical, and philosophical problems. The final chapter of the book explore how this theory of numerosities can be exploited to provide surprisingly novel perspectives on neo-logicism.--

Baker Berry Cook QA9 .M2945 2016

Competition math for middle school

Batterson, J

[Alpine, Calif.] : Art of Problem Solving, ©2010

Introduction -- Algebra -- Counting -- Probability -- Number theory -- Geometry -- Solutions -- Appendix.

"Written for the gifted math student, the new math coach, the teacher in search of problems and materials to challenge exceptional students, or anyone else interested in advanced mathematical problems like those found in the nation's major national math competitions, Competition Math contains over 700 examples and problems in the areas of Algebra, Counting, Probability, Number Theory, and Geometry. Examples and full solutions present clear concepts and provide helpful tips and tricks ..."--Back cover.

Baker Berry Cook QA43 .B38 2010

Periods and Nori motives

Huber, Annette, author

Cham, Switzerland : Springer, [2017]

General set-up -- Singular cohomology -- Algebraic de Rham cohomology -- Holomorphic de Rham Cohomology -- The period isomorphism -- Categories of (mixed) motives -- Nori's diagram category -- More on diagrams -- Nori motives -- Weights and pure Nori motives -- Periods of varieties -- Kontsevich-Zagier periods -- Formal periods and the period conjecture -- Elementary examples -- Multiple zeta values -- Miscellaneous periods : an outlook.

"This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives. It develops Nori's approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties. Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori's unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting. Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained."--Provided by publisher.

Baker Berry Cook QA612.3 .H83 2017

Stochastic modeling

Lanchier, Nicolas, author

Cham, Switzerland : Springer, [2017]

Baker Berry Cook QA274.2 .L35 2017

A basic course in probability theory

Bhattacharya, R. N. 1937- author

Cham, Switzerland : Springer, 2016

I. Random Maps, Distribution, and Mathematical Expectation -- II. Independence, Conditional Expectation -- III. Martingales and Stopping Times -- IV. Classical Central Limit Theorems -- V. Classical Zero-One Laws, Laws of Large Numbers and Large Deviations -- VI. Fourier Series, Fourier Transform, and Characteristic Functions -- VII. Weak Convergence of Probability Measures on Metric Spaces -- VIII. Random Series of Independent Summands -- IX. Kolmogorov's Extension Theorem and Brownian Motion -- X. Brownian Motion: The LIL and Some Fine-Scale Properties -- XI. Strong Markov Property, Skorokhod Embedding and Donsker's Invariance Principle -- XII. A Historical Note on Brownian Motion -- XIII. Some Elements of the Theory of Markov Processes and their Convergence to Equilibrium -- A. Measure and Integration -- B. Topology and Function Spaces -- C. Hilbert Spaces and Applications in Measure Theory.

This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded. General Markov dependent sequences and their convergence to equilibrium is the subject of an entirely new chapter. The introduction of conditional expectation and conditional probability very early in the text maintains the pedagogic innovation of the first edition; conditional expectation is illustrated in detail in the context of an expanded treatment of martingales, the Markov property, and the strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of large deviation and/or concentration inequalities ranging from those of Chebyshev, Cramer--Chernoff, Bahadur--Rao, to Hoeffding have been added, with illustrative comparisons of their use in practice. This also includes a treatment of the Berry--Esseen error estimate in the central limit theorem. The authors assume mathematical maturity at a graduate level; otherwise the book is suitable for students with varying levels of background in analysis and measure theory. For the reader who needs refreshers, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference. Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored numerous books, including a series of four upcoming graduate textbooks in stochastic processes with applications.

Baker Berry Cook QA273 .B43 2016

Homotopy of operads and Grothendieck-Teichmüller groups

Fresse, Benoit, author

Providence, Rhode Island : American Mathematical Society, [2017]

Part 1. The algebraic theory and its topological background -- I. From operads to Grothendeck-Teichmüller groups -- I(a). The general theory of operads -- I(b). Braids and E2-operads -- I(c). Hopf algebras and the Malcev completion -- I(d). The operadic definition of the Grothendieck-Teichmüller group -- Part 2. The applications of (rational) homotopy theory methods -- II. Homotopy theory and its applications to operads -- II(a). General methods of homotopy theory -- II(b). Modules, algebras, and the rational homotopy of spaces -- II(c). The (rational) homotopy of operads -- II(d). Applications of the rational homotopy to En-operads -- III. The computation of homotopy automorphism spaces of operads -- Introduction to the results of the computations for E2-operads -- III(a). The applications of homotopy spectral sequences -- III(b). The case of En-operads -- Conclusion : a survey of further research on operadic mapping spaces and their applications.

Baker Berry Cook QA612.7 .F74 2017

Foundations of arithmetic differential geometry

Buium, Alexandru, 1955- author

Providence, Rhode Island : American Mathematical Society, [2017]

Algebraic background -- Classical differential geometry revisted -- Arithmetic differential geometry : generalities -- Arithmetic differential geometry : the case of GLn -- Curvature and Galois groups of Ehresmann connections -- Curvature of Chern connections -- Curbature of Levi-Cività connections -- Curvature of Lax connections -- Open problems.

"The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is 'intrinsically curved'; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before"--Back cover.

Baker Berry Cook QA641 .B774 2017

String-Math 2014 : S tring-math 2014, June 9-13, 2014, University of Alberta, Edmonton, Alberta, Canada

Vincent Bouchard and three others, editors

Providence, Rhode Island : American Mathematical Society, [2016]

All genus mirror symmetry for toric Calabi-Yau 3-orbifolds -- Symmetries and defects in three-dimensional topological field theory -- Quantum curves and topological recursion -- A few recent developments in 2d (2,2) and (0,2) theories -- Codimension two defects and the Springer correspondence -- Higher spin AdS₃ holography and superstring theory -- Humbert surfaces and the moduli of lattice polarized K3 surfaces -- Superconformal field theories and cyclic homology -- Differential K-characters and D-branes -- Integral pentagon relations for 3d superconformal indices -- Wilson Surfaces in 6D (2,0) Theory and AdS--/CFT₆ -- Motivic zeta functions of the quartic and its mirror dual -- Semistability and Instability in Products and Applications -- Local and relative BPS state counts for del Pezzo surfaces -- Resurgence and topological strings -- Chern-Simons splitting of 2+1D gauge theories -- A strange family of Calabi-Yau 3-folds -- Calabi-Yau threefolds fibred by Kummer surfaces associated to products of elliptic curves -- Weighted Hurwitz numbers and hypergeometric [tau]-functions: an overview -- Calabi-Yau threefolds with infinite fundamental group -- Logarithmic invariants of links -- Positivity of Hochster theta over C -- Cohomological Donaldson-Thomas theory.

The conference String-Math 2014 was held from June 9-13, 2014, at the University of Alberta. This edition of String-Math is the first to include satellite workshops: "String-Math Summer School" (held from June 2-6, 2014, at the University of British Columbia), "Calabi-Yau Manifolds and their Moduli" (held from June 14-18, 2014, at the University of Alberta), and "Quantum Curves and Quantum Knot Invariants" (held from June 16-20, 2014, at the Banff International Research Station). This volume presents the proceedings of the conference and satellite workshops. For mathematics, string theory has been a source of many significant inspirations, ranging from Seiberg-Witten theory in four-manifolds, to enumerative geometry and Gromov-Witten theory in algebraic geometry, to work on the Jones polynomial in knot theory, to recent progress in the geometric Langlands program and the development of derived algebraic geometry and n-category theory. In the other direction, mathematics has provided physicists with powerful tools, ranging from powerful differential geometric techniques for solving or analyzing key partial differential equations, to toric geometry, to K-theory and derived categories in D-branes, to the analysis of Calabi-Yau manifolds and string compactifications, to modular forms and other arithmetic techniques. Articles in this book address many of these topics.

Baker Berry Cook QA564 .S77 2014

Lie algebras, lie superalgebras, vertex algebras, and related topics : 2012-2014 Southeastern Lie Theory Workshop Series : Categorification of Quantum Groups and Representation Theory, April 21-22, 2012, North Carolina State University : Lie Algebras, Vertex Algebras, Integrable Systems and Applications, December 16-18, 2012, College of Charleston : Noncommutative Algebraic Geometry and Representation Theory, May 10-12, 2013, Louisiana State University : Representation Theory of Lie Algebras and Lie Superalgebras, May 16-17, 2014, University of Georgia

Kailash C. Misra, Daniel K. Nakano, Brian J. Parshall, editors

Providence, Rhode Island : American Mathematical Society, [2016]

Modular affine vertex algebras and baby Wakimoto modules / Tomoyuki Arakawa and Weiqiang Wang -- Howe correspondence and Springer correspondence for dual pairs over a finite field / A.-M. Aubert, W. Kraśkiewicz, and T. Przebinda -- Twisted modules for tensor product vertex operator superalgebras and permutation automorphisms of odd order / Katrina Barron -- Third cohomology for Frobenius kernels and related structures / Christopher P. Bendel, Daniel K. Nakano, and Cornelius Pillen -- Invariant theory for quantum Weyl algebras under finite group action / S. Ceken, J.H. Palmieri, Y.-H. Wang, and J.J. Zhang -- Bounded highest weight modules of osp(1,2n) / Thomas Ferguson, Maria Gorelik, and Dimitar Grantcharov -- A combinatorial description of the affine Gindikin-Karpelevich formula of type An(¹) / Seok-Jin Kang, Kyu-Hwan Lee, Hansol Ryu, and Ben Salisbury -- Canonical bases of Cartan-Borcherds type, II: Constructible functions on singular supports / Yiqiang Li -- Krichever-Novikov type algebras. An introduction / Martin Schlichenmaier -- Lax operator algebras and Lax equations / Oleg K. Sheinman -- From forced gradings to Q-Koszul algebras / Brian J. Parshall and Leonard L. Scott -- Perverse sheaves on the nilpotent cone and Lusztig's generalized Springer correspondence / Laura Rider and Amber Russell -- Categorifying the tensor product of a level 1 highest weight and perfect crystal in type A / Monica Vazirani -- On the unitary representations of the affine ax + b-group, sl(2,R) and their relatives / Anton M. Zeitlin.

"This book contains the proceedings of the 2012-2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras"--Publisher's website.

Baker Berry Cook QA252.3 .L5534 2016

Algebraic groups : structure and actions : 2015 Clifford lectures, Algebraic groups: structure and actions, March 2-5, 2015, Tulane University, New Orleans, Louisiana

Mahir Bilen Can, editor

Providence, Rhode Island : American Mathematical Society, [2017]

Preface -- Computing torus-equivariant K-theory of singular varieties / Dave Anderson -- Algebraic structures of groups of birational transformations / Jérémy Blanc -- The Hermite-Joubert problem over p-closed fields / Matthew Brassil and Zinovy Reichstein -- Some structure theorems for algebraic groups / Michel Brion -- Structure and classification of pseudo-reductive groups / Brian Conrad and Gopal Prasad -- Invariants of algebraic groups and retract rationality of classifying spaces / Alexander S. Merkurjev.

Baker Berry Cook QA247.4 .C55 2015

From Frenet to Cartan : the method of moving frames

Clelland, Jeanne N., 1970- author

Providence, Rhode Island : American Mathematical Society, [2017]

Baker Berry Cook QA433 .C564 2017

Calculus and analysis in Euclidean space

Shurman, Jerry Michael, author

Cham, Switzerland : Springer, [2016]

Preface -- 1. Results from One-Variable Calculus -- Part I. Multivariable Differential Calculus ; 2. Euclidean Space ; 3. Linear Mappings and Their Matrices ; 4. The Derivative ; 5. Inverse and Implicit Functions -- Part II. Multivariable Integral Calculus. 6. Integration ; 7. Approximation by Smooth Functions ; 8. Parameterized Curves ; 9. Integration of Differential Forms -- Index.

The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skills of geometric intuition (the visual cortex being quickly instinctive) algebraic manipulation (symbol-patterns being precise and robust) incisive use of natural language (slogans that encapsulate central ideas enabling a large-scale grasp of the subject). Thinking in these ways renders mathematics coherent, inevitable, and fluid. The prerequisite is single-variable calculus, including familiarity with the foundational theorems and some experience with proofs.

Baker Berry Cook QA278 .S52 2016

Episodes in the mathematics of medieval Islam

Berggren, J. L., author

New York, NY, U.S.A. : Springer, [2016]

Arithmetic in the Islamic world -- Geometry in the Islamic world -- Algebra in the Islamic world -- Trigonometry in the Islamic world -- Spherical trigonometry in the Islamic world -- Number theory and combinatorics in the Islamic world.

Baker Berry Cook QA27.A67 B46 2016

Introduction to nonlinear thermomechanics of solids

Kleiber, Michał, author

Switzerland : Springer, 2016

Kresge QA808 .K54 2016

Identity and play in interactive digital media : ergodic ontogeny

Cole, Sara M., author

New York, NY : Routledge, 2017

Baker Berry Cook QA76.76.I59 C6528 2017

Advanced penetration testing : hacking the world's most secure networks

Allsopp, Wil, author

Indianapolis, IN : John Wiley & Sons, Inc., [2017]

Medical records (in)security -- Stealing research -- Twenty-first century heist -- Pharma karma -- Guns and ammo -- Criminal intelligence -- War games -- Hack journalists -- Northern exposure.

Baker Berry Cook QA76.9.A25 A3686 2017

Latent variable models : an introduction to factor, path, and structural equation analysis

Loehlin, John C

New York, NY : Routledge, 2017

Baker Berry Cook QA278.6 .L64 2017

Fractals in probability and analysis

Bishop, Christopher J., author

Cambridge, United Kingdom ; Cambridge University Press, 2017

Baker Berry Cook QA614.86 .B57 2017

Galois representations and (Phi, Gamma)-modules

Schneider, P. 1953- author

Cambridge, United Kingdom : Cambridge University Press, 2017

Baker Berry Cook QA247.3 .S36 2017

A generalized framework of linear multivariable control

Tan, Liansheng, author

Kidlington, Oxford, United Kingdom : Butterworth-Heinemann is an imprint of Elsevier, 2017

Mathematical preliminaries -- Generalized inverse of matrix and solution of linear system equation -- Polynomial fraction description -- Stability -- Fundamental approaches to control system analysis -- Determination of finite and infinite frequency structure of a rational matrix -- The solution of a regular PMD and the set of impulsive free initial conditions -- A refined resolvent decomposition of a regular polynomial matrix and application to the solution of regular PMDs -- Frequency structures of generalized companion form and application to the solution of regular PMDs -- A generalized chain-scattering representation and its algebraic system properties -- Realization of behavior -- Related extensions to system well-posedness and internal stability -- Nonstandard H [infinity symbol] control problem : a generalized chain-scattering representation approach -- Internet congestion control : a linear multivariable control look.

Baker Berry Cook QA402.3 .T35 2017

The learning and teaching of geometry in secondary schools : a modeling perspective

Herbst, Pat., author

Abingdon, Oxon ; Routledge, an imprint of the Taylor & Francis Group, 2017

The Discourse of Teaching and Learning Secondary Geometry through History -- Geometric Figures and Their Representations -- Students' Thinking and Learning in Geometry -- Teaching Practice and Teacher Knowledge in Geometry Instruction -- Improving the Teaching and Learning of Geometry in Secondary School Classrooms -- A Conclusion and a Beginning: Doing Research on The Teaching and Learning of Secondary Geometry

IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Geometry in Secondary Schools reviews past and present research on the teaching and learning of geometry in secondary schools and proposes an approach for design research on secondary geometry instruction. Areas covered include: teaching and learning secondary geometry through history; the representations of geometric figures; students' cognition in geometry; teacher knowledge, practice and, beliefs; teaching strategies, instructional improvement, and classroom interventions; research designs and problems for secondary geometry. Drawing on a team of international authors, this new text will be essential reading for experienced teachers of mathematics, graduate students, curriculum developers, researchers, and all those interested in exploring students' study of geometry in secondary schools. -- Provided by publisher.

Baker Berry Cook QA461 .H43 2017

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