IAS/PCMI-The Teacher Program Series, Volume: 1
2015; approx. 175 pp; softcover
ISBN-13: 978-1-4704-1925-7
Expected publication date is October 19, 2015.
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Probability through Algebra is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute.
But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves.
The specific themes developed in Probability through Algebra introduce readers to the algebraic properties of expected value and variance through analysis of games, to the use of generating functions and formal algebra as combinatorial tools, and to some applications of these ideas to questions in probabilistic number theory.
Probability through Algebra is a volume of the book series "IAS/PCMI-The Teacher Program Series" published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest.
Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
In-service secondary school teachers; students training to become secondary school teachers.
Problem sets
Facilitator notes
Teaching notes
Mathematical overview
Solutions
IAS/PCMI-The Teacher Program Series, Volume: 3
2015; approx. 216 pp; softcover
ISBN-13: 978-1-4704-2195-3
Expected publication date is October 9, 2015.
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Famous Functions in Number Theory is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute.
But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves.
Famous Functions in Number Theory introduces readers to the use of formal algebra in number theory. Through numerical experiments, participants learn how to use polynomial algebra as a bookkeeping mechanism that allows them to count divisors, build multiplicative functions, and compile multiplicative functions in a certain way that produces new ones. One capstone of the investigations is a beautiful result attributed to Fermat that determines the number of ways a positive integer can be written as a sum of two perfect squares.
Famous Functions in Number Theory is a volume of the book series "IAS/PCMI-The Teacher Program Series" published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest.
Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
In-service secondary school teachers; students training to become secondary school teachers.
Problem sets
Facilitaor notes
Teaching notes
Mathematical overview
Solutions
University Lecture Series, Volume: 63
2015; 114 pp; softcover
ISBN-13: 978-1-4704-2397-1
Expected publication date is October 9, 2015.
The theory of motives began in the early 1960s when Grothendieck envisioned the existence of a "universal cohomology theory of algebraic varieties". The theory of noncommutative motives is more recent. It began in the 1980s when the Moscow school (Beilinson, Bondal, Kapranov, Manin, and others) began the study of algebraic varieties via their derived categories of coherent sheaves, and continued in the 2000s when Kontsevich conjectured the existence of a "universal invariant of noncommutative algebraic varieties".
This book, prefaced by Yuri I. Manin, gives a rigorous overview of some of the main advances in the theory of noncommutative motives. It is divided into three main parts. The first part, which is of independent interest, is devoted to the study of DG categories from a homotopical viewpoint. The second part, written with an emphasis on examples and applications, covers the theory of noncommutative pure motives, noncommutative standard conjectures, noncommutative motivic Galois groups, and also the relations between these notions and their commutative counterparts. The last part is devoted to the theory of noncommutative mixed motives. The rigorous formalization of this latter theory requires the language of Grothendieck derivators, which, for the reader's convenience, is revised in a brief appendix.
Graduate students and research mathematicians interested in algebraic geometry, including non-commutative algebraic geometry.
Introduction
Differential graded categories
Additive invariants
Background on pure motives
Noncommutative pure motives
Noncommutative (standard) conjugates
Noncommutative motivic Galois groups
Jacobians of noncommutative Chow motives
Localizing invariants
Noncommutative mixed motives
Noncommutative motivic Hopf dg algebras
Appendix
Bibliography
Index
Student Mathematical Library, Volume: 76
2015; 269 pp; softcover
ISBN-13: 978-1-4704-2198-4
Expected publication date is October 2, 2015.
The winding number is one of the most basic invariants in topology. It measures the number of times a moving point P goes around a fixed point Q, provided that P travels on a path that never goes through Q and that the final position of P is the same as its starting position. This simple idea has far-reaching applications. The reader of this book will learn how the winding number can
help us show that every polynomial equation has a root (the fundamental theorem of algebra),
guarantee a fair division of three objects in space by a single planar cut (the ham sandwich theorem),
explain why every simple closed curve has an inside and an outside (the Jordan curve theorem),
relate calculus to curvature and the singularities of vector fields (the Hopf index theorem),
allow one to subtract infinity from infinity and get a finite answer (Toeplitz operators),
generalize to give a fundamental and beautiful insight into the topology of matrix groups (the Bott periodicity theorem).
All these subjects and more are developed starting only from mathematics that is common in final-year undergraduate courses.
Undergraduates and beginning graduate students interested in (and trying to learn) ideas concentrated around the notion of the winding number and its appearance in such areas of mathematics as analysis, differential geometry, and topology.
Prelude: Love, hate, and exponentials
Paths and homotopies
The winding number
Topology of the plane
Integrals and the winding number
Vector fields and the rotation number
The winding number in functional analysis
Coverings and the fundamental group
Coda: The Bott periodicity theorem
Linear algebra
Metric spaces
Extension and approximation theorems
Measure zero
Calculus on normed spaces
Hilbert space
Groups and graphs
Bibliography
Index
Proceedings of Symposia in Pure Mathematics, Volume: 90
2015; approx. 341 pp; hardcover
ISBN-13: 978-0-8218-9495-8
Expected publication date is October 8, 2015.
This volume contains the proceedings of the conference String-Math 2012, which was held July 16-21, 2012, at the Hausdorff Center for Mathematics, Universitat Bonn. This was the second in a series of annual large meetings devoted to the interface of mathematics and string theory. These meetings have rapidly become the flagship conferences in the field.
Topics include super Riemann surfaces and their super moduli, generalized moonshine and K3 surfaces, the latest developments in supersymmetric and topological field theory, localization techniques, applications to knot theory, and many more.
The contributors include many leaders in the field, such as Sergio Cecotti, Matthias Gaberdiel, Rahul Pandharipande, Albert Schwarz, Anne Taormina, Johannes Walcher, Katrin Wendland, and Edward Witten.
This book will be essential reading for researchers and students in this area and for all mathematicians and string theorists who want to update themselves on developments in the math-string interface.
Graduate students and research mathematicians interested in string theory.
Plenary talks
S. Cecotti -- The quiver approach to the BPS spectrum of a 4dN=2 gauge theory
R. Donagi and E. Witten -- Supermoduli space is not projected
M. R. Gaberdiel, D. Persson, and R. Volpato -- Generalised moonshine and holomorphic orbifolds
A. Marian, D. Oprea, and R. Pandharipande -- The first Chern class of the Verlinde bundles
A. Schwarz, V. Vologodsky, and J. Walcher -- Framing the di-logarithm (over Z)
A. Taormina and K. Wendland -- Symmetry-surfing the moduli space of Kummer K3s
A. Torrielli -- Secret symmetries of AdS/CFT
Contributed talks
I. Adam -- On the marginal deformations of general (0,2) non-linear sigma-models
S. Alexandrov, J. Manschot, D. Persson, and B. Pioline -- Quantum hypermultiplet moduli spaces in N=2 string vacua: A review
D. Andriot -- Non-geometric fluxes versus (non)-geometry
C. I. Lazaroiu, E. M. Babalic, and I. A. Coman -- The geometric algebra of supersymmetric backgrounds
N. Carqueville and D. Murfet -- A toolkit for defect computations in Landau-Ginzburg models
W. Donovan -- Grassmannian twists, derived equivalences, and brane transport
P. Fleig and A. Kleinschmidt -- Perturbative terms of Kac-Moody-Eisenstein series
H. Fuji and P. Su?kowski -- Super-A-polynomial
M. Huang -- On gauge theory and topological string in Nekrasov-Shatashvili limit
A.-K. Kashani-Poor -- AGT and the topological string
M. V. Movshev and A. Schwarz -- Generalized Chern-Simons action and maximally supersymmetric gauge theories