Softcover ISBN: 978-1-4704-6978-8
Product Code: CONM/795
Expected availability date: April 05, 2024
Contemporary Mathematics Volume: 795;
2024; 197 pp
MSC: Primary 91; 90;
This volume contains the proceedings of the virtual AMS Special Session on Mathematics of Decisions, Elections and Games, held on April 8, 2022.
Decision theory, voting theory, and game theory are three related areas of mathematics that involve making optimal decisions in different contexts. While these three areas are distinct, much of the recent research in these fields borrows techniques from other branches of mathematics such as algebra, combinatorics, convex geometry, logic, representation theory, etc. The papers in this volume demonstrate how the mathematics of decisions, elections, and games can be used to analyze problems from the social sciences.
Graduate students and research mathematicians interested in apportionment theory, decision theory, game theory, and social choice theory.
D. Marc Kilgour and Steven J. Brams ? When to stop consulting
Steven J. Brams and Ben D. Mor ? How lies induced cooperation in Golden Balls: A game-theoretic analysis
Adam Graham-Squire ? Conditions for fairness anomalies in instant-runoff voting
Kristen Mazur, Mutiara Sondjaja, Matthew Wright and Carolyn Yarnall ? Piercing numbers in circular societies
Karl-Dieter Crisman, Abraham Holleran, Micah Martin and Josephine Noonan ? Voting on cyclic orders, group theory, and ballots
Wesley H. Holliday, Chase Norman, Eric Pacuit and Saam Zahedian ? Impossibility theorems involving weakenings of expansion consistency and resoluteness in voting
Donald G. Saari ? Connecting Arrow’s Theorem, voting theory, and the Traveling Salesperson Problem
Michael A. Jones, David McCune and Jennifer Wilson ? An iterative procedure for apportionment and its use in the 2016 Georgia Republican primary
Steven J. Brams and Mehmet S. Ismail ? Double moves by each player in chess openings make the game fairer
Softcover ISBN: 978-1-4704-7398-3
Product Code: AMSTEXT/64
Expected availability date: April 27, 2024
Pure and Applied Undergraduate Texts Volume: 64;
2024; 371 pp
MSC: Primary 11; 68; 81; 94;
Quantum algorithms are among the most important, interesting, and promising innovations in information and communication technology. They pose a major threat to today's cybersecurity and at the same time promise great benefits by potentially solving previously intractable computational problems with reasonable effort. The theory of quantum algorithms is based on advanced concepts from computer science, mathematics, and physics.
Introduction to Quantum Algorithms offers a mathematically precise exploration of these concepts, accessible to those with a basic mathematical university education, while also catering to more experienced readers. This comprehensive book is suitable for self-study or as a textbook for one- or two-semester introductory courses on quantum computing algorithms. Instructors can tailor their approach to emphasize theoretical understanding and proofs or practical applications of quantum algorithms, depending on the course's goals and timeframe.
Undergraduate and graduate students and researchers interested in learning the foundations of quantum computing.
Classical computation
Hilbert spaces
Quantum mechanics
The theory of quantum algorithms
The algorithms of Deutsch and Simon
The algorithms of Shor
Quantum search and quantum counting
The HHL algorithm
Foundations
Linear algebra
Probability theory
Solutions of selected exercises
Bibliography
Index
Hardcover ISBN: 978-1-4704-7302-0
Product Code: GSM/236
Expected availability date: April 30, 2024
Graduate Studies in Mathematics Volume: 236;
2024; 277 pp
MSC: Primary 53; 30;
Alexandrov spaces are defined via axioms similar to those of the Euclid axioms but where certain equalities are replaced with inequalities. Depending on the signs of the inequalities, we obtain Alexandrov spaces with curvature bounded above (CBA) and curvature bounded below (CBB). Even though the definitions of the two classes of spaces are similar, their properties and known applications are quite different.
The goal of this book is to give a comprehensive exposition of the structure theory of Alexandrov spaces with curvature bounded above and below. It includes all the basic material as well as selected topics inspired by considering Alexandrov spaces with CBA and with CBB simultaneously. The book also includes an extensive problem list with solutions indicated for every problem.
Graduate students and researchers interested in geometry.
Preliminaries
Model plane
Metric spaces
Maps and functions
Ultralimits
Space of spaces
The ghost of Euclid
Dimension theory
Fundamentals
Fundamentals of curvature bounded below
Fundamentals of curvature bounded above
Kirszbraun revisited
Warped products
Polyhedral spaces
Structure and tools
First order differentiation
Dimension of CAT spaces
Dimension of CBB spaces
Gradient flow
Semisolutions
Bibliography
Index
Softcover ISBN: 978-1-4704-7260-3
Product Code: CONM/796
Expected availability date: April 05, 2024
Contemporary Mathematics Volume: 796;
2024; 373 pp
MSC: Primary 11; 14;
This book will be published Open Access with a Creative Commons Attribution 4.0 International License (CC BY 4.0). The eBOOK will be available to download electronically for free when published.
This volume contains the proceedings of the LuCaNT (LMFDB, Computation, and Number Theory) conference held from July 10?14, 2023, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island and affiliated with Brown University.
This conference provided an opportunity for researchers, scholars, and practitioners to exchange ideas, share advances, and collaborate in the fields of computation, mathematical databases, number theory, and arithmetic geometry. The papers that appear in this volume record recent advances in these areas, with special focus on the LMFB (the L-Functions and Modular Forms Database), an online resource for mathematical objects arising in the Langlands program and the connections between them.
Graduate students and research mathematicians interested in number theory, arithmetic geometry, and computation.
Christian Bagshaw, Michael J. Jacobson, Renate Scheidler and Nickolas Rollick ? Improved methods for finding imaginary quadratic fields with high n
-rank
Ce Bian, Andrew R. Booker, Austin Docherty, Michael J. Jacobson Jr. and Andrei Seymour-Howell ? Unconditional computation of the class groups of real quadratic fields
Kiran S. Kedlaya ? The relative class number one problem for function fields, III
John E. Cremona and Andrew V. Sutherland ? Computing the endomorphism ring of an elliptic curve over a number field
Jacob Mayle and Rakvi ? Serre curves relative to obstructions modulo 2
Barinder S. Banwait, Armand Brumer, Hyun Jong Kim, Zev Klagsbrun, Jacob Mayle, Padmavathi Srinivasan and Isabel Vogt ? Computing nonsurjective primes associated to Galois representations of genus 2
curves
Noam D. Elkies ? Families of genus-2 curves with 5-torsion
Raymond van Bommel, Shiva Chidambaram, Edgar Costa and Jean Kieffer ? Computing isogeny classes of typical principally polarized abelian surfaces over the rationals
Francesca Bianchi and Oana Padurariu ? Rational points on rank 2 genus 2 bielliptic curves in the LMFDB
Eran Assaf, Watson Ladd, Gustavo Rama, Gonzalo Tornaria and John Voight ? A database of paramodular forms from quinary orthogonal modular forms
Havard Damm-Johnsen ? Modular algorithms for Gross?Stark units and Stark?Heegner points
Eran Assaf, Angelica Babei, Ben Breen, Edgar Costa, Juanita Duque-Rosero, Aleksander Horawa, Jean Kieffer, Avinash Kulkarni, Grant Molnar, Sam Schiavone and John Voight ? A database of basic numerical invariants of Hilbert modular surfaces
David W. Farmer, Sally Koutsoliotas, Stefan Lemurell and David P. Roberts ? The landscape of L-functions: degree 3 and conductor 1
Jonathan Komada Eriksen, Lorenz Panny, Jana Sotakova and Mattia Veroni ? Deuring for the people: Supersingular elliptic curves with prescribed endomorphism ring in general characteristic
Softcover ISBN: 978-1-4704-7469-0
Product Code: SURV/278
Expected availability date: May 02, 2024
Mathematical Surveys and Monographs Volume: 278;
2024; 141 pp
MSC: Primary 94; 81; 20;
This book is intended as a comprehensive treatment of group-based cryptography accessible to both mathematicians and computer scientists, with emphasis on the most recent developments in the area. To make it accessible to a broad range of readers, the authors started with a treatment of elementary topics in group theory, combinatorics, and complexity theory, as well as providing an overview of classical public-key cryptography. Then some algorithmic problems arising in group theory are presented, and cryptosystems based on these problems and their respective cryptanalyses are described. The book also provides an introduction to ideas in quantum cryptanalysis, especially with respect to the goal of post-quantum group-based cryptography as a candidate for quantum-resistant cryptography.
The final part of the book provides a description of various classes of groups and their suitability as platforms for group-based cryptography.
The book is a monograph addressed to graduate students and researchers in both mathematics and computer science.
Graduate students and researchers interested in algebraic methods of cryptography.
Background information
Group theory
Algorithmic problems in group theory
Classical cryptography
Post-quantum cryptography and cryptanalysis
Noncommutative cryptographic protocols
Attacks
Quantum cryptanalysis
Cryptographic platforms
Braid groups
Hyperbolic groups
Small cancellation groups
Polycyclic groups
Graph groups
Arithmetic groups
Engel groups
Self-similar groups
Bibliography
Index
Paperback ISBN: 9780443187209
An Introduction to Probability and Statistical Inference, Third Edition guides the reader through probability models and statistical methods to develop critical-thinking skills. Written by award-winning author George Roussas, this valuable text introduces a thinking process to help users obtain the best solution to a posed question or situation and provides a plethora of examples and exercises to illustrate applying statistical methods to different situations.
1. Some Motivating Examples and Some Fundamental Concepts
2. The Concept of Probability and Some Basic Results
3. Numerical Characteristics of a Random Variable, Some Special Random Variables
4. Joint and Conditional p.d.f.'s, Conditional Expectation and Variance, Moment Generating Function, Covariance and Correlation Coefficient
5. Independence of Random Variables and Some Applications
6. Transformation of Random Variables
7. Some Modes of Convergence of Random Variables, Applications
8. An Overview of Statistical Inference
9. Point Estimation
10. Confidence Intervals and Confidence Regions
11. Testing Hypotheses
12. More About Testing Hypotheses
13. A Simple Linear Regression Model
14. Two Models of Analysis of Variance
15. Some Topics in Nonparametric Inference
16. Appendix