The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1?3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island.
The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions.
On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.
Readership
Graduate students and research mathematicians interested in computational mathematics.
Contemporary Mathematics, Volume: 754
2020; 364 pp; Softcover
MSC: Primary 11; 16; 35; 41; 65;
Print ISBN: 978-1-4704-5163-9
Product Code: CONM/754
MAA Press: An Imprint of the American Mathematical Society
Bicycle or Unicycle? is a collection of 105 mathematical puzzles whose defining characteristic is the surprise encountered in their solutions. Solvers will be surprised, even occasionally shocked, at those solutions. The problems unfold into levels of depth and generality very unusual in the types of problems seen in contests. In contrast to contest problems, these are problems meant to be savored; many solutions, all beautifully explained, lead to unanswered research questions. At the same time, the mathematics necessary to understand the problems and their solutions is all at the undergraduate level. The puzzles will, nonetheless, appeal to professionals as well as to students and, in fact, to anyone who finds delight in an unexpected discovery.
These problems were selected from the Macalester College Problem of the Week archive. The Macalester tradition of a weekly problem was started by Joseph Konhauser in 1968. In 1993 Stan Wagon assumed problem-generating duties. A previous book written by Wagon, Konhauser, and Dan Velleman, Which Way Did the Bicycle Go?, gathered problems from the first twenty-five years of the archive. The title problem in that collection was inspired by an error in logic made by Sherlock Holmes, who attempted to determine the direction of a bicycle from the tracks of its wheels. Here the title problem asks whether a bicycle track can always be distinguished from a unicycle track. You'll be surprised by the answer.
Readership
Undergraduate and graduate students and researchers interested in problem solving.
Problem Books, Volume: 36
2020; 286 pp; Softcover
MSC: Primary 00;
Print ISBN: 978-1-4704-4759-5
Product Code: PRB/36
This is a text for students who have had a three-course calculus sequence and who are ready to explore the logical structure of analysis as the backbone of calculus. It begins with a development of the real numbers, building this system from more basic objects (natural numbers, integers, rational numbers, Cauchy sequences), and it produces basic algebraic and metric properties of the real number line as propositions, rather than axioms. The text also makes use of the complex numbers and incorporates this into the development of differential and integral calculus. For example, it develops the theory of the exponential function for both real and complex arguments, and it makes a geometrical study of the curve (expit), for real t, leading to a self-contained development of the trigonometric functions and to a derivation of the Euler identity that is very different from what one typically sees. Further topics include metric spaces, the Stone?Weierstrass theorem, and Fourier series.
Readership
Undergraduates interested in analysis in one variable.
Pure and Applied Undergraduate Texts Volume: 47
2020; 247 pp; Softcover
MSC: Primary 26;
Print ISBN: 978-1-4704-5668-9
Product Code: AMSTEXT/47
Not yet published - available from December 2020
FORMAT: Hardback
ISBN: 9781107003736
This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.
A necessary update of the Bateman Manuscript Project for the twenty-first century
Gives an encyclopedic survey of multivariable special functions, providing an excellent starting point for readers who need guidance to the scattered literature
Emphasizes the connections between multivariable special functions and other fields, in particular, Lie theory and mathematical physics
Not yet published - available from January 2021
FORMAT: Hardback
ISBN: 9781108482950
This is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine regression on B-splines with simple, discrete, roughness penalties. They were introduced by the authors in 1996 and have been used in many diverse applications. The regression basis makes it straightforward to handle non-normal data, like in generalized linear models. The authors demonstrate optimal smoothing, using mixed model technology and Bayesian estimation, in addition to classical tools like cross-validation and AIC, covering theory and applications with code in R. Going far beyond simple smoothing, they also show how to use P-splines for regression on signals, varying-coefficient models, quantile and expectile smoothing, and composite links for grouped data. Penalties are the crucial elements of P-splines; with proper modifications they can handle periodic and circular data as well as shape constraints. Combining penalties with tensor products of B-splines extends these attractive properties to multiple dimensions. An appendix offers a systematic comparison to other smoothers.
Readers will learn how to recognize and avoid potential problems with large data sets
111 color illustrations and graphs demonstrate the flexibility and applicability of P-splines
The source code (in R), a supporting software package, and interactive programs are available on the companion website
1. Introduction
2. Bases, penalties, and likelihoods
3. Optimal smoothing in action
4. Multidimensional smoothing
5. Smoothing of scale and shape
6. Complex counts and composite links
7. Signal regression
8. Special subjects
A. P-splines for the impatient
B. P-splines and competitors
C. Computational details
D. Array algorithms
E. Mixed model equations
F. Standard errors in detail
G. The website.
Copyright Year 2021
ISBN 9780367194840
September 28, 2020 Forthcoming by Chapman and Hall/CRC
224 Pages 35 B/W Illustrations
This textbook presents techniques for statistical analysis in the absence of strong assumptions about the distributions generating the data. Rank-based and resampling techniques are heavily represented, but robust techniques are considered as well. These techniques include one-sample testing and estimation, multi-sample testing and estimation, and regression.
Attention is payed to the intellectual development of the field, with a thorough review of bibliographical references. Computational tools, in R and SAS, are developed and illustrated via examples. Exercises designed to reinforce examples are included.
Important techniques covered include
Rank-based techniques, including sign, Kruskal-Wallis, Friedman, Mann-Whitney and Wilcoxon tests, are presented.
Tests are inverted to produce estimates and confidence intervals.
Multivariate tests are explored.
Techniques reflecting the dependence of a response variable on explanatory variables are presented.
Density estimation is explored.
The bootstrap and jackknife are discussed.
This text is intended for a graduate student in applied statistics. The course is best taken after an introductory course in statistical methodology, a course in elementary probability, and a course in regression. Mathematical prerequisites include calculus through multivariate differentiation and integration, and, ideally, a course in matrix algebra.