Textbook – Mathematical Association of America

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The Chain That Binds

By Lew Ludwig An Administrator’s Quip “If they want to ruin their education, that is up to them. We can’t stop them.” Someone recently shared this remark from an administrator who was responding to a question about whether they were concerned about what AI is doing to student learning. The exact circumstances and preceding exchange that...

The Putnam Exam: Why do we compete?

By Doug Ensley The MAA’s annual William Lowell Putnam Mathematical Competition has been running since 1938, and in the past 50 years, only 10 different institutions have won first place, with Harvard and MIT achieving the feat in two-thirds of those years. The competition is considered to be the most prestigious undergraduate mathematics competition in...

Experimental Mathematics: A Computational Perspective

The term “experimental mathematics” refers to the use of computation to discover and explore mathematical concepts. It has a long tradition that includes the laborious calculations by hand of Gauss, Euler, and many other notables, but the current usage applies to computation mostly with modern software and computer-related investigations. The authors have assembled a collection...

Book cover of Experimental Mathematics: A Computational Perspective by Matthew P. Richey and Matthew L. Wright, part of the AMS/MAA Textbooks series (Volume 74). The design features a purple header with the title and authors’ names, and the MAA Press and AMS logos at the bottom. The main background shows mathematical visuals: a grid of blue dots, a snippet of pseudocode for coin flips, a circular graph diagram with numbered nodes and connecting lines, several colorful line plots, and a small Fibonacci number table.

Bifurcation Theory

Bifurcation theory is a component of the study of dynamical systems that analyzes the changes in dynamics that occur when there is a qualitative change of behavior arising from varying parameters. Poincaré introduced the term bifurcation in the late nineteenth century to mean the splitting of equilibria for a family of differential equations. A great...

Fixed Point Theory in Generalized Metric Spaces

Fixed point theory is one of the major research areas in nonlinear functional analysis, topologyand real analysis, which deals with the study of fixed points of functions. A fixed point of afunction is a point in the domain of the function that is mapped to itself by the function. Fixedpoint theory also has several applications...

Book cover of "Fixed Point Theory in Generalized Metric Spaces" by Erdal Karapinar and Ravi P. Agarwal. The background is a gradient of purple hues with white and black text. The series title, “Synthesis Lectures on Mathematics & Statistics,” appears at the top under a red and navy banner. The publisher logos for "Synthesis Collection of Technology" and "Springer" are displayed at the top and bottom respectively.

Numerical Mathematics 3×9

This book presents an alternative standard first course in numerical analysis or “numerics” as the author calls it. It is subtitled “Three subject areas in 27 short chapters”. The author’s introduction emphasizes his intent to explore unexpected effects that arise in the course of developing numerical methods. The structure of the text suggest that is...

Cover of the book Numerical Mathematics: 3 x 9 by Sören Bartels, part of the UNITEXT series (volume 160),

Random Explorations

This book is part of the AMS Student Mathematical Library series and was developed followinga course the author offered in a 2020 Research Experiences for Undergraduates (REU) setting.The author explains that the title can be interpreted as both a random sampling of some objectsthat arise in probability and statistical mechanics, and as a prevailing theme...

An Introduction to Piecewise Smooth Dynamics

The study of piecewise smooth dynamics incorporates both theory and applications of those dynamical systems, smooth almost everywhere, which encounter discontinuities in isolated places, usually at some kind of threshold condition. The authors present an informal graduate course for studying models that involve such a discontinuity. The material provided here is derived from presentations given...

An Introduction to Convexity, Optimization and Algorithms

The authors’ goal in this book is to describe the basics of convex analysis, convex optimization, and the algorithms they enable. Convex optimization looks at the question of minimizing a convex function over a convex set. This study has ramifications across many disciplines of applied mathematics. Algorithms for convex optimization have become very important for...

Quantum Computation and Quantum Information: A Mathematical Perspective

This book is designed to be a textbook for a one-semester course in quantum computing and quantum information theory. Recommended prerequisites includes basic undergraduate finite probability theory, linear algebra, and some abstract algebra up through group theory. Some parts of the book are more challenging – particularly the later ones - and probably a better...

Inverse Problems and Data Assimilation

Inverse problems and the associated questions of data assimilation are of considerable interest in our data-intensive world. This book offers a concise introduction to these subjects from a mathematical perspective. The authors suggest it is most appropriate for advanced undergraduates and graduate students in mathematics as well as researchers in the sciences and engineering interested...

Symplectic and Contact Geometry

This introduction to symplectic and contact geometry is intended for advanced mathematics undergraduates, graduate students and other interested researchers with some background in differential geometry, manifold theory, and a bit of Lie theory and algebraic topology. Symplectic and contact geometry had their origins in classical mechanics but have developed broadly beyond that. This book stays...

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