Michael A. Jones - Böcker

Math Affinity Puzzles highlights the patterns and relationships that appear throughout mathematics. Rather than treating mathematics as a collection of separate topics or isolated courses, the puzzles here look beyond boundaries to discover links among different areas of knowledge. The book uses analogies to explore connections between mathematical terms and concepts, where solving a puzzle requires unraveling the relationships between the mathematical ideas. Solving this kind of mathematical puzzle is thus not about assessing understanding, but deepening it, making the connections, and having fun doing it.Each puzzle is followed by a short description and further discussion, touching on the different choices while going more deeply into historical or other aspects of the relationships. In some cases, there may be multiple relationships present and the suggested answer is one of many.The puzzles in this book can be enjoyed on their own or as supplements in a course setting. The authors have used them in calculus and upper-level classes as homework assignments and for in-class discussions, offering opportunities for noncomputational critical thinking, speaking, and writing about mathematics. Regardless of their use, the puzzles will deepen the reader’s understanding and appreciation of the relationships among mathematical ideas.

Math Affinity Puzzles highlights the patterns and relationships that appear throughout mathematics. Rather than treating mathematics as a collection of separate topics or isolated courses, the puzzles here look beyond boundaries to discover links among different areas of knowledge. The book uses analogies to explore connections between mathematical terms and concepts, where solving a puzzle requires unraveling the relationships between the mathematical ideas. Solving this kind of mathematical puzzle is thus not about assessing understanding, but deepening it, making the connections, and having fun doing it.Each puzzle is followed by a short description and further discussion, touching on the different choices while going more deeply into historical or other aspects of the relationships. In some cases, there may be multiple relationships present and the suggested answer is one of many.The puzzles in this book can be enjoyed on their own or as supplements in a course setting. The authors have used them in calculus and upper-level classes as homework assignments and for in-class discussions, offering opportunities for noncomputational critical thinking, speaking, and writing about mathematics. Regardless of their use, the puzzles will deepen the reader’s understanding and appreciation of the relationships among mathematical ideas.

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.

This book provides a comprehensive mathematical description and analysis of the delegate allocation processes in the US Democratic and Republican presidential primaries, focusing on the role of apportionment methods and the effect of thresholds—the minimum levels of support required to receive delegates.  The analysis involves a variety of techniques, including theoretical arguments, simplicial geometry, Monte Carlo simulation, and examination of presidential primary data from 2004 to 2020. The book is divided into two parts: Part I defines the classical apportionment problem and explains how the implementation and goals of delegate apportionment differ from those of apportionment for state representation in the US House of Representatives and for party representation in legislatures based on proportional representation. The authors then describe how delegates are assigned to states and congressional districts and formally define the delegate apportionment methods usedin each state by the two major parties to allocate delegates to presidential candidates. Part II analyzes and compares the apportionment methods introduced in Part I based on their level of bias and adherence to various notions of proportionality. It explores how often the methods satisfy the quota condition and quantifies their biases in favor or against the strongest and weakest candidates. Because the methods are quota-based, they are susceptible to classical paradoxes like the Alabama and population paradoxes. They also suffer from other paradoxes that are more relevant in the context of delegate apportionment such as the elimination and aggregation paradoxes. The book evaluates the extent to which each method is susceptible to each paradox. Finally, it discusses the appointment of delegates based on divisor methods and notions of regressive proportionality.This book appeals to scholars and students interested in mathematical economics and political science, with an emphasis on apportionment and social choice theory.