Jennifer M. Wilson

Instead of treating mathematics as a collection of separate topics or isolated courses, this book highlights the patterns and relationships that appear throughout mathematics. Rather than keeping studies confined to a single field, the puzzles here look beyond boundaries and discover links among different areas of knowledge. Within the domain of mathematics, this book focuses on the fun of finding such connections through puzzles. Math Affinity Puzzles 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. Because there may be multiple relationships present, one answer is not claimed to be correct. Instead, which answer is best comes from one point of view. The short descriptions follow, touching on the different choices while going more deeply into historical or other aspects of the relationships. The puzzles will deepen the reader’s understanding and appreciation of, as well as foster discussion about, the relationships among mathematical ideas. 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. Students have been asked to justify the one they have chosen, offering opportunities for noncomputational critical thinking, speaking, and writing about mathematics.

Instead of treating mathematics as a collection of separate topics or isolated courses, this book highlights the patterns and relationships that appear throughout mathematics. Rather than keeping studies confined to a single field, the puzzles here look beyond boundaries and discover links among different areas of knowledge. Within the domain of mathematics, this book focuses on the fun of finding such connections through puzzles. Math Affinity Puzzles 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. Because there may be multiple relationships present, one answer is not claimed to be correct. Instead, which answer is best comes from one point of view. The short descriptions follow, touching on the different choices while going more deeply into historical or other aspects of the relationships. The puzzles will deepen the reader’s understanding and appreciation of, as well as foster discussion about, the relationships among mathematical ideas. 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. Students have been asked to justify the one they have chosen, offering opportunities for noncomputational critical thinking, speaking, and writing about mathematics.

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.

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.

This is the life story of Bridget Bishop, the first woman executed for witchcraft in Salem in 1692. At the time of her death, she was one of the most prosperous tavern owners in the colonies. Here is an account of the journey she traveled - through three marriages, the birth of a daughter, extremes of both poverty and wealth, and accusations of murder and witchcraft. It is the story of one woman, living life on her own terms, and discovering for herself the varied meanings of heaven and hell.