This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.

Count Dracula orders take-out, Italian When the unsuspecting porn star arrives at Dracula's door, she is amused by his unusual fantasy. He wines and dines her until late into the night. She has the one thing he needs. She doesn't believe in real vampires, but for the right amount of money she will do anything the Count requests, even letting him bite her neck.

If you like vampire stories, this book is packed with them. Here, you'll discover five of Glenn's classic bone-chilling tales of blood-lust. If you enjoy vampire poetry, there are seven exclusive vampire themed poems. If you were to purchase these stories and poems separately, you would easily spend over $30. Also included is a bonus short story about a vampire teddy-bear that bites. Ouch Halloween Ball at Dracula's Castle It's Halloween night and the Count is throwing a party for his undead friends. Guess who the main course is Join Jill and Vickie, two college cheerleaders, as they accept Dracula's special invitation to the Ball. Can two cheerleaders fight back against the evil forces surrounding them this Halloween night? Babysitting a Vampire It's late at night and your strange pale next door neighbor needs someone to watch little Johnny. What happens during a thunderstorm when little Johnny is hungry and you're fresh out of baby formula? Will Karen be able to keep him under control until sunrise? For someone so young, little Johnny seems to have incredible strength. Living Next Door to a Vampire A new neighbor moves in to the apartment next door about the same time a woman is murdered nearby. Her body, drained of blood, and there are puncture wounds on her neck. The new neighbor is identified as the killer, but manages to get out of jail. He's knocking on Karen's door. He wants to be friends. He swears he's not the killer. Can she save herself or does she become his next meal? The Vamp and the Tramp Count Dracula orders take-out, Italian When the unsuspecting porn star arrives, he wines and dines her. She has something that he wants. She doesn't believe in vampires, but something happens that night and changes her mind. The Black Widow It's Halloween night and a werewolf is loose in downtown Chicago. Can the police stop this creature before the body count stacks up. The Valentine Gift - Bonus Story Joe gets his wife something special for their first Valentines Day, except this gift has fangs and bites Vampire Poems A collection of seven exclusive vampire themed poems. Vampire Feast, A Vampire's Agony, A Vampire is No Beast, Our New Day, Vamp and the Tramp, I'm a Vampire, and A Vampire's Needs.

A new neighbor moves in to the apartment next door about the same time a woman is murdered nearby. Her body, drained of blood, and there are puncture wounds on her neck. The new neighbor is identified as the killer, but manages to get out of jail. He's knocking on Karen's door. He wants to be friends. He swears he's not the killer. Can she save herself or does she become his next meal?

It's late at night and your strange pale neighbor next door needs someone to watch little Johnny. What happens during a thunderstorm when little Johnny is hungry and you're fresh out of baby formula? Will Karen be able to keep him under control until sunrise? For someone so young, little Johnny seems to have incredible strength.

It's Halloween night and the Count is throwing a party for his undead friends. Guess who the main course is Join Jill and Vickie, two college cheerleaders, as they accept Dracula's special invitation to the Ball. Can two cheerleaders fight back against the evil forces surrounding them this Halloween night and escape with their prize money?

It's Halloween night and a monster is loose in downtown Chicago. Can the police stop this creature before it's too late?

This is the eighth book in the Teacher Program Series. Each book includes a full course in a mathematical focus topic. The topic for this book is the study of continued fractions, including important results involving the Euclidean algorithm, the golden ratio, and approximations to rational and irrational numbers. The course includes 14 problem sets designed for low-threshold, high-ceiling access to the topic, building on one another as the concepts are explored. The book also includes solutions for all the main problems and detailed facilitator notes for those wanting to use this book with students at any level. The course is based on one delivered at the Park City Math Institute in Summer 2018.

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Fractions, Tilings, and Geometry is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. The overall goal of the course is an introduction to non-periodic tilings in two dimensions and space-filling polyhedra. While the course does not address quasicrystals, it provides the underlying mathematics that is used in their study. Because of this goal, the course explores Penrose tilings, the irrationality of the golden ratio, the connections between tessellations and packing problems, and Voronoi diagrams in 2 and 3 dimensions. These topics all connect to precollege mathematics, either as core ideas (irrational numbers) or enrichment for standard topics in geometry (polygons, angles, and constructions). But this book isn't a ``course'' in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes. These materials provide participants with the opportunity for authentic mathematical discovery--participants build mathematical structures by investigating patterns, use reasoning to test and formalize their ideas, offer and negotiate mathematical definitions, and apply their theories and mathematical machinery to solve problems. Fractions, Tilings, and Geometry is a volume of the book series IAS/PCMI--The Teacher Program Series published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Moving Things Around is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a ``course'' in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The goal of Moving Things Around is to help participants make what might seem to be surprising connections among seemingly different areas: permutation groups, number theory, and expansions for rational numbers in various bases, all starting from the analysis of card shuffles. Another goal is to use these connections to bring some coherence to several ideas that run throughout school mathematics-rational number arithmetic, different representations for rational numbers, geometric transformations, and combinatorics. The theme of seeking structural similarities is developed slowly, leading, near the end of the course, to an informal treatment of isomorphism. Moving Things Around is a volume of the book series IAS/PCMI-The Teacher Program Series published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Some Applications of Geometric Thinking is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a ``course'' in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The goal of Some Applications of Geometric Thinking is to help teachers see that geometric ideas can be used throughout the secondary school curriculum, both as a hub that connects ideas from all parts of secondary school and beyond-algebra, number theory, arithmetic, and data analysis-and as a locus for applications of results and methods from these fields. Some Applications of Geometric Thinking is a volume of the book series IAS/PCMI-The Teacher Program Series' published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Applications of Algebra and Geometry to the Work of Teaching is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a ``course'' in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The specific theme developed in Applications of Algebra and Geometry to the Work of Teaching is the use of complex numbers-especially the arithmetic of Gaussian and Eisenstein integers-to investigate some questions that are at the intersection of algebra and geometry, like the classification of Pythagorean triples and the number of representations of an integer as the sum of two squares. Applications of Algebra and Geometry to the Work of Teaching is a volume of the book series IAS/PCMI-The Teacher Program Series published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest.

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Probability through Algebra is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a ``course'' in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The specific themes developed in Probability through Algebra introduce readers to the algebraic properties of expected value and variance through analysis of games, to the use of generating functions and formal algebra as combinatorial tools, and to some applications of these ideas to questions in probabilistic number theory. Probability through Algebra is a volume of the book series IAS/PCMI-The Teacher Program Series published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest.

American political development (APD) is a core subfield in American political science, and focuses on political and policy history. For a variety of reasons, most of the focus in the twentieth century APD has been on liberal policymaking. Yet since the 1970s, conservatives have gradually assumed control over numerous federal policymaking institutions. This edited book will be the first to offer a comprehensive overview of the impact of conservatism on twentieth century American political development, locating its origins in the New Deal and then focusing on how conservatives acted within government once they began to achieve power in the late 1960s. The book is divided into three eras, and in each it focuses on three core issues: social security, the environment, and education. Throughout, the authors emphasize the ironic role of conservatism in the expansion of the American state. Scholars of the state have long focuses on liberalism because liberals were the architects of state expansion. However, as conservatives increased their presence in the federal apparatus, they were frequently co-opted into maintaining of even expanding public fiscal and regulatory power. At times, conservatives also came to accept the existence of the liberal state, but attempted to use it to achieve conservative policy ends. Despite conservatives' power in the US politics and governance, the American state remains gargantuan. As Conservatism and American Political Development shows, the new right has not only helped shape the state, but has been shaped by it as well.