In Expression vs. Equality, J. Tobin Grant and Thomas J. Rudolph argue that although public opinion plays a vital role in judicial rulings on the legalities of various finance reform options, political scientists have yet to realize fully the complexities and nuances of public attitudes toward campaign financing. The issue of campaign finance reform exposes a real conflict between the core democratic values of equality and expression. Economic inequalities, reformers argue, allow certain groups and individuals to exert undue influence in the political process, thereby threatening the democratic value of political equality. Opponents tend to frame the issue as a question of free speech: restrictions on campaign contributions are viewed as a threat to the democratic value of political expression. In the context of campaign finance, how do committed Americans rank the importance of equality and expression? How do they resolve the conflict between these competing democratic values? The answers to these questions, say the authors, depend heavily on whose influence and whose rights are perceived to be at stake. Using a series of unique experiments embedded in a national survey of the American electorate, they find that citizens' commitment to the values of expression and equality in the campaign finance system is strongly influenced by their feelings or affect toward those whose rights and influence are perceived to be at stake. Freedom of speech is more highly valued in contexts where the respondent agrees with the issue in question; equity, on the other hand, is more highly valued when the respondent disagrees with the issue. These findings have implications not only for the continuingpublic debate over campaign finance reform, but also for our understanding of how citizens make tradeoffs between competing democratic values.

How should a liberal democracy respond to hate groups and others that oppose the ideal of free and equal citizenship? The democratic state faces the hard choice of either protecting the rights of hate groups and allowing their views to spread, or banning their views and violating citizens' rights to freedoms of expression, association, and religion. Avoiding the familiar yet problematic responses to these issues, political theorist Corey Brettschneider proposes a new approach called value democracy. The theory of value democracy argues that the state should protect the right to express illiberal beliefs, but the state should also engage in democratic persuasion when it speaks through its various expressive capacities: publicly criticizing, and giving reasons to reject, hate-based or other discriminatory viewpoints. Distinguishing between two kinds of state action--expressive and coercive--Brettschneider contends that public criticism of viewpoints advocating discrimination based on race, gender, or sexual orientation should be pursued through the state's expressive capacities as speaker, educator, and spender. When the state uses its expressive capacities to promote the values of free and equal citizenship, it engages in democratic persuasion. By using democratic persuasion, the state can both respect rights and counter hateful or discriminatory viewpoints. Brettschneider extends this analysis from freedom of expression to the freedoms of religion and association, and he shows that value democracy can uphold the protection of these freedoms while promoting equality for all citizens.

How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.

The images in this book are in color. For a less-expensive grayscale paperback version, see ISBN 9781680923254. Prealgebra 2e is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. Students who are taking basic mathematics and prealgebra classes in college present a unique set of challenges. Many students in these classes have been unsuccessful in their prior math classes. They may think they know some math, but their core knowledge is full of holes. Furthermore, these students need to learn much more than the course content. They need to learn study skills, time management, and how to deal with math anxiety. Some students lack basic reading and arithmetic skills. The organization of Prealgebra makes it easy to adapt the book to suit a variety of course syllabi.

This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.

The first detailed examination of African Americans and First Amendment rights, from the colonial era to the present. African Americans and the First Amendment is the first book to explore in detail the relationship between African Americans and our “first freedoms,” especially freedom of speech. Timothy C. Shiell utilizes an interdisciplinary approach to demonstrate that a strong commitment to civil liberty and to racial equality are mutually supportive, as they share an opposition to orthodoxy and a commitment to greater inclusion and participation. This crucial connection is evidenced throughout US history, from the days of colonial and antebellum slavery to Jim Crow: in the landmark US Supreme Court decision in 1937 freeing the black communist Angelo Herndon; in the struggles and victories of the civil rights movement, from the late 1930s to the late ’60s; and in the historical and modern debates over hate speech restrictions. Liberty and equality can conflict in individual cases, Shiell argues, but there is no fundamental conflict between them. Robust First Amendment values protect and encourage demands for racial equality while weak First Amendment values, in contrast, lead to censorship and a chilling of demands for racial equality. “A splendid book on all accounts, and a necessary one in today’s heated debate over free speech.” — Donald Alexander Downs, author of Restoring Free Speech and Liberty on Campus

ALL people have the right to be treated fairly, no matter who they are, what they look like or where they come from. This is called equality. An ABC of Equality introduces complicated concepts to the youngest of children.