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Attaining Excellence
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Integer and Polynomial Algebra
This book is a concrete introduction to abstract algebra and number theory. Starting from the basics, it develops the rich parallels between the integers and polynomials, covering topics such as Unique Factorization, arithmetic over quadratic number fields, the RSA encryption scheme, and finite fields. In addition to introducing students to the rigorous foundations of mathematical proofs, the authors cover several specialized topics, giving proofs of the Fundamental Theorem of Algebra, the transcendentality of $e$, and Quadratic Reciprocity Law. The book is aimed at incoming undergraduate students with a strong passion for mathematics.
Pursuing Excellence
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Philosophical and Foundational Issues in Measurement Theory
Measurement theory has only recently become recognized as a legitimate, specialized field of inquiry. This text covers a wide range of issues of central concern to contemporary measurement theorists, and a broad range of philosophical perspectives are represented. The formalist, representationalist approach defines measurement as the assignment of numbers to entities and events to represent their properties and relations. It also states that measurement theory is supposed to analyze the concept of a scale of measurement, describe various types of scales and their uses, and formulate the conditions required for the existence of scales of various types. Since this approach dominates contemporary measurement theory, the volume begins with essays by some of its leading architects. In order to allow for diverse points of view, the book also includes articles that attempt to broaden this approach, and several that even criticize the approach.
The Mathematics of Voting and Elections: A Hands-On Approach
The Mathematics of Voting and Elections: A Hands-On Approach, Second Edition, is an inquiry-based approach to the mathematics of politics and social choice. The aim of the book is to give readers who might not normally choose to engage with mathematics recreationally the chance to discover some interesting mathematical ideas from within a familiar context, and to see the applicability of mathematics to real-world situations. Through this process, readers should improve their critical thinking and problem solving skills, as well as broaden their views of what mathematics really is and how it can be used in unexpected ways. The book was written specifically for non-mathematical audiences and r...
Discrete Mathematics in the Schools
A collection of articles written by experienced primary, secondary, and collegiate educators. It explains why discrete mathematics should be taught in K-12 classrooms and offers guidance on how to do so. It offers school and district curriculum leaders material that addresses how discrete mathematics can be introduced into their curricula.
