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This little book makes serious math simple—with more than 120 laws, theorems, paradoxes, and more explained in jargon-free terms. The Little Book of Mathematical Principles provides simple, clear explanations for the principles, equations, paradoxes, laws, and theorems that form the basis of modern mathematics. It is a refreshingly engaging tour of Fibonacci numbers, Euclid's Elements, and Zeno's paradoxes, as well as other fundamental principles such as chaos theory, game theory, and the game of life. Renowned mathematics author Dr. Robert Solomon simplifies the ancient discipline of mathematics and provides fascinating answers to intriguing questions, such as: What is the greatest pyramid?, What is a perfect number?, and Is there a theory for stacking oranges?
This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning.
A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.
An analysis of how educational research is applied in the process of setting standards for school mathematics. The text focuses on research derived from a wide array of areas, including professional development of teachers, mathematics assessment, and literature on curriculum topics.
Social Science Quotations has been prepared to meet an evident, unmet need in the literature of the social sciences. Writings on the lives and theories of individual social scientists abound, but there has been no fully documented collection of memorable quotations from the social sciences as a whole. The frequent use of quotations in scientific as well as literary writings that are mere summaries or paraphrases typically fail to capture the full force of formulations that have made quotations memorable. This book of quotations invites the further reading or rereading of the original texts, beyond the quotations themselves. Sills and Merton draw extensively upon the writings that constitute the historical core of the social sciences and social thought; those works with staying power often described as the "classical texts." Many quotations have been drawn from these classical texts because the quotations contain memorable ideas memorably expressed. Both consequential and memorable, these words have been quoted over the generations, entering into the collective memory of social scientists everywhere and at times diffusing into popular thought and into the vernacular as well. This book is useful to social scientists, anthropologists, economists, historians, political scientists, psychiatrists, psychologists, sociologists and statisticians, and for all who want to learn or verify memorable formulations and phrases concerning social thought and social theories. It is particularly useful for graduate students taking courses that examine the history of their discipline.
Mathematical Principles of Fuzzy Logic provides a systematic study of the formal theory of fuzzy logic. The book is based on logical formalism demonstrating that fuzzy logic is a well-developed logical theory. It includes the theory of functional systems in fuzzy logic, providing an explanation of what can be represented, and how, by formulas of fuzzy logic calculi. It also presents a more general interpretation of fuzzy logic within the environment of other proper categories of fuzzy sets stemming either from the topos theory, or even generalizing the latter. This book presents fuzzy logic as the mathematical theory of vagueness as well as the theory of commonsense human reasoning, based on the use of natural language, the distinguishing feature of which is the vagueness of its semantics.