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Carl Boyer B. A History of Mathematics


The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.

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Brian Evans The Development of Mathematics Throughout the Centuries. A Brief History in a Cultural Context


Throughout the book, readers take a journey throughout time and observe how people around the world have understood these patterns of quantity, structure, and dimension around them. The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Contex provides a brief overview of the history of mathematics in a very straightforward and understandable manner and also addresses major findings that influenced the development of mathematics as a coherent discipline. This book: Highlights the contributions made by various world cultures including African, Egyptian, Babylonian, Chinese, Indian, Islamic, and pre-Columbian American mathematics Features an approach that is not too rigorous and is ideal for a one-semester course of the history of mathematics. Includes a Resources and Recommended Reading section for further exploration and has been extensively classroom-tested

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Michael K. J. Goodman An Introduction to the Early Development of Mathematics


An easy-to-read presentation of the early history of mathematics Engaging and accessible, An Introduction to the Early Development of Mathematics provides a captivating introduction to the history of ancient mathematics in early civilizations for a nontechnical audience. Written with practical applications in a variety of areas, the book utilizes the historical context of mathematics as a pedagogical tool to assist readers working through mathematical and historical topics. The book is divided into sections on significant early civilizations including Egypt, Babylonia, China, Greece, India, and the Islamic world. Beginning each chapter with a general historical overview of the civilized area, the author highlights the civilization’s mathematical techniques, number representations, accomplishments, challenges, and contributions to the mathematical world. Thoroughly class-tested, An Introduction to the Early Development of Mathematics features: Challenging exercises that lead readers to a deeper understanding of mathematics Numerous relevant examples and problem sets with detailed explanations of the processes and solutions at the end of each chapter Additional references on specific topics and keywords from history, archeology, religion, culture, and mathematics Examples of practical applications with step-by-step explanations of the mathematical concepts and equations through the lens of early mathematical problems A companion website that includes additional exercises An Introduction to the Early Development of Mathematics is an ideal textbook for undergraduate courses on the history of mathematics and a supplement for elementary and secondary education majors. The book is also an appropriate reference for professional and trade audiences interested in the history of mathematics. Michael K. J. Goodman is Adjunct Mathematics Instructor at Westchester Community College, where he teaches courses in the history of mathematics, contemporary mathematics, and algebra. He is also the owner and operator of The Learning Miracle, LLC, which provides academic tutoring and test preparation for both college and high school students.

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Roger L. Cooke The History of Mathematics. A Brief Course


Praise for the Second Edition «An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential.» —CHOICE This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include: Material arranged in a chronological and cultural context Specific parts of the history of mathematics presented as individual lessons New and revised exercises ranging between technical, factual, and integrative Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book) An emphasis on geography, culture, and mathematics In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.

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Donald Bindner Mathematics for the Liberal Arts


Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life. Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features: A detailed explanation of why mathematical principles are true and how the mathematical processes work Numerous figures and diagrams as well as hundreds of worked examples and exercises, aiding readers to further visualize the presented concepts Various real-world practical applications of mathematics, including error-correcting codes and the space shuttle program Vignette biographies of renowned mathematicians Appendices with solutions to selected exercises and suggestions for further reading Mathematics for the Liberal Arts is an excellent introduction to the history and concepts of mathematics for undergraduate liberal arts students and readers in non-scientific fields wishing to gain a better understanding of mathematics and mathematical problem-solving skills.

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Carl Lotus Becker The Declaration of Independence: A Study in the History of Political Ideas

Carl Dixon Strange Way to Live


As a member of Canada’s most famous rock band, The Guess Who, Carl Dixon has an unparalleled view of the history of Canadian rock Carl Dixon, one of the most frequently quoted musicians in the recent title Metal on Ice (Dundurn, 2013), tells his own story Dixon’s injuries in his 2008 auto crash were truly terrible, and his recovery is a remarkable story of determination and faith Author keeps a busy touring schedule as a musician and inspirational speaker and is a great interviewee

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Friedrich Waismann Introduction to Mathematical Thinking


This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition of mathematic fundamentals. Rather than a system of theorems with completely developed proofs or examples of applications, readers will encounter a coherent presentation of mathematical ideas that begins with the natural numbers and basic laws of arithmetic and progresses to the problems of the real-number continuum and concepts of the calculus.Contents include examinations of the various types of numbers and a criticism of the extension of numbers; arithmetic, geometry, and the rigorous construction of the theory of integers; the rational numbers, the foundation of the arithmetic of natural numbers, and the rigorous construction of elementary arithmetic. Advanced topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers.In issues of mathematical philosophy, the author explores basic theoretical differences that have been a source of debate among the most prominent scholars and on which contemporary mathematicians remain divided. «With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics.» — Carl B. Boyer, Brooklyn College. 27 figures. Index.

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Carl B. Boyer The History of the Calculus and Its Conceptual Development


This book, for the first time, provides laymen and mathematicians alike with a detailed picture of the historical development of one of the most momentous achievements of the human intellect ― the calculus. It describes with accuracy and perspective the long development of both the integral and the differential calculus from their early beginnings in antiquity to their final emancipation in the 19th century from both physical and metaphysical ideas alike and their final elaboration as mathematical abstractions, as we know them today, defined in terms of formal logic by means of the idea of a limit of an infinite sequence.But while the importance of the calculus and mathematical analysis ― the core of modern mathematics ― cannot be overemphasized, the value of this first comprehensive critical history of the calculus goes far beyond the subject matter. This book will fully counteract the impression of laymen, and of many mathematicians, that the great achievements of mathematics were formulated from the beginning in final form. It will give readers a sense of mathematics not as a technique, but as a habit of mind, and serve to bridge the gap between the sciences and the humanities. It will also make abundantly clear the modern understanding of mathematics by showing in detail how the concepts of the calculus gradually changed from the Greek view of the reality and immanence of mathematics to the revised concept of mathematical rigor developed by the great 19th century mathematicians, which held that any premises were valid so long as they were consistent with one another. It will make clear the ideas contributed by Zeno, Plato, Pythagoras, Eudoxus, the Arabic and Scholastic mathematicians, Newton, Leibnitz, Taylor, Descartes, Euler, Lagrange, Cantor, Weierstrass, and many others in the long passage from the Greek «method of exhaustion» and Zeno's paradoxes to the modern concept of the limit independent of sense experience; and illuminate not only the methods of mathematical discovery, but the foundations of mathematical thought as well.

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Marcus du Sautoy Brief History Of Mathematics

J. Patrick Boyer Direct Democracy in Canada


Direct Democracy in Canada: The History and Future of Referendums surveys Canada’s century-long record of plebiscites and referendums. J. Patrick Boyer analyzes the effects of the three national referendums and the development of a consensus. This companion volume to The People’s Mandate studies some of the major provincial and municipal referendums, examines existing legal frameworks and speculates on the future of direct democracy in Canada.

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Patricia M. Boyer The March of Days


Although Patricia M. Boyer won a scholarship to McMaster University with the highest mathematics marks in Ontario and graduated at age 19, literature and languages were her specialty. She first worked as a public librarian, next as a secondary school teacher, then as a newspaper editor. A community leader in arts and theatre, Patricia was devoted to human rights action in her local community and around the world, church work, drama, the education of children with disabilities, and music. Each week she wrote a newspaper column inspired by episodes in the world around her, both local and global. She rewarded readers through articles infused with learning from literature, astute sensibility to human psychology, and balanced insights on the tragedies and comedies of life’s passing parade. Patricia Boyer summed up her approach to life as «optimistic realism». This collection of the best of her celebrated columns, organized through the twelve months of the year or «the march of days», includes reflections on seasonal celebrations, changing atmospheres of nature, and calendar milestones in the human cycle. A number of these concise yet poignant writings will move many readers with nostalgia as they evoke the happy events and tragic developments of the Sixties and Seventies. All of them, however, convey the wisdom of a woman whose message of optimistic realism endures like a timeless guide to living a satisfying life in the real world today.

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Timothy D. Kanold Balancing the Equation


Copublished with the National Council of Teachers of Mathematics, this book focuses on individuals involved in K–12 mathematics education who seek to help children achieve success. The authors tackle popular misconceptions and misguided discourse about mathematics education and draw on peer-reviewed research about instruction that can significantly improve students’ conceptual understanding.   Benefits   Explore reasons why expectations for mathematics teaching and learning must be raised. Study the history of the progression, changes, and disputes in K–12 mathematics education. Discover insights about mathematics education in an era of mathematics reform. Define mathematical literacy and what elements are part of effective mathematics instruction. Learn the steps that must be taken to support the teaching and learning of mathematics so all students can be college and career ready.   Contents   Introduction Why Mathematics Education Needs to Improve A Brief History of Mathematics Education: Lessons to Learn The Equilibrium Position and Effective Mathematics Instruction How to Help Your Child Learn Mathematics Conclusion and Action Steps for Educators and Parents Epilogue: Conclusion and Action Steps for Educators and Parents Appendix: Additional Resources for Parents

1946.38 RUR

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Engel Carl Musical Myths and Facts (Vol. 1&2)


"Musical Myths and Facts" in 2 volumes is one of the best-known works by a German author Carl Engel. This carefully crafted e-artnow ebook is formatted for your eReader with a functional and detailed table of contents. Volume 1: A Musical Library Elsass-Lothringen Music and Ethnology Collections of Musical Instruments Musical Myths and Folk-lore The Studies of our Great Composers Superstitions concerning Bells Curiosities in Musical Literature The English Instrumentalists Musical Fairies and their Kinsfolk Sacred Songs of Christian Sects… Volume 2: Mattheson on Handel Diabolic Music Royal Musicians Composers and Practical Men Music and Medicine Popular Stories with Musical Traditions Dramatic Music of Uncivilized Races A Short Survey of the History of Music Chronology of the History of Music The Musical Scales in Use at the Present Day…

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Jonathan A. Wood Did it Really Happen?


The Bible makes remarkable claims about people and events in world history. Creation, Adam and Eve, Israel's escape from Egypt, the rise and fall of Israel's kingdom, the birth of the Messiah, Jesus Christ's life, death, and resurrection, the growth of the church–all points of interest by scholars for the historical veracity of the Scriptures. Yet, the Bible does not appear to present the acts of God in history for the purpose of vindicating historical accuracy of the text. The Bible is a story that reveals the living God through inspired writings that communicate the meaning of historical events. In light of the Bible as the revelation of God, and the high stakes of historical veracity for the claims of the Bible, how should Christians approach the interpretation of the Scriptures in a faithful way? Carl F. H. Henry offers guidance as a foremost theologian regarding God, revelation, and the Scriptures. In Did it Really Happen? Jonathan Wood engages the thought of Carl Henry in dialogue with the major alternatives to revelation, history, and the biblical text. The value of Carl Henry's approach is shown to provide a path forward for affirming the historicity of the Bible while interpreting the text well.

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Carl L. DeVito Science, Seti, and Mathematics

Vladimir Lepetic Principles of Mathematics. A Primer


Presents a uniquely balanced approach that bridges introductory and advanced topics in modern mathematics An accessible treatment of the fundamentals of modern mathematics, Principles of Mathematics: A Primer provides a unique approach to introductory andadvanced mathematical topics. The book features six main subjects, whichcan be studied independently or in conjunction with each other including: settheory; mathematical logic; proof theory; group theory; theory of functions; andlinear algebra. The author begins with comprehensive coverage of the necessary building blocks in mathematics and emphasizes the need to think abstractly and develop an appreciation for mathematical thinking. Maintaining a useful balance of introductory coverage and mathematical rigor, Principles of Mathematics: A Primer features: Detailed explanations of important theorems and their applications Hundreds of completely solved problems throughout each chapter Numerous exercises at the end of each chapter to encourage further exploration Discussions of interesting and provocative issues that spark readers’ curiosity and facilitate a better understanding and appreciation of the field of mathematics Principles of Mathematics: A Primer is an ideal textbook for upper-undergraduate courses in the foundations of mathematics and mathematical logic as well as for graduate-level courses related to physics, engineering, and computer science. The book is also a useful reference for readers interested in pursuing careers in mathematics and the sciences. Vladimir Lepetic, PhD, is Professor in the Department of Mathematical Sciences at DePaul University. His research interests include mathematical physics, set theory, foundations of mathematics, and the philosophy of mathematics.

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Mona Toncheff Activating the Vision


In order to build and sustain a successful mathematics program, mathematics leaders need to collaboratively establish a cohesive vision for teaching and learning and put that vision into action. This book details the necessary steps mathematics leaders must take to change traditional practices; meet new curricular, instructional, and assessment challenges; and engage students, families, and community members in mathematics education. Benefits Discover the big ideas and essential understandings of the four keys of effective mathematics leadership and how the four keys connect to each other. Answer questions to assess mathematics leadership. Consider scenarios that illustrate how mathematics leaders can take the visionary leadership actions described in this book. Explore the relationships among district-, site-, and team-level engagement. Appraise the necessary steps to move mathematics leadership from vision to action. Use appendices that present planning templates and menus of professional development opportunities. Contents Foreword by Timothy D. Kanold Introduction Part I: Establish a Clear Vision for Mathematics Teaching and Learning Take Stock of Your Mathematics Program’s Health Develop a Collaborative Vision for an Exemplary Mathematics Program Establish Measures of Success Part II: Support Visionary Professional Learning for Teachers and Teacher Leaders Engage Teachers in Worthwhile and Differentiated Professional Learning Develop Highly Skilled and Highly Effective Mathematics Leaders Build Capacity of Site-Based Administrators and District Leaders Part III: Develop Systems for Activating the Vision Leverage Team Actions Create and Implement Well-Designed Curriculum and Assessments Monitor Consistent Expectations for Exemplary Instruction Part IV: Empower the Vision of Family and Community Engagement Activate the Student Voice to Check Alignment Between Vision and Reality Empower Families as Informed Advocates Build and Engage a Strong Network of Partnerships Epilogue Appendix A: Vision for Teaching and Learning Mathematics Appendix B: Cognitive Demand Appendix C: Planning Template for Change Appendix D: Mathematics Professional Development Plan for a School Year

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Группа авторов The History of Mathematics


This new edition brings the fascinating and intriguing history of mathematics to life The Second Edition of this internationally acclaimed text has been thoroughly revised, updated, and reorganized to give readers a fresh perspective on the evolution of mathematics. Written by one of the world's leading experts on the history of mathematics, the book details the key historical developments in the field, providing an understanding and appreciation of how mathematics influences today's science, art, music, literature, and society. In the first edition, each chapter was devoted to a single culture. This Second Edition is organized by subject matter: a general survey of mathematics in many cultures, arithmetic, geometry, algebra, analysis, and mathematical inference. This new organization enables students to focus on one complete topic and, at the same time, compare how different cultures approached each topic. Many new photographs and diagrams have been added to this edition to enhance the presentation. The text is divided into seven parts: The World of Mathematics and the Mathematics of the World, including the origin and prehistory of mathematics, cultural surveys, and women mathematicians Numbers, including counting, calculation, ancient number theory, and numbers and number theory in modern mathematics Color Plates, illustrating the impact of mathematics on civilizations from Egypt to Japan to Mexico to modern Europe Space, including measurement, Euclidean geometry, post-Euclidean geometry, and modern geometrics Algebra, including problems leading to algebra, equations and methods, and modern algebra Analysis, including the calculus, real, and complex analysis Mathematical Inference, including probability and statistics, and logic and set theory As readers progress through the text, they learn about the evolution of each topic, how different cultures devised their own solutions, and how these solutions enabled the cultures to develop and progress. In addition, readers will meet some of the greatest mathematicians of the ages, who helped lay the groundwork for today's science and technology. The book's lively approach makes it appropriate for anyone interested in learning how the field of mathematics came to be what it is today. It can also serve as a textbook for undergraduate or graduate-level courses. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

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J. B. Bury A History of Freedom of Thought

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