Concrete Mathematics

Concrete Mathematics

Author: Ronald L. Graham

Publisher: Addison-Wesley Professional

Published: 1994-02-28

Total Pages: 811

ISBN-13: 0134389980

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This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.


Mathematics and Computation

Mathematics and Computation

Author: Avi Wigderson

Publisher: Princeton University Press

Published: 2019-10-29

Total Pages: 434

ISBN-13: 0691189137

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From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography


What's Happening in the Mathematical Sciences

What's Happening in the Mathematical Sciences

Author: Barry Cipra

Publisher: American Mathematical Soc.

Published:

Total Pages: 108

ISBN-13: 9780821890431

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Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.


Student Solutions Manual for Wackerly/Mendenhall/Scheaffer's Mathematical Statistics with Applications, 7th

Student Solutions Manual for Wackerly/Mendenhall/Scheaffer's Mathematical Statistics with Applications, 7th

Author: Dennis Wackerly

Publisher: Cengage Learning

Published: 2007-09

Total Pages: 0

ISBN-13: 9780495385066

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Prepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring worked out-solutions to the problems in MATHEMATICAL STATISTICS WITH APPLICATIONS, 7th Edition, this manual shows you how to approach and solve problems using the same step-by-step explanations found in your textbook examples.


School, Family, and Community Partnerships

School, Family, and Community Partnerships

Author: Joyce L. Epstein

Publisher: Corwin Press

Published: 2018-07-19

Total Pages: 508

ISBN-13: 1483320014

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Strengthen programs of family and community engagement to promote equity and increase student success! When schools, families, and communities collaborate and share responsibility for students′ education, more students succeed in school. Based on 30 years of research and fieldwork, the fourth edition of the bestseller School, Family, and Community Partnerships: Your Handbook for Action, presents tools and guidelines to help develop more effective and more equitable programs of family and community engagement. Written by a team of well-known experts, it provides a theory and framework of six types of involvement for action; up-to-date research on school, family, and community collaboration; and new materials for professional development and on-going technical assistance. Readers also will find: Examples of best practices on the six types of involvement from preschools, and elementary, middle, and high schools Checklists, templates, and evaluations to plan goal-linked partnership programs and assess progress CD-ROM with slides and notes for two presentations: A new awareness session to orient colleagues on the major components of a research-based partnership program, and a full One-Day Team Training Workshop to prepare school teams to develop their partnership programs. As a foundational text, this handbook demonstrates a proven approach to implement and sustain inclusive, goal-linked programs of partnership. It shows how a good partnership program is an essential component of good school organization and school improvement for student success. This book will help every district and all schools strengthen and continually improve their programs of family and community engagement.


Introductory Statistics 2e

Introductory Statistics 2e

Author: Barbara Illowsky

Publisher:

Published: 2023-12-13

Total Pages: 2106

ISBN-13:

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Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others. The material supports students with conceptual narratives, detailed step-by-step examples, and a wealth of illustrations, as well as collaborative exercises, technology integration problems, and statistics labs. The text assumes some knowledge of intermediate algebra, and includes thousands of problems and exercises that offer instructors and students ample opportunity to explore and reinforce useful statistical skills. This is an adaptation of Introductory Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License.


Math in Society

Math in Society

Author: David Lippman

Publisher:

Published: 2012-09-07

Total Pages: 0

ISBN-13: 9781479276530

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Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course.This book is an open textbook; it can be read free online at http://www.opentextbookstore.com/mathinsociety/. Editable versions of the chapters are available as well.