Mathematics and Computation

Mathematics and Computation
Author: Avi Wigderson
Publisher: Princeton University Press
Total Pages: 434
Release: 2019-10-29
Genre: Computers
ISBN: 0691189137

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

The Complete Idiot's Guide to Algebra

The Complete Idiot's Guide to Algebra
Author: W. Michael Kelley
Publisher: Penguin
Total Pages: 340
Release: 2004
Genre: Juvenile Nonfiction
ISBN: 9781592571611

The complete hands-on, how-to guide to engineering an outstanding customer experience! Beyond Disney and Harley-Davidson - Practical, start-to-finish techniques to be used right now, whatever is sold. Leverages the latest neuroscience to help readers assess, audit, design, implement and steward any customer experience. By Lou Carbone, CEO of Experience Engineering, Inc., the world's #1 customer experience consultancy.

Flip Your Classroom

Flip Your Classroom
Author: Jonathan Bergmann
Publisher: International Society for Technology in Education
Total Pages: 123
Release: 2012-06-21
Genre: Education
ISBN: 1564844684

Learn what a flipped classroom is and why it works, and get the information you need to flip a classroom. You’ll also learn the flipped mastery model, where students learn at their own pace, furthering opportunities for personalized education. This simple concept is easily replicable in any classroom, doesn’t cost much to implement, and helps foster self-directed learning. Once you flip, you won’t want to go back!

SRA Real Math

SRA Real Math
Author: Sharon Griffin
Publisher:
Total Pages: 0
Release: 2007-08
Genre: Mathematics
ISBN: 9780076124268

A standards-based, comprehensive math intervention curriculum for the state of California. Designed for students identified with math deficiencies who have not responded to reteaching efforts or who have a sustained lack of adquate progress in mathematics. This program provides intensive focus on developing foundational understanding and skills. It provides explicit, scientifically based instruction emphasizing the five critical elements of mathematics proficiency: understanding, computing, applying reasoning/problem solving , and engagement.

Early Childhood Mathematics Education Research

Early Childhood Mathematics Education Research
Author: Julie Sarama
Publisher: Routledge
Total Pages: 440
Release: 2009-04-01
Genre: Education
ISBN: 1135592497

This important new book synthesizes relevant research on the learning of mathematics from birth into the primary grades from the full range of these complementary perspectives. At the core of early math experts Julie Sarama and Douglas Clements's theoretical and empirical frameworks are learning trajectories—detailed descriptions of children’s thinking as they learn to achieve specific goals in a mathematical domain, alongside a related set of instructional tasks designed to engender those mental processes and move children through a developmental progression of levels of thinking. Rooted in basic issues of thinking, learning, and teaching, this groundbreaking body of research illuminates foundational topics on the learning of mathematics with practical and theoretical implications for all ages. Those implications are especially important in addressing equity concerns, as understanding the level of thinking of the class and the individuals within it, is key in serving the needs of all children.

81 Fresh & Fun Critical-thinking Activities

81 Fresh & Fun Critical-thinking Activities
Author: Laurie Rozakis
Publisher: Scholastic Inc.
Total Pages: 124
Release: 1998
Genre: Education
ISBN: 9780590375269

Help children of all learning styles and strengths improve their critical thinking skills with these creative, cross-curricular activities. Each engaging activity focuses on skills such as recognizing and recalling, evaluating, and analyzing.

Transforming the Workforce for Children Birth Through Age 8

Transforming the Workforce for Children Birth Through Age 8
Author: National Research Council
Publisher: National Academies Press
Total Pages: 587
Release: 2015-07-23
Genre: Social Science
ISBN: 0309324882

Children are already learning at birth, and they develop and learn at a rapid pace in their early years. This provides a critical foundation for lifelong progress, and the adults who provide for the care and the education of young children bear a great responsibility for their health, development, and learning. Despite the fact that they share the same objective - to nurture young children and secure their future success - the various practitioners who contribute to the care and the education of children from birth through age 8 are not acknowledged as a workforce unified by the common knowledge and competencies needed to do their jobs well. Transforming the Workforce for Children Birth Through Age 8 explores the science of child development, particularly looking at implications for the professionals who work with children. This report examines the current capacities and practices of the workforce, the settings in which they work, the policies and infrastructure that set qualifications and provide professional learning, and the government agencies and other funders who support and oversee these systems. This book then makes recommendations to improve the quality of professional practice and the practice environment for care and education professionals. These detailed recommendations create a blueprint for action that builds on a unifying foundation of child development and early learning, shared knowledge and competencies for care and education professionals, and principles for effective professional learning. Young children thrive and learn best when they have secure, positive relationships with adults who are knowledgeable about how to support their development and learning and are responsive to their individual progress. Transforming the Workforce for Children Birth Through Age 8 offers guidance on system changes to improve the quality of professional practice, specific actions to improve professional learning systems and workforce development, and research to continue to build the knowledge base in ways that will directly advance and inform future actions. The recommendations of this book provide an opportunity to improve the quality of the care and the education that children receive, and ultimately improve outcomes for children.

Secrets of Mental Math

Secrets of Mental Math
Author: Arthur Benjamin
Publisher: Crown
Total Pages: 306
Release: 2006-08-08
Genre: Mathematics
ISBN: 0307338401

These simple math secrets and tricks will forever change how you look at the world of numbers. Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun. Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.