At the interface between chemistry and mathematics, this book brings together research on the use mathematics in the context of undergraduate chemistry courses. These university-level studies also support national efforts expressed in the Next Generation Science Standards regarding the importance of skills, such as quantitative reasoning and interpreting data. Curated by award-winning leaders in the field, this book is useful for instructors in chemistry, mathematics, and physics at the secondary and university levels.
Most books on fractals focus on deterministic fractals as the impact of incorporating randomness and time is almost absent. Further, most review fractals without explaining what scaling and self-similarity means. This book introduces the idea of scaling, self-similarity, scale-invariance and their role in the dimensional analysis. For the first time, fractals emphasizing mostly on stochastic fractal, and multifractals which evolves with time instead of scale-free self-similarity, are discussed. Moreover, it looks at power laws and dynamic scaling laws in some detail and provides an overview of modern statistical tools for calculating fractal dimension and multifractal spectrum.
Unlocking Creativity in Solving Novel Mathematics Problemsdelivers a fascinating insight into thinking and feeling approaches used in creative problem solving and explores whether attending to 'feeling' makes any difference to solving novelproblems successfully. With a focus on research throughout, this book reveals ways of identifying, describing and measuring 'feeling' (or 'intuition') in problem-solving processes. It details construction of a new creative problem-solving conceptual framework using cognitive and non-cognitive elements, including the brain's visuo-spatial and linguistic circuits, conscious and non-conscious mental activity, and the generation of feeling in listening to the self, identified from verbal data. This framework becomes the process model for developing a comprehensive quantitative model of creative problem solving incorporating the Person, Product, Process and Environment dimensions of creativity. In a world constantly seeking new ideas and new approaches to solving complex problems, the application of this book's findings will revolutionize the way students, teachers, business and industry approach novel problem solving, and mathematics learning and teaching. In a world constantly seeking new ideas and new approaches to solving complex problems, the application of this book's findings will revolutionize the way students, teachers, business and industry approach novel problem solving, and mathematics learning and teaching.
"The third edition of this significant and groundbreaking book summarizes current research into how young children learn mathematics, and how best to develop foundational knowledge to realize more effective teaching. Using straightforward, practical language, early math experts Douglas Clements and Julie Sarama show how learning trajectories help teachers understand children's level of mathematical understanding and lead to better teaching. By focusing on the inherent delight and curiosity behind young children's mathematical reasoning, learning trajectories ultimately make teaching more joyous: in helping teachers understand the varying levels of knowledge exhibited by individual students, it allows them to better meet the learning needs of all children. This thoroughly revised and contemporary third edition of Learning and Teaching Early Math remains the definitive, research-based resource to help teachers understand the learning trajectories of early mathematics, and become confident, credible professionals. The new edition draws on numerous new research studies, offers expanded international examples, and includes updated illustrations throughout. This new edition is closely linked with Learning and Teaching with Learning Trajectories - [LT]² - an open-access, web-based tool for early childhood educators to learn about how children think and learn about mathematics. Head to LearningTrajectories.org for on-going updates, interactive games, and practical tools that support classroom learning. Douglas H. Clements is Distinguished University Professor, the Kennedy Endowed Chair in Early Childhood Learning, and co-Executive Director of the Marsico Institute of Early Learning, at the University of Denver. Julie Sarama is Distinguished University Professor, the Kennedy Endowed Chair in Innovative Learning Technologies, and co-Executive Director of the Marsico Institute of Early Learning, at the University of Denver"--
Day-by-Day Math Thinking Routines in Fourth Grade helps you provide students with a review of the foundational ideas in math, every day of the week! Based on the bestselling Daily Math Thinking Routines in Action, the book follows the simple premise that frequent, rigorous, engaging practice leads to mastery and retention of concepts, ideas, and skills. These worksheet-free, academically rigorous routines and prompts follow the grade level priority standards and include whole group, individual, and partner work. The book can be used with any math program, or for small groups, workstations, or homework. Inside you will find: 40 weeks of practice 1 activity a day 200 activities total Answer Key For each week, the Anchor Routines cover these key areas: Monday: General Thinking Routines; Tuesday: Vocabulary; Wednesday: Place Value; Thursday: Fluency; and Friday: Problem Solving. Get your students' math muscles moving with the easy-to-follow routines in this book!
The subject of Finite Geometries is a central part of discrete mathematics. Structures from Finite Geometries have led to solutions of open problems in extremal combinatorics, design theory, and coding theory and cryptography. However, there are no recent textbooks in finite geometry that have a broad scope. This book discusses non-Desarguesian planes and explains the recent proof techniques using polynomials in case of Desarguesian planes. Some applications in extremal combinatorics are also mentioned.
This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The first part describes the use of tools from potential theory to establish the classification and to show that the analytic and algebraic approaches to the classification are equivalent. Part II covers geometric theory of the same classification and a proof that it is equivalent to the algebraic approach. Part III is a new approach to the geometric classification that requires more advanced geometric technology, namely homotopy, homology and the theory of currents. Using these methods, a more direct, but also more sophisticated, approach to the equivalence of the geometric and algebraic classification is made. Background material is introduced gradually to familiarise readers with ideas from areas such as Lie groups, differential topology and probability, in particular, random walks on groups. Numerous open problems inspire students to explore further.
The contributions by leading experts in this book focus on a variety of topics of current interest related to information-based complexity, ranging from function approximation, numerical integration, numerical methods for the sphere, and algorithms with random information, to Bayesian probabilistic numerical methods and numerical methods for stochastic differential equations.
This volume is a reorganized edition of Kei Takeuchi's works on various problems in mathematical statistics based on papers and monographs written since the 1960s on several topics in mathematical statistics and published in various journals in English and in Japanese. They are organized into seven parts, each of which is concerned with specific topics and edited to make a consistent thesis. Sometimes expository chapters have been added. The topics included are as follows: theory of statistical prediction from a non-Bayesian viewpoint and analogous to the classical theory of statistical inference; theory of robust estimation, concepts, and procedures, and its implications for practical applications; theory of location and scale covariant/invariant estimations with derivation of explicit forms in various cases; theory of selection and testing of parametric models and a comprehensive approach including the derivation of the Akaike's Information Criterion (AIC); theory of randomized designs, comparisons of random and conditional approaches, and of randomized and non-randomized designs, with random sampling from finite populations considered as a special case of randomized designs and with some separate independent papers included. Theory of asymptotically optimal and higher-order optimal estimators are not included, since most of them already have been published in the Joint Collected Papers of M. Akahira and K. Takeuchi. There are some topics that are not necessarily new, do not seem to have attracted many theoretical statisticians, and do not appear to have been systematically dealt with in textbooks or expository monographs. One purpose of this volume is to give a comprehensive view of such problems as well.
Help your students learn math and get results by working smarter, not harder This book provides a research-based, classroom-tested framework that helps make teaching easier. Learn how to design your classroom physical space, develop productive routines, plan effective lessons and facilitate meaningful discussions by using formative assessment to help students learn. This framework naturally integrates the Standards for Mathematical Practice in the Common Core Standards into the process of teaching. Spend your time working smarter not harder to get results in student learning This book is perfect for individual teachers, Professional Learning Communities (PLC's), math coaches, for pre-service or in-service math methods courses.
Building Big Data Applications helps data managers and their organizations make the most of unstructured data with an existing data warehouse. It provides readers with what they need to know to make sense of how Big Data fits into the world of Data Warehousing. Readers will learn about infrastructure options and integration and come away with a solid understanding on how to leverage various architectures for integration. The book includes a wide range of use cases that will help data managers visualize reference architectures in the context of specific industries (healthcare, big oil, transportation, software, etc.). Explores various ways to leverage Big Data by effectively integrating it into the data warehouse Includes real-world case studies which clearly demonstrate Big Data technologies Provides insights on how to optimize current data warehouse infrastructure and integrate newer infrastructure matching data processing workloads and requirements
NATIONAL BESTSELLER From the award-winning founder of JUMP Math, All Things Being Equal is a proven guide to succeeding in math, and a passionate argument for why this success can and must be available to the majority instead of the privileged few. For two decades, John Mighton has developed strategies for fostering intellectual potential in all children through learning math. Math, Mighton says, provides us with mental tools of incredible power. When we learn math we learn to see patterns, to think logically and systematically, to draw analogies, to perceive risk, to understand cause and effect--among many other critical skills. Yet we tolerate and in fact expect a vast performance gap in math among students, and live in a world where many adults aren't equipped with these crucial tools. This learning gap is unnecessary, dangerous and tragic, he cautions, and it has led us to a problem of intellectual poverty which is apparent everywhere--in fake news, political turmoil, floundering economies, even in erroneous medical diagnoses. In All Things Being Equal, Mighton argues that math study is an ideal starting point to break down social inequality and empower individuals to build a smarter, kinder, more equitable world. Bringing together the latest cognitive research and incremental learning strategies, Mighton goes deep into the classroom and beyond to offer a hopeful--and urgent--vision for a numerate society.
A guide to changing how you think about numbers and mathematics, from the prodigy changing the way the world thinks about math. We all know math is important: we live in the age of big data, our lives are increasingly governed by algorithms, and we're constantly faced with a barrage of statistics about everything from politics to our health. But what might be less obvious is how math factors into your daily life, and what memorizing all of those formulae in school had to do with it. Math prodigy Stefan Buijsman is beginning to change that through his pioneering research into the way we learn math. Plusses and Minuses is based in the countless ways that math is engrained in our daily lives, and shows readers how math can actually be used to make problems easier to solve. Taking readers on a journey around the world to visit societies that have developed without the use of math, and back into history to learn how and why various disciples of mathematics were invented, Buijsman shows the vital importance of math, and how a better understanding of mathematics will give us a better understanding of the world as a whole. Stefan Buijsman has become one of the most sought-after experts in math education after he completed his PhD at age 20. In Plusses and Minuses, he puts his research into practice to help anyone gain a better grasp of mathematics than they have ever had.
Using strengths-based approaches to support development in mathematics It's time to re-imagine what's possible and celebrate the brilliance multilingual learners bring to today's classrooms. Innovative teaching strategies can position these learners as leaders in mathematics. Yet, as the number of multilingual learners in North American schools grows, many teachers have not had opportunities to gain the competencies required to teach these learners effectively, especially in disciplines such as mathematics. Multilingual learners--historically called English Language Learners--are expected to interpret the meaning of problems, analyze, make conjectures, evaluate their progress, and discuss and understand their own approaches and the approaches of their peers in mathematics classrooms. Thus, language plays a vital role in mathematics learning, and demonstrating these competencies in a second (or third) language is a challenging endeavor. Based on best practices and the authors' years of research, this guide offers practical approaches that equip grades K-8 teachers to draw on the strengths of multilingual learners, partner with their families, and position these learners for success. Readers will find: *A focus on multilingual students as leaders*A strength-based approach that draws on students' life experiences and cultural backgrounds*An emphasis on maintaining high expectations for learners' capacity for mastering rigorous content*Strategies for representing concepts in different formats *Stop and Think questions throughout and reflection questions at the end of each chapter*Try It! Implementation activities, student work examples, and classroom transcripts
Learn how to provide rich, online mathematics instruction that maximizes the screen time you have with students and includes parents without overwhelming them. Marian Small shows teachers how to use open questions and parallel tasks as ideal strategies for teaching math in a virtual environment, how to adapt existing materials, how to build and maintain community with students online, and how and when to use "office hours" to assist students and parents. This practical resource examines the benefits that online learning affords, such as recorded lessons that families can access for reteaching and tasks that use home environments as resources for counting, measuring, geometry, data analysis, and more. Students absorb the deep message that math is indeed everywhere. Readers will find clear explanations, engaging teaching examples, and troubleshooting tips. Teaching Math Online is essential for anyone teaching K-8 math either wholly online or in blended classrooms. Book Features: Provides immediate assistance for teachers with either little or extensive experience teaching math online. Offers specific suggestions for supporting parents in their new partnership role. Addresses both logistical and pedagogical issues important to successful online learning. Includes access to teaching videos and scripts for teachers to create their own at tcpress.com/teachingmathonline. Provides reproducibles for creating math manipulatives and tools. Discusses distanced formative assessment. Suggests additional online resources.
In order best exploit the incredible quantities of data being generated in most diverse disciplines data sciences increasingly gain worldwide importance. The book gives the mathematical foundations to handle data properly. It introduces basics and functionalities of the R programming language which has become the indispensable tool for data sciences. Thus it delivers the reader the skills needed to build own tool kits of a modern data scientist.
This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.
The most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of machine learning and data science by considering math problems and building R programs. As the preliminary part, Chapter 1 provides a concise introduction to linear algebra, which will help novices read further to the following main chapters. Those succeeding chapters present essential topics in statistical learning: linear regression, classification, resampling, information criteria, regularization, nonlinear regression, decision trees, support vector machines, and unsupervised learning. Each chapter mathematically formulates and solves machine learning problems and builds the programs. The body of a chapter is accompanied by proofs and programs in an appendix, with exercises at the end of the chapter. Because the book is carefully organized to provide the solutions to the exercises in each chapter, readers can solve the total of 100 exercises by simply following the contents of each chapter. This textbook is suitable for an undergraduate or graduate course consisting of about 12 lectures. Written in an easy-to-follow and self-contained style, this book will also be perfect material for independent learning.
Math teachers will find the classroom-tested lessons and strategies in this book to be accessible and easily implemented in the classroom The Teacher's Toolbox series is an innovative, research-based resource providing teachers with instructional strategies for students of all levels and abilities. Each book in the collection focuses on a specific content area. Clear, concise guidance enables teachers to quickly integrate low-prep, high-value lessons and strategies in their middle school and high school classrooms. Every strategy follows a practical, how-to format established by the series editors. The Math Teacher's Toolbox contains hundreds of student-friendly classroom lessons and teaching strategies. Clear and concise chapters, fully aligned to Common Core math standards, cover the underlying research, required technology, practical classroom use, and modification of each high-value lesson and strategy. This book employs a hands-on approach to help educators quickly learn and apply proven methods and techniques in their mathematics courses. Topics range from the planning of units, lessons, tests, and homework to conducting formative assessments, differentiating instruction, motivating students, dealing with "math anxiety," and culturally responsive teaching. Easy-to-read content shows how and why math should be taught as a language and how to make connections across mathematical units. Designed to reduce instructor preparation time and increase student engagement and comprehension, this book: Explains the usefulness, application, and potential drawbacks of each instructional strategy Provides fresh activities for all classrooms Helps math teachers work with ELLs, advanced students, and students with learning differences Offers real-world guidance for working with parents, guardians, and co-teachers The Math Teacher's Toolbox: Hundreds of Practical ideas to Support Your Students is an invaluable source of real-world lessons, strategies, and techniques for general education teachers and math specialists, as well as resource specialists/special education teachers, elementary and secondary educators, and teacher educators.
One of the central challenges facing early childhood teachers is how to meet academic standards while creating learning environments that honor young children's mathematical ideas, curiosity, and playfulness. In Early Childhood Math Routines, Toni Cameron introduces us to a set of short whole-group and partner routines designed to engage young children in meaningful math thinking and build problem-solving communities. Toni reimagines traditional math routines and introduces brand new routines that focus on the important mathematical ideas of early childhood. Through stories, classroom examples, and resources, Toni offers you the tools to get started right away with these routines. Inside you'll find the following resources: Innovative routines featuring student-teacher dialogue and teaching analysis to support you in planning and facilitating Clear explanations of the big mathematical ideas in early childhood math Access to a robust companion website, which includes downloadable and printable cards and gameboards; over 30 slide decks for facilitating routines, additional practice routines, supplemental readings, and a place value interview assessment A day-by-day suggested planning guide to introducing and developing each routine in your classroom Learn from Toni's experience in classrooms supporting the complexities of early childhood mathematics while also building communities that foster social, emotional, and cognitive development in young children. Get the tools and routines that will help you connect children to mathematics in a way that is exciting and powerful.
Mathematics today is the fruit of centuries of brilliant insights by men and women whose personalities and life experiences were often as extraordinary as their mathematical achievements. This entertaining history of mathematics chronicles those achievements through fifty short biographies that bring these great thinkers to life while making their contributions understandable to readers with little math background. Among the fascinating characters profiled are Isaac Newton (1642-1727), the founder of classical physics and infinitesimal calculus--he frequently quarreled with fellow scientists and was obsessed by alchemy and arcane Bible interpretation; Sophie Germain (1776 - 1831), who studied secretly at the cole Polytechnique in Paris, using the name of a previously enrolled male student--she is remembered for her work on Fermat's Last Theorem and on elasticity theory; Emmy Noether (1882 - 1935), whom Albert Einstein described as the most important woman in the history of mathematics--she made important contributions to abstract algebra and in physics she clarified the connection between conservation laws and symmetry; and Srinivasa Ramanujan (1887-1920), who came from humble origins in India and had almost no formal training, yet made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions. The unusual behavior and life circumstances of these and many other intriguing personalities make for fascinating reading and a highly enjoyable introduction to mathematics.
Reinforce your understanding of data science and data analysis from a statistical perspective to extract meaningful insights from your data using Python programming Key Features Work your way through the entire data analysis pipeline with statistics concerns in mind to make reasonable decisions Understand how various data science algorithms function Build a solid foundation in statistics for data science and machine learning using Python-based examples Book Description Statistics remain the backbone of modern analysis tasks, helping you to interpret the results produced by data science pipelines. This book is a detailed guide covering the math and various statistical methods required for undertaking data science tasks. The book starts by showing you how to preprocess data and inspect distributions and correlations from a statistical perspective. You'll then get to grips with the fundamentals of statistical analysis and apply its concepts to real-world datasets. As you advance, you'll find out how statistical concepts emerge from different stages of data science pipelines, understand the summary of datasets in the language of statistics, and use it to build a solid foundation for robust data products such as explanatory models and predictive models. Once you've uncovered the working mechanism of data science algorithms, you'll cover essential concepts for efficient data collection, cleaning, mining, visualization, and analysis. Finally, you'll implement statistical methods in key machine learning tasks such as classification, regression, tree-based methods, and ensemble learning. By the end of this Essential Statistics for Non-STEM Data Analysts book, you'll have learned how to build and present a self-contained, statistics-backed data product to meet your business goals. What you will learn Find out how to grab and load data into an analysis environment Perform descriptive analysis to extract meaningful summaries from data Discover probability, parameter estimation, hypothesis tests, and experiment design best practices Get to grips with resampling and bootstrapping in Python Delve into statistical tests with variance analysis, time series analysis, and A/B test examples Understand the statistics behind popular machine learning algorithms Answer questions on statistics for data scientist interviews Who this book is for This book is an entry-level guide for data science enthusiasts, data analysts, and anyone starting out in the field of data science and looking to learn the essential statistical concepts with the help of simple explanations and examples. If you're a developer or student with a non-mathematical background, you'll find this book useful. Working knowledge of the Python programming language is required.
Performing Math tells the history of expectations for math communication--and the conversations about math hatred and math anxiety that occurred in response. Focusing on nineteenth-century American colleges, this book analyzes foundational tools and techniques of math communication: the textbooks that supported reading aloud, the burnings that mimicked pedagogical speech, the blackboards that accompanied oral presentations, the plays that proclaimed performers' identities as math students, and the written tests that redefined "student performance." Math communication and math anxiety went hand in hand as new rules for oral communication at the blackboard inspired student revolt and as frameworks for testing student performance inspired performance anxiety. With unusual primary sources from over a dozen educational archives, Performing Math argues for a new, performance-oriented history of American math education, one that can explain contemporary math attitudes and provide a way forward to reframing the problem of math anxiety.
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