Understanding Applied Statistics by 
The Five Practices in Practice [High School] by
Enhance your fluency in the five practices―anticipating, monitoring, selecting, sequencing, and connecting―to bring powerful discussions of mathematical concepts to life in your high school classroom. This book unpacks the five practices for deeper understanding and empowers you to use each practice effectively.
The Five Practices in Practice [Middle School] by
Enhance your fluency in the five practices―anticipating, monitoring, selecting, sequencing, and connecting―to bring powerful discussions of mathematical concepts to life in your middle school classroom. This book unpacks the five practices for deeper understanding and empowers you to use each practice effectively.
The Five Practices in Practice [Elementary] by
Enhance your fluency in the five practices―anticipating, monitoring, selecting, sequencing, and connecting―to bring powerful discussions of mathematical concepts to life in your elementary classroom. This book unpacks the five practices for deeper understanding and empowers you to use each practice effectively.
Using R for Biostatistics by
This book introduces the open-source R software language that can be implemented in biostatistics for data organization, statistical analysis, and graphical presentation. In the years since the authors' 2014 work Introduction to Data Analysis and Graphical Presentation in Biostatistics with R, the R user community has grown exponentially, and the R language has increased in maturity and functionality.
The Biggest Number in the World: A Journey to the Edge of Mathematics by
From cells in our bodies to measuring the universe, big numbers are everywhere We all know that numbers go on forever, that you could spend your life counting and never reach the end of the line, so there can't be such a thing as a 'biggest number'. Or can there? To find out, David Darling and Agnijo Banerjee embark on an epic quest, revealing the answers to questions like: are there more grains of sand on Earth or stars in the universe? Is there enough paper on Earth to write out the digits of a googolplex? And what is a googolplex? Then things get serious. Enter the strange realm between the finite and the infinite, and float through a universe where the rules we cling to no longer apply. Encounter the highest number computable and infinite kinds of infinity. At every turn, a cast of wild and wonderful characters threatens the status quo with their ideas, and each time the numbers get larger.
Putting Two and Two Together by
Putting Two and Two Together is a humorous and quirky collection of unusual, ingenious, and beautiful morsels of mathematics. Authors Burkard Polster (YouTube's Mathologer) and Marty Ross delve into mathematical puzzles and phenomena in engaging stories featuring current events, sports, and history, many flavored with a distinctive bit of Australiana. Each chapter ends with “puzzles to ponder" that will spur further reflection. These stories were written for a general audience, and originally appeared in the Maths Masters column in The Age newspaper.
Partial Differential Equations by
While partial differential equations (PDEs) are fundamental in mathematics and throughout the sciences, most undergraduate students are only exposed to PDEs through the method of separation of variations. This text is written for undergraduate students from different cohorts with one sole purpose: to facilitate a proficiency in many core concepts in PDEs while enhancing the intuition and appreciation of the subject. For mathematics students this will in turn provide a solid foundation for graduate study. A recurring theme is the role of concentration as captured by Dirac's delta function. This both guides the student into the structure of the solution to the diffusion equation and PDEs involving the Laplacian and invites them to develop a cognizance for the theory of distributions. Both distributions and the Fourier transform are given full treatment. The book is rich with physical motivations and interpretations, and it takes special care to clearly explain all the technical mathematical arguments, often with pre-motivations and post-reflections. Through these arguments the reader will develop a deeper proficiency and understanding of advanced calculus. While the text is comprehensive, the material is divided into short sections, allowing particular issues/topics to be addressed in a concise fashion. Sections which are more fundamental to the text are highlighted, allowing the instructor several alternative learning paths. The author's unique pedagogical style also makes the text ideal for self-learning.
Numb and number : how to avoid being mystified by the mathematics of modern life by
Like it or not, our lives are dominated by mathematics. Our daily diet of news regales us with statistical forecasts, opinion polls, risk assessments, inflation figures, weather and climate predictions and all sorts of political decisions and advice backed up by supposedly accurate numbers. Most of us do not even pause and question such figures even to ask what they really mean and whether they raise more questions than they answer. We let the figures wash over us with no more than a glance. In this simple guide for anyone numbed by numbers, William Hartston explains with clarity and humour how to steer a safe path through the minefield of mathematics that surrounds us.
Shape : the hidden geometry of information, biology, strategy, democracy, and everything else by
"Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. Geometry doesn't just measure the world--it explains it. Shape shows us how"-- Provided by publisher.How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play GO, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of minuscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? These are important questions. The word "goemetry" comes from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world--it explains it. Shape shows us how. -- From dust jacket.
Understanding lesson study for mathematics : a practical guide for improving teaching and learning by
"Using the latest research, this book provides an insight into how learning in mathematics can be improved through a lesson study approach. This highly practical resource explores the research and theory that underpins lesson study, and shows the significant impact it can have on teacher development. Divided into ten accessible main chapters that focus in depth on an individual mathematics lesson, each chapter provides research and background to the lesson, an outline of key features, a detailed description and analysis of the lesson in practice, post-lesson discussions and reflections which generalise from the experience, as well as links to helpful resources. Some of the key topics explored include: Fractions; Proportional relationships; Probability and statistics; Geometry; Modelling; Algebra; Dialogic reasoning. Understanding Lesson Study for Mathematics is the perfect resource for all mathematics teachers, trainee teachers, and professional developers who are looking to develop the use of lesson study in their own practice or for those simply seeking new inspiring ideas for the mathematics classroom"-- Provided by publisher.
Statistical Foundations of Data Science by
Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning. -- Provided by publisher.
Quick(er) calculations : how to add, subtract, multiply, divide, square, and square root more swiftly by
How fast can you calculate? Would you like to be faster? This book presents the time honored tricks and tips of calculation, from a fresh perspective, to boost the speed at which you can add -- whether a couple of numbers, or columns so long an accountant may faint. Find out how to subtract, multiply, divide, and find square roots more quickly.
Bayesian Statistical Methods by
Bayesian Statistical Methods provides data scientists with the foundational and computational tools needed to carry out a Bayesian analysis. This book focuses on Bayesian methods applied routinely in practice including multiple linear regression, mixed effects models and generalized linear models (GLM). The authors include many examples with complete R code and comparisons with analogous frequentist procedures. In addition to the basic concepts of Bayesian inferential methods, the book covers many general topics: Advice on selecting prior distributions Computational methods including Markov chain Monte Carlo (MCMC) Model-comparison and goodness-of-fit measures, including sensitivity to priors Frequentist properties of Bayesian methods Case studies covering advanced topics illustrate the flexibility of the Bayesian approach: Semiparametric regression Handling of missing data using predictive distributions Priors for high-dimensional regression models Computational techniques for large datasets Spatial data analysis The advanced topics are presented with sufficient conceptual depth that the reader will be able to carry out such analysis and argue the relative merits of Bayesian and classical methods. A repository of R code, motivating data sets, and complete data analyses are available on the book's website. Brian J. Reich, Associate Professor of Statistics at North Carolina State University, is currently the editor-in-chief of the Journal of Agricultural, Biological, and Environmental Statistics and was awarded the LeRoy & Elva Martin Teaching Award. Sujit K. Ghosh, Professor of Statistics at North Carolina State University, has over 22 years of research and teaching experience in conducting Bayesian analyses, received the Cavell Brownie mentoring award, and served as the Deputy Director at the Statistical and Applied Mathematical Sciences Institute.
Euler's pioneering equation : the most beautiful theorem in mathematics by
In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a'score for beauty'. While there were many worthy competitors, the winner was'Euler's equation'. In 2004 Physics World carried out a similar poll of'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as'like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence'. What is it that makes Euler's identity, eiπ + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.
The joy of statistics : a treasury of elementary statistical tools and their applications by
The vast majority of statistics books delineate techniques used to analyze collected data. The Joy of Statistics is not one of these books. It consists of a series of 42'short stories', each illustrating how statistical methods applied to data produce insight and solutions to the questions the data were collected to answer. Real-life and sometimes artificial data are used to demonstrate the often painless method and magic of statistics. In addition, the text contains brief histories of the evolution of statistical methods and a number of brief biographies of the most famous statisticians of the 20th century. Sprinkled throughout are statistical jokes, puzzles and traditional stories. The levels of statistical texts span a spectrum, from elementary to introductory to application to theoretical to advanced mathematical. This book explores a variety of statistical applications using graphs and plots, along with detailed and intuitive descriptions, and occasionally a bit of 10th grade mathematics. Examples of a few of the topics included among these short stories are pet ownership, gambling games such as roulette, blackjack and lotteries, as well as more serious subjects such as comparison of black/white infant mortality risk, infant birth weight and maternal age, estimation of coronary heart disease risk and racial differences in Hodgkin disease. The statistical descriptions of these topics are in many cases accompanied by easy to understand explanations labelled 'How it Works.'
Bayesian Statistics for Beginners : A Step-By-step Approach by
Bayesian statistics is currently undergoing something of a renaissance. At its heart is a method of statistical inference in which Bayes'theorem is used to update the probability for a hypothesis as more evidence or information becomes available. It is an approach that is ideally suited to making initial assessments based on incomplete or imperfect information; as that information is gathered and disseminated, the Bayesian approach corrects or replaces the assumptions and alters its decision-making accordingly to generate a new set of probabilities. As new data/evidence becomes available the probability for a particular hypothesis can therefore be steadily refined and revised. It is very well-suited to the scientific method in general and is widely used across the social, biological, medical, and physical sciences. Key to this book's novel and informal perspective is its unique pedagogy, a question and answer approach that utilizes accessible language, humor, plentiful illustrations, and frequent reference to on-line resources. Bayesian Statistics for Beginners is an introductory textbook suitable for senior undergraduate and graduate students, professional researchers, and practitioners seeking to improve their understanding of the Bayesian statistical techniques they routinely use for data analysis in the life and medical sciences, psychology, public health, business, and other fields.
Statistical Testing Strategies in the Health Sciences by
Statistical Testing Strategies in the Health Sciences provides a compendium of statistical approaches for decision making, ranging from graphical methods and classical procedures through computationally intensive bootstrap strategies to advanced empirical likelihood techniques. It bridges the gap between theoretical statistical methods and practical procedures applied to the planning and analysis of health-related experiments. The book is organized primarily based on the type of questions to be answered by inference procedures or according to the general type of mathematical derivation. It establishes the theoretical framework for each method, with a substantial amount of chapter notes included for additional reference. It then focuses on the practical application for each concept, providing real-world examples that can be easily implemented using corresponding statistical software code in R and SAS. The book also explains the basic elements and methods for constructing correct and powerful statistical decision-making processes to be adapted for complex statistical applications. With techniques spanning robust statistical methods to more computationally intensive approaches, this book shows how to apply correct and efficient testing mechanisms to various problems encountered in medical and epidemiological studies, including clinical trials. Theoretical statisticians, medical researchers, and other practitioners in epidemiology and clinical research will appreciate the book's novel theoretical and applied results. The book is also suitable for graduate students in biostatistics, epidemiology, health-related sciences, and areas pertaining to formal decision-making mechanisms.
Understanding applied statistics by
The Business Reference Guide series is designed to provide a solid foundation for the research of various business topics.
Statistical Process Control by
People with minimal math skills, and even those with advanced math skills, have difficulty grasping the intuitive concepts behind Statistical Process Control (SPC). Many practitioners do not understand the concepts behind Control Charts, the differences of out of control and out of specification, and the process variation on Control Charts. This book will explain these concepts by using a simple methodology that will bring a much greater level of understanding to those that use it by providing a detailed description of the method, using common language, real-world examples to illustrate the concept, and instructions on easy implementation.
Learn R for applied statistics : with data visualizations, regressions, and statistics by
Gain the R programming language fundamentals for doing the applied statistics useful for data exploration and analysis in data science and data mining. This book covers topics ranging from R syntax basics, descriptive statistics, and data visualizations to inferential statistics and regressions. After learning R's syntax, you will work through data visualizations such as histograms and boxplot charting, descriptive statistics, and inferential statistics such as t-test, chi-square test, ANOVA, non-parametric test, and linear regressions. Learn R for Applied Statistics is a timely skills-migration book that equips you with the R programming fundamentals and introduces you to applied statistics for data explorations. What you will learn/discover R, statistics, data science, data mining, and big dataMaster the fundamentals of R programming, including variables and arithmetic, vectors, lists, data frames, conditional statements, loops, and functionsWork with descriptive statistics Create data visualizations, including bar charts, line charts, scatter plots, boxplots, histograms, and scatterplots use inferential statistics including t-tests, chi-square tests, ANOVA, non-parametric tests, linear regressions, and multiple linear regressions Who This Book Is For Those who are interested in data science, in particular data exploration using applied statistics, and the use of R programming for data visualizations.
Mathematical Interest Theory by
Mathematical Interest Theory provides an introduction to how investments grow over time. This is done in a mathematically precise manner. The emphasis is on practical applications that give the reader a concrete understanding of why the various relationships should be true. Among the modern financial topics introduced are: arbitrage, options, futures, and swaps. Mathematical Interest Theory is written for anyone who has a strong high-school algebra background and is interested in being an informed borrower or investor. The book is suitable for a mid-level or upper-level undergraduate course or a beginning graduate course. The content of the book, along with an understanding of probability, will provide a solid foundation for readers embarking on actuarial careers. The text has been suggested by the Society of Actuaries for people preparing for the Financial Mathematics exam. To that end, Mathematical Interest Theory includes more than 260 carefully worked examples. There are over 475 problems, and numerical answers are included in an appendix. A companion student solution manual has detailed solutions to the odd-numbered problems. Most of the examples involve computation, and detailed instruction is provided on how to use the Texas Instruments BA II Plus and BA II Plus Professional calculators to efficiently solve the problems. This Third Edition updates the previous edition to cover the material in the SOA study notes FM-24-17, FM-25-17, and FM-26-17.
Financial Mathematics for Actuarial Science by
Financial Mathematics for Actuarial Science: The Theory of Interest is concerned with the measurement of interest and the various ways interest affects what is often called the time value of money (TVM). Interest is most simply defined as the compensation that a borrower pays to a lender for the use of capital. The goal of this book is to provide the mathematical understandings of interest and the time value of money needed to succeed on the actuarial examination covering interest theory Key Features Helps prepare students for the SOA Financial Mathematics Exam Provides mathematical understanding of interest and the time value of money needed to succeed in the actuarial examination covering interest theory Contains many worked examples, exercises and solutions for practice Provides training in the use of calculators for solving problems A complete solutions manual is available to faculty adopters online
