Why were most historically important mathematicians wealthy? Why were they often lawyers and many had pastors for fathers? Why were original results sometimes discovered by two mathematicians independently within a short time of each other? Why did the Italian Fibonacci, speak Arabic?It all began a couple of years ago, when one of the authors started to write short biographies of important historical mathematicians for the teaching journal Australian Primary Mathematics Classroom. It was felt that teachers generally knew very little about the way the subject developed or the people who developed it. And it was felt that historical knowledge would help them see how the subject progressed and enable them to fit in with the historical episodes that would be of interest to students.Clearly, the book that developed contains mathematics up to the 17th century, but we are keen to set the subject in those times, to try to give short biographies of the people involved, as well as provide a perspective of the events that led up to the times and led up to the mathematics. Importantly, it is shown that the maths enterprise was not undertaken by a small few, but worked like a relay race. One or a few might take up an idea and develop it, but it often gets only so far. Later, others would take up the idea, the baton, and the relay race to find results continues.Readership: Teachers and educators at all levels from primary to tertiary. Secondary and tertiary students. This book is also aimed at the general readership to enhance their appreciation of mathematics. Read more

"Modern Statistics: Intuition, Math, Python, R" is an authoritative and comprehensive textbook designed to guide university students and professionals through the intricate world of statistics, data science, and machine learning. This extensive 700-page volume, with its impressive array of 390 figures and over 35,000 lines of code (all code and a sample chapter are freely available on github), offers a unique blend of theoretical and practical knowledge, making it an indispensable resource for those seeking to deepen their understanding of statistical methodologies and their applications in the modern digital era.Beginning with foundational concepts, the book delves into what data are and how they can be visualized, setting the stage for more complex subjects. It covers key areas such as descriptive statistics, data simulation, transformations, and data quality assessment and improvement, providing a robust framework for data analysis. The exploration of probability theory, sampling, and distributions paves the way for an in-depth discussion of hypothesis testing, including a detailed examination of the t-test family.The book places a strong emphasis on the practical implementation of statistical techniques, with extensive Python and R code examples that bring to life the concepts of correlations, confidence intervals, ANOVA, and regression analysis. The chapters on permutation tests, power and sample size calculations, biases, and data communication underscore the importance of robust statistical practice and effective data storytelling in research and professional settings.This textbook is not only a rich source of statistical knowledge but also a practical guide to applying these concepts using the latest software tools. It bridges the gap between statistical theory and real-world data analysis, ensuring readers are equipped to tackle complex data challenges with confidence.Whether you are a student embarking on your statistical journey or a seasoned professional looking to refine your skills, "Modern Statistics: Intuition, Math, Python, R" is a vital addition to your educational toolkit.Targeted at those who appreciate the rigor of statistical analysis and the nuances of data interpretation, this book is a testament to the ever-evolving field of statistics and its pivotal role in the age of data science and machine learning.*Note about the ebook version: Formatting a textbook with equations and figures is challenging. Everything should be clear and legible in this ebook version, but the print version will have the best formatting. Read more

This book has a lot of useful information related to calculation, from tricks to multiply by the first natural numbers without the need of a calculator to methods to raise a number to any other, or to calculate by hand the nth root of a number or its logarithm, passing through uncommon curious ways of multiplying and dividing, the detection of errors in the operations, the decomposition in factors of the first 1000 numbers (highlighting among them those that are prime), the simplification of fractions, rules to determine the significant figures of a number and its rounding and a cursory look at the ABN method that complements traditional education. Read more

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market! The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist. Read more

Combining the latest thinking in the field with practical, step-by-step guidance, the Third Edition of John W. Creswell and Vicki L. Plano Clark’s Designing and Conducting Mixed Methods Research now includes seven mixed methods designs with accompanying journal articles illustrating each design. The authors walk readers through the entire research process and present updated examples from published mixed methods studies drawn from multiple disciplines. In addition, this new edition includes information about the dynamic and evolving nature of the field of mixed methods research, four additional methodological approaches, and coverage of new directions in mixed methods. Read more

You are about to download the Kindle Ebook version of E.W. Bullinger's classic work, 'Number in Scripture'. Number in Scripture provides a complete and exhaustive synopsis of the spiritual significance of every number found in the Bible. This book is one of the most famous and helpful reference books on biblical number study ever written.This is not a book on numerology which is a false religion, this is exactly what the title says - this is a book about numbers in the scriptures. Anything that God creates can be perverted for an evil purpose, and numerology is not what this book is about. This book shows the intelligent design of the Scriptures by showing the supernatural use of numbers in the biblical texts as well as in nature. If you want to read this book it won't take you much time. If you want to truly study this book, it could take you a year. Great book! Bullinger shows through numerical values, gematria, and other mathematical means that "the Bible has but one Author...carrying out His own infinite plans". He makes the mathematician love the scriptures and the religious love math. One of my favorite parts is when he is explaining Dr. Milo Mahan's work on the principle of number 8 and number 13, and he gets passionate with the validity of the Bible, as over and over he demonstrates with gematria that every single name of the Lord's people are multiples of 8 and every one who were His enemies, are multiples of 13. It is one of the only books of its genre that wasn't exclusively written for Jews.Don't miss reading the book along with the Bible. Some of the tidbits in this book are worth a king's ransom, such as where 360 degrees came from, why there are 12 zodiac signs, why certain numbers are used in the Bible, etc.Bullinger shows the magnificent orderliness of the Word of the God. The book shows how God uses numbers to symbolize various concepts. Each number is always used to show the same concept throughout the entire 66 books. The number 7 is a good place to begin study as it is emphasized. Certain names and words are repeated 7 times throughout the 66 books even though various men set down the words to paper. Only the Holy Spirit could have designed such order. No man nor computer could have produced such results. Bullinger gives many examples. He provides the original Greek and Hebrew texts in his examples.This is yet another great book by the insightful E.W. Bullinger. Number is Scripture is fascinating and shocking, as it sheds light on the hidden footprints of the Holy Spirit in the scripture. Readers learn about the significance of what previously seemed like meaningless numbers. Everything in the Bible has a meaning, numbers included.Don't pass up this opportunity to obtain a copy of this awesome Bible reference book! Original hardcopy editions of these works have sold for many times the cost of this download. Buy now! Read more

One of the greatest changes in the sports world in the past 20 years has been the use of mathematical methods to analyze performances, recognize trends and patterns, and predict results. Analytic Methods in Sports: Using Mathematics and Statistics to Understand Data from Baseball, Football, Basketball, and Other Sports, Second Editionprovides a concise yet thorough introduction to the analytic and statistical methods that are useful in studying sports. The book gives you all the tools necessary to answer key questions in sports analysis. It explains how to apply the methods to sports data and interpret the results, demonstrating that the analysis of sports data is often different from standard statistical analyses. The book integrates a large number of motivating sports examples throughout and offers guidance on computation and suggestions for further reading in each chapter. Features Covers numerous statistical procedures for analyzing data based on sports results Presents fundamental methods for describing and summarizing data Describes aspects of probability theory and basic statistical concepts that are necessary to understand and deal with the randomness inherent in sports data Explains the statistical reasoning underlying the methods Illustrates the methods using real data drawn from a wide variety of sports Offers many of the datasets on the author’s website, enabling you to replicate the analyses or conduct related analyses New to the Second EditionR code included for all calculationsA new chapter discussing several more advanced methods, such as binary response models, random effects, multilevel models, spline methods, and principal components analysis, and moreExercises added to the end of each chapter, to enable use for courses and self-studyFull solutions manual available to course instructors. Read more

What do Bach's compositions, Rubik's Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history. Read more

Las matemáticas ocultas de los Mapuche, es una invitación a conocer la riqueza cultural del Pueblo mapuche, el cual no sólo se encuentra en la historia como un pueblo que enfrentó con éxito a dos grandes imperios, primero a los Incas y luego a la Corona Española, sino a entender su filosofía y la manera práctica de utilizar las matemáticas.Para el mapuche, las matemáticas no son un invento, ni un descubrimiento, es simplemente parte de su esencia social, natural y espiritual. Desde los números, pasando por la arquitectura, el diseño y la astronomía, las matemáticas se ponen a disposición para construir viviendas resistentes a las exigencias de la naturaleza, dibujar hermosas figuras geométricas en sus tejidos y medir el tiempo utilizando los astros como grandes relojes y calendarios.En este escrito Javier Lefiman, siendo él un mapuche y al mismo tiempo un Ingeniero, nos presenta una explicación de algunas actividades características del Pueblo Mapuche donde se utilizan las matemáticas, ratificándolo con herramientas de sistemas numéricos, geometría euclidiana, geometría analítica, trigonometría, métodos numéricos y teoría de ondas.Por último, a partir de cierta evidencia y racionamiento, se proponen algunas hipótesis respecto a la existencia de un Calendario Mapuche, el cual podría haber estado frente a nuestros ojos por siglos, sin darnos cuenta. Además, se propone un conjunto de símbolos para representar los números mapuche. Read more

Discrete Mathematics for Computer Science Made EasyEmbark on a journey through the essential concepts of discrete mathematics with "Discrete Mathematics for Computer Science Made Easy," a definitive guide designed to empower computer science students and professionals. This book breaks down the complexities of discrete math into digestible, easy-to-understand sections, making it accessible to learners at all levels.Key Features:Comprehensive Coverage: From foundational principles like sets, logic, and proofs to advanced topics such as graph theory, number theory, and formal languages, this book covers all the essential topics in discrete mathematics.Practical Examples and Applications: Real-world examples and applications demonstrate how discrete mathematics underpins core computer science concepts, including algorithms, data structures, cryptography, and more.Clear and Concise Explanations: Complex topics are presented in a straightforward manner, with clear explanations and minimal jargon, making it easy to grasp even the most challenging concepts.Visual Aids: Diagrams, charts, and tables are used throughout to enhance understanding and provide visual representations of key ideas.Exercises and Solutions: Each chapter includes exercises designed to reinforce learning and provide hands-on practice, with solutions available to check your work.Who Should Read This Book?Students: Ideal for undergraduate and graduate computer science students seeking a solid foundation in discrete mathematics.Professionals: A valuable resource for software engineers, data scientists, cybersecurity experts, and other professionals looking to deepen their understanding of the mathematical principles that underpin their work.Enthusiasts: Anyone with an interest in the mathematical foundations of computer science will find this book engaging and informative.Unlock the Potential of Discrete MathematicsWith "Discrete Mathematics for Computer Science Made Easy," you'll gain the knowledge and skills needed to excel in the dynamic field of computer science. Whether you're preparing for exams, tackling complex projects, or simply looking to enhance your mathematical toolkit, this book is your go-to resource for mastering discrete mathematics. Read more

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This book takes a first step toward describing the complete structure, functions, and connections of the nervous system with the hope being to work toward understanding consciousness. An important feature of the book is the hierarchically structured table of components of the nervous system including a description of the function or functions that each performs. The hierarchically structured list in the book of all the components of the nervous system can be accessed at RWS Publications Website (www.rwspublications.com).The large square connection matrix shows where the signal transmissions between nuclei and ganglia occur. We offer two ways to access the matrix. The first is an Excel spreadsheet that can be downloaded from https://www.creativedecisions.net/resources/index.php?section=showResources&action=showFullRes&id=80. The second is a searchable interactive database that can be accessed online from https://www.rwspublications.com/extras/.The second unique feature of this book is the hypermatrix that extends the connection matrix of the brain. The hypermatrix is a conceptual mathematical tool composed of nested connection matrices that will become ever more complete as neural science advances. Every neural cluster in the connection matrix connects to the book’s interactive web based database (www.rwspublications.com/extras/) that can show the currently known neural firing paths of links one, two, or more to and from it. Read more

Majorana 1: The Enigma is an in-depth research study investigating the architecture, fabrication, and operational principles of the Majorana 1 quantum chip—a pioneering device that leverages the exotic properties of Majorana fermions for topological quantum computing. This research meticulously examines:Chip Design and Architecture: Detailed exploration of the chip’s layout, including the integration of superconducting and semiconducting materials designed to stabilize Majorana bound states. The study explains how the device's architecture exploits the non-Abelian statistics of Majorana fermions to achieve fault tolerance and robust error correction.Fabrication Techniques: An analysis of the advanced nano-engineering methods used in the chip's production. This includes the deposition processes for superconducting layers and the precision patterning required to create interfaces where Majorana modes can emerge, emphasizing the critical role of material science in enhancing device performance.Quantum Coherence and Error Suppression: Investigation into the mechanisms by which the chip maintains quantum coherence. The research addresses the challenges of decoherence and noise in quantum systems and describes how the topological nature of Majorana modes contributes to intrinsic error resilience.Theoretical and Experimental Correlations: A comprehensive review of simulation models and experimental data that validate the chip's operation. This section bridges theoretical predictions with empirical observations, providing insights into the quantum behavior exhibited by the chip and highlighting potential scalability issues.Implications for Future Quantum Computing: Discussion on how the Majorana 1 quantum chip could pave the way for scalable, fault-tolerant quantum computing architectures. The study evaluates its performance benchmarks, potential integration into larger quantum networks, and its overall impact on advancing quantum technology.By combining rigorous experimental investigation with theoretical analysis, Majorana 1: The Enigma aims to demystify the complexities of Majorana-based quantum devices and set the stage for the next generation of quantum computing innovations. Read more

The Pulitzer Prize–winning magazine’s stories of mathematical explorations show that inspiration strikes haphazardly, revealing surprising solutions and exciting discoveries—with a foreword by James Gleick These stories from Quanta Magazine map the routes of mathematical exploration, showing readers how cutting-edge research is done, while illuminating the productive tension between conjecture and proof, theory and intuition. The stories show that, as James Gleick puts it in the foreword, “inspiration strikes willy-nilly.” One researcher thinks of quantum chaotic systems at a bus stop; another suddenly realizes a path to proving a theorem of number theory while in a friend's backyard; a statistician has a “bathroom sink epiphany” and discovers the key to solving the Gaussian correlation inequality. Readers of The Prime Number Conspiracy, says Quanta editor-in-chief Thomas Lin, are headed on “breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge.”Winner of the 2022 Pulitzer Prize for Explanatory Reporting, Quanta is the only popular publication that offers in-depth coverage of the latest breakthroughs in understanding our mathematical universe. It communicates mathematics by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves. Readers of this volume will learn that prime numbers have decided preferences about the final digits of the primes that immediately follow them (the “conspiracy” of the title); consider whether math is the universal language of nature (allowing for “a unified theory of randomness”); discover surprising solutions (including a pentagon tiling proof that solves a century-old math problem); ponder the limits of computation; measure infinity; and explore the eternal question “Is mathematics good for you?” Contributors Ariel Bleicher, Robbert Dijkgraaf, Kevin Hartnett, Erica Klarreich, Thomas Lin, John Pavlus, Siobhan Roberts, Natalie Wolchover Copublished with Quanta Magazine Read more

"Paranoia: The Hypervigilant Paradox"Dear reader,This book is more than a study of the human mind; it is a personal journey that has challenged and transformed me. Throughout my life, I have faced moments when the need to control every detail and anticipate every move led me to fall into the traps of hypervigilance and paranoia. It was a difficult path, full of doubts and learnings, but also of discoveries that changed me forever.I wrote these pages not as an expert who knows everything, but as someone who has been in the fight, someone who understands what it means to feel trapped by one's own thoughts. Here I share with you what I have learned: that even our weaknesses can become strengths, and that our greatest battles are not against the world, but against ourselves.My wish is that this book be a guide for you, a beacon in the midst of uncertainty. I want you to find in these pages tools, reflections, and, above all, the hope that there is always a way forward. Because in the end, it's not about winning every game, but about learning to play the game of life with confidence, clarity and balance.This is my gift to you, my invitation to explore together the most complex board of all: our own mind.With gratitude,Óscar de los Reyes Marín Read more

Low mathematics scores are a good predictor of high school dropout rates. Even when students do graduate, only 1 out of 4 are proficient at high-school level mathematics. In college, 69% of STEM majors switch to fields with fewer mathematics requirements. Math anxiety is real, and it prevents many adults from pursuing careers in math-related fields. America has a real problem with math illiteracy. That problem largely results from the way we teach our children math in school. All too often, math is reduced to memorization, in an environment that doesn’t accommodate students’ individual learning speeds. In Rethinking Math Learning, Dr. Aditya Nagrath shows how you can empower your child with the tools needed to overcome math illiteracy. Using a proven system of six basic concepts, steeped in years of research, Dr. Nagrath explains how to banish math anxiety forever and ensure that your child has the math skills necessary for their future economic success. Read more

The substantially updated and revised Fifth Edition of this landmark handbook presents the state-of-the-art theory and practice of qualitative inquiry. Representing top scholars from around the world, the editors and contributors continue the tradition of synthesizing existing literature, defining the present, and shaping the future of qualitative research. The Fifth Edition contains 19 new chapters, with 16 revised—making it virtually a new volume—while retaining six classic chapters from previous editions. New contributors to this edition include Jamel K. Donnor and Gloria Ladson-Billings; Margaret Kovach; Paula Saukko; Bryant Keith Alexander; Thomas A. Schwandt and Emily F. Gates; Johnny Saldaña; Uwe Flick; Mirka Koro-Ljungberg, Maggie MacLure, and Jasmine Ulmer; Maria Elena Torre, Brett G. Stoudt, Einat Manoff, and Michelle Fine; Jack Bratich; Svend Brinkmann; Eric Margolis and Renu Zunjarwad; Annette N. Markham; Alecia Y. Jackson and Lisa A. Mazzei; Jonathan Wyatt, Ken Gale, Susanne Gannon, and Bronwyn Davies; Janice Morse; Peter Dahler-Larsen; Marc Spooner; and David A. Westbrook. Read more

Despite the increasing use of computers, the basic need for mathematical tables continues. Tables serve a vital role in preliminary surveys of problems before programming for machine operation, and they are indispensable to thousands of engineers and scientists without access to machines. Because of automatic computers, however, and because of recent scientific advances, a greater variety of functions and a higher accuracy of tabulation than have been available until now are required. In 1954, a conference on mathematical tables, sponsored by M.I.T. and the National Science Foundation, met to discuss a modernization and extension of Jahnke and Emde's classical tables of functions. This volume, published 10 years later by the U.S. Department of Commerce, is the result. Designed to include a maximum of information and to meet the needs of scientists in all fields, it is a monumental piece of work, a comprehensive and self-contained summary of the mathematical functions that arise in physical and engineering problems. The book contains 29 sets of tables, some to as high as 20 places: mathematical constants; physical constants and conversion factors (6 tables); exponential integral and related functions (7); error function and Fresnel integrals (12); Bessel functions of integer (12) and fractional (13) order; integrals of Bessel functions (2); Struve and related functions (2); confluent hypergeometric functions (2); Coulomb wave functions (2); hypergeometric functions; Jacobian elliptic and theta functions (2); elliptic integrals {9); Weierstrass elliptic and related functions; parabolic cylinder functions {3); Mathieu functions (2); spheroidal wave functions (5); orthogonal polynomials (13); combinatorial analysis (9); numerical interpolation, differentiation and integration (11); probability functions (ll); scales of notation (6); miscellaneous functions (9); Laplace transforms (2); and others. Each of these sections is prefaced by a list of related formulas and graphs: differential equations, series expansions, special functions, and other basic relations. These constitute an unusually valuable reference work in themselves. The prefatory material also includes an explanation of the numerical methods involved in using the tables that follow and a bibliography. Numerical examples illustrate the use of each table and explain the computation of function values which lie outside its range, while the editors' introduction describes higher-order interpolation procedures. Well over100 figures illustrate the text. In all, this is one of the most ambitious and useful books of its type ever published, an essential aid in all scientific and engineering research, problem solving, experimentation and field work. This contains every page of the original government publication.   Read more

Imre Lakatos' philosophical and scientific papers are published here in two volumes. Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics (much of it unpublished), together with some critical essays on contemporary philosophers of science and some famous polemical writings on political and educational issues. Read more