Mathematics of Deep Learning
This course aims at providing a mathematical perspective to some key elements of the so-called deep neural networks (DNNs). Much of the interest on deep learning has focused on the implementation of DNN-based algorithms. Our hope is that this compact textbook will offer a complementary point of view that emphasizes the underlying mathematical ideas. We believe that a more foundational perspective will help to answer important questions that have only received empirical answers so far. Our goal is to introduce basic concepts from deep learning in a rigorous mathematical fashion, e.g. introduce mathematical definitions of deep neural networks (DNNs), loss functions, the backpropagation algorithm, etc. We attempt to identify for each concept the simplest setting that minimizes technicalities but still contains the key mathematics. The book focuses on deep learning techniques and introduces them almost immediately. Other techniques such as regression and SVM are briefly introduced and used as a steppingstone for explaining basic ideas of deep learning. Throughout these notes, the rigorous definitions and statements are supplemented by heuristic explanations and figures. The book is organized so that each chapter introduces a key concept. When teaching this course, some chapters could be presented as a part of a single lecture whereas the others have more material and would take several lectures.
Calculus of One Variable
This book is a textbook about calculus of one variable. It contains proofs of all the theorems, propositions etc but also Python codes in order to solve many calculus problems. To produce these codes we use AI and show to the reader how to do that. This book aims to supplement the existing bibliography concerning single-variable calculus. Material including Python code for both symbolic and approximate computations. Our goal is to appropriately use artificial intelligence to generate this code and demonstrate to students how this is approximately done. This book is extremely useful for first-year science students, their professors, and others.
Creative Activities in Mathematics - Book 1
Problem-based learning is a powerful alternative to drill-and practice or skills-based learning, especially within maths, but it can be difficult to source rich materials that engage an entire class.The Creative Activities in Mathematics series provides a wealth of investigations and open-ended active learning activities, designed to engage students with mathematics and develop their problem solving, collaboration and mathematical skills.Book One provides 12 different class activities suitable for students in lower and middle primary school (Foundation to Year 4), along with teaching notes and staged lesson plans. Each activity is a whole-class investigation with open-ended answers that takes a particular scenario and develops it over three levels. This enables it to be used both at different year levels and with students of differing ability in the same class. All activities are firmly rooted in the Australian Curriculum: Mathematics and linked to the content descriptors of the Number and Algebra, Measurement and Geometry, and Statistics and Probability strands.
Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research
Decision-making is a constant feature in the lives of individuals and organizations. Choices, whether simple or complex, are shaped by preferences, experiences and available data, and often involve reconciling multiple points of view. Formally, a decision is the selection of a course of action based on information to solve a problem. In this context, Multicriteria Decision Analysis (MCDA) plays a vital role in evaluating options to identify the most favorable alternative or to rank them. MCDA is fundamental in allocating finite resources in the face of competing interests, a daily challenge in organizational and domestic environments. This Reprint presents new methods and applications that support decision-making in various organizational contexts, such as law enforcement agencies and the education sector, featuring the integration of multi-criteria methods, and contextualizes the theory through application to real-world problems.
Numerical Analysis
Internationalization of mathematics education has become an inevitable trend, and bilingual education is a booster for achieving internationalization of mathematics education. Due to the vast territory of our country, there are significant differences in the foreign language proficiency and mathematical thinking ability of students in different regions and universities. Therefore, we cannot blindly establish unified standards for all mathematics courses in universities and choose some mathematics courses as bilingual teaching objects. In terms of content, "Numerical Analysis" is the most ideal choice for implementing bilingual education, and numerical analysis originates from practice. It is a discipline with a systematic theoretical system and is widely used as a powerful tool in many natural science fields such as automation control, communication and control, and electronic engineering. This book is divided into six chapters, which systematically introduces the basic theory and methods of numerical analysis, including mathematical foundations and error analysis, calculus review, error sources and precision control, direct/iterative methods for solving systems of linear equations, interpolation and polynomial approximation, curve fitting, numerical differentiation and integration, convergence, and precision. This book is suitable for teachers and students of science and engineering major in colleges and universities all over the country, and can also be read and referenced by engineering and technical personnel.
Math Mammoth Grade 7-B Worktext, Canadian Version
Math Mammoth Grade 7-B Worktext (2025 Edition, Canadian Version) is the student book for the latter half of 7th grade mathematics studies or the latter half of a pre-algebra course (Math Mammoth Grade 7 is a pre-algebra curriculum). This is the full-color version of the worktext. Please note: The worktext does not include the answer key. The answer keys for grade 7 are sold as a separate book.The main areas of study in Math Mammoth Grade 7-B are: ratios, rates, proportions, and percentgeometry: angle relationships, compass & ruler constructions, drawing problems, pi and the area and circumference of a circle, cross-sections formed when cutting solids, surface area, and volumeprobabilitystatisticsFeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is very little teacher preparation required.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.This curriculum is essentially the same as the U.S. version of Math Mammoth Grade 7, only customized for the Canadian audience in these aspects: The curriculum uses mostly the metric measurement units. Since Canadians do use some imperial units (e.g. miles, pounds) in some contexts, the curriculum does infrequently use them.The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.Page (paper) size is Letter.
Math Mammoth Grade 7 Tests and Cumulative Reviews, Canadian Version
Math Mammoth Grade 7 Tests and Cumulative Reviews (2025 edition, Canadian Version) includes consumable student copies of end-of-chapter tests, the end-of-year test, and additional cumulative review lessons that match the Math Mammoth Grade 7 curriculum. Please note: The answer keys are not included. They are sold in a separate book that includes all answer keys for the Math Mammoth Grade 7 Complete Curriculum.
Math Mammoth Grade 7 Answer Keys, Canadian Version
Math Mammoth Grade 7 Answer Keys (2025 edition, Canadian Version) contains answers to Math Mammoth Grade 7-A and 7-B student worktexts, to chapter tests, to the end-of-year test, and to the cumulative review lessons. This is the full-color version.
Math Mammoth Grade 7-A Worktext, Canadian Version
Math Mammoth Grade 7-A Worktext (2025 Edition, Canadian Version) is the student book for the first half of 7th grade mathematics studies or the first half of a pre-algebra course (Math Mammoth grade 7 is a pre-algebra curriculum). This is the full-color version of the worktext. Please note: The worktext does not include the answer key. The answer keys for grade 7 are sold as a separate book.The main areas of study in Math Mammoth Grade 7-A are: introduction to basic algebra conceptsintegers and their operationssolving one-step equations, including with negative numbersoperations with negative rational numberssolving linear equations and writing equations for word problemsFeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.It requires very little teacher preparation required.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.This curriculum is essentially the same as the U.S. version of Math Mammoth Grade 7, only customized for the Canadian audience in these aspects: The curriculum uses mostly the metric measurement units. Since Canadians do use some imperial units (e.g. miles, pounds) in some contexts, the curriculum does infrequently use them.The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.Page (paper) size is Letter.
Enterprise Transformation
Hello, I'm Jerry Torres. Over 75% of all enterprise transformation initiatives fail. This means they're halted before solutions are delivered but not before substantial time, money, resources and confidence are lost and wasted. Those that do succeed are mostly second, third or fourth go-rounds of previously failed efforts. Transformation program failure doesn't discriminate. It's common to both public and commercial sector enterprises and to every business space regardless of the initiative's size, location, complexity, cost or objectives.Whether you're transforming the fundamental ways you conduct and carry out business processes or procedures or enforce standards of performance; redefine your organizational or team structures; integrate emerging or cutting edge technologies such as Artificial Intelligence (AI), Robotics or Quantum solutions; transition from traditional Data Center or Network Operation Center (NOC) to Cloud Based Computing (CBC) architectures; or re-define your business cultures, values or belief systems, your enterprise faces momentous challenges and roadblocks to success. This book provides the magic you need to achieve your transformational objectives. This book is a practical methodological guide that defines how to deliver transformational enterprise solutions right the first time. This approach, named "Enterprise Transformation Methodology" (ETM), details proven practices that consistently result in comprehensive, sustained, precise and predictable results. It also describes the forces and dynamics that cause initiatives to fail and explains how to avoid, mitigate and manage them. Initiatives that succeed almost always protect themselves against these challenges, while those that fall victim to them fail.
Multigrid Methods
This book introduces the theory of multigrid methods for the fast numerical solution of linear and weakly nonlinear elliptic PDE. We use the finite element method to discretize the PDE problems, as this is the most natural choice, and the reader will get a thorough treatment of finite elements. No previous exposure to numerical discretization methods is assumed. All that is required of the reader is some knowledge of matrix theory. Coding the multigrid method is difficult. This book will help the reader build basic multigrid codes using easy-to-read sample Matlab codes. We use a matrix-based approach in the first part of the book, both as a way of presenting the theory in a natural way, and as a means for translating the theory into practical codes. The operators in the text and codes have the same names, which makes reading the sample codes simple, even if the reader has never coded. We deviate from the matrix-based approach only in the presentation of the nonlinear theory in the second part, which represents an area of current research. The book takes the reader from the basics and simple implementation issues all the way to the front lines of research.
Mathematical Biology
Very Short Introductions: Brilliant, Sharp, Inspiring Why are English Premier League football shirt patterns very similar to animal coat markings? And what do invasive species have in common with cancer cells in the body? Mathematical biology develops models which answer these questions, as they are applied to processes from the spread of a gene in a population, to predator-prey dynamics in an ecosystem, to the growth of tumours. In this Very Short Introduction Philip K. Maini describes the art of modelling, what it is, why we do it, and illustrates how the abstract way of thinking that is the essence of mathematics enables us to transfer knowledge from one area of research to another. Using numerous examples, he explains how the same fundamental ideas have been used in different fields, and shows how mathematics is the language of science. The author also points to cases in science where the traditional scientific modelling approach - verbal reasoning - is incorrect and shows how mathematics can uncover, and correct, such flawed reasoning while, at the same time, enhance our intuition. This book provides a guide to the trajectory of mathematical biology from a niche subject in the 1970s to a well-established, popular subject that is truly inter-disciplinary, and points to exciting future challenges. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Analysis with Mathematica(r)
A computer algebra system such as Mathematica(R) is able to do much more than just numerics: This revised text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica(R) represents domains, qualifiers and limits to implement actual proofs - a requirement to unlock the huge potential of Mathematica(R) for a variety of applications.
Functional and Harmonic Analysis
This book provides a comprehensive exploration of weighted function spaces, a fundamental topic in modern analysis. Beginning with the basics of weighted Lebesgue spaces, it systematically develops key properties such as duality, convexity, and interpolation. It delves into Muckenhoupt weights, Hardy and Carlson inequalities, and Calder籀n-Zygmund decompositions, highlighting their applications in harmonic analysis. With a structured and didactic approach, this work serves as an essential reference for researchers and graduate students in mathematical analysis, functional spaces, and related areas.
Probably Overthinking It
An essential guide to the ways data can improve decision making. Statistics are everywhere: in news reports, at the doctor's office, and in every sort of forecast, from the stock market to the weather. Blogger, teacher, and computer scientist Allen B. Downey knows well that people have an innate ability both to understand statistics and to be fooled by them. As he makes clear in this accessible introduction to statistical thinking, the stakes are big. Simple misunderstandings have led to incorrect medical prognoses, underestimated the likelihood of large earthquakes, hindered social justice efforts, and resulted in dubious policy decisions. There are right and wrong ways to look at numbers, and Downey will help you see which are which. Probably Overthinking It uses real data to delve into real examples with real consequences, drawing on cases from health campaigns, political movements, chess rankings, and more. He lays out common pitfalls--like the base rate fallacy, length-biased sampling, and Simpson's paradox--and shines a light on what we learn when we interpret data correctly, and what goes wrong when we don't. Using data visualizations instead of equations, he builds understanding from the basics to help you recognize errors, whether in your own thinking or in media reports. Even if you have never studied statistics--or if you have and forgot everything you learned--this book will offer new insight into the methods and measurements that help us understand the world.
The Great Math War
A stirring account of the mathematicians who went looking for the bedrock philosophical foundations of their field and witnessed a house of cards collapse instead "A fascinating romp through one of the most consequential conflicts of the early 20th century."--Johnjoe McFadden, author of Life on the Edge As the nineteenth century ended, mathematicians were celebrating a century of triumphs that--surprisingly--made clear how little they knew: What is the nature of infinity? Is math free from self-contradiction? And what does math have to do with reality? This was the Foundational Crisis in mathematics. In The Great Math War, Jason Socrates Bardi tells the story of three competing efforts by mathematicians to resolve it--and the firefight that ensued. Bertrand Russell thought we could achieve certainty if we treated math as an extension of logic. David Hilbert believed redemption lay in accepting mathematics as a formal game of arbitrary rules, no different from the moves and pieces in chess. And L. E. J. Brouwer argued math is entirely rooted in human intuition--and that math is not based on logic but rather logic is based on math. It was a bitter struggle, intellectually and personally, as the three vied to set the course for mathematics in the twentieth century. Set against the backdrop of international warfare unfolding alongside it, The Great Math War brings the Foundational Crisis to radiant life--and shows how it indelibly shaped twentieth-century intellectual life.
The Indisputable Existence of Santa Claus
In The Indisputable Existence of Santa Claus, two distinguished mathematicians explain, with humor and clarity, mathematical concepts through one very merry motif: Christmas. Lighthearted and diverting with Christmasy diagrams, sketches and graphs, equations, Markov chains, and matrices, The Indisputable Existence of Santa Claus brightens up the bleak midwinter with stockingsful of mathematical marvels. How do you apply game theory to select who should be on your Christmas shopping list? What equations should you use to decorate the Christmas tree? Will calculations show Santa is getting steadily thinner--shimmying up and down chimneys for a whole night--or fatter--as he munches on cookies and milk in billions of houses across the world? In their quest to provide mathematical proof for the existence of Santa, the authors take readers on a festive journey through a traditional holiday season. Every activity, from wrapping presents to playing board games to cooking the perfect turkey, is analyzed through the lens of math. Because who hasn't always wondered how to set up a mathematically perfect Secret Santa? This book belongs under your Christmas tree if you enjoy a spice of math in your eggnog.
Groups Of The Order P^M Which Contain Cyclic Subgroups Of Order P^(M-3)
A hidden cornerstone of algebra returns rediscovered, restored, and reborn by Alpha Editions. Groups Of The Order P^M Which Contain Cyclic Subgroups Of Order P^(M-3) is a rigorous, illuminating classic in mathematical group theory that probes the fine architecture of p-groups and their internal symmetries. This compact yet deep work guides readers through a precise analysis of order P^M groups, centering on P^(M-3) subgroup analysis and the role of cyclic subgroups in shaping algebraic structures. With clear proofs, carefully classified cases, and thoughtful exploration of cyclic group properties, Neikirk s group theory investigation advances subgroup classification and group order analysis in ways that still inform contemporary research. Scholars will find exacting results and techniques; curious learners will discover the logic and beauty behind abstract algebra. Historically significant and long out of print, this edition has been restored for today s and future generations. Alpha Editions presents more than a reprint this is a collector s item and a cultural treasure, prepared for mathematicians, libraries, and lovers of classic mathematical research alike. Whether you re assembling a reference shelf or seeking clarity on advanced mathematics, this volume offers enduring insight into algebraic structures and the foundations of subgroup theory. Rediscover Neikirk s contributions to mathematical group theory a must-have for anyone passionate about cyclic subgroups, subgroup classification, and the anatomy of p-groups.
A Textbook of Partial Differential Equation
Partial differential equations provide a generic description of the majority of physical events, whether they are related to heat flow, fluid dynamics, electricity, magnetism, mechanics, or optics. Such equations are, in fact, essential to mathematical physics. Even if these equations can be simplified to become ordinary differential equations, the full description of physical systems can be found in the general field of partial differential equations. This extremely helpful literature demonstrates to the reader how to create a mathematical model of the physical problem, how to generate a partial differential equation from it, and how to solve the equation (along with initial and boundary conditions).This succinct guide is devoted to assisting engineering students in solving problems in their profession that include partial differential equations and only requires a basic understanding of ordinary differential equations. Questions of existence, uniqueness, and convergence are not emphasised; instead, the treatment concentrates solely on the useful solution of partial differential equations. The more prevalent partial differential equations related to phenomena, including vibration, heat transport, electricity, and elasticity, are derived.For more details, please visit https: //centralwestpublishing.com
Multiple Integrals in Calculus
The book consists of eight chapters, each focusing on different aspects of multiple integrals and related topics in mathematical analysis.In Chapter 1, multiple integrals are defined and developed. The Jordan measure in n-dimensional unit balls is introduced, along with the definition and criteria for multiple integrals, as well as their properties. Chapter 2 delves into advanced techniques for computing multiple integrals. It introduces the Taylor formula, discusses linear maps on measurable sets, and explores the metric properties of differentiable maps. In Chapter 3, we focus on improper multiple integrals and their properties. The chapter deduces criteria for the integrability of functions of several variables and develops concepts such as improper integrals of nonnegative functions, comparison criteria, and absolute convergence. Chapter 4 investigates the Stieltjes integral and its properties. Topics covered include the differentiation of monotone functions of finite variation and the Helly principle of choice, as well as continuous functions of finite variation. Chapter 5 addresses curvilinear integrals, defining line integrals of both the first and second kinds. It also discusses the independence of line integrals from the path of integration. In Chapter 6, surface integrals of the first and second kinds are introduced. The chapter presents the Gauss-Ostrogradsky theorem and Stokes' formulas, along with advanced practical problems to practice these concepts.
Foundations of Numerical Methods and Data Analysis
This book offers a comprehensive journey into the world of numerical methods, beginning with the essential mathematical preliminaries: calculus, vectors, matrices, and programming concepts before moving into deeper areas such as error analysis, curve fitting, interpolation, and the numerical solution of ordinary and partial differential equations. Advanced chapters extend into systems of equations, finite element methods, and spectral techniques, ensuring that readers not only understand the fundamentals but also gain exposure to methods at the frontier of computational practice. A distinguishing feature of the book is the integration of theory with practice. Each concept is accompanied by carefully chosen examples, figures, and end- of-chapter exercises designed to strengthen understanding and encourage hands-on application. Historical notes and bibliographical references enrich the discussion, situating modern numerical methods in their broader intellectual context. In addition, the book pays special attention to the use of contemporary computational tools such as MATLAB, Python, and other numerical libraries, thereby bridging traditional methods with current software-driven practice. In short, it is both a textbook and a reference, meant to serve readers across different stages of their academic or professional journey. For more details, please visit https: //centralwestpublishing.com
Advanced Analytical and Numerical Methods with their Application to Industrial Problems
This book covers the models of different real-world problems that include the models using ordinary and partial differential equations and dynamical systems, uncertainty quantifications using fuzzy systems, computational methods for differential equations, modern control theory and applications, neural networks and neural computing, computational heat and mass transfer and computational fluid dynamics. It also includes various research problems on developing advanced analytical and numerical methods for solving real-world situations, with its theoretical derivations and engineering and science applications. For more details, please visit https: //centralwestpublishing.com
Evidence for Dark Numbers
This book contains several arguments for the existence of dark numbers, i.e., numbers which cannot be manipulated as individuals but only collectively. Their existence depends on the premise of actual infinity. Whether actually infinite sets exist is unknown and cannot be proven; it can only be assumed as an axiom. But if actually infinite sets exist then dark elements are unavoidable. This concept helps to explain many paradoxes of set theory like Zeno's paradox or the paradox of the binary tree or the completely scattered space of the real axis.
The Hidden Poetry & Music of Mathematics for Teaching Professionals
When poetry and music are interlinked with mathematics to provide phenomenal strategies to teaching mathematics. This would invite a plethora of thinking beyond classical frames to exceptional intelligent practice for teaching mathematics, including thinking outside classical frames to innovatively and creatively teach mathematics. This book is an open invite to all teaching professionals of mathematics.
Compound Poisson Distributions
This book presents a comprehensive overview of compound Poisson distributions. All of the distributions listed in this book were derived, or invented, by the original authors as ""new"" statistical distributions, to fit a dataset(s) of experimental data. The properties of each newly proposed distribution were derived ab initio, sometimes with much effort by the original authors. Hence the title and motivation for this book: the primary focus here is the compound Poisson distributions themselves. We show that they are all exemplars of a common underlying formalism. General formulas (this includes both exact results and recurrences) are presented which apply to all compound Poisson distributions. In individual chapters, we apply that underlying formalism to selected compound Poisson distributions. We also derive new formulas not published in the literature. Having said the above, this book also presents a new technique for parameter estimation for a set of widely used compound Poisson distributions. The new technique is applied to several published experimental datasets, i.e. real data, not simulations. It yields equal or better fits to the data than those obtained by the original authors (in some cases, significantly better). Numerous graphs are plotted, to demonstrate the good/better fits obtained by the new technique. Hence this book contains not only pure theory, but also visually demonstrates the merits of the new formalism for fitting experimental data.
Wonderlic Math Workbook
Complete math workbook, prepared by exam experts, with over 200 questions. You have arrived!Here is everything you need to pass the WONDERLIC(R)! We have helped thousands of students and we can help you!WONDERLIC(R) Basic Skills Math Practice Questions and Tutorials for: Fractions, Decimals and PercentWord ProblemsBasic AlgebraBasic GeometryWonderlic is a registered trademark of WONDERLIC, INC CORPORATION, who are not involved in the pro-duction of, and do not endorse this product. You also receive: - Math Multiple-Choice Strategy - How to Study for a Math Test - How to make a WONDERLIC(R) study plan - How to Take a TestHere is what the WONDERLIC(R) Math Workbook can do for you: - Learn then practice your math skills! Practice test questions are the best way to prepare for an exam and this is the book that you need to fully prepare for the WONDERLIC(R) - Practice tests are a critical self-assessment tool that reveals your strengths and weaknesses.- Practice reduces test anxiety, one of the main reasons for low marks on an exam. - Learn powerful multiple-choice strategies designed by exam experts! Includes tips and multiple-choice strategies to increase your score you won't find anywhere else!You can get a Great Score with the Least Amount of Studying! Study Smarter, Not Harder!You receive the benefit of our dedicated team of exam experts. All the material in the math workbook, including every practice question, are designed increase your score on the WONDERLIC(R) exam with the least amount of studying. Heard it all before? Maybe you have read this kind of thing before, and maybe feel you don't need it, and you are not sure if you are going to buy this book. Remember though, it only a few percentage points divide the PASS from the FAIL students. Even if our test tips increase your score by a few percentage points, isn't that worth it?I will be honest - it will require real effort and dedication, but if you are willing to focus your energy and devote the study time necessary, (don't worry - we help every step of the way) then before you know it you will be opening that letter of acceptance to the school or the job of your dreams. Do everything to get the best score on the WONDERLIC(R)!
Pentagons and Pentagrams
A fascinating exploration of the pentagon and its role in various cultures The pentagon and its close cousin, the pentagram, have inspired individuals for the last two and half millennia, from mathematicians and philosophers to artists and naturalists. Despite the pentagon's wide-ranging history, no single book has explored the important role of this shape in various cultures, until now. Richly illustrated, Pentagons and Pentagrams offers a sweeping view of the five-sided polygon, revealing its intriguing geometric properties and its essential influence on a variety of fields. Traversing time, Eli Maor narrates vivid stories, both celebrated and unknown, about the pentagon and pentagram. He discusses the early Pythagoreans, who ascribed to the pentagon mythical attributes, adopted it as their emblem, and figured out its construction with a straightedge and compass. Maor looks at how a San Diego housewife uncovered four previously unknown types of pentagonal tilings, and how in 1982 a scientist's discovery of fivefold symmetries in certain alloys caused an uproar in crystallography and led to a Nobel Prize. Maor also discusses the pentagon's impact on many buildings, from medieval fortresses to the Pentagon in Washington, D.C. Eugen Jost's superb illustrations provide sumptuous visual context, and the book's puzzles and mazes offer fun challenges for readers, with solutions given in an appendix.
Complex Function Theory
The text book gives a clear and concise analysis of the fundamentals of complex function theory. It presents various illustrative and motivating examples to make the concepts clearer and to help the students to acquire a basic understanding of the subject and learn the techniques of problem solving, which will help him/her enormously in the examinations like GATE, NET, CSIR etc.We hope this book would appeal not only to post graduate students of Mathematics and Physics (including research mathematicians) but also to those engineering students who are highly motivated.Salient Features* The concepts are emphasized in each chapter to make the students learn them thoroughly.* Applications of most of the theorems are shown through various solved examples.* Theorems and Propositions are stated in the maximum possible generality and much stress has been given to help the readers to compare and understand how vastly different the subjects Complex Analysis and Real Analysis are.* The exercise sets given at the end of each chapter shall sharpen the student's intellectual ability.* Nearly 80 figures are drawn to illustrate the results which will help the students for visualization.* The book is more exhaustive than most of the existing books.* The solved examples and exercises will better prepare students for different competitive examinations like GATE, NET, CSIR, NBHM etc.
TASC Math Mastery
TASC Math Mastery: Complete Tutorials & Practice Workbook with 200+ QuestionsYou have arrived!Here is everything you need to pass this tough test!We have helped thousands of students and we can help you! Over 200 TASC math practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple choice strategies! TASC Math Practice Questions and Tutorials for: Basic MathScientific NotationExponents and Radicals Square RootFractions, Decimals and PercentMeans, Median and ModesAlgebra Solve real world problems with ratio and proportion Solve one and two variable equations Identify and solve quadratic equations given values or graphs Solve quadratic using different methods Translate real world problems into quadratic equa-tions and solve Basic Geometry Slope of a line Identify linear equations from a graph Calculate perimeter, circumference and volume Solve problems using the Pythagorean theorem Determine geometric transformations Solve real world problems using the properties of geometric shapesTASC(R) is a registered trademark of the Educational Testing Service (ETS), who are not involved in the production of, and do not endorse this product.Remember though, it only a few percentage points divide the PASS from the FAIL students! Even if our test tips increase your score by a few percentage points, isn't that worth it?
A Philosophical Essay On Probabilities
A philosophical essay on probabilities begins by establishing that much of what is considered human knowledge rests on the principles of probability rather than certainty. The essay presents a structured investigation into the nature and utility of probability, showing how it extends beyond games of chance into fields such as astronomy, jurisprudence, and social behavior. It emphasizes that probability emerges from ignorance of true causes and that rational decisions should be based on the best available data and inference. The early sections consider how prior beliefs influence our understanding and how probability serves as a bridge between ignorance and reasonable expectation. By tracing the evolution of the concept from superstition to science, the work affirms that what was once deemed chance can often be calculated, interpreted, and applied with mathematical rigor. The writing examines the philosophical implications of uncertainty and advocates for the application of probabilistic reasoning as a key method for approaching reality, whether through empirical study or moral judgment. Through this lens, the work outlines a vision where probability becomes a central tool in shaping knowledge, expectations, and action.
SSAT Math Workbook
Over 200 SSAT(R) math practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple choice strategies! You have arrived! We have helped thousands of students and we can hlep you!SSAT(R) Math Practice Questions and Tutorials for: AlgebraBasic MathGeometryWord ProblemsProbabilityStatisticsSSAT(c) and the Specialized High School Admissions Test(c) are administered by the New York Department of Education, who are not involved in the produc-tion of, and do not endorse this publication.You also receive: - Math Multiple Choice Strategy - How to Study for a Math Test - How to make a SSAT(R) study plan - How to Take a TestHere is what the SSAT(R) Math Workbook can do for you: - Learn then practice your math skills! Practice test questions are the best way to prepare for an exam and this is the book that you need to fully prepare for the SSAT(R) math test.- Practice Tests familiarize you with the exam format and types of questions, giving you more confidence when you take the exam.- Practice tests are a critical self-assessment tool that reveals your strengths and weaknesses.SSAT(R) Practice tests allow you to practice your exam time management - a critical exam-writing skill that can easily improve your grade substantially.- Practice tests reduce Test Anxiety, one of the main reasons for low marks on an exam. Hundreds of questions with detailed solutions and explanations to improve your understand of the basic concepts behind the questions.- Learn powerful multiple choice strategies designed by exam experts! Includes tips and multiple choice strategies to increase your score you won't find anywhere else!Practice Really Does Make Perfect! The more questions you see, the more likely you are to pass the test. And between our study guide and practice tests, you'll have over 200 practice questions that cover every category. Our SSAT(R) Math practice test questions have been developed by our dedicated team of experts. All the material in the study guide, including every practice question, are designed to engage your critical thinking skills needed to pass the test! Heard it all before? Maybe you have heard this kind of thing before, and don't feel you need it. Maybe you are not sure if you are going to buy this book. Remember though, it only a few percentage points divide the PASS from the FAIL students! Even if our test tips increase your score by a few percentage points, isn't that worth it?
NLN PAX Math Workbook
Over 200 NLN PAX math practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple-choice strategies! ou have arrived! We have helped thousands of students and we can help you! Practice questions and tutorials for: Basic MathFractions and DecimalsWord ProblemsMetric ConversionBasic AlgebraGeometrySpeed, Force and MomentumMode, Mean and MedianAnd more!NLN PAX and the National Nursing League are not involved in the production of, and do not endorse this publication.You also receive: Math Multiple Choice StrategyHow to Study for a Math TestHow to make a NLN PAX study planHow to Take a TestPlease note that the PAX RN is administered by the National League of Nursing which is not involved in the production of, and does not endorse, this product. Here is what the NLN PAX Math Workbook can do for you: Learn then practice your math skills! Practice test questions are the best way to prepare for an exam and this is the book that you need to fully prepare for the NLN PAX math test.Practice Tests familiarize you with the exam format and types of questions, giving you more confidence when you take the exam.Practice tests are a critical self-assessment tool that reveals your strengths and weaknesses.NLN PAX Practice tests allow you to practice your exam time management - a critical exam-writing skill that can easily improve your grade substantially.Practice tests reduce Test Anxiety, one of the main reasons for low marks on an exam. Hundreds of questions with detailed solutions and explanations to improve your understand of the basic concepts behind the questions.Heard it all before? Maybe you have heard this kind of thing before, and don't feel you need it. Maybe you are not sure if you are going to buy this book.Remember though, it only a few percentage points divide the PASS from the FAIL students!Even if our test tips increase your score by a few percentage points, isn't that worth it?
HOAE PSB Math Workbook
Over 200 PSB math practice questions, prepared by a dedicated team of exam experts!You have arrived! We have helped thousands of students and we can help you! Practice questions and tutorials for: Basic Math Fractions and DecimalsWord ProblemsMetric ConversionBasic AlgebraGeometrySpeed, Force and MomentumMode, Mean and MedianAnd more!The PSB Health Occupations Aptitude Exam is administered by the Psychological Services Bureau, who are not involved in the production of this book and do not endorse this product. You also receive: Math Multiple Choice StrategyHow to Study for a Math TestHow to make a PSB study planHow to Take a TestHere is what the PSB Math Workbook can do for you: Learn then practice your math skills! Practice test questions are the best way to prepare for an exam and this is the book that you need to fully prepare for the PSB math test.Practice Tests familiarize you with the exam format and types of questions, giving you more confidence when you take the exam.PSB Practice tests allow you to practice your exam time management - a critical exam-writing skill that can easily improve your grade substantially.Practice tests reduce Test Anxiety, one of the main reasons for low marks on an exam. Hundreds of questions with detailed solutions and explanations to improve your understand of the basic concepts behind the questions.Learn powerful multiple-choice strategies designed by exam experts! Includes tips and multiple-choice strategies to increase your score you won't find anywhere else!Heard it all before? Maybe you have heard this kind of thing before, and don't feel you need it. Maybe you are not sure if you are going to buy this book. Remember though, it only a few percentage points divide the PASS from the FAIL students! Even if our test tips increase your score by a few percentage points, isn't that worth it?
Artificial Intelligence Technologies for Education
This Reprint presents a collection of cutting-edge research and reviews on the application of artificial intelligence (AI) technologies in education, focusing on both theoretical advancements and practical implementations. It examines how AI can be leveraged to enhance personalized learning, support adaptive assessment, enable intelligent learning environments, and facilitate more effective human-computer interaction in educational contexts. The contributions cover a broad spectrum of topics, including student and cognitive modeling, educational data mining, natural language processing for educational purposes, learning analytics, and the design of automated assistants and intelligent tutoring systems.The works featured in this Reprint address key challenges and opportunities in integrating AI into diverse educational domains. They explore innovative methods and tools for analyzing learning data, delivering targeted instructional support, and adapting pedagogical strategies to meet the needs of individual learners. The collection also highlights the interplay between AI-driven systems and educators, emphasizing collaborative and human-centered approaches to technology-enhanced learning. By bringing together original research, comprehensive surveys, and case studies, this Reprint provides valuable insights into the evolving role of AI in shaping the future of education, making it a useful resource for researchers, practitioners, and policymakers alike.
Calculus I
This Calculus I workbook is designed to provide structure to the Peer-Led Team Learning (PLTL) Workshop. These materials, originally developed from courses at the University of Maine, Morehouse College, and Prince George's Community College in Maryland, have been tested and provide students with many valuable tools for success.Each unit in this publication falls into one of three categories: (1) a discovery workshop, best offered before discussion of a concept occurs in class, with the goal that your learning will be enhanced through discovering an idea with peers; (2) an exploratory workshop, best offered after a concept is discussed in class so you can explore concepts in more depth with the goal of deepening your understanding of the idea; (3) a review workshop that is offered so you can practice important skills. You may be asked to complete the entire workshop, or selected parts because of the extensive nature of the topic and/or time constraints.
Blueprints
"A stunning book ... a thrilling read" (Peter Frankopan) that reveals how creative people can harness the profound and productive relationship between mathematics and the arts When Shakespeare has the Three Witches cast Macbeth's lot, he uses something very weird to do it: not simply "eye of newt and toe of frog," but the number seven. And when Hamlet claims, "To be or not to be, that is the question," Shakespeare reaches for eleven. For Shakespeare, prime numbers were magical. And he is not alone. As Marcus du Sautoy showcases in Blueprints, creativity is inseparable from mathematics. The designs of Le Corbusier and Leonardo; the music of Glass, Bach, and Debussy; the wild visions of Dali, the choreography of Laban, the animation of Pixar--all are shot through with mathematics, from primes and fractals to the weirder worlds of Hamiltonian cycles and hyperbolic geometry. And Du Sautoy argues that the relationship runs both ways. Just as mathematics inspires new art, the artistic mindset is a necessity for discovering new mathematics. Blueprints will expand your mind, but more importantly, it shows how to ignite your imagination. Anyone who wants to create needs this book.
Master HiSET Math
HiSET Math Mastery: Complete Tutorials & Practice Workbook with 200+ QuestionsYou have arrived! We have helped thousands of students and we can help you! Over 200 HiSET math practice questions, prepared by a dedicated team of exam experts, with detailed answer key, Math shortcuts, tips and tricks, tutorials and multiple choice strategies! HiSET Math Practice Questions and Tutorials for: Basic MathScientific NotationExponents and Radicals Square RootFractions, Decimals and PercentMeans, Median and ModesAlgebra Real world problems with ratio and proportion One and two variable equations Solve quadratic equations given values or graphs Quadratic using different methods Basic Geometry Slope of a line Linear equations from a graph Perimeter, circumference and volume Pythagorean theorem Geometric transformations Real world problems using the properties of geometric shapesYou also receive: Math Multiple Choice Strategy- How to Study for a Math Test- How to make a study plan- How to Take a TestHiSET(R) is a registered trademark of the Educational Testing Service (ETS), who are not involved in the production of, and do not endorse this product.Remember though, it only a few percentage points divide the PASS from the FAIL students! Even if our test tips increase your score by a few percentage points, isn't that worth it?
Making Democracy Count
How we can repair our democracy by rebuilding the mechanisms that power it What's the best way to determine what most voters want when multiple candidates are running? What's the fairest way to allocate legislative seats to different constituencies? What's the least distorted way to draw voting districts? Not the way we do things now. Democracy is mathematical to its very foundations. Yet most of the methods in use are a historical grab bag of the shortsighted, the cynical, the innumerate, and the outright discriminatory. Making Democracy Count sheds new light on our electoral systems, revealing how a deeper understanding of their mathematics is the key to creating civic infrastructure that works for everyone. In this timely guide, Ismar Volic empowers us to use mathematical thinking as an objective, nonpartisan framework that rises above the noise and rancor of today's divided public square. Examining our representative democracy using powerful clarifying concepts, Volic shows why our current voting system stifles political diversity, why the size of the House of Representatives contributes to its paralysis, why gerrymandering is a sinister instrument that entrenches partisanship and disenfranchisement, why the Electoral College must be rethought, and what can work better and why. Volic also discusses the legal and constitutional practicalities involved and proposes a road map for repairing the mathematical structures that undergird representative government. Making Democracy Count gives us the concrete knowledge and the confidence to advocate for a more just, equitable, and inclusive democracy.
Statistics for Composite Indicators
This book provides a systematic and integrated approach to construct measures of complex and multidimensional concepts called composite indicators. One of the most pressing needs of scientists and policy makers is to measure phenomena that are important to our lives in society using numbers, to observe their evolution over time, and to analyse the relationships between them in order to understand the complex reality and decide on the right actions to achieve specific goals. Many socio-economic phenomena, as well as ecological, biological and of other sciences, are multidimensional and, to be measured, require the use of statistical-mathematical techniques that facilitate their reading and use for studies and analyses. This book is a guide to the knowledge and application of statistical tools suitable for the construction of "optimal" composite indicators, i.e. indicators that provide the most accurate measure of multidimensional reality. The book is aimed at all those - statisticians, sociologists, economists, and policy makers - who wish to construct composite indicators to measure and evaluate the complex reality that surrounds us.
Unequal
An exciting "new perspective on equality and difference" (Stephon Alexander) that shows why the familiar equal sign isn't just a marker of sameness but a gateway into math's--and humanity's--most profound questions "Eugenia Cheng has opened up my mind to the wondrous world of pure mathematics in a way that I never thought was possible."―Willow Smith, singer and actress A New Scientist Best Book of the Year Math is famous for its equations: 1 + 1 = 2, a^2 + b^2 = c^2, or y = mx + b. Much of the time it can seem like that's all mathematics is: following steps to show that what's on one side of an equation is the same as what's on the other. In Unequal, Eugenia Cheng shows that's just part of the story, and the boring part to boot. Mathematics isn't only about showing how numbers and symbols are the same. It isn't even just about numbers and symbols at all, but a world of shapes, symmetries, logical ideas, and more. And in that world, the boundary between things being equal and unequal is a gray area, or perhaps a rainbow of beautiful, vibrant, subtly nuanced color. As Unequal shows, once you go over that rainbow, almost everything can be considered equal and unequal at the same time, whether it's shapes (seen from the right perspective, a circle is the same as an ellipse), words (synonyms), or people--even numbers! It all depends on what features we care about. And it's up to us what we do about it. That's because mathematics isn't a series of rules, facts, or answers. It's an invitation to a more powerful way of thinking.
Artificial Intelligence in Healthcare
The two-volume set constitutes the proceedings of the Second International Conference on Artificial Intelligence in Healthcare, AIiH 2025, which took place in Cambridge, UK, in September 2025. The 60 full papers included in this book were carefully reviewed and selected from 83 submissions. They were organized in topical sections as follows: Health informatics, Personalised Healthcare, Robotics, Assisted Living Technology, Computational Medicine, Long-term Health Conditions, Maternity and Women's Health and Wellbeing.
Artificial Intelligence in Healthcare
The two-volume set constitutes the proceedings of the Second International Conference on Artificial Intelligence in Healthcare, AIiH 2025, which took place in Cambridge, UK, in September 2025. The 60 full papers included in this book were carefully reviewed and selected from 83 submissions. They were organized in topical sections as follows: Health informatics, Personalised Healthcare, Robotics, Assisted Living Technology, Computational Medicine, Long-term Health Conditions, Maternity and Women's Health and Wellbeing.
The Pattern of Change
One of life's most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.
The Pattern of Change
One of life's most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.
Banach Algebras and Harmonic Analysis
The book includes recent articles on various topics studied recently in Banach algebras and abstract harmonic analysis. On the Banach algebra side, the reader will find idempotents and socle of a Banach algebra; closed subspaces of a Banach space, including the classical sequence spaces, which are realized as the kernel of a bounded operator; the connection between the stable rank one and Dedekind-finite property of the algebra of operators on a Banach space; spectral synthesis properties in convolution Sobolev algebras on the real line. The harmonic analysis side includes a generalization of the famous Beurling theorem; groups with few finite-dimensional unitary representations; relations between ideals of the Figa-Talamanca Herz algebra of a locally compact group and ideals of Figa-Talamanca Herz algebra of its closed subgroup; the tame functionals on Banach algebras and in harmonic analysis; and cancellation, factorization, and isometries in algebras on a locally compact group. The book also includes four surveys written by leaders in the area of full sheaf cohomology theory for noncommutative C - algebras; one-parameter semigroups of bounded operators on a Banach space which are weakly continuous in the sense of Arveson.
Partial Differential Equations
Partial Differential Equations: Foundations and Applications offers a clear, precise, and conceptually rich introduction to one of the most fundamental areas of mathematics. Far beyond abstract formalism, partial differential equations form the language through which the laws of nature are expressed, governing phenomena in physics, engineering, and the life sciences - from heat diffusion and wave propagation to fluid motion, electromagnetism, and quantum systems.This volume is designed for undergraduate and postgraduate students in mathematics, physics, and engineering, as well as for motivated self-learners and researchers seeking a unified and reliable reference. It balances mathematical depth with conceptual clarity, integrating theory and application so that abstract methods emerge from physical motivations.This book includes: Fundamental definitions, classification, and formation of partial differential equations First-order partial differential equations: method of characteristics, Lagrange's method, Charpit's method, and applications such as transport equations and Burgers' equation Second-order partial differential equations: classification into hyperbolic, parabolic, and elliptic types, canonical forms, and associated physical models Separation of variables and Sturm-Liouville theory, with orthogonal functions and eigenfunction expansions Fourier series and Fourier transforms, convergence theorems, Parseval's identity, and applications to the heat and wave equations The heat, wave, and Laplace equations in one or more dimensions, steady-state and time-dependent solutions, and coordinate-based techniques Laplace transform methods for problems on semi-infinite domains, impulsive sources, and delta function initial conditions Each chapter is structured to develop both analytical techniques and physical insight, supported by solved examples and graded exercises with answers. Special attention is given to connecting mathematical derivations with their physical interpretations, ensuring the reader gains not only procedural skill but also a comprehensive insight of the underlying principles of the subject.
