Statistical Analyses for Criminal Justice and Criminology
This book is a how-to guide for statistical analyses designed for undergraduates and others new to the subject. It uses a conceptual framework, starting with the most basic concepts of statistics and moving up through the capacity to perform bivariate regression.
Mathematics of Tabletop Games
This book provides a bridge between mathematics and hobby tabletop gaming. Readers interested in either mathematics or tabletop games will find this book an engaging way to begin exploring the other topic or the connection between the topics.
Numerical Approaches to Optimal Control
Optimal control has been widely applied to modern control systems design and has drawn great attention for decades. In the optimal control theory, the control problem is formulated as an optimization problem, and the control law is calculated by solv-ing the optimal control problem (OCP). Comparing with traditional control methods like PID control, optimal control is capable of providing an optimal control law in a systematic way. However, optimal control can achieve an analytic expression of the optimal control law only for some relatively simpler cases, for instance, unconstrained linear systems. Specifically, the optimal feedback control law for unconstrained linear systems with a quadratic cost function is in a simple linear form, and the optimal control gain is obtained by solving a Riccati equation. In practical systems, most of the physical plants are essentially nonlinear systems subject to physical constraints. For these cases, it is difficult to obtain an analytical solution to the optimal control problems. In order to find the optimum to an intractable optimization problem, ap-proximate solutions have to be taken into account.
Bayesian Modeling of Spatio-Temporal Data with R
This book is designed to make spatio-temporal modeling and analysis understandable to students and researchers, mathematicians and statisticians and practitioners in the applied sciences. By avoiding hardcore math and calculus, this book aims to be a bridge that removes the statistical knowledge gap from among the applied scientists.
Parabolic Problems
Parabola is a mathematics magazine published by UNSW, Sydney. Among other things, each issue of Parabola has contained a collection of puzzles/problems, on various mathematical topics and at a suitable level for younger (but mathematically sophisticated) readers.Parabolic Problems: 60 Years of Mathematical Puzzles in Parabola collects the very best of almost 1800 problems and puzzles into a single volume. Many of the problems have been re-mastered, and new illustrations have been added. Topics covered range across geometry, number theory, combinatorics, logic, and algebra. Solutions are provided to all problems, and a chapter has been included detailing some frequently useful problem-solving techniques, making this a fabulous resource for education and, most importantly, fun!Features Hundreds of diverting and mathematically interesting problems and puzzles. Accessible for anyone with a high school-level mathematics education. Wonderful resource for teachers and students of mathematics from high school to undergraduate level, and beyond.
API Design for C++
API Design for C++, Second Edition provides a comprehensive discussion of Application Programming Interface (API) development, from initial design through implementation, testing, documentation, release, versioning, maintenance, and deprecation. It is the only book that teaches the strategies of C++ API development, including interface design, versioning, scripting, and plug-in extensibility. Drawing from the author's experience on large scale, collaborative software projects, the text offers practical techniques of API design that produce robust code for the long-term. It presents patterns and practices that provide real value to individual developers as well as organizations. The Second Edition includes all new material fully updated for the latest versions of C++, including a new chapter on concurrency and multithreading, as well as a new chapter discussing how Objective C++ and C++ code can co-exist and how a C++ API can be accessed from Swift programs. In addition, it explores often overlooked issues, both technical and non-technical, contributing to successful design decisions that produce high quality, robust, and long-lived APIs. It focuses on various API styles and patterns that will allow you to produce elegant and durable libraries. A discussion on testing strategies concentrates on automated API testing techniques rather than attempting to include end-user application testing techniques such as GUI testing, system testing, or manual testing.
Make: Math Teacher's Supplement
Make: Math Teacher's Supplement is the essential guide for teachers, parents, and other educators wanting to supplement their curriculum with Joan Horvath and Rich Cameron's Make: Geometry, Make: Trigonometry, and Make: Calculus books. This book is a companion to the three math books, and does not duplicate the content in them. Drawing on the authors' experience guiding both students and teachers, it covers: The philosophy behind the Make: math book series, including the key inclusion of universal design principles to make the material accessible to those who learn differently A list of topics, projects, and needed maker skills, tied to the math book chapters Key learning objectives and associated assessment ideas A practical primer on 3D printing in an educational environment Helpful tips to manage student 3D printed workflow Five specific examples of ways to use content from the math books, including studying geometry with castles and using LEGO bricks to demonstrate calculus concepts Packed with tips and links to online resources, Make: Math Teacher's Supplement will let you see how to build math intuition to create a solid base for your learner's future.
Math Mammoth Square Roots & the Pythagorean Theorem
Math Mammoth Square Roots & The Pythagorean Theorem is a relatively short worktext focusing on irrational numbers, square roots, and the Pythagorean Theorem and its applications.First, students learn about taking a square root as the opposite operation to squaring a number. They learn about irrational numbers, and how to find approximations to square roots both with a calculator and with a guess-and-check method. Students also practice placing irrational numbers on the number line, using mental math to find their approximate location.Next, the book has a review lesson on how to convert fractions to decimals. The following lesson has to do with writing decimals as fractions, and teaches a method for converting repeating decimals to fractions.Then it is time to learn to solve simple equations that involve taking a square or cube root, over the course of two lessons. After learning to solve such equations, students are now fully ready to study the Pythagorean Theorem and apply it.The Pythagorean Theorem is introduced in the lesson by that name. Students learn to verify that a triangle is a right triangle by checking whether it fulfills the Pythagorean Theorem. They apply their knowledge about square roots and solving equations to solve for an unknown side in a right triangle when two of the sides are given.Next, students solve a variety of geometric and real-life problems that require the Pythagorean Theorem. This theorem is extremely important in many practical situations. Students should show their work for these word problems to include the equation that results from applying the Pythagorean Theorem to the problem and its solution.There are literally hundreds of proofs for the Pythagorean Theorem. In this book, we present one easy proof based on geometry (not algebra). As an exercise, students are asked to supply the steps of reasoning to another geometric proof of the theorem. Students also study a proof for the converse of the theorem, which says that if the sides of a triangle fulfill the equation a2 + b2 = c2 then the triangle is a right triangle.Our last topic is distance between points in the coordinate grid, as this is another simple application of the Pythagorean Theorem.
Applied Nonlinear Functional Analysis
The second edition covers the introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. The new edition includes some new topics on Banach spaces of functions and measures and nonlinear analysis.
Surveys in Geometry II
The book is the second volume of a collection which consists of surveys that focus on important topics in geometry which are at the heart of current research. The topics in the present volume include the conformal and the metric geometry of surfaces, Teichm羹ller spaces, immersed surfaces of prescribed extrinsic curvature in 3-dimensional manifolds, symplectic geometry, the metric theory of Grassmann spaces, homogeneous metric spaces, polytopes, the higher-dimensional Gauss-Bonnet formula, isoperimetry in finitely generated groups and Coxeter groups.Each chapter is intended for graduate students and researchers. Several chapters are based on lectures given by their authors to middle-advanced level students and young researchers. The whole book is intended to be an introduction to important topics in geometry.
Financial Data Analytics with R
This book is an exploration of statistical methodologies and their applications in finance. Readers are taken on a journey in each chapter through practical explanations and examples, enabling them to develop a solid foundation of these methods in R and their applications in finance.
Optimization Problems in Transportation and Logistics
This educational guide will help students and practitioners seeking to understand the fundamentals and practice of linear programming. The exercises contained within demonstrate how to solve classical optimization problems with an emphasis on spatial analysis in supply chain management and transport logistics. All exercises describe the Python programs and optimization libraries that can be used to solve them. The first chapter introduces key concepts in linear programming and establishes a new cognitive framework to help students and practitioners set up each optimization problem. This cognitive framework organizes the decision variables, constraints, objective function, and variable bounds in a format that allows for direct application to optimization software. The second chapter introduces two types of mobility optimization problems (shortest path in a network and minimum cost tour) in the context of delivery and service planning logistics. The third chapter introduces four types of spatial optimization problems (neighborhood coverage, flow capturing, zone heterogeneity, service coverage) and provides a workflow for visualizing the optimized solutions in maps. The workflow creates decision variables from maps by using the free geographic information systems (GIS) programs QGIS and GeoDA. The fourth chapter introduces three types of spatial logisticsproblems (spatial distribution, flow maximization, warehouse location optimization) and demonstrates how to scale the cognitive framework in software to reach solutions. The final chapter summarizes lessons learned and provides insights about how students and practitioners can modify the Python programs and GIS workflows to solve their own optimization problem andvisualize the results.
Math Mammoth Grade 2 Answer Keys, International Version
This book includes the answers for the Math Mammoth International Version Grade 2-A and 2-B student worktexts, for all of the chapter tests, and for the cumulative revisions for grade 2. The other parts of the curriculum may be purchased separately.
Math Mammoth Grade 2 Tests and Cumulative Revisions, International Version
Math Mammoth Grade 2 Tests and Cumulative Revisions (International Version) contains the chapter tests, end-of-year test, and cumulative revision worksheets for Math Mammoth grade 2 complete curriculum. It does not contain answers; the answer key book may be purchased separately.
Math Mammoth Grade 4 Tests and Cumulative Revisions, International Version
Math Mammoth Grade 4 Tests and Cumulative Revisions (International Version) contains the chapter tests, end-of-year test, and cumulative revision lessons for Math Mammoth grade 4 complete curriculum. Note: this book does not contain answers. The answer key book for grade 4 may be purchased as a separate book.
Math Mammoth Grade 2-A Worktext, International Version
Math Mammoth Grade 2-A Worktext (International Version) is the student worktext for the first half of grade 2, and part of the Math Mammoth Grade 2 complete curriculum. This book, 2-A, covers some revision, even and odd numbers, doubling, reading the clock, addition and subtraction facts within 0 - 18, adding two-digit numbers, geometry and fractions. The rest of the topics for 2nd grade are covered in the student book 2-B. Please note: this is a student worktext and does not contain the answers. The answer key book is available separately.Being a worktext, the book contains both the necessary instruction and the problems and exercises (the 'text' and the 'work'; thus a "worktext"), and is for the most part self-teaching.Some main features of Math Mammoth complete curriculum (Light Blue series) are: focuses on conceptual understanding;uses lots of visual models and pattern exercises;mastery-oriented, focusing at length on a topic;emphasizes mental maths and number senserequires little preparation from the teacher.This curriculum is essentially the same as the US version of Math Mammoth Grade 2, only customised for the international audience in these aspects: The currency used in the money chapters in grades 1-3 is the Australian dollar.The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds, are not used.The spelling conforms to British international standards (British English).Page (paper) size is A4.Please note this is a student worktext and does not contain the answers. The answer key book is available separately.The other parts of Math Mammoth Grade 2 curriculum (International Version) are: grade 2-B student worktext, grade 2 answer keys, and grade 2 tests and cumulative revisions.
Math Mammoth Grade 2-B Worktext, International Version
Math Mammoth Grade 2-B International Version is the student worktext (in full color) for the second half of grade 2, and part of the Math Mammoth Grade 2 complete curriculum. This book covers three-digit numbers, measuring, regrouping in addition and subtraction, money (using Australian money) and the introduction to multiplication. The rest of the topics for 2nd grade are covered in the student book 2-A. Please note: this is a student worktext and does not contain the answers. The answer key book is available separately.Being a worktext, the book contains both the necessary instruction and the problems and exercises (the 'text' and the 'work'; thus a "worktext"), and is for the most part self-teaching.Some main features of Math Mammoth complete curriculum (Light Blue series) are: focuses on conceptual understanding;uses lots of visual models and pattern exercises;mastery-oriented, focusing at length on a topic;emphasizes mental maths and number senserequires little preparation from the teacher.This curriculum is essentially the same as the US version of Math Mammoth Grade 2, only customised for the international audience in these aspects: The currency used in the money chapters in grades 1-3 is the Australian dollar.The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds, are not used.The spelling conforms to British international standards (British English).Page (paper) size is A4.The other parts of Math Mammoth International Version Grade 2 curriculum are: grade 2-A student worktext, grade 2 answer keys, and grade 2 tests and cumulative revisions.
Math Mammoth Grade 4-A Worktext, International Version
Math Mammoth Grade 4-A Worktext (International Version) is the student worktext for the first half of grade 4 mathematics, and part of the Math Mammoth Grade 4 complete curriculum. This book covers addition, subtraction, patterns, graphs, large numbers and place value, multi-digit multiplication, time, and measuring.The worktext contains both the necessary instruction and the problems and exercises (the 'text' and the 'work'; thus a "worktext"), and is for the most part self-teaching.Please note this is a student worktext and does not contain the answers.Features: Math Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the maths, 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 a strong emphasis on mental maths and number sense.It requires very little teacher preparation, which is a big help to most parents.: )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.For multiplication tables and division facts, you can use our online practice program (free).The other parts of Math Mammoth Grade 4 (International Version) are: grade 4-B student worktext, grade 4 answer keys, and grade 4 tests and cumulative revisions.
Math Mammoth Grade 4 Answer Keys, International Version
This book includes the answers for the Math Mammoth Grade 4-A and 4-B (International Version) student worktexts, for all of the chapter tests, and for the cumulative revisions. The A and B worktexts, and a book containing the cumulative revisions, chapter tests and the end-of-the-year test may be purchased as separate books.
Math Mammoth Grade 1 Answer Keys, International Version
This book includes the answers for the Math Mammoth Grade 1-A and 1-B student worktexts (International Version), for all of the chapter tests, and for the cumulative revisions for grade 1. The other parts of the curriculum may be purchased as separate books.
Math Mammoth Grade 1-B Worktext, International Version
Math Mammoth Grade 1-B Worktext (International Version) is the student worktext for the second half of grade 1 mathematics studies. In this part B, the main areas of study are: addition and subtraction facts within 10;clock to the half hour;geometric shapes and measuring length;adding and subtracting within 100; andcounting coins (Australian currency).The worktext is in full color, and contains both the necessary instruction and the problems & exercises (the 'text' and the 'work'), and is for the most part self-teaching. It does not contain the answers.Features of the curriculum: Math Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the maths, 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 a strong emphasis on mental maths and number sense. Requires very little teacher preparation, which is a big benefit to most teachers/parents.: ) 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. For addition and subtraction facts, you can use our online practice program (free). A companion to this book, Math Mammoth Grade 1-A worktext, covers the first half of 1st grade maths (available separately). Also available are the answer keys and a book containing cumulative revisions and end-of-chapter tests.
Math Mammoth Grade 1-A Worktext, International Version
Math Mammoth Grade 1-A Worktext (International Version) is the student worktext for the first half of grade 1 mathematics studies. In this part A, the main areas of study are: The concepts of addition and subtraction;strategies for addition and subtraction facts; anddeveloping understanding of whole number relationships and place value till 100.The worktext is in full color, and contains both the necessary instruction and the problems & exercises (the 'text' and the 'work'), and is for the most part self-teaching. It does not contain the answers.Features of the curriculum: Math Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the maths, 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 a strong emphasis on mental maths and number sense. Requires very little teacher preparation, which is a big benefit to most teachers/parents.: ) 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. For addition and subtraction facts, you can use our online practice program (free). A companion to this book, Math Mammoth Grade 1-B worktext, covers the second half of 1st grade maths (available separately). Also available are the answer keys and a book containing cumulative revisions and end-of-chapter tests..
Math Mammoth Grade 1 Tests and Cumulative Revisions, International Version
Math Mammoth Grade 1 Tests and Cumulative Revisions (International Version) contains the chapter tests, the end-of-year test, and cumulative revision worksheets for Math Mammoth Grade 1 curriculum. This book does not contain answers; the answer key book may be purchased separately.
Computational Methods for Coupled Problems in Science and Engineering
The ninth edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2021) was organized to take place on 13-16 June 2021. Due to the pandemic, COUPLED 2021 was a fully online and completely synchronous conference. The previous eight editions of this conference were held on the islands of Santorini (Greece) on 25-28 May 2005; Ibiza (Spain) on 21-23 May 2007; Ischia (Italy) on 8-11 June 2009; Kos (Greece) on 20-22 June 2011; Ibiza (Spain) on 17-19 June 2013; San Servolo, Venice (Italy), on 18-20 May 2015; Rhodes Island (Greece) on 12-14 June 2017; and Sitges (Spain) on 3-5 June 2019. The objectives of COUPLED PROBLEMS 2021 were to present and discuss the state of the art in mathematical models, numerical methods and computational techniques for solving coupling problems of a multidisciplinary character in science and engineering. The conference's goal was to make advances in the formulation and solution of real-life problems with a multidisciplinary perspective, accounting for all the complex couplings involved in the physical description of the problem. The conference was one of the Thematic Conferences of the European Community on Computational Methods in Applied Sciences (ECCOMAS) and a Special Interest Conference of the International Association for Computational Mechanics (IACM). It was also supported by other scientific organizations in Europe and across the globe.
Risk Revealed
Explore the concept of risk through numerous examples and their statistical modeling, traveling from a historical perspective all the way to an up-to-date technical analysis. Written with a wide readership in mind, this book begins with accounts of a selection of major historical disasters, such as the North Sea flood of 1953 and the L'Aquila earthquake. These tales serve to set the scene and to motivate the second part of the book, which describes the mathematical tools required to analyze these events, and how to use them. The focus is on the basic understanding of the mathematical modeling of risk and what types of questions the methods allow one to answer. The text offers a bridge between the world of science and that of everyday experience. It is written to be accessible to readers with only a basic background in mathematics and statistics. Even the more technical discussions are interspersed with historical comments and plentiful examples.
Change Point Analysis for Time Series
This volume provides a comprehensive survey that covers various modern methods used for detecting and estimating change points in time series and their models. The book primarily focuses on asymptotic theory and practical applications of change point analysis. The methods discussed in the book go beyond the traditional change point methods for univariate and multivariate series. It also explores techniques for handling heteroscedastic series, high-dimensional series, and functional data. While the primary emphasis is on retrospective change point analysis, the book also presents sequential "on-line" methods for detecting change points in real-time scenarios. Each chapter in the book includes multiple data examples that illustrate the practical application of the developed results. These examples cover diverse fields such as economics, finance, environmental studies, and health data analysis. To reinforce the understanding of the material, each chapter concludes with several exercises.Additionally, the book provides a discussion of background literature, allowing readers to explore further resources for in-depth knowledge on specific topics. Overall, "Change Point Analysis for Time Series" offers a broad and informative overview of modern methods in change point analysis, making it a valuable resource for researchers, practitioners, and students interested in analyzing and modeling time series data.
Linear Algebra in Data Science
This textbook explores applications of linear algebra in data science at an introductory level, showing readers how the two are deeply connected. The authors accomplish this by offering exercises that escalate in complexity, many of which incorporate MATLAB. Practice projects appear as well for students to better understand the real-world applications of the material covered in a standard linear algebra course. Some topics covered include singular value decomposition, convolution, frequency filtering, and neural networks. Linear Algebra in Data Science is suitable as a supplement to a standard linear algebra course.
The families of prime numbers
The book introduces innovative approaches to conjectures and established knowledge in the realm of prime numbers. It explores how famous mathematicians like Sophie Germain and Mersenne, among others, conceptualized prime numbers Not only does the text clarify Fermat's Little Theorem, but it also offers an explanation for the existence of pseudoprimes. Furthermore, it sheds light on the effectiveness of the Lucas-Lehmer algorithm in discovering Mersenne Primes. By elucidating fundamental concepts, the book provides fresh insights into the study of prime numbers within Number Theory. While its primary audience consists of enthusiasts and mathematicians in search of new patterns and analytical methodologies for prime numbers, the book is designed to be accessible to a broader audience. With over 70 explanatory figures and clear prose, it appeals to anyone intrigued by the intricate world of prime numbers.
Tangles
Tangles offer a precise way to identify structure in imprecise data. By grouping qualities that often occur together, they not only reveal clusters of things but also types of their qualities: types of political views, of texts, of health conditions, or of proteins. Tangles offer a new, structural, approach to artificial intelligence that can help us understand, classify, and predict complex phenomena. This has become possible by the recent axiomatization of the mathematical theory of tangles, which has made it applicable far beyond its origin in graph theory: from clustering in data science and machine learning to predicting customer behaviour in economics; from DNA sequencing and drug development to text and image analysis. Such applications are explored here for the first time. Assuming only basic undergraduate mathematics, the theory of tangles and its potential implications are made accessible to scientists, computer scientists, and social scientists.
Harmonic Functions and Random Walks on Groups
Research in recent years has highlighted the deep connections between the algebraic, geometric, and analytic structures of a discrete group. New methods and ideas have resulted in an exciting field, with many opportunities for new researchers. This book is an introduction to the area from a modern vantage point. It incorporates the main basics, such as Kesten's amenability criterion, Coulhon and Saloff-Coste inequality, random walk entropy and bounded harmonic functions, the Choquet-Deny Theorem, the Milnor-Wolf Theorem, and a complete proof of Gromov's Theorem on polynomial growth groups. The book is especially appropriate for young researchers, and those new to the field, accessible even to graduate students. An abundance of examples, exercises, and solutions encourage self-reflection and the internalization of the concepts introduced. The author also points to open problems and possibilities for further research.
Ecosystem Modelling with EwE
This textbook provides a basis for courses in ecosystem modelling based on the Ecopath with Ecosim (EwE) modelling framework and software. EwE is a versatile approach with a low but very long (and gradually steeper) learning curve.The authors have been central to the development of EwE for more than thirty years, and during that time the simple Ecopath mass-balance approach it started with has through the addition of time and spatial-dynamic models, among others, been expanded to become a dynamic toolbox that can be used to address anything from simple fundamental research questions to very complex management and policy questions related to ecosystem based management.It's been a guiding principle throughout the development of EwE to provide an easy-to-access approach that does not require extensive mathematical or programming capabilities to get start. Model first, ask later is the philosophy. By just getting started with modelling, you gain insight and can start asking fundamental questions about how components of ecosystems interplay. Diving deeper is important, but this textbook makes the initial getting-started as simple and accessible as possible.
Probability Theory
This book is intended as an introduction to Probability Theory and Mathematical Statistics for students in mathematics, the physical sciences, engineering, and related fields. It is based on the author's 25 years of experience teaching probability and is squarely aimed at helping students overcome common difficulties in learning the subject. The focus of the book is an explanation of the theory, mainly by the use of many examples. Whenever possible, proofs of stated results are provided. All sections conclude with a short list of problems. The book also includes several optional sections on more advanced topics. This textbook would be ideal for use in a first course in Probability Theory. Contents: ProbabilitiesConditional Probabilities and IndependenceRandom Variables and Their DistributionOperations on Random VariablesExpected Value, Variance, and CovarianceNormally Distributed Random VectorsLimit Theorems Introduction to Stochastic ProcessesMathematical StatisticsAppendixBibliographyIndex
Higher Special Functions
Higher special functions emerge from boundary eigenvalue problems of Fuchsian differential equations with more than three singularities. This detailed reference provides solutions for singular boundary eigenvalue problems of linear ordinary differential equations of second order, exploring previously unknown methods for finding higher special functions. Starting from the fact that it is the singularities of a differential equation that determine the local, as well as the global, behaviour of its solutions, the author develops methods that are both new and efficient and lead to functional relationships that were previously unknown. All the developments discussed are placed within their historical context, allowing the reader to trace the roots of the theory back through the work of many generations of great mathematicians. Particular attention is given to the work of George Cecil Jaff矇, who laid the foundation with the calculation of the quantum mechanical energy levels of the hydrogen molecule ion.
Practical Machine Learning with R
This textbook is a comprehensive guide to machine learning and artificial intelligence tailored for students in business and economics. It takes a hands-on approach to teach machine learning, emphasizing practical applications over complex mathematical concepts. Students are not required to have advanced mathematics knowledge such as matrix algebra or calculus.The author introduces machine learning algorithms, utilizing the widely used R language for statistical analysis. Each chapter includes examples, case studies, and interactive tutorials to enhance understanding. No prior programming knowledge is needed. The book leverages the tidymodels package, an extension of R, to streamline data processing and model workflows. This package simplifies commands, making the logic of algorithms more accessible by minimizing programming syntax hurdles. The use of tidymodels ensures a unified experience across various machine learning models.With interactive tutorials that students can download and follow along at their own pace, the book provides a practical approach to apply machine learning algorithms to real-world scenarios.In addition to the interactive tutorials, each chapter includes a Digital Resources section, offering links to articles, videos, data, and sample R code scripts. A companion website further enriches the learning and teaching experience: https: //ai.lange-analytics.com.This book is not just a textbook; it is a dynamic learning experience that empowers students and instructors alike with a practical and accessible approach to machine learning in business and economics. Key Features: Unlocks machine learning basics without advanced mathematics -- no calculus or matrix algebra required. Demonstrates each concept with R code and real-world data for a deep understanding -- no prior programming knowledge is needed. Bridges the gap between theory and real-world applications with hands-on interactive projects and tutorials in every chapter, guided with hints and solutions. Encourages continuous learning with chapter-specific online resources--video tutorials, R-scripts, blog posts, and an online community. Supports instructors through a companion website that includes customizable materials such as slides and syllabi to fit their specific course needs.
Linear Partial Differential and Difference Equations and Simultaneous Systems with Constant or Homogeneous Coefficients
Linear Partial Differential and Difference Equations and Simultaneous Systems: With Constant or Homogeneous Coefficients is part of the series "Mathematics and Physics for Science and Technology," which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. Volume V presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions, and includes applications to: acoustic, elastic, water, electromagnetic and other waves; the diffusion of heat, mass, and electricity; and their interactions. This is the third book of the volume.The book starts with six different methods of solution of linear partial differential equations (p.d.e.) with constant coefficients. One of the methods, namely characteristic polynomial, is then extended to a further five classes, including linear p.d.e. with homogeneous power coefficients and finite difference equations and simultaneous systems of both (simultaneous partial differential equations [s.p.d.e.] and simultaneous finite difference equations [s.f.d.e.]). The applications include detailed solutions of the most important p.d.e. in physics and engineering, including the Laplace, heat, diffusion, telegraph, bar, and beam equations. The free and forced solutions are considered together with boundary, initial, asymptotic, starting, and other conditions.The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical, and other branches of engineering dealing with advanced technology, and also in the physical sciences and applied mathematics.
Vector Calculus
A calculus book must tell the truth. This book is carefully written in the accepted language of mathematics in a readable exposition. It includes useful and fascinating applications, acquaints students with the history of the subject and offers a sense of what mathematics is all about.
Math Mammoth The Four Operations (with a Touch of Algebra)
Math Mammoth The Four Operations (with a Touch of Algebra) is a mathematics worktext meant primarily for fifth and sixth grades. Being a worktext means that this book is a textbook and workbook together: the lessons include both the explanations of the concepts, as well as practice exercises.The main topics of this book are mental math strategies, simple equations and expressions, the order of operations, partial products, using all four operations in solving problems, and number patterns in the coordinate grid.Students encounter the exact definition of an equation and an expression. They practice the order of operations with problems that also reinforce the idea of the equal sign ("=") as denoting equality of the right and left sides of an equation. These kinds of exercises are needed because students may think that an equal sign signifies the act of finding the answer to a problem (such as 134 + 23 = ?), which is not so.Students solve simple equations with the help of a bar model. They also use the pan balance model to solve simple one and two-step equations and even some three-step equations.We review the thought of partial products (multiplying and dividing in parts), including how those partial products are seen in the multiplication algorithm, and how to use mental math to divide numbers in parts.Although the book is named "The Four Operations," the idea is not to practice each of the four operations separately, but rather to see how they are used together in solving problems and in simple equations. We are trying to develop the student's algebraic thinking, including the abilities to: translate problems into mathematical operations, comprehend the many operations needed to yield an answer to a problem, "undo" operations, and so on. Many of the ideas in this book are preparing students for algebra.The answers are appended.
Current topics in Logic and the Philosophy of Science. Papers from SILFS 2022 postgraduate conference
Logic and the Philosophy of Science are disciplines that avoid stopping and wandering around in circles on the same topics. Their role in dedicating themselves to scientific and applicative subjects always makes them extraordinarily fruitful and productive, in step with the developments of scientific and technological knowledge. The writings contained in this volume are proof of this. The set of research selected for this publication, starting from the 2022 Postgraduate Conference of SILFS (the Italian Society for Logic and the Philosophy of Science), testifies to a lively and rich knowledge widespread among young scholars of this area who combine pure logic and philosophy to the analysis of cutting-edge knowledge produced by current scientific and technological disciplines. The result is a kaleidoscope of research on updated logical and philosophical-scientific topics, which gives rise to promising developments on the part of young scholars who are contributing today to the logic and philosophy of science to create further perspectives in the future.
The Code of Mathematics
Inspired by recent developments in dependent type theory and infinity categories, this book presents a history of ideas around the topics of truth, proof, equality and equivalence. Besides selected ideas of Platon, Aristoteles, Leibniz, Kant, Frege and others, the results of G繹del and Tarski on incompleteness, undecidability and truth in deductive systems and their semantic models are covered. The main focus of this textbook is on dependent type theory and its recent variant homotopy type theory. Such theories contain identity types, which give a new understanding of equality, symmetry, equivalence and isomorphism in a conceptual way. The interaction of type theory and infinity category theory yields a new paradigm for a structural view on mathematics. This supports the tendencies towards formalising mathematics with the help of proof assistants. This book was first published in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
Bridging Gaps In Elementary Mathematics
Bridging Gaps in Elementary Mathematics is a Mathematics study supplement created to improve upon the appreciation and fundamental understanding of Mathematics by employing the "why" of Mathematics approach. It was also created to ensure that those who did not have an opportunity in their earlier years to study Mathematics, or those who did but need better understanding, would be able to "bridge" the gaps formed in their education. The material covers topics found in the curriculum at the Primary to the pre-Junior High School level. It is not intended to substitute for formally prescribed schooling study materials and textbooks. Still, it is a supplement that provides a more profound understanding, real-life applications and different perspectives of the universal elements of the Mathematics curriculum. It effectively approaches the subject from the root to help make it less abstract.
Inverse Gravity Cosmology
The book is about the inverse gravity cosmology hypothesis which is based on three of the author's published papers which past peer review. Hence, the book presents the inverse gravity concept, its mathematical structure, and its incorporation to established and proven aspects of physics. New developments and mathematics of the theoretical concept are expressed. Moreover, the book cites mistakes/deficiencies and omissions in previous publications. Lastly, the book's introduction includes information about the author's background that inspired the inception of the theoretical concept.
Mathematical Puzzles
Research in maths is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing maths. This book makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem.
Model-Based Monitoring and Statistical Control
Available in English for the first time, this classic and influential book by the late Kohei Otshu presents real examples of ships in motion under irregular ocean waves, helping to expalin fluctuations of stochastic phenomena through spectral analysis methods and statistical modeling.
