The Joy of Abstraction
Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no formal mathematical background needed. The book brings abstract mathematical ideas down to earth using examples of social justice, current events, and everyday life - from privilege to COVID-19 to driving routes. The journey begins with the ideas and workings of abstract mathematics, after which you will gently climb toward more technical material, learning everything needed to understand category theory, and then key concepts in category theory like natural transformations, duality, and even a glimpse of ongoing research in higher-dimensional category theory. For fans of How to Bake Pi, this will help you dig deeper into mathematical concepts and build your mathematical background.
Galois Theory
Since 1973, Galois Theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory, Fifth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for today's algebra students.
The Energy of Data and Distance Correlation
Energy statistics are functions of distances between statistical observations in metric spaces. The authors hope this book will spark the interest of most statisticians who so far have not explored E-statistics and would like to apply these new methods using R.
The Fabulous Fibonacci Numbers
The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.
Fundamentals of Statistical Inference
This book provides a coherent description of foundational matters concerning statistical inference and shows how statistics can help us make inductive inferences about a broader context, based only on a limited dataset such as a random sample drawn from a larger population. By relating those basics to the methodological debate about inferential errors associated with p-values and statistical significance testing, readers are provided with a clear grasp of what statistical inference presupposes, and what it can and cannot do. To facilitate intuition, the representations throughout the book are as non-technical as possible.The central inspiration behind the text comes from the scientific debate about good statistical practices and the replication crisis. Calls for statistical reform include an unprecedented methodological warning from the American Statistical Association in 2016, a special issue "Statistical Inference in the 21st Century: A World Beyond p The American Statistician in 2019, and a widely supported call to "Retire statistical significance" in Nature in 2019.The book elucidates the probabilistic foundations and the potential of sample-based inferences, including random data generation, effect size estimation, and the assessment of estimation uncertainty caused by random error. Based on a thorough understanding of those basics, it then describes the p-value concept and the null-hypothesis-significance-testing ritual, and finally points out the ensuing inferential errors. This provides readers with the competence to avoid ill-guided statistical routines and misinterpretations of statistical quantities in the future.Intended for readers with an interest in understanding the role of statistical inference, the book provides a prudent assessment of the knowledge gain that can be obtained from a particular setof data under consideration of the uncertainty caused by random error. More particularly, it offers an accessible resource for graduate students as well as statistical practitioners who have a basic knowledge of statistics. Last but not least, it is aimed at scientists with a genuine methodological interest in the above-mentioned reform debate.
A Primer of Subquasivariety Lattices
Preface.- Introduction.- Varieties and quasivarieties in general languages.- Equaclosure operators.- Preclops on finite lattices.- Finite lattices as Sub(S,∧, 1,����): The case J(L) ⊆ ���� (L).- Finite lattices as Sub(S,∧, 1,����): The case J(L) ̸⊆ ���� (L).- The six-step program: From (L, ����) to (Lq(����), Γ).- Lattices 1 + L as Lq(����).- Representing distributive dually algebraic lattices.- Problems and an advertisement.- Appendices.
Intermediate Algebra
Intermediate Algebra provides precollege algebra students with the essentials for understanding what algebra is, how it works, and why it so useful. It is written with plain language and includes annotated examples and practice exercises so that even students with an aversion to math will understand these ideas and learn how to apply them. This textbook expands on algebraic concepts that students need to progress with mathematics at the college level, including linear, exponential, logarithmic, and quadratic functions; sequences; and dimensional analysis. Written by faculty at Chemeketa Community College for the students in the classroom, Intermediate Algebra is a classroom-tested textbook that sets students up for success.
An Essay on the Foundations of Geometry
An Essay on the Foundations of Geometry was first published in 1897 and marks Bertrand Russell's first foray into analytic philosophy, a movement in which Russell is one of the founding members and figurehead. This Routledge Classics edition includes a new Foreword by Michael Potter.
Harmonic Analysis and the Theory of Probability
Harmonic Analysis and the Theory of Probability by Salomon Bochner is a landmark monograph that rigorously links two central domains of modern mathematics: Fourier analysis and probability theory. Written during the author's time at the Statistical Laboratory at Berkeley under the direction of Jerzy Neyman, the book develops a unified account of approximation, Fourier expansions, Laplace and Mellin transforms, stochastic processes, and their deep interrelations. Bochner's treatment moves fluidly from classical tools--kernels, summability formulas, spherical harmonics--to more advanced concepts such as infinitely divisible processes, characteristic functionals, and the closure properties of Fourier transforms, always with an eye to their probabilistic interpretations. This volume demonstrates how probability theory gains analytic depth when recast in the language of harmonic analysis, and how harmonic methods are enriched by probabilistic intuition. It offers precise theorems on convergence, moment conditions, and stochastic functionals, while also exploring zeta integrals, random paths, and the analysis of stationary processes. As part of the California Monographs in Mathematical Sciences series, it speaks to mathematicians, statisticians, and theoretical physicists seeking rigorous frameworks for randomness and structure. Bochner's synthesis not only advanced mid-twentieth-century probability but also laid groundwork for contemporary research in functional analysis, statistical mechanics, and stochastic modeling. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.
Elementary Algebra
Elementary Algebra provides precollege algebra students with the essentials for understanding what algebra is, how it works, and why it so useful. It is written with plain language and includes annotated examples and practice exercises so that even students with an aversion to math will understand these ideas and learn how to apply them. This textbook expands on algebraic concepts that students need to progress with mathematics at the college level, including linear models and equations, polynomials, and quadratic equations. Written by faculty at Chemeketa Community College for the students in the classroom, Elementary Algebra is a classroom-tested textbook that sets students up for success.
Studies in Inductive Logic and Probability, Volume I
Rudolf Carnap and Richard C. Jeffrey's Studies in Inductive Logic and Probability, Volume I gathers seminal work charting Carnap's late-career re-architecture of inductive logic. Moving beyond the single preferred c\*-method of Logical Foundations of Probability (1950), this volume documents the shift to a "continuum" of c-functions and then to a still broader framework sensitive to analogy and similarity, informed by de Finetti's representation theorem and contemporary probability/statistics. Anchored by Carnap's "Basic System" (presented here in detail) and complemented by foundational essays--including the programmatic "Inductive Logic and Rational Decisions"--the collection recasts logical probability in the idiom of events, models, and conditionalization, aligning formal inductive methods with Bayesian decision theory while distinguishing logical from statistical notions of information and entropy. Framed by Jeffrey's editorial introduction and Carnap's own historical notes, the book doubles as an intellectual roadmap through the 1950s-60s renaissance in formal epistemology: collaborations with John Kemeny, dialogue with Savage and Putnam, and the systematic adoption of mathematical tools that were absent from Carnap's earlier work. For philosophers of science, statisticians, and decision theorists, Volume I offers both a definitive statement of Carnap's mature foundations and a launch pad for the unfinished upper stories--issues of confirmation, learning from analogy, and representation--that Volume II continues. It's essential reading for anyone who wants to see how inductive logic became conversant with modern probability while retaining a distinctly logical--normative--conception of rational belief. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1971.
Partial Differential Equations: Spectral and High Order Methods
Partial differential equations (PDEs) are mathematical equations that relate a function of several variables to its partial derivatives. A partial derivative of a function of many variables describes how fast the function changes when one variable is altered, keeping the others constant. The task of discovering a partial derivative can be applied to a function that is itself a partial derivative of another function to obtain a second-order partial derivative. The order and degree of partial differential equations are determined in the same way as ordinary differential equations. Different approaches, evaluations and methodologies on partial differential equations have been included in this book. It strives to provide a fair idea about this discipline and to help develop a better understanding of the latest advances within this field. Coherent flow of topics, student-friendly language and extensive use of examples make this book an invaluable source of knowledge.
The Didactics of Mathematics: Approaches and Issues
Didactics of mathematics is a scientific discipline between math and teaching which deals with various matters of teaching math at individual as well as various school levels. This includes the content and methods on how to teach and learn math. It defines aims and content of a math curriculum, and recommends appropriate methods, procedures and organizational forms of teaching. Didactics of mathematics takes into account psychological relations of learning and provides the necessary teaching technology. At present, there are questions as to the role of a pupil and teacher in an educational process. Didactics of mathematics studies the processes which take place in the minds of the student and teacher when teaching math. This book discusses the fundamentals as well as modern approaches and issues of this field. Different approaches, evaluations, methodologies and advanced studies on the didactics of math have been included herein. This book will help the readers in keeping pace with the rapid changes in this field.
Field Engineering
Field Engineering - A Handbook of the Theory and Practice of Railway Surveying, Location, and Construction is an unchanged, high-quality reprint of the original edition of 1882. Hansebooks is editor of the literature on different topic areas such as research and science, travel and expeditions, cooking and nutrition, medicine, and other genres. As a publisher we focus on the preservation of historical literature. Many works of historical writers and scientists are available today as antiques only. Hansebooks newly publishes these books and contributes to the preservation of literature which has become rare and historical knowledge for the future.
Harmonic Analysis and the Theory of Probability
Harmonic Analysis and the Theory of Probability by Salomon Bochner is a landmark monograph that rigorously links two central domains of modern mathematics: Fourier analysis and probability theory. Written during the author's time at the Statistical Laboratory at Berkeley under the direction of Jerzy Neyman, the book develops a unified account of approximation, Fourier expansions, Laplace and Mellin transforms, stochastic processes, and their deep interrelations. Bochner's treatment moves fluidly from classical tools--kernels, summability formulas, spherical harmonics--to more advanced concepts such as infinitely divisible processes, characteristic functionals, and the closure properties of Fourier transforms, always with an eye to their probabilistic interpretations. This volume demonstrates how probability theory gains analytic depth when recast in the language of harmonic analysis, and how harmonic methods are enriched by probabilistic intuition. It offers precise theorems on convergence, moment conditions, and stochastic functionals, while also exploring zeta integrals, random paths, and the analysis of stationary processes. As part of the California Monographs in Mathematical Sciences series, it speaks to mathematicians, statisticians, and theoretical physicists seeking rigorous frameworks for randomness and structure. Bochner's synthesis not only advanced mid-twentieth-century probability but also laid groundwork for contemporary research in functional analysis, statistical mechanics, and stochastic modeling. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1955.
Principles of Statistical Analysis
This compact course is written for the mathematically literate reader who wants to learn to analyze data in a principled fashion. The language of mathematics enables clear exposition that can go quite deep, quite quickly, and naturally supports an axiomatic and inductive approach to data analysis. Starting with a good grounding in probability, the reader moves to statistical inference via topics of great practical importance - simulation and sampling, as well as experimental design and data collection - that are typically displaced from introductory accounts. The core of the book then covers both standard methods and such advanced topics as multiple testing, meta-analysis, and causal inference.
Introduction to Matrix Theory
Matrix Operations.- Systems of Linear Equations.- Matrix as a Linear Map.- Orthogonality.- Eigenvalues and Eigenvectors.- Canonical Forms.- Norms of Matrices.- Short Bibliography.- Index.
Studies in Inductive Logic and Probability, Volume I
Rudolf Carnap and Richard C. Jeffrey's Studies in Inductive Logic and Probability, Volume I gathers seminal work charting Carnap's late-career re-architecture of inductive logic. Moving beyond the single preferred c\*-method of Logical Foundations of Probability (1950), this volume documents the shift to a "continuum" of c-functions and then to a still broader framework sensitive to analogy and similarity, informed by de Finetti's representation theorem and contemporary probability/statistics. Anchored by Carnap's "Basic System" (presented here in detail) and complemented by foundational essays--including the programmatic "Inductive Logic and Rational Decisions"--the collection recasts logical probability in the idiom of events, models, and conditionalization, aligning formal inductive methods with Bayesian decision theory while distinguishing logical from statistical notions of information and entropy. Framed by Jeffrey's editorial introduction and Carnap's own historical notes, the book doubles as an intellectual roadmap through the 1950s-60s renaissance in formal epistemology: collaborations with John Kemeny, dialogue with Savage and Putnam, and the systematic adoption of mathematical tools that were absent from Carnap's earlier work. For philosophers of science, statisticians, and decision theorists, Volume I offers both a definitive statement of Carnap's mature foundations and a launch pad for the unfinished upper stories--issues of confirmation, learning from analogy, and representation--that Volume II continues. It's essential reading for anyone who wants to see how inductive logic became conversant with modern probability while retaining a distinctly logical--normative--conception of rational belief. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1971.
Principles of Statistical Analysis
This compact course is written for the mathematically literate reader who wants to learn to analyze data in a principled fashion. The language of mathematics enables clear exposition that can go quite deep, quite quickly, and naturally supports an axiomatic and inductive approach to data analysis. Starting with a good grounding in probability, the reader moves to statistical inference via topics of great practical importance - simulation and sampling, as well as experimental design and data collection - that are typically displaced from introductory accounts. The core of the book then covers both standard methods and such advanced topics as multiple testing, meta-analysis, and causal inference.
Computational Optimization
This textbook offers a guided tutorial reviewing the theoretical fundamentals while going through the practical examples used for constructing the computational frame, applied to various real-life models.
Bloch-Type Periodic Functions
This monograph aims to provide for the first time a unified and homogenous presentation of the recent works on the theory of Bloch periodic functions, their generalizations, and their applications to evolution equations. It is useful for graduate students and beginning researchers as seminar topics, graduate courses and reference text in pure and applied mathematics, physics, and engineering.
Environmental Data Analysis with MATLAB or Python
Environmental Data Analysis with MATLAB, Third Edition, is a new edition that expands fundamentally on the original with an expanded tutorial approach, more clear organization, new crib sheets, and problem sets providing a clear learning path for students and researchers working to analyze real data sets in the environmental sciences. The work teaches the basics of the underlying theory of data analysis and then reinforces that knowledge with carefully chosen, realistic scenarios, including case studies in each chapter. The new edition is expanded to include applications to Python, an open source software environment. Significant content in Environmental Data Analysis with MATLAB, Third Edition is devoted to teaching how the programs can be effectively used in an environmental data analysis setting. This new edition offers chapters that can both be used as self-contained resources or as a step-by-step guide for students, and is supplemented with data and scripts to demonstrate relevant use cases.
Algebra II All-In-One for Dummies
Every intermediate algebra lesson, example, and practice problem you need in a single, easy-to-use reference Algebra II can be a tough nut to crack when you first meet it. But with the right tools...well, she's still tough but she gets a heckuva lot easier to manage. In Algebra II All-in-One For Dummies you'll find your very own step-by-step roadmap to solving even the most challenging Algebra II problems, from conics and systems of equations to exponential and logarithmic functions. In the book, you'll discover the ins and outs of function transformation and evaluation, work out your brain with complex and imaginary numbers, and apply formulas from statistics and probability theory. You'll also find: Accessible and practical lessons and practice for second year high-school or university algebra students End-of-chapter quizzes that help you learn - and remember! - key algebraic concepts, such as quadratic equations, graphing techniques, and matrices One-year access to additional chapter quizzes online, where you can track your progress and get real-time feedback! Your own personal mathematical toolbox for some of the most useful and foundational math you'll learn in school, this Algebra II All-in-One For Dummies combines hands-on techniques, methods, and strategies from a variety of sources into one, can't-miss reference. You'll get the insights, formulas, and practice you need, all in a single book (with additional quizzes online!) that's ideal for students and lifelong learners alike!
Partial Differential Equations
This book is an attempt to make available to the student a coherent modern view of the theory of partial differential equations. Here equations of the first order and linear second order equations are treated with the tensor calculus, which combines generality and insight, in mind. Since the book is self-contained, much of the material is classical, but an effort has been made to achieve a modern outlook on these topics. A number of significant recent developments are introduced, and treated in relation to the natural background formed by geometry and physics.Special features of the exposition are: (a) the simplified general treatment of first order equations; (b) the geometrical foundations of the theory of linear second order equations (c) unified treatment of boundary value problems and related topics by integral equations; (d) the theory of generalized hyperbolic potentials.
Linear Algebra II: Advanced Topics for Applications
This is the second volume of the two-volume book on linear algebra in the University of Tokyo (UTokyo) Engineering Course.The objective of this second volume is to branch out from the standard mathematical results presented in the first volume to illustrate useful specific topics pertaining to engineering applications. While linear algebra is primarily concerned with systems of equations and eigenvalue problems for matrices and vectors with real or complex entries, this volumes covers other topics such as matrices and graphs, nonnegative matrices, systems of linear inequalities, integer matrices, polynomial matrices, generalized inverses, and group representation theory.The chapters are, for the most part, independent of each other, and can be read in any order according to the reader's interest. The main objective of this book is to present the mathematical aspects of linear algebraic methods for engineering that will potentially be effective in various application areas.
Make: Calculus
When Isaac Newton developed calculus in the 1600s, he was trying to tie together math and physics in an intuitive, geometrical way. But over time math and physics teaching became heavily weighted toward algebra, and less toward geometrical problem solving. However, many practicing mathematicians and physicists will get their intuition geometrically first and do the algebra later. Make: Calculus imagines how Newton might have used 3D printed models, construction toys, programming, craft materials, and an Arduino or two to teach calculus concepts in an intuitive way. The book uses as little reliance on algebra as possible while still retaining enough to allow comparison with a traditional curriculum. This book is not a traditional Calculus I textbook. Rather, it will take the reader on a tour of key concepts in calculus that lend themselves to hands-on projects. This book also defines terms and common symbols for them so that self-learners can learn more on their own.
Mathematics in Ancient Jaina Literature
The volume contains selected articles presented in the ZOOM conference on History of Mathematics in Jain Literature, December 2020, and also contains articles invited by the editors on specific topics.The main objective for the conference was to bring to the attention of historians in mathematics that there is a plenty of literature written by monks and scholars in Jaina literature that contains elements of arithmetic, algebra and geometry, independent of discoveries by other cultures in the past. The talks and the discussions at the conference highlighted a need for a volume that can be recommended as a reference book for a course on History of Mathematics in the Departments of Mathematics and Education in colleges and universities. This is our hope that the present volume would fill up the gap on the lack of knowledge of past Jaina contributions.
The Eigenbook
​This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory.For graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research. For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs.Written in an engaging and educational style, the book also includes exercises and provides their solution.
Mathematics Applied to Engineering in Action
Mathematics Applied to Engineering in Action: Advanced Theories, Methods, and Models focuses on material relevant to solving the kinds of mathematical problems regularly confronted by engineers. This new volume explains how an engineer should properly define the physical and mathematical problem statements, choose the computational approach, and solve the problem by a proven reliable approach. It presents the theoretical background necessary for solving problems, including definitions, rules, formulas, and theorems on the particular theme.The book aims to apply advanced mathematics using real-world problems to illustrate mathematical ideas. This approach emphasizes the relevance of mathematics to engineering problems, helps to motivate the reader, and gives examples of mathematical concepts in a context familiar to the research students. The volume is intended for professors and instructors, scientific researchers, students, and industry professionals. It will help readers to choose the most appropriate mathematical modeling method to solve engineering problems.
Mathematics as a Laboratory Tool
The second edition of Mathematics as a Laboratory Tool reflects the growing impact that computational science is having on the career choices made by undergraduate science and engineering students. The focus is on dynamics and the effects of time delays and stochastic perturbations ("noise") on the regulation provided by feedback control systems. The concepts are illustrated with applications to gene regulatory networks, motor control, neuroscience and population biology. The presentation in the first edition has been extended to include discussions of neuronal excitability and bursting, multistability, microchaos, Bayesian inference, second-order delay differential equations, and the semi-discretization method for the numerical integration of delay differential equations. Every effort has been made to ensure that the material is accessible to those with a background in calculus. The text provides advanced mathematical concepts such as the Laplace and Fourier integral transforms in the form of Tools. Bayesian inference is introduced using a number of detective-type scenarios including the Monty Hall problem.
Kontsevich's Deformation Quantization and Quantum Field Theory
- 1. Introduction. - 2. Foundations of Differential Geometry. - 3. Symplectic Geometry. - 4. Poisson Geometry. - 5. Deformation Quantization. - 6. Quantum Field Theoretic Approach to Deformation Quantization.
Bootstrap Methods
This book provides a compact introduction to the bootstrap method. In addition to classical results on point estimation and test theory, multivariate linear regression models and generalized linear models are covered in detail. Special attention is given to the use of bootstrap procedures to perform goodness-of-fit tests to validate model or distributional assumptions. In some cases, new methods are presented here for the first time. The text is motivated by practical examples and the implementations of the corresponding algorithms are always given directly in R in a comprehensible form. Overall, R is given great importance throughout. Each chapter includes a section of exercises and, for the more mathematically inclined readers, concludes with rigorous proofs. The intended audience is graduate students who already have a prior knowledge of probability theory and mathematical statistics.
Advances in Modal Logic 14
Ever since antiquity, philosophers have recognized that truth comes in many "modes", so that a proposition may not only be true or false, but also e.g. "necessary" or "possible". These ideas led to the modern field of modal logic, a lively are of research at the intersection of philosophy, mathematics, and computer science. Nowadays, the term "modal logic" is understood in a broad sense, which allows it to be used for reasoning about seemingly unrelated phenomena such as knowledge, obligations, time, space, and proofs, among many others. Actual research in modal logic draws on techniques from many disciplines including complexity theory, combinatorics, universal algebra, category theory, topology, and proof theory. These proceedings record the papers presented at the 2022 Advances in Modal Logic, a biennial conference series with an aim to report on important new developments in pure and applied modal logic. The topics in this edition include constructive and substructural modal logic, unification, algebraic and neighbourhood semantics, proof theory and complexity of modal logics, and verification in modal logic.
The Logica Yearbook 2021
This volume of the Logica Yearbook series brings together articles based on selected abstracts accepted for presentation at the annual international symposium Logica 2021, in Hejnice, the Czech Republic. The articles range over mathematical and philosophical logic, history and philosophy of logic, and the analysis of natural language.
Introduction to Number Theory
Introduction to Number Theory covers the essential content of an introductory number theory course including divisibility and prime factorization, congruences, and quadratic reciprocity. The instructor may also choose from a collection of additional topics.
Math in Society
Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course.This book is an open textbook; it can be read free online at http: //www.opentextbookstore.com/mathinsociety/
Precalculus 1
The first half of the second edition of Precalculus: An Investigation of Functions. This is an open textbook, available free online. This first portion of the book (Chapters 1-4) is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.
EQAO Grade 6 Math Test Prep!
Created to help Grade 6 students prepare for the EQAO Mathematics Assessment Test.The 10 practice tests were designed to be similar to the actual test the students will be taking. The questions are either multiple choice or open response so that students can get familiar with the question/answer format.The first 5 tests each feature a different key math skill for targeted practice: number sense & numeration, patterning & algebra, measurement, geometry & spatial sense, and data management & probability. Students struggling in any of these areas will benefit from this skill-specific practice.The following 5 tests feature mixed math skills with questions that are a combination of all the math skills. There is no particular sequence to the tests. They can be used in whatever order you choose to fit your student's needs.
Fundamentals of Mathematical Statistics
This books is meant for a standard one-semester advanced undergraduate or graduate level course on Mathematical Statistics. It covers all the key topics - statistical models, linear normal models, exponential families, estimation, asymptotics of maximum likelihood, significance testing, and models for tables of counts.
Optimal Control Problems Related to the Robinson-Solow-Srinivasan Model
This book is devoted to the study of classes of optimal control problems arising in economic growth theory, related to the Robinson-Solow-Srinivasan (RSS) model. The model was introduced in the 1960s by economists Joan Robinson, Robert Solow, and Thirukodikaval Nilakanta Srinivasan and was further studied by Robinson, Nobuo Okishio, and Joseph Stiglitz. Since then, the study of the RSS model has become an important element of economic dynamics. In this book, two large general classes of optimal control problems, both of them containing the RSS model as a particular case, are presented for study. For these two classes, a turnpike theory is developed and the existence of solutions to the corresponding infinite horizon optimal control problems is established. The book contains 9 chapters. Chapter 1 discusses turnpike properties for some optimal control problems that are known in the literature, including problems corresponding to the RSS model. The first class of optimal control problems is studied in Chaps. 2-6. In Chap. 2, infinite horizon optimal control problems with nonautonomous optimality criteria are considered. The utility functions, which determine the optimality criterion, are nonconcave. This class of models contains the RSS model as a particular case. The stability of the turnpike phenomenon of the one-dimensional nonautonomous concave RSS model is analyzed in Chap. 3. The following chapter takes up the study of a class of autonomous nonconcave optimal control problems, a subclass of problems considered in Chap. 2. The equivalence of the turnpike property and the asymptotic turnpike property, as well as the stability of the turnpike phenomenon, is established. Turnpike conditions and the stability of the turnpike phenomenon for nonautonomous problems are examined in Chap. 5, with Chap. 6 devoted to the study of the turnpike properties for the one-dimensional nonautonomous nonconcave RSS model. The utility functions, which determine the optimality criterion, are nonconcave. The class of RSS models is identified with a complete metric space of utility functions. Using the Baire category approach, the turnpike phenomenon is shown to hold for most of the models. Chapter 7 begins the study of the second large class of autonomous optimal control problems, and turnpike conditions are established. The stability of the turnpike phenomenon for this class of problems is investigated further in Chaps. 8 and 9.
Big Data Analytics and Knowledge Discovery
This volume LNCS 13428 constitutes the papers of the 24 th International Conference on Big Data Analytics and Knowledge Discovery, held in August 2022 in Vienna, Austria. The 12 full papers presented together with 12 short papers in this volume were carefully reviewed and selected from a total of 57 submissions. The papers reflect a wide range of topics in the field of data integration, data warehousing, data analytics, and recently big data analytics, in a broad sense. The main objectives of this event are to explore, disseminate, and exchange knowledge in these fields.
Simplicial and Dendroidal Homotopy Theory
This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories. Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences. Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization.
Gamma Solution
The Gamma Function is a generalisation of the factorial for use with complex numbers. The plane of complex numbers subsumes fractions including transcendental numbers, some of which have especially elegant Gamma forms. The Gamma Function has a number of applications in advanced science including quantum physics, astrophysics and fluid dynamics An analytical and experimental study was undertaken to assess how theoretical and experimental code and performance metrics might assist the choice of published Complete Gamma Function ( CGF ) solution algorithms, or inform the development of new CGF methods. Accuracy, speed and component timing statistics were computed for thirteen methods or method variations, and new empirical metrics proposed. Empirical metrics and component time profiles disclosed significant algorithm properties and assisted coding optimisations. Halstead metrics did not apply, but code token ratios correlated with other CGF algorithm features. Further research could involve recently discovered Elliptic, Laplacian or Zeta Function avenues. Enjoy the work and I hope you find it useful as a starting point.Extensive equations and diagrams are included, as well as program code in Visual Basic
Tensor Algebra and Analysis for Engineers: With Applications to Differential Geometry of Curves and Surfaces
In modern theoretical and applied mechanics, tensors and differential geometry are two almost essential tools. Unfortunately, in university courses for engineering and mechanics students, these topics are often poorly treated or even completely ignored. At the same time, many existing, very complete texts on tensors or differential geometry are so advanced and written in abstract language that discourage young readers looking for an introduction to these topics specifically oriented to engineering applications.This textbook, mainly addressed to graduate students and young researchers in mechanics, is an attempt to fill the gap. Its aim is to introduce the reader to the modern mathematical tools and language of tensors, with special applications to the differential geometry of curves and surfaces in the Euclidean space. The exposition of the matter is sober, directly oriented to problems that are ordinarily found in mechanics and engineering. Also, the language and symbols are tailored to those usually employed in modern texts of continuum mechanics.Though not exhaustive, as any primer textbook, this volume constitutes a coherent, self-contained introduction to the mathematical tools and results necessary in modern continuum mechanics, concerning vectors, 2nd- and 4th-rank tensors, curves, fields, curvilinear coordinates, and surfaces in the Euclidean space. More than 100 exercises are proposed to the reader, many of them complete the theoretical part through additional results and proofs. To accompany the reader in learning, all the exercises are entirely developed and solved at the end of the book.
Numerical Analysis on Time Scales
Mathematical models cannot be solved using the traditional analytical methods for dynamic equations on time scales. These models must be dealt with using computational methods. This textbook introduces numerical methods for initial value problems for dynamic equations on time scales. Hands-on examples utilizing MATLAB and practical problems illustrate a wide variety of solution techniques.
Teaching and Research in Mathematics
The author's goal is to help the transition from graduate studies and make it less diffcult and time-consuming. Part I covers techniques on teaching and conducting research and in Part II, the author has introduced some modern research in mathematics in various industries.
Precalculus
An open textbook covering pre-calculus including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisited more extensively in the third chapter. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.
