# 510 Mathematics

## Dublin Core

### Title

510 Mathematics

## Collection Items

### The Data Renaissance: Analyzing the Disciplinary Effects of Big Data, Artificial Intelligence, and Beyond

The Data Renaissance delves into the complexities of data's role in various industries and its broader impact on society. It highlights the challenges in investigating data practices, citing examples like TikTok, where algorithms and data handling…

### From theORy to application: learning to optimize with Operations Research in an interactive way

This book serves as a comprehensive roadmap for navigating the realm of Operations Research (OR). From laying down fundamental mathematical principles to crafting precise modeling techniques and their solution methods, it culminates in a panoramic…

### Adjustment theory: an introduction

Adjustment theory can be regarded as the part of mathematical geodesy that deals with the optimal combination of redundant measurements together with the estimation of unknown parameters. It is essential for a geodesist, its meaning comparable to…

### Advanced Mathematical Science for Mobility Society

This open access book presents the mathematical methods for huge data and network analysis. The automotive industry has made steady progress in technological innovations under the names of Connected Autonomous-Shared-Electric (CASE) and Mobility as a…

### Big Data for Epidemiology: Applied Data Analysis Using National Health Surveys

National data sets provide an avenue for students to practice data analytic skills while also answering meaningful research questions. This open education resource was developed to train future public health professionals how to conduct secondary…

### Mathematics for Biomedical Physics

Mathematics for Biomedical Physics is an open access peer-reviewed textbook geared to introduce several mathematical topics at the rudimentary level so that students can appreciate the applications of mathematics to the interdisciplinary field of…

### Data Analysis in the Psychological Sciences: A Practical, Applied, Multimedia Approach

This open resources textbook contains 10 Units that describe and explain the main concepts in statistical analysis of psychological data. In addition to conceptual descriptions and explanations of the basic analyses for descriptive statistics, this…

### Counting Rocks! An Introduction to Combinatorics

This textbook, Counting Rocks!, is the written component of an interactive introduction to combinatorics at the undergradaute level. Throughout the text, we link to videos where we describe the material and provide examples; see the Youtube playlist…

### Introduction to Probability

This is an introduction to probability theory, designed for self-study. It covers the same topics as the one-semester introductory courses which I taught at the University of Minnesota, with some extra discussion for reading on your own. The reasons…

### Classical Numerical Methods in Scientific Computing

Partial differential equations are paramount in mathematical modelling with applications in engineering and science. The book starts with a crash course on partial differential equations in order to familiarize the reader with fundamental properties…

### Numerical Methods in Scientific Computing

This is a book about numerically solving partial differential equations occurring in technical and physical contexts and the authors have set themselves a more ambitious target than to just talk about the numerics. Their aim is to show the place of…

### An Invitation to Statistics in Wasserstein Space

This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also…

### Introducing Mathematical Biology

Mathematical modelling plays an increasingly important role in almost any area of life sciences, and this interactive textbook focuses on the areas of population ecology, infectious diseases, immunology and cell dynamics, gene networks and…

### Analysis of Reaction-Diffusion Models with the Taxis Mechanism

This open access book deals with a rich variety of taxis-type cross-diffusive equations. Particularly, it intends to show the key role played by quasi-energy inequality in the derivation of some necessary a priori estimates. This book addresses…

### Algorithms for Sparse Linear Systems

Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are…

### Calculus in Context - 2008 Edition

We believe that calculus can be for students what it was for Euler and the Bernoullis: a language and a tool for exploring the whole fabric of science. We also believe that much of the mathematical depth and vitality of calculus lies in connections…

### Advanced Algebra v. 1.0

Intermediate Algebra is the second part of a two-part course in Algebra. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study of…

### Control Problems for Conservation Laws with Traffic Applications

Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different…

### The Application of Ant Colony Optimization

The application of advanced analytics in science and technology is rapidly expanding, and developing optimization technics is critical to this expansion. Instead of relying on dated procedures, researchers can reap greater rewards by utilizing…

### Sublinear Computation Paradigm

This open access book gives an overview of cutting-edge work on a new paradigm called the “sublinear computation paradigm,” which was proposed in the large multiyear academic research project “Foundations of Innovative Algorithms for Big Data.” That…

### Matching minors in bipartite graphs

In this thesis we adapt fundamental parts of the Graph Minors series of Robertson and Seymour for the study of matching minors and investigate a connection to the study of directed graphs. We develope matching theoretic to established results of…

### International Symposium on Mathematics, Quantum Theory, and Cryptography

This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics…

### Values and Valuing in Mathematics Education

This engaging open access book discusses how a values and valuing perspective can facilitate a more effective mathematics pedagogical experience, and allows readers to explore multiple applications of the values perspective across different education…

### Boundary Value Problems, Weyl Functions, and Differential Operators

This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension…

### Mathematics Methods for Early Childhood

Welcome to Early Childhood Mathematics! This course satisfies the Early Childhood Unified requirements in the state of Kansas for a teaching license Birth to Grade 3.

Most people agree that early childhood includes the period from infancy until…

Most people agree that early childhood includes the period from infancy until…

### Introduction to Statistical Thinking

The target audience for this book is college students who are required to learn statistics, students with little background in mathematics and often no motivation to learn more. It is assumed that the students do have basic skills in using computers…

### Elementary Calculus

This textbook covers calculus of a single variable, suitable for a year-long (or two-semester) course. Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II. The book is designed for students who have completed courses in high-school…

### Technical Mathematics

This developmental-level mathematics textbook is intended for career-technical students. It was made possible by a grant from Open Oregon Educational Resources, which supports the development and implementation of high-quality materials at low or no…

### Mostly Harmless Statistics

This text is for an introductory level probability and statistics course with an intermediate algebra prerequisite. The focus of the text follows the American Statistical Association’s Guidelines for Assessment and Instruction in Statistics Education…

### Informal Calculus with Applications to Biological and Environmental Sciences

This book is an approachable introduction to calculus with applications to biology and environmental science. For example, one application in the book is determining the volume of earth moved in the 1959 earthquake that created Quake Lake. Another…

### Optimal, Integral, Likely Optimization, Integral Calculus, and Probability for Students of Commerce and the Social Sciences

Optimal, Integral, Likely is a free, open-source textbook intended for UBC’s course MATH 105: Integral Calculus with Applications to Commerce and Social Sciences. It is shared under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0…

### Austenitic TRIP/TWIP Steels and Steel-Zirconia Composites

This open access book presents a collection of the most up-to-date research results in the field of steel development with a focus on pioneering alloy concepts that result in previously unattainable materials properties. Specifically, it gives a…

### Statistics Hight School

This Statistics resource was developed under the guidance and support of experienced high school teachers and subject matter experts. It is presented here in multiple formats: PDF, online, and low-cost print. Statistics offers instruction in…

### Transition to Higher Mathematics: Structure and Proof - Second Edition

This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics. This is the…

### Transition to Higher Mathematics: Structure and Proof - Second Edition

This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics. This is the…

### Turbulence: Numerical Analysis, Modelling and Simulation

The problem of accurate and reliable simulation of turbulent flows is a central and intractable challenge that crosses disciplinary boundaries. As the needs for accuracy increase and the applications expand beyond flows where extensive data is…

### Symmetry in Graph Theory

This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in…

### Stochastic Processes: Theory and Applications

The aim of this special issue is to publish original research papers that cover recent advances in the theory and application of stochastic processes. There is especial focus on applications of stochastic processes as models of dynamic phenomena in…

### Polyhedral Structures, Symmetry, and Applications

Symmetry is an intriguing phenomenon manifesting itself in art, nature, and the mind. This Special Issue book features 19 articles about discrete geometric and combinatorial polyhedral structures, with symmetry as the unifying theme. These articles…

### New Trends in Differential and Difference Equations and Applications

This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The…

### Neutrosophic Multi-Criteria Decision Making

Neutrosophic logic and set are gaining significant attention in solving many real-life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. A number of new neutrosophic theories have been…

### Lie and non-Lie Symmetries: Theory and Applications for Solving Nonlinear Models

Since the end of the 19th century when the prominent Norwegian mathematician Sophus Lie created the theory of Lie algebras and Lie groups and developed the method of their applications for solving differential equations, his theory and method have…

### Intermittency and Self-Organisation in Turbulence and Statistical Mechanics

There is overwhelming evidence, from laboratory experiments, observations, and computational studies, that coherent structures can cause intermittent transport, dramatically enhancing transport. A proper description of this intermittent phenomenon,…

### Discrete Time Analysis of Consolidated Transport Processes

The objective of this work is to develop models for the analysis of consolidated transport processes. With the discrete time queuing models developed for inventory and vehicle consolidation, in particular milkrun systems, a detailed performance…

### Advances in Food Analysis

This Topical Collection of Molecules provides the most recent advancements and trends within the framework of food analysis, confirming the growing public, academic, and industrial interest in this field. The articles broach topics related to sample…

### Advanced Numerical Methods in Applied Sciences

The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and…

### Social and Political Dimensions of Mathematics Education: Current Thinking

This book examines the current thinking on five critical social and political areas in mathematics education. It focuses on material conditions in teaching and learning, and details features of social life and their influence on mathematics teaching,…

### Semiotics in Mathematics Education

This volume discusses semiotics in mathematics education as an activity with a formal sign system, in which each sign represents something else. Theories presented by Saussure, Peirce, Vygotsky and other writers on semiotics are summarized in their…

### Projection-Based Clustering through Self-Organization and Swarm Intelligence: Combining Cluster Analysis with the Visualization of High-Dimensional Data

This book covers aspects of unsupervised machine learning used for knowledge discovery in data science and introduces a data-driven approach to cluster analysis, the Databionic swarm (DBS). DBS consists of the 3D landscape visualization and…

### The Philosophy of Mathematics Education

This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall…

### Advances in Discrete Differential Geometry

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex…

### Wearable Electronics and Embedded Computing Systems

Wearable electronics and embedded computing systems have been receiving a great deal of interest over the last two decades in research and commercial fields, with a special focus on biomedical applications. The key benefits introduced by these…

### Uses of Technology in Upper Secondary Mathematics Education

This survey addresses the use of technology in upper secondary mathematics education from four points of view: theoretical analysis of epistemological and cognitive aspects of activity in new technology mediated learning environments, the changes…

### Turbulence: Numerical Analysis, Modelling and Simulation

The problem of accurate and reliable simulation of turbulent flows is a central and intractable challenge that crosses disciplinary boundaries. As the needs for accuracy increase and the applications expand beyond flows where extensive data is…

### Transitions in Mathematics Education

This book examines the kinds of transitions that have been studied in mathematics education research. It defines transition as a process of change, and describes learning in an educational context as a transition process. The book focuses on research…

### Symmetry with Operator Theory and Equations

A plethora of problems from diverse disciplines such as Mathematics, Mathematical: Biology, Chemistry, Economics, Physics, Scientific Computing and also Engineering can be formulated as an equation defined in abstract spaces using Mathematical…

### Symmetry Measures on Complex Networks

Symmetry is found everywhere, to a greater or lesser degree. It is essential in all sciences and also as the basic substrate in all arts. The same happens with Complex Networks, which are the majority of all those that interest for advanced…

### Symmetry in Vision

Symmetry has a central role in the study of vision. The concept of symmetry has an ancient origin in considerations of visual appearance; in modern times, abstracted and formalized into Group Theory, it has found spectacular applications, far beyond…

### Symmetry in Graph Theory

This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in…

### Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks

his Special Issue focuses on recent progress in a new area of mathematical physics and applied analysis, namely, on nonlinear partial differential equations on metric graphs and branched networks. Graphs represent a system of edges connected at one…

### Stochastic Processes: Theory and Applications

The aim of this special issue is to publish original research papers that cover recent advances in the theory and application of stochastic processes. There is especial focus on applications of stochastic processes as models of dynamic phenomena in…

### Stochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists…

### Social and Political Dimensions of Mathematics Education: Current Thinking

This book examines the current thinking on five critical social and political areas in mathematics education. It focuses on material conditions in teaching and learning, and details features of social life and their influence on mathematics teaching,…

### Scaling of Differential Equations

The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models,…

### Finite Difference Computing with Exponential Decay Models

This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary…

### Progress in Mathematical Ecology

Mathematical ecology is an area of applied mathematics concerned with the application of mathematical concepts, tools and techniques, usually in the form of mathematical models, to problems arising in population dynamics, ecology and evolution. This…

### Problem Solving in Mathematics Education

This survey book reviews four interrelated areas: (i) the relevance of heuristics in problem-solving approaches – why they are important and what research tells us about their use; (ii) the need to characterize and foster creative problem-solving…

### New Trends in Differential and Difference Equations and Applications

This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The…

### Neutrosophic Multi-Criteria Decision Making

Neutrosophic logic and set are gaining significant attention in solving many real-life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. A number of new neutrosophic theories have been…

### Advances in Proof-Theoretic Semantics

This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of…

### The method of densities for non-isotropic Boolean models

This book deals with the Boolean model, a basic model of stochastic geometry for the description of porous structures like the pore space in sand stone. The main result is a formula which gives in two and three dimensions a series representation of…

### Metasurfaces: Physics and Applications

Metasurfaces, the two-dimensional analog of metamaterials, have attracted progressively increasing attention in recent years due to their planar configurations and, thus, ease of fabrication, while enabling an unprecedented control over optical…

### Measurement and Control of Charged Particle Beams

This advanced textbook and reference is the first comprehensive and systematic review of all methods used for the measurement, correction, and control of the beam dynamics of modern particle accelerators. Based on material presented in several…

### The Mathematics Education of Prospective Secondary Teachers Around the World

This volume shares and discusses significant new trends and developments in research and practices related to various aspects of preparing prospective secondary mathematics teachers from 2005–2015. It provides both an overview of the current…

### Mathematical Modelling in Engineering & Human Behaviour 2018

This book includes papers in cross-disciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cutting-edge research, each chapter is focused on a different problem of modelling human…

### Mathematical Analysis and Applications

Investigations involving the theory and applications of mathematical analytic tools and techniques are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue,…

### Iterative Methods for Solving Nonlinear Equations and Systems

Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not…

### International Comparative Studies in Mathematics: Lessons for Improving Students’ Learning

This open access book examines the cultural and educational factors that influence how successfully students learn mathematics; focuses on international comparative studies as a means of generating theories and improving students’ learning; and…

### Interdisciplinary Mathematics Education

This book provides an essential introduction to the state-of the-art in interdisciplinary Mathematics Education. First, it begins with an outline of the field’s relevant historical, conceptual and theoretical backgrounds, what “discipline” means and…

### Information Geometry

This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information…

### Guided-Wave Optics

The topic of guided wave (GW) propagation comprises a vast research area overlapping with photonics, matter waves in macroscopic quantum media (ultracold gases of bosonic and fermionic atoms, condensates of quasiparticles, such as…

### Geometry and topology of wild translation surfaces

A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the…

### Geometric Regularization in Bioluminescence Tomography

Bioluminescence tomography is a recent biomedical imaging technique which allows to study molecular and cellular activities in vivo. From a mathematical point of view, it is an ill-posed inverse source problem: the location and the intensity of a…

### Fuzzy Techniques for Decision Making

This book contains the successful invited submissions to a Special Issue of Symmetry in the subject area of “Fuzzy Techniques for Decision Making”. We invited contributions addressing novel techniques and tools for decision making (e.g., group or…

### Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of…

### Fractional Order Systems

This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital.…

### Fractional Differential Equations: Theory, Methods and Applications

Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as…

### Fractional Calculus: Theory and Applications

Fractional calculus is allowing integrals and derivatives of any positive order (the term fractional is kept only for historical reasons). It can be considered a branch of mathematical physics that deals with integro-differential equations, where…

### Early Geometrical Thinking in the Environment of Patterns, Mosaics and Isometries

This book discusses the learning and teaching of geometry, with a special focus on kindergarten and primary education. It examines important new trends and developments in research and practice, and emphasizes theoretical, empirical and developmental…

### Dynamic risk management with Markov decision processes

An important tool in risk management is the implementation of risk measures. We study dynamic models where risk measures and dynamic risk measures can be applied. In particular, we solve various portfolio optimization problems and introduce a class…

### Differential Geometry

The present book contains 14 papers published in the Special Issue “Differential Geometry” of the journal Mathematics. They represent a selection of the 30 submissions. This book covers a variety of both classical and modern topics in differential…

### Current Trends in Symmetric Polynomials with their Applications

This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and…

### Applied Analysis of Ordinary Differential Equations

One might say that ordinary differential equations (notably, in Isaac Newton’s analysis of the motion of celestial bodies) had a central role in the development of modern applied mathematics. This book is devoted to research articles which build upon…

### Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets ( 2 )

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them,…

### Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them,…

### Advances in Mechanical Problems of Functionally Graded Materials and Structures

The book deals with novel aspects and perspectives in functionally graded materials (FGMs), which are advanced engineering materials designed for a specific performance or function with spatial gradation in structure and/or composition. The…

### Building the Foundation: Whole Numbers in the Primary Grades: The 23rd ICMI Study

This twenty-third ICMI Study addresses for the first time mathematics teaching and learning in the primary school (and pre-school) setting, while also taking international perspectives, socio-cultural diversity and institutional constraints into…

### Uses of Technology in Upper Secondary Mathematics Education

This survey addresses the use of technology in upper secondary mathematics education from four points of view: theoretical analysis of epistemological and cognitive aspects of activity in new technology mediated learning environments, the changes…

### Empirical Research in Statistics Education

This ICME-13 Topical Survey provides a review of recent research into statistics education, with a focus on empirical research published in established educational journals and on the proceedings of important conferences on statistics education. It…

### Early Algebra: Research into its Nature, its Learning, its Teaching

This survey of the state of the art on research in early algebra traces the evolution of a relatively new field of research and teaching practice. With its focus on the younger student, aged from about 6 years up to 12 years, this volume reveals the…

### Current and Future Perspectives of Ethnomathematics as a Program

This survey on the modernity of ethnomathematics addresses numerous themes related to both ethnomathematics and mathematics education. It offers a broader view of mathematics, including ideas, procedures, concepts, processes, methods, and practices…

### Early Algebra: Research into its Nature, its Learning, its Teaching

This survey of the state of the art on research in early algebra traces the evolution of a relatively new field of research and teaching practice. With its focus on the younger student, aged from about 6 years up to 12 years, this volume reveals the…

### Algebra in Cuneiform: Introduction to an Old Babylonian Geometrical Technique

his textbook analyzes a number of texts in “conformal translation,” that is, a translation in which the same Babylonian term is always translated in the same way and, more importantly, in which different terms are always translated differently.…

### Mathematical Modelling in Engineering & Human Behaviour 2018

This book includes papers in cross-disciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cutting-edge research, each chapter is focused on a different problem of modelling human…

### Multivariable Calculus

This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of…

### Flood Forecasting Using Machine Learning Methods

Flood disasters have had a great impact on city development. Early flood warning systems (EFWS) are promising countermeasures against flood hazards and losses. Machine learning (ML) is the kernel for building a satisfactory EFWS. This paper first…

### Theory and Applications of Ordered Fuzzy Numbers: A Tribute to Professor Witold Kosiński

The subject of this chapter is fuzzy sets and the basic issues related to them. The first section discusses concepts of sets: classic and fuzzy, and presents various ways of describing fuzzy sets. The second section is dedicated to t-norms, s-norms,…

### Scaling of Differential Equations

Finding proper values of physical parameters in mathematical models is often quite a challenge. While many have gotten away with using just the mathematical symbols when doing science and engineering with pen and paper, the modern world of numerical…

### Wearable Electronics and Embedded Computing Systems

The application of wearable electronics in the biomedical research and commercial fields has

been gaining great interest over the last several decades. Small-sized, lightweight monitoring systems

with low-power consumption and, of course,…

been gaining great interest over the last several decades. Small-sized, lightweight monitoring systems

with low-power consumption and, of course,…

### Finite Difference Computing with Exponential Decay Models

Throughout industry and science it is common today to study nature or technological devices through models on a computer. With such models the computer acts as a virtual lab where experiments can be done in a fast, reliable, safe, and cheap way. In…

### Algorithms for Scheduling Problems

Optimal scheduling is an important area of operations research, as it has both theoretical and

practical aspects. It is clear that efficient algorithms are most desirable for practical applications,

since most real-world scheduling problems have…

practical aspects. It is clear that efficient algorithms are most desirable for practical applications,

since most real-world scheduling problems have…

### Quantitative Problem Solving in Natural Resources

This text is intended to support courses that bridge the divide between mathematics typically encountered in U.S. high school curricula and the practical problems that natural resource students might engage with in their disciplinary coursework and…

### Advanced Numerical Methods in Applied Sciences

The generalized Schur algorithm (GSA) allows computing well-known matrix decompositions,

such as QR and LU factorizations [1]. In particular, if the involved matrix is structured, i.e., Toeplitz, block-Toeplitz or Sylvester, the GSA computes the R…

such as QR and LU factorizations [1]. In particular, if the involved matrix is structured, i.e., Toeplitz, block-Toeplitz or Sylvester, the GSA computes the R…

### Introduction to Louis Michel’s lattice geometry through group action

This chapter describes the outline of the book and explains the interrelations between different chapters and appendices. The specificity of this book is an intensive use of group action ideas and terminology when discussing physical and mathematical…

### An Introduction to the Theory of Numbers

This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory.…

### Statistical Thinking for the 21st Century

Statistical thinking is a way of understanding a complex world by describing it in relatively simple terms that nonetheless capture essential aspects of its structure, and that also provide us some idea of how uncertain we are about our knowledge.…

### Introduction to Financial Mathematics Concepts and Computational Methods

Introduction to Financial Mathematics: Concepts and Computational Methods serves as a primer in financial mathematics with a focus on conceptual understanding of models and problem solving. It includes the mathematical background needed for risk…

### Tea Time Numerical Analysis

Numerical methods are designed to approximate one thing or another. Sometimes roots, sometimes derivatives or definite integrals, or curves, or solutions of differential equations. As numerical methods produce only approximations to these things, it…

### Geometry with an Introduction to Cosmic Topology

Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the…

### Teaching Mathematics at Secondary Level

Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help…

### The Essence of Mathematics Through Elementary Problems

The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics…

### BUSINESS MATH: A Step-By-Step Handbook

Business Mathematics was written to meet the needs of a twenty-first century student. It takes a systematic approach to helping students learn how to think and centers on a structured process termed the PUPP Model (Plan, Understand, Perform, and…

### First Semester in Numerical Analysis with Julia

First Semester in Numerical Analysis with Julia presents the theory and methods, together with the implementation of the algorithms using the Julia programming language (version 1.1.0). The book covers computer arithmetic, root-finding, numerical…

### An Introduction to Psychological Statistics

We are constantly bombarded by information, and finding a way to filter that information in an objective way is crucial to surviving this onslaught with your sanity intact. This is what statistics, and logic we use in it, enables us to do. Through…

### Adult Literacy Fundamentals Mathematics: Book 1

This is book one in a six-book series on fundamental mathematics for adult learners. These books include glossaries, self tests, practice requests, grades records, and unit tests. Ancillary Resources include the Instructor's Manual.

### Mathematics for Elementary Teachers

This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable…

### Linear Regression Using R: An Introduction to Data Modeling

Linear Regression Using R: An Introduction to Data Modeling presents one of the fundamental data modeling techniques in an informal tutorial style. Learn how to predict system outputs from measured data using a detailed step-by-step process to…

### Prealgebra

Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text introduces the fundamental concepts of algebra while…

### Topics in Applied Mathematics

The concepts and basic topics in elementary Linear Algebra and Calculus are reviewed and generalized to Linear Analysis in this first unit. In particular, the dot product, the vector space of R 2(that is, the x − y plane in Plane Geometry), and…

### An Introductory Course in Elementary Number Theory

Integers are the building blocks of the theory of numbers. This chapter contains somewhat very simple and obvious observations starting with properties of integers and yet the proofs behind those observations are not as simple. In this chapter

we…

we…

### Linear Algebra with Applications. Open Edition

This textbook is an introduction to the ideas and techniques of linear algebra for first- or second-year

students with a working knowledge of high school algebra. The contents have enough flexibility to present

a traditional introduction to the…

students with a working knowledge of high school algebra. The contents have enough flexibility to present

a traditional introduction to the…

### Linear Algebra, Theory And Applications

This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more…

### Mathematical Analysis. Volume I

This text is an outgrowth of lectures given at the University of Windsor, Canada. One of our main objectives is updating the undergraduate analysis as a rigorous postcalculus course. While such excellent books as Dieudonn´e’s Foundations of Modern…

### Elementary Linear Algebra

This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms. At the end, the more abstract notions of vector spaces and linear…

### APEX Pre Calculus

This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is de-signed to…

### An Introduction to Matlab and Mathcad

This textbook, or really a “coursebook” for a college freshman-level class, has been updated for Spring 2014 and provides an introduction to programming and problem solving using both Matlab and Mathcad. We provide a balanced selection of…

### Fundamentals of Matrix Algebra

A college (or advanced high school) level text dealing with the basic principles of matrix and linear algebra. It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations. Numerous…

### Algebra and Mathematics. Explained with easy to understand 3D animations.

Explains variables, systems of equations, Cartesian coordinates, and many other concepts. Fun and educational for all ages.

### Trigonometry

This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just…

### Precalculus

From the preface, "These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the…

### Elementary Differential Equations

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of…

### Applied Calculus

Calculus was first developed more than three hundred years ago by Sir Isaac Newton and Gottfried Leibniz to help them describe and understand the rules overning the motion of planets and moons. Since then, thousands of other men and women have…

### Basic Arithmetic Workbook

This workbook was created through the efforts of three instructors at Scottsdale Community College in Scottsdale, Arizona, has been used by thousands of students, and is continually improved. This workbook contains have lessons that were carefully…

### Contemporary Calculus I . For the students

This is a textbook for differential calculus with explanations, examples, worked solutions, problem sets and answers. It has been reviewed by calculus instructors and class-tested by them and the author.

Topics are typically introduced by way of…

Topics are typically introduced by way of…

### Solving Linear Equations - Basic Algebra Shortcut Tricks!

This algebra video tutorial shows you how to solve linear equations that contain fractions and variables on both sides of the equation. This video contains plenty of examples and practice problems for you to work on.

### Linear Regression Using R: An Introduction to Data Modeling

Linear Regression Using R: An Introduction to Data Modeling presents one of the fundamental data modeling techniques in an informal tutorial style. Learn how to predict system outputs from measured data using a detailed step-by-step process to…

### Trigonometry

This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just…

### Ordinary Differential Equations

This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these…

Linear Algebra

We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be…

### Lies, Damned Lies, or Statistics: How to Tell the Truth with Statistics

Mathematical definitions should be perfectly precise because they do not describe something which is observed out there in the world, since such descriptive definitions might have fuzzy edges. In biology, for example, whether a virus is considered…

### Precalculus

Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by…

### Statistics Using Technology

You are exposed to statistics regularly. If you are a sports fan, then you have the statistics for your favorite player. If you are interested in politics, then you look at the polls to see how people feel about certain issues or candidates. If you…

### Elementary Algebra Textbook

The Mayans used arithmetic to make astronomical computations, and developed the concept of zero over 2,000 years ago. The word “arithmetic” is derived from the Greek word arithmos (translated as

“number”). It is the oldest and most elementary branch…

“number”). It is the oldest and most elementary branch…

### LINEAR ALGEBRA

This book helps students to master the material of a standard US undergraduate first course in Linear Algebra. The material is standard in that the subjects covered are Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and…

### Elementary Differential Equations

In order to apply mathematical methods to a physical or “real life” problem, we must formulate the problem in mathematical terms; that is, we must construct a mathematical model for the problem. Many

physical problems concern relationships between…

physical problems concern relationships between…

### A First Course in LINEAR ALGEBRA an Open Text

A First Course in Linear Algebra presents an introduction to the fascinating subject of linear algebra for students who have a reasonable understanding of basic algebra. Major topics of linear algebra are presented in detail, with proofs of important…

### Elementary Algebra

Elementary Algebra is licensed under a Creative Commons Attribution 4.0 International (CC BY) license, which means that you can distribute, remix, and build upon the content, as long as you provide attribution to OpenStax and its content…

### College Algebra

It’s a cold day in Antarctica. In fact, it’s always a cold day in Antarctica. Earth’s southernmost continent, Antarctica experiences the coldest, driest, and windiest conditions known. The coldest temperature ever recorded, over one hundred degrees…

### ACTIVE CALCULUS

In Active Calculus, we endeavor to actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students. Where many texts present a general theory of calculus…

### Calculus

Gilbert Strang's clear, direct style and detailed, intensive explanations make this textbook ideal as both a course companion and for self-study. Single variable and multivariable calculus are covered in depth. Key examples of the application of…

### Trigonometry

The precursors to what we study today as Trigonometry had their origin in ancient Mesopotamia, Greece and India. These cultures used the concepts of angles and lengths as an aid to understanding the movements of the heavenly bodies in the night sky.…

### Calculus -- The foundation of modern science

Easy to understand explanation of integrals and derivatives using 3D animations.

### Elementary Algebra

Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. Use of this book will help the student develop the insight and intuition necessary to master algebraic techniques and manipulative…

### Logaritma

Open Educational Resource (OER) Unsyiah adalah satu satu Portal yang dikembangkan oleh Perpustakaan Universitas Syiah Kuala. OER Unsyiah berbasis Open Acces untuk siapa saja dan di mana saja. Bahkan Kami juga akan menerima kontribusi yang ingin ikut…

### My Math GPS: Elementary Algebra Guided Problem Solving (2016 Edition)

My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into…

### Proofs and Concepts: The Fundamentals of Abstract Mathematics

This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract…

### Statistical Inference For Everyone

This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a…

### The Simple Math of Writing Well: Writing for the 21st Century

Writing guides abound, but The Simple Math of Writing Well is one of a kind. Readers will find its practical approach affirming, encouraging, and informative, and its focus on the basics of linguistic structure releases 21st-century writers to…

### Linear Algebra, Theory And Applications

This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more…

### Introduction to Real Analysis

This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also…

### Fundamentals of Mathematics

Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who:

have had…

have had…

### Fast Fourier Transforms

This book focuses on the discrete Fourier transform (DFT), discrete convolution, and, particularly, the fast algorithms to calculate them. These topics have been at the center of digital signal processing since its beginning, and new results in…

### Elementary Differential Equations with Boundary Value Problems

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.

An elementary text should be written so the student…

An elementary text should be written so the student…

### Elementary College Geometry

This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra.

The…

The…

### Applied Finite Mathematics

Applied Finite Mathematics covers topics including linear equations, matrices, linear programming, the mathematics of finance, sets and counting, probability, Markov chains, and game theory.

### College Algebra

College Algebra is an introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The…

### Applied Probability

This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are…

### Advanced Algebra II: Conceptual Explanations

This module contains a table of every module within the three books of Kenny Felder's course on "Algebra II", with links to the modules.

### A Primer of Real Analysis

This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus…

### A Computational Introduction to Number Theory and Algebra

All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by…

### Applied Combinatorics

As we hope you will sense right from the beginning, we believe that combinatorial

mathematics is one of the most fascinating and captivating subjects on the planet.

Combinatorics is very concrete and has a wide range of applications, but it also…

mathematics is one of the most fascinating and captivating subjects on the planet.

Combinatorics is very concrete and has a wide range of applications, but it also…

### A Foundation In Pure Mathematics

Everyone in Hong Kong has heard of the Mark Six! Players select six different numbers from 49 possibilities in the hope of winning a small fortune - or possibly even a large one.

So how many different choices of six numbers out of 49 are there? If…

So how many different choices of six numbers out of 49 are there? If…

### A Foundation In Applied Mathematics

This module develops concepts and techniques for studying functions. You will learn about one of the foundations of applied mathematics, i.e. the algebraic and graphic methods for studying functions.

You'll be introduced to clear define and…

You'll be introduced to clear define and…

### Collaborative Statistics

Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino, California. The textbook was developed over several years and has been used in regular and honors-level classroom settings and…

### Calculus Volume 2

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those…

### Calculus Volume 1

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those…

### Algebra and Trigonometry

lgebraic principles. The text is suitable for a typical introductory Algebra & Trigonometry course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of…

### The Curious Country

By definition scientists are an inquisitive lot. But what are the scientific curiosities and concerns on the minds of Australians? What worries them, baffles them, and sets their curiosity meter to 10 out of 10? To find out, the Office of the Chief…

### Discrete Mathematics

his text was written to be used as the primary text for the class Discrete Mathematics (Math 228) at the University of Northern Colorado. The course serves as the role of a transitions course (introduction to proof), as well as an introduction to…

### Combinatorics Through Guided Discovery

This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as "counting." The book consist almost entirely of…

### A Story of Real Analysis

The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a…

### Introduction to the Modeling and Analysis of Complex Systems

Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a…

### Dalton State College APEX Calculus

This text for Analytic Geometry and Calculus I, II, and III is a Dalton State College remix of APEX Calculus 3.0. The text was created through a Round Six ALG Textbook Transformation Grant.

Topics covered in this text include:

Limits

…

Topics covered in this text include:

Limits

…

### Armstrong Calculus

The text is mostly an adaptation of two other excellent open- source calculus textbooks: Active Calculus by Dr. Matt Boelkins of Grand Valley State University and Drs. Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar, and…

### A Spiral Workbook for Discrete Mathematics

This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains…

### Linear Algebra with Applications

This textbook is an introduction to the ideas and techniques of linear algebra for ﬁrst- or second-year students with a working knowledge of high school algebra. The contents have enough ﬂexibility to present

a traditional introduction to the…

a traditional introduction to the…

### Geometry

Geometry is used in many areas—from art to science. For example, geometry plays a key role in construction, fashion design, architecture, and computer graphics. This course focuses on the main ideas of geometry that are the foundation of applications…

### Calculus

This text comprises a three–volume series on Calculus. The ﬁrst part covers material taught in many “Calc ” courses: limits, derivaves, and the basics of integraon, found in Chapters through . The second text covers material oen taught in “Calc :”…

### Precalculus

There are key differences between the way teaching and learning takes place in high schools and universities. Our goal is much more than just getting you to reproduce what was done in the classroom. Here are some key points to keep in mind:

• The…

• The…

### Notes on Diffy Qs: Differential Equations for Engineers

This book originated from my class notes for teaching Math 286 at the University of Illinois at Urbana-Champaign in Fall 2008 and Spring 2009. It is a ﬁrst course on differential equations for

engineers. I also taught Math 285 at UIUC and Math 20D…

engineers. I also taught Math 285 at UIUC and Math 20D…

### Mathematical Reasoning: Writing and Proof

Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs. Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics.…

### Math in Society

Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are…

### Introduction to Modern Set Theory

Introduction to Modern Set Theory is designed for a one-semester course in set theory at the advanced undergraduate or beginning graduate level. Three features are the full integration into the text of the study of models of set theory, the use of…

### Introduction to Differential Equations

Much of the material of Chapters 2-6 and 8 has been adapted from thewidely used textbook “Elementary differential equations and boundary value problems” by Boyce & DiPrima (John Wiley & Sons, Inc., Seventh Edition, ○c 2001). Many of the examples…

### Combinatorics

Combinatorics is a subfield of "discrete mathematics," so we should begin by asking what discrete mathematics means. The differences are to some extent a matter of opinion, and various mathematicians might classify specific topics…

### Calculus for The Life Sciences A Modeling Approach Volume II

In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and…

### Calculus For the Life Sciences: A Modeling Approach Volume I

In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and…

### Applied Discrete Structures

Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The…

### Applied Calculus

An openly licensed applied calculus textbook, covering derivatives, integrals, and an intro to multivariable calculus. This book is heavily remixed from Dale Hoffman's Contemporary Calculus textbook, and retains the same conceptual focus from that…

### Statistical Analysis with The General Linear Model

This course is about a large and complex set of statistical methods tied together by a unifying conceptual framework known as “The General Linear Model” (GLM). This model can be used to answer an amazing variety of research questions within an…

### Vector Calculus

This book covers calculus in two and three variables. It is suitable for a one-semester course, normally known as “Vector Calculus”, “Multivariable Calculus”, or simply “Calculus III”. The prerequisites are the standard courses in single-variable…

### Active Calculus Multivariable

In Active Calculus - Multivariable, we endeavor to actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students. Where many texts present a general theory of…

### Abstract Algebra

This text is intended for a one or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several…

### Introduction to Logic and Critical Thinking Version 1.4

This is an introductory textbook in logic and critical thinking. The goal of the

textbook is to provide the reader with a set of tools and skills that will enable

them to identify and evaluate arguments. The book is intended for an

introductory…

textbook is to provide the reader with a set of tools and skills that will enable

them to identify and evaluate arguments. The book is intended for an

introductory…

### Fundamental Methods of Logic

There’s an ancient view, still widely held, that what makes human beings special—what distinguishes us from the “beasts of the field”—is that we are rational. What does rationality consist in? That’s a vexed question, but one possible response…

### Introduction to Probability

Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continued to…

### Analysis of Variance (ANOVA)

A description of the concepts behind Analysis of Variance. Also, see this site: http://www.psych.utah.edu/stat/introstats/anovaflash.html for a "hands-on" experience.

### Probability and Statistics

We discuss probability and do some basic examples to refresh our memory on practice problems involving probability. Next video we focus on expectation values/ mean and the second moment of distribution.

### Calculus using Matlab - Laplace Transform

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### Calculus - Derivative of an Inverse Function

Calculus lecture explaining the derivative of an inverse function.

Gives a graphical explanation of how the derivative of an inverse function is related to the reciprocal of the derivative of the original function.

Uses the example y = x^2 + 1…

Gives a graphical explanation of how the derivative of an inverse function is related to the reciprocal of the derivative of the original function.

Uses the example y = x^2 + 1…

### Statistical Mechanics

This is a book about statistical mechanics at the advanced undergraduate level. It assumes a background in

classical mechanics through the concept of phase space, in quantum mechanics through the Pauli exclusion

principle, and in mathematics…

classical mechanics through the concept of phase space, in quantum mechanics through the Pauli exclusion

principle, and in mathematics…

### Introduction to Numerical Methods and Matlab Programming for Engineers

These notes were developed by the firsht author in the process of teaching a course on applied

numerical methods for Civil Engineering majors during 2002-2004 and was modified to include

Mechanical Engineering in 2005. The materials have been…

numerical methods for Civil Engineering majors during 2002-2004 and was modified to include

Mechanical Engineering in 2005. The materials have been…

### Introduction to Numerical Methods

What follows are my lecture notes for Math 3311: Introduction to Numerical Methods, taught at the Hong Kong University of Science and Technology. Math 3311, with two lecture hours per week, is primarily for non-mathematics majors and is required by…

### Basic Analysis: Introduction to Real Analysis

A first course in mathematical analysis. Covers the real number system, sequences and series, continuous functions, the derivative, the Riemann integral, sequences of functions, and metric spaces.

### Elementary Diferrential Equantions

Elementary Differential Equations by William F. Trench Andrew G. Cowles Distinguished Professor Emeritus, Department of Mathematics, Trinity University, San Antonio, Texas, USA,Previously published by Brooks/Cole Thomson Learning, 2000. This book has…

### For All X; The Lorain County Remix

This book was created by combining two previous books on logic and critical thinking, both made available under a Creative Commons license, and then adding some material so that the coverage matched that of commonly used logic textbooks.

### Introductory Statistics

ntroductory Statistics is designed for the one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it…

### Active Calculus 2.0

Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live…

### Precalculus: An Investigation of Functions (Includes Trig) 2nd Ed

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. An emphasis is placed on…

### Precalculus: An Investigation of Functions (Includes Trig) 1st Ed

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. An emphasis is placed on…

### Active Calculus 1.0

Active Calculus is different from most existing calculus texts in at least the following ways: the text is free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html…

### Elementary Algebra

This is the Elementary Algebra textbook used by the Department of Mathematics in their Elementary Algebra course at College of the Redwoods, Eureka, California.

License: Creative Commons Attribution Sharealike Noncommercial. This license is very…

License: Creative Commons Attribution Sharealike Noncommercial. This license is very…

### OpenIntro Statistics

The OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. The inaugural effort is OpenIntro Statistics. Probability is…

### Introductory Algebra Student Workbook

This workbook was created through the efforts of instructors at Scottsdale Community College in Scottsdale, Arizona, has been used by thousands of students, and is continually improved. This workbook contains have lessons that were carefully and…

### Beginning and Intermediate Algebra

Beginning and Intermediate Algebra was designed to reduce textbook costs to students while not reducing the quality of materials. This text includes many detailed examples for each section along with several problems for students to practice and…

### Prealgebra

A clear, methodical approach to topics in prealgebra, with good explanations of concepts. This book includes plenty of examples and then exercises. Equation solving is started earlier and used throughout.

Geometric topics (e.g., area and…

Geometric topics (e.g., area and…

### Pre-Algebra

A pre-algebra text, written by Angela Milano from American River College. For each section the text includes a student activity, narrative text with examples, and exercises.

License: Creative Commons Attribution Sharealike Noncommercial. This…

License: Creative Commons Attribution Sharealike Noncommercial. This…

### Basic Arithmetic Student Workbook

This workbook was created through the efforts of three instructors at Scottsdale Community College in Scottsdale, Arizona, has been used by thousands of students, and is continually improved. This workbook contains have lessons that were carefully…

### Arithmetic for College Students

This book is a course on arithmetic designed for college students. It covers whole numbers, fractions, decimals, percents, ratios and proportions, measurement, and integers. Geometry and statistics are integrated throughout the text rather than…

### Calculus Early Transcendental: an Open Text

Calculus: Early Transcendentals, originally by D. Guichard, has been redesigned by the Lyryx editorial team. Substantial portions of the content, examples, and diagrams have been redeveloped, with additional contributions provided by experienced and…

### A Friendly Introduction to Differential Equations

n this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations,…

### A First Course in Linear Algebra

In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students practice…

### Introduction to Mathematical Analysis I

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels.…

### Foundations in Statistical Reasoning

This book starts by presenting an overview of the statistical thought process. By the end of chapter 2, students are already familiar with concepts such as hypotheses, level of significance, p-values, errors. Normally these topics are not introduced…

### Contemporary Calculus

How to Succeed in Beginning Calculus

Calculus is the mathematics of CHANGE and almost everything in our world is changing.

Calculus is among the most important and useful developments of human thought, and, even though it is over 300 years old, it…

Calculus is the mathematics of CHANGE and almost everything in our world is changing.

Calculus is among the most important and useful developments of human thought, and, even though it is over 300 years old, it…

### Exact Trig Values - Hand Trick

There are some key angles that have exact values in trigonometry. The ones we need to know are 0, 30, 45, 60 and 90.

In this video we will discover one method of remember what these values are - by counting fingers on our hand!

In the first…

In this video we will discover one method of remember what these values are - by counting fingers on our hand!

In the first…

### Pure Mathematics

What is PURE MATHEMATICS? What does PURE MATHEMATICS mean? PURE MATHEMATICS meaning - PURE MATHEMATICS definition - PURE MATHEMATICS explanation.

Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/…

Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/…

### Functions and Relations

Part of the NCSSM Online AP Calculus Collection: This video deals with transformations of functions including parent functions and the library of functions and relations. http://www.dlt.ncssm.edu

Please attribute this work as being created by the…

Please attribute this work as being created by the…