510 Mathematics

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…

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…

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…

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.

College Trigonometry

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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…

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…

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…

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…

Principles of Business Statistics

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…

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…

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…

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…

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…

Intro to Logic

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…

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…

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 3

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…

Brief Calculus

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
…

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…

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…

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…

Precalculus An Investigation of Functions Edition 1.5

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…

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…

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…

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…

Trigonometry

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…

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…

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…

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…

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…

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…

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…

Calculus Based Physics II

From Algorithms to Z-Scores: Probabilistic and Statistical Modeling in Computer Science

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…

Mathematical Analysis Volume I

Intermediate Algebra

mathematic foccus on algebra

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…

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