Elementary Algebra
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 skills. Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.
Wade Ellis
Denny Burzynski
OpenStax CNX
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Proofs and Concepts: The Fundamentals of Abstract Mathematics
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 mathematics, but it is also suitable for independent study by undergraduates (or mathematically mature high-school students), or for use as a very inexpensive supplement to undergraduate courses in any field of abstract mathematics.
Dave Morris
Joy Morris
Independent
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Linear Algebra, Theory And Applications
Linear Algebra
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 analysis than this, however.
This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants.
The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.
Kenneth Kuttler
Saylor Foundation
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Advanced Problems in Mathematics: Preparing for University
Mathematics
" This book is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge colleges as the basis for conditional offers. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics. "
Stephen Siklos
https://www.openbookpublishers.com/reader/342#page/10/mode/2up
Open Book Publishers
2016
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English
Textbooks
Introduction to Real Analysis
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 benefit from the mathematical maturity that can be gained from an introductory real analysis course.
The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.
William Trench
Independent
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Fundamentals of Mathematics
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 previous courses in prealgebra
wish to meet the prerequisites of higher level courses such as elementary algebra
need to review fundamental mathematical concenpts and techniques
This text will help the student devlop the insight and intuition necessary to master arithmetic techniques and manipulative skills. It was written with the following main objectives:
to provide the student with an understandable and usable source of information
to provide the student with the maximum oppurtinity to see that arithmetic concepts and techniques are logically based
to instill in the student the understanding and intuitive skills necessary to know how and when to use particular arithmetic concepts in subsequent material cources and nonclassroom situations
to give the students the ability to correctly interpret arithmetically obtained results
We have tried to meet these objects by presenting material dynamically much the way an instructure might present the material visually in a classroom. (See the development of the concept of addition and subtraction of fractions in section 5.3 for examples) Intuition and understanding are some of the keys to creative thinking, we belive that the material presented in this text will help students realize that mathematics is a creative subject.
Denny Burzynski
Wade Ellis
OpenStax CNX
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Fast Fourier Transforms
Transforms
Mathematics
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 hardware, theory and applications continue to keep them important and exciting.
C. Sidney Burrus
Matteo Frigo
Steven G. Johnson
Markus Pueschel
Ivan Selesnick
Connexions
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Elementary Differential Equations with Boundary Value Problems
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.
An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough.
An elementary text can’t be better than its exercises. This text includes 1695 numbered exercises, many with several parts. They range in difficulty from routine to very challenging.
An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and definitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 250 completely worked out examples. Where appropriate, concepts and results are depicted in 144 figures.
Although I believe that the computer is an immensely valuable tool for learning, doing, and writing mathematics, the selection and treatment of topics in this text reflects my pedagogical orientation along traditional lines. However, I have incorporated what I believe to be the best use of modern technology, so you can select the level of technology that you want to include in your course. The text includes 336 exercises – identified by the symbols C and C/G – that call for graphics or computation and graphics. There are also 73 laboratory exercises – identified by L – that require extensive use of technology. In addition, several sections include informal advice on the use of technology. If you prefer not to emphasize technology, simply ignore these exercises and the advice.
William Trench
Independent
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Elementary College Geometry
Geometry
Mathematics
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 emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem-proving or formal methods of reasoning. However the topics are ordered so that they may be taught deductively.
The problems are arranged in pairs so that just the odd-numbered or just the even-numbered can be assigned. For assistance, the student may refer to a large number of completely worked-out examples. Most problems are presented in diagram form so that the difficulty of translating words into pictures is avoided. Many problems require the solution of algebraic equations in a geometric context. These are included to reinforce the student's algebraic and numerical skills, A few of the exercises involve the application of geometry to simple practical problems. These serve primarily to convince the student that what he or she is studying is useful. Historical notes are added where appropriate to give the student a greater appreciation of the subject.
This book is suitable for a course of about 45 semester hours. A shorter course may be devised by skipping proofs, avoiding the more complicated problems and omitting less crucial topics.
Henry Africk
CUNY Academic Works
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Applied Finite Mathematics
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.
OpenStax CNX
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Textbooks
College Algebra
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 authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely.
Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended). Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it.
The authors also offer a Precalculus version of this text, which has two extra chapters covering Trigonometry.
Carl Stitz
Jeff Zeager
Stitz Zeager Open Source Mathematics
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Applied Probability
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 evaluated as iterated integrals. The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation. Appendix B provides a convenient compendium of mathematical facts used frequently in this work. And the symbolic toolbox, implementing MAPLE, may be used to evaluate integrals, if desired.
In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user defined MATLAB procedures and functions (which we refer to as m-programs, or simply programs) to solve many important problems in basic probability. This should make the work useful as a stand-alone exposition as well as a supplement to any of several current textbooks.
Most of the programs developed here were written in earlier versions of MATLAB, but have been revised slightly to make them quite compatible with MATLAB 7. In a few cases, alternate implementations are available in the Statistics Toolbox, but are implemented here directly from the basic MATLAB program, so that students need only that program (and the symbolic mathematics toolbox, if they desire its aid in evaluating integrals).
Since machine methods require precise formulation of problems in appropriate mathematical form, it is necessary to provide some supplementary analytical material, principally the so-called minterm analysis. This material is not only important for computational purposes, but is also useful in displaying some of the structure of the relationships among events.
Paul Pfeiffer
OpenStax CNX
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Advanced Algebra II: Conceptual Explanations
Algebra
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.
Kenny M. Felder
Connexions
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A Primer of Real Analysis
Real Analysis
Mathematics
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 courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.
Dan Sloughter
Independent
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A Computational Introduction to Number Theory and Algebra
Computational
Number Theory
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 one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.
The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures.
There are a few sections that are marked with a “(∗),” indicating that the material covered in that section is a bit technical, and is not needed else- where.
There are many examples in the text, which form an integral part of the book, and should not be skipped.
There are a number of exercises in the text that serve to reinforce, as well as to develop important applications and generalizations of, the material presented in the text.
Some exercises are underlined. These develop important (but usually simple) facts, and should be viewed as an integral part of the book. It is highly recommended that the reader work these exercises, or at the very least, read and understand their statements.
In solving exercises, the reader is free to use any previously stated results in the text, including those in previous exercises. However, except where otherwise noted, any result in a section marked with a “(∗),” or in §5.5, need not and should not be used outside the section in which it appears.
There is a very brief “Preliminaries” chapter, which fixes a bit of notation and recalls a few standard facts. This should be skimmed over by the reader.
There is an appendix that contains a few useful facts; where such a fact is used in the text, there is a reference such as “see §An,” which refers to the item labeled “An” in the appendix.
Victor Shoup
Independent
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Applied Combinatorics
Combinatorics
Mathematics
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 has
an intellectually appealing theoretical side. Our goal is to give you a taste of both. In
order to begin, we want to develop, through a series of examples, a feeling for what types of problems combinatorics addresses.
Mitchel T. Keller
William T. Trotter
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Intro to Logic
Logic
Mathematics
Matthias Felleisen
John Grenier
Moshe Vardi
Phokion Kolaitis
Ian Barland
Connexions
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A Foundation In Applied Mathematics
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 recognize functions, see how they constitute a special type of relation, and then move on to consider the simple, useful class of functions called linear functions.
Along the way you'll have plenty of chances to practise what you're learning in examples and exercises.
The Open University of Hong Kong
The Open University of Hong Kong
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Collaborative Statistics
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 in distance learning classes. Courses using this textbook have been articulated by the University of California for transfer of credit. The textbook contains full materials for course offerings, including expository text, examples, labs, homework, and projects. A Teacher’s Guide is currently available in print form and on the Connexions site at and supplemental course materials including additional problem sets and video lectures are available. The on-line text for each of these collections collections will meet the Section 508 standards for accessibility.
An on-line course based on the textbook was also developed by Illowsky and Dean. It has won an award as the best on-line California community college course. The on-line course will be available at a later date as a collection in Connexions, and each lesson in the on-line course will be linked to the on-line textbook chapter. The on-line course will include, in addition to expository text and examples, videos of course lectures in captioned and non-captioned format.
The original preface to the book as written by professors Illowsky and Dean, now follows:
This book is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it. The text is named Collaborative Statistics because students learn best by doing. In fact, they learn best by working in small groups. The old saying “two heads are better than one” truly applies here.
Our emphasis in this text is on four main concepts:
thinking statistically
incorporating technology
working collaboratively
writing thoughtfully
These concepts are integral to our course. Students learn the best by actively participating, not by just watching and listening. Teaching should be highly interactive. Students need to be thoroughly engaged in the learning process in order to make sense of statistical concepts. Collaborative Statistics provides techniques for students to write across the curriculum, to collaborate with their peers, to think statistically, and to incorporate technology.
This book takes students step by step. The text is interactive. Therefore, students can immediately apply what they read. Once students have completed the process of problem solving, they can tackle interesting and challenging problems relevant to today’s world. The problems require the students to apply their newly found skills. In addition, technology (TI-83 graphing calculators are highlighted) is incorporated throughout the text and the problems, as well as in the special group activities and projects. The book also contains labs that use real data and practices that lead students step by step through the problem solving process.
At De Anza, along with hundreds of other colleges across the country, the college audience involves a large number of ESL students as well as students from many disciplines. The ESL students, as well as the non-ESL students, have been especially appreciative of this text. They find it extremely readable and understandable. Collaborative Statistics has been used in classes that range from 20 to 120 students, and in regular, honor, and distance learning classes.
Barbara Illowsky
Susan Dean
OpenStax CNX
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Calculus Volume 3
Calculus
Gilbert Strang
OpenStax
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Calculus Volume 2
Calculus
Mathematics
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 concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.
Gilbert Strang
OpenStax
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Calculus Volume 1
Calculus
Mathematics
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 concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration.
OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
Gilbert Strang
Edwin Herman
OpenStax
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Textbooks
Brief Calculus
Calculus
Benjamin Crowell
Open Textbooks
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Algebra and Trigonometry
Algebra
Trigonometry
Mathematics
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 programs. Algebra and Trigonometry guides and supports students with differing levels of preparation and experience with mathematics. Ideas are presented as clearly as possible, and progress to more complex understandings with considerable reinforcement along the way. A wealth of examples – usually several dozen per chapter – offer detailed, conceptual explanations, in order to build in students a strong, cumulative foundation in the material before asking them to apply what they’ve learned.
Multiple Authors
OpenStax
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Discrete Mathematics
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 topics in discrete mathematics. While we have a few students each semester who will go on to study computer science, pure mathematics or applied mathematics, the majority of students are studying to be elementary or secondary math teachers. For this reason, most of the standard discrete textbooks are not appropriate for us. For many years we used Discrete and Combinatorial Mathematics by Richard Grassl and Tabitha Mingus. This is a very nice book in many ways (Grassl taught at UNC) but the print-on-demand publishing was expensive for students and some sections needed updating and (as I saw it) rearranging.
While the book began as a set of lecture notes, it now contains a number of features that should support its use as a primary textbook:
363 exercises, including 233 with answers or full solutions, as well as 130 more involved problems suitable for homework.
Investigate! activities throughout the text to support active, inquiry based learning.
A full index and list of symbols.
Consistent and (hopefully) helpful page layout and formatting (i.e., examples are easy to identify, important definitions and theorems in boxes, etc.)
Oscar Levin
Oscar Levin
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Combinatorics Through Guided Discovery
Combinatorics
Mathematics
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 problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. Above all, this book is dedicated to the principle that doing mathematics is fun. As long as you know that some of the problems are going to require more than one attempt before you hit on the main idea, you can relax and enjoy your successes, knowing that as you work more and more problems and share more and more ideas, problems that seemed intractable at first become a source of satisfaction later on.
There are six chapters as well as an appendix with three additional topics:
What is Combinatorics?
Applications of Induction and Recursion in Combinatorics and Graphy Theory
Distribution Problems
Generating Functions
The Principle of Inclusion and Exclusion
Groups Acting on Sets
The three supplmental sections deal with relations, mathematical induction, and exponential generating functions.
Kenneth P. Bogart
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A Story of Real Analysis
Real Analysis
Mathematics
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 reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found
in analysis.
This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context.
This book covers the major topics typically addressed in an introductory undergraduate
course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.
Robert Rogers
Eugene Boman
Open SUNY Textbooks
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Introduction to the Modeling and Analysis of Complex Systems
Modeling
Analysisof Complex Systems
Mathematics
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 large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.
Hiroki Sayama
Open SUNY Textbooks
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Dalton State College APEX Calculus
Calculus
Mathematics
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
Derivatives
Integration
Antidifferentiation
Sequences
Vectors
Thomas Gonzalez
Michael Hilgemann
Jason Schmurr
Dalton State College
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A Spiral Workbook for Discrete Mathematics
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 and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students’ problem-solving and writing skills.
Harris Kwong
Open SUNY Textbooks
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Explaining Criminal Career
Society and social sciences
Explaining Criminal Careers presents a simple quantitative theory of crime, conviction and reconviction, the assumptions of the theory are derived directly from a detailed analysis of cohort samples drawn from the “UK Home Office” Offenders Index (OI). Mathematical models based on the theory, together with population trends, are used to make: exact quantitative predictions of features of criminal careers; aggregate crime levels; the prison population; and to explain the age-crime curve, alternative explanations are shown not to be supported by the data. Previous research is reviewed, clearly identifying the foundations of the current work. Using graphical techniques to identify mathematical regularities in the data, recidivism (risk) and frequency (rate) of conviction are analysed and modelled. These models are brought together to identify three categories of offender: high-risk / high-rate, high-risk / low-rate and low-risk / low-rate. The theory is shown to rest on just 6 basic assumptions. Within this theoretical framework the seriousness of offending, specialisation or versatility in offence types and the psychological characteristics of offenders are all explored suggesting that the most serious offenders are a random sample from the risk/rate categories but that those with custody later in their careers are predominantly high-risk/high-rate. In general offenders are shown to be versatile rather than specialist and can be categorised using psychological profiles. The policy implications are drawn out highlighting the importance of conviction in desistance from crime and the absence of any additional deterrence effect of imprisonment. The use of the theory in evaluation of interventions is demonstrated.
John F. Macleod,
Peter G. Grove,
David P. Farringtz
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Oxford University Press
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Geometry
Geometry
Mathematics
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 of geometry used everywhere. In this chapter, you’ll study the basic elements of geometry. Later you will prove things about geometric shapes using the vocabulary and ideas in this chapter—so make sure that you completely understand each of the concepts presented here before moving on.
Victor Cifarelli
Andrew Gloag
Dan Greenberg
Jim Sconyers
Bill Zahner
CK-12 Foundation
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Calculus
Calculus
Mathematics
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 :” integraon and its applicaons, along with an introducon to sequences, series and Taylor Polynomials, found in Chapters through
. The third text covers topics common in “Calc ” or “mulvariable calc:” parametric
equaons, polar coordinates, vector–valued funcons, and funcons of more than one variable, found in Chapters through.
Gregory Hartman, Ph.D.
Troy Siemers, Ph.D.
Brian Heinold, Ph.D.
Dimplekumar Chalishajar, Ph.D.
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Precalculus An Investigation of Functions Edition 1.5
Precalculus
Mathematics
David Lippman
Melonie Rasmussen
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Precalculus
Precalculus
Mathematics
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 pace of this course will be faster than a high school class in
precalculus. Above that, we aim for greater command of the material, especially the ability to extend what we have learned to new situations.
• This course aims to help you build the stamina required to solve
challenging and lengthy multi-step problems.
• As a rule of thumb, this course should on average take 15 hours
of effort per week. That means that in addition to the 5 classroom hours per week, you would spend 10 hours extra on the class. This is only an average and my experience has shown that 12–15 hours of study per week (outside class) is a more typical estimate. In other words, for many students, this course is the equivalent of a halftime job!
• Because the course material is developed in a highly cumulative
manner, we recommend that your study time be spread out evenly over the week, rather than in huge isolated blocks. An analogy with athletics is useful: If you are preparing to run a marathon, you must train daily; if you want to improve your time, you must continually push your comfort zone.
David H. Collingwood
K. David Prince
Matthew M. Conroy
University of Washington
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Textbooks
Physical Modeling in MATLAB
MATLAB
Computer Science
Mathematics
Most books that use MATLAB are aimed at readers who know how to program. This book is for people who have never programmed before.
As a result, the order of presentation is unusual. The book starts with scalar values and works up to vectors and matrices very gradually. This approach is good for beginning programmers, because it is hard to understand composite objects until you understand basic programming semantics. But there are
problems:
• The MATLAB documentation is written in terms of matrices, and so are the error messages. To mitigate this problem, the book explains the necessary vocabulary early and deciphers some of the messages that beginners ﬁnd confusing.
• Many of the examples in the ﬁrst half of the book are not idiomatic MATLAB. I address this problem in the second half by translating the examples into a more standard style.
The book puts a lot of emphasis on functions, in part because they are an important mechanism for controlling program complexity, and also because they are useful for working with MATLAB tools like fzero and ode45.
I assume that readers know calculus, diﬀerential equations, and physics, but not linear algebra. I explain the math as I go along, but the descriptions might not be enough for someone who hasn’t seen the material before.
There are small exercises within each chapter, and a few larger exercises at the end of some chapters.
Allen B. Downey
Green Tea Press
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Textbooks
Introduction to Modern Set Theory
Modern Set Theory
Mathematics
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 illustrative examples both in the text and in the exercises, and the integration of consistency results and large cardinals into the text early on. This book is aimed at two audiences: students who are interested in studying set theory for its own sake, and students in other areas who may be curious about applications of set theory to their field. In particular, great care is taken to develop the intuitions that lie behind modern, as well as classical, set theory, and to connect set theory with the rest of mathematics.
Judith Roitman
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Textbooks
Introduction to Differential Equations
Mathematics
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 presented in these notes may be found in this book. The material of Chapter 7 is adapted from the textbook “Nonlinear dynamics and chaos” by Steven H. Strogatz (Perseus Publishing, ○c 1994)
Jeffrey R. Chasnov
The Hong Kong University of Science and Technology
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Textbooks
Calculus for The Life Sciences A Modeling Approach Volume II
Calculus
Mathematics
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 from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There is a chapter on systems of two difference equations.
James L. Cornette
Ralph A. Ackerman
Flooved.com on behalf of the author
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Textbooks
Calculus For the Life Sciences: A Modeling Approach Volume I
Calculus
Mathematics
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 from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There is a chapter on systems of two difference equations.
James L. Cornette
Ralph A. Ackerman
Flooved.com on behalf of the author
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Textbooks
Applied Discrete Structures
Discrete Structures
Mathematics
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 algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http://www.aimath.org/textbooks/. This version was created using Mathbook Xml (https://mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at Umass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at Umass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.
Alan Doerr
Kenneth Levasseur
University of Massachusetts Lowell
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Textbooks
Active Calculus Multivariable
Calculus
Mathematics
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 calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore. Following key activities or examples, the presentation normally includes some overall perspective and a brief synopsis of general trends or properties, followed by formal statements of rules or theorems. While we often offer plausibility arguments for such results, rarely do we include formal proofs. It is not the intent of this text for the instructor or author to demonstrate to students that the ideas of calculus are coherent and true, but rather for
students to encounter these ideas in a supportive, leading manner that enables them to begin to understand for themselves why calculus is both coherent and true.
Steven Schlicker
David Austin
Matthew Boelkins
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Textbooks
Fundamental Methods of Logic
Fundamental Methods of Logic
Logic
Fundamental Methods
Math
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 goes roughly like this: we manifest
our rationality by engaging in activities that involve reasoning—making claims and backing them up with reasons, acting in accord with reasons and beliefs, drawing inferences from available evidence, and so on.
This reasoning activity can be done well and it can be done badly—it can be done correctly or
incorrectly. Logic is the discipline that aims to distinguish good reasoning from bad. Since reasoning is central to all fields of study—indeed, since it’s arguably central to being
human—the tools developed in logic are universally applicable. Anyone can benefit from studying
logic by becoming a more self-aware, skillful reasoner.
This covers a variety of topics at an introductory level. Chapter One introduces basic notions, such as arguments and explanations, validity and soundness, deductive and inductive reasoning; it also covers basic analytical techniques, such as distinguishing premises from conclusions and diagramming arguments. Chapter Two discusses informal logical fallacies. Chapters Three and
Four concern deductive logic, introducing the basics of Aristotelian and Sentential Logic, respectively. Chapters Five and Six concern inductive logic. Chapter Five deals with analogical and causal reasoning, including a discussion of Mill’s Methods. Chapter Six covers basic
probability calculations, Bayesian inference, fundamental statistical concepts and techniques, and common statistical fallacies.
Matthew Knachel
https://dc.uwm.edu/cgi/viewcontent.cgi?referer=http://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=491&httpsredir=1&article=1000&context=phil_facbooks
UWM Libraries
Rahmah Agustira
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Textbooks
Introduction to Probability
Introduction to Probability
Probability
Mathematical Probability
Mathematics
Math
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 inﬂuence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a wellestablished
branch of mathematics that ﬁnds applications in every area of scholarly activity from music to physics, and in daily experience from weather prediction to predicting the risks of new medical treatments.
Charles M. Grinstead
J. Laurie Snell
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf
Swarthmore College
Rahmah Agustira
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Textbooks
Statistical Mechanics
Statistical Mechanics
Statistic
Statistics
Mathematics
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 through multivariate calculus. (Section 9.2 also assumes that you can can
diagonalize a 2 x 2 matrix.)
Daniel F. Styer
http://www2.oberlin.edu/physics/dstyer/StatMech/book.pdf
Rahmah Agustira
Creative Commons
Textbooks
Introduction to Numerical Methods and Matlab Programming for Engineers
Introduction to Numerical Methods
Matlab Programming for Engineers
Mathematics
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 periodically updated since then and
underwent a major revision by the second author in 2006-2007.
The main goals of these lectures are to introduce concepts of numerical methods and introduce
Matlab in an Engineering framework. By this we do not mean that every problem is a \real life"
engineering application, but more that the engineering way of thinking is emphasized throughout
the discussion.
Todd Young
Martin J. Mohlenkamp
http://www.math.ohiou.edu/courses/math3600/book.pdf
Ohio University
Rahmah Agustira
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Textbooks
Introduction to Numerical Methods
Numerical Methods
Mathematics
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 several engineering departments. All web surfers are welcome to download these notes at
http://www.math.ust.hk/~machas/numerical-methods.pdf
and to use the notes freely for teaching and learning. I welcome any comments, suggestions or corrections sent by email to jeffrey.chasnov@ust.hk.
Jeffrey R. Chasno
https://www.math.ust.hk/~machas/numerical-methods.pdf
The Hong Kong University of Science and Technology
Rahmah Agustira
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Textbooks
Calculus-Based Physics I
Calculus-Based
Physics
Mathematics
Calculus-Based Physics is an introductory physics textbook designed for use in the two-semester introductory physics course typically taken by science and engineering students. This is the first of two textbooks for this course.
Jeffrey W. Schnick, Ph.D
http://solr.bccampus.ca:8001/bcc/file/b3cd0dd6-f46f-4178-b29d-4a26be81f7f5/1/cbPhysicsIa18%281%29.pdf
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Textbooks
An Introduction to MATLAB and Mathcad
MATLAB and Mathcad
Mathematics
Computer Science
An introduction to programming and problem solving using both MATLAB and Mathcad.
Troy J. Siemers
http://www.vmi.edu/media/content-assets/documents/academics/appliedmath/110_MATLAB_MATHCAD_Text.pdf
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Textbooks
An Introduction to Combinatorics and Graph Theory
Graph Theory
Combinatorics
Mathematics
David Guichard
https://www.whitman.edu/mathematics/cgt_online/cgt.pdf
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Textbooks
Graph Theory
Mathematics
This is a set of lecture notes for Math 485–Penn State’s undergraduate Graph Theory course. Readers should have taken a course in combinatorial proof and ideally matrix algebra.
Christopher Griffin
http://www.freetechbooks.com/graph-theory-penn-state-math-485-lecture-notes-t1236.html
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Textbooks
A First Course in Electrical and Computer Engineering
Electrical and Computer Engineering
Engineering & Electronics
Mathematics
Statistics Science
Technology
Louis Scharf
https://cnx.org/contents/fpkWedRh@2.3:tQa_RWkY@3/Dedication-of-A-First-Course-i
Louis Scharf, Daniel Williamson, C. Sidney Burrus, Richard Baraniuk
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Textbooks
Elementary Diferrential Equantions
Elementary Diferrential
Mathematics
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 been judged to meet the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute’s Open Textbook Initiative.
William F. Trench
https://florida.theorangegrove.org/og/file/1449b08c-b0be-4984-8e3d-6eafd0f649fe/1/TRENCH_FREE_DIFFEQ_I.pdf
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Textbooks
Calculus Based Physics II
Calculus
Physics
Mathematics
Jeffrey W. Schnick
https://florida.theorangegrove.org/og/file/e153a870-4e35-41f0-868d-11727676a502/1/cbPhysicsIIb24.pdf
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Textbooks
Mathematical Analysis Volume I
Analysis
Real Numbers
Sets
Vectors
Sequences
Mathematics
Elias Zakon
https://florida.theorangegrove.org/og/file/5fa982a6-2c68-8570-1147-801c0d137365/1/Real-Analysis-I-Zakon-1-30-11-OTC.pdf
The Saylor Foundation
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Textbooks
Mathematics for Computer Science
Mathematics
Computer
Eric Lehman
F Tom Leighton
Albert R Meyer
https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2015/readings/MIT6_042JS15_textbook.pdf
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Textbooks
OpenIntro Statistics
Statistics
Mathematics
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 optional, inference is key, and we feature real data whenever possible.
License: Creative Commons Attribution Sharealike. This license is considered to be some to be the most open license. It allows reuse, remixing, and distribution (including commercial), but requires any remixes use the same license as the original. This limits where the content can be remiThe 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 optional, inference is key, and we feature real data whenever possible.
License: Creative Commons Attribution Sharealike. This license is considered to be some to be the most open license. It allows reuse, remixing, and distribution (including commercial), but requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license.xed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license.
Diez, Barr
Cetinkaya-Rundel
http://www.opentextbookstore.com/details.php?id=12
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Textbooks
Introductory Algebra Student Workbook
Algebra
Mathematics
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 thoughtfully crafted to lead students on a path to understanding numbers and arithmetic.
License: Creative Commons Attribution Sharealike. This license is considered to be some to be the most open license. It allows reuse, remixing, and distribution (including commercial), but requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license.
Jenifer Bohart
William Meacham
Amy Volpe
James Sousa
Judy Sutor
Donna Gaudet
http://www.opentextbookstore.com/details.php?id=25
Scottsdale Community College
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Textbooks
Beginning and Intermediate Algebra
Intermediate Algebra
Algebra
Mathematics
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 master concepts. Complete answers are included for students to check work and receive immediate feedback on their progress.
Topics covered include: pre-algebra review, solving linear equations, graphing linear equations, inequalities, systems of linear equations, polynomials, factoring, rational expressions and equations, radicals, quadratics, and functions including exponential, logarithmic and trigonometric.
License: Creative Commons Attribution. This license is considered to be some to be the most open license since it is the least restrictive. It allows reuse, remixing, and distribution (including commercial), only requiring attribution. The content can be remixed into content of other license, but on the other hand it allows the remix to be put under a more restrictive license.
Tyler Wallace
http://www.opentextbookstore.com/details.php?id=6
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Textbooks
Prealgebra
Algebra
Mathematics
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 perimeter) are presented throughout the text so students might actually remember them. The applications (word problems) are mostly realistic, and the applications are spread throughout the text, not isolated in a few sections.
License: Creative Commons Attribution Sharealike Noncommercial. This license is very open. It allows reuse, remixing, and distribution, but prohibits commercial use and requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license. The non-commercial clause can make getting printed copies of remixes challenging depending upon how strictly the authors interpret the clause.
David Arnold
Bruce Wagner
http://www.opentextbookstore.com/details.php?id=5
Department of Mathematics, College of the Redwoods
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Textbooks
Pre-Algebra
Algebra
Mathematics
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 is very open. It allows reuse, remixing, and distribution, but prohibits commercial use and requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license. The non-commercial clause can make getting printed copies of remixes challenging depending upon how strictly the authors interpret the clause.
Angela Milano
http://www.opentextbookstore.com/details.php?id=22
American River College
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Textbooks
Basic Arithmetic Student Workbook
Basic Arithmetic
Arithmetic
Mathematics
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 and thoughtfully crafted to lead students on a path to understanding numbers and arithmetic.
License: Creative Commons Attribution Sharealike. This license is considered to be some to be the most open license. It allows reuse, remixing, and distribution (including commercial), but requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license.
Donna Gaudet
Amy Volpe
Jenifer Bohart
http://www.opentextbookstore.com/details.php?id=24
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Textbook
Arithmetic for College Students
Arithmetic
Mathematics
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 covered in independent sections. The textbook does not include exercises. Instead, a collection of handouts/worksheets is available, as well as online homework.
License: Creative Commons Attribution. This license is considered to be some to be the most open license since it is the least restrictive. It allows reuse, remixing, and distribution (including commercial), only requiring attribution. The content can be remixed into content of other license, but on the other hand it allows the remix to be put under a more restrictive license.
MITE
David Lippman
http://www.opentextbookstore.com/details.php?id=13
Scottsdale Community College
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Textbooks
A First Course in Linear Algebra
Algebra
Linear Algebra
Mathematics
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 additional sets of problems other than examples, and they can also check their solutions to some of these exercises by looking at “Answers to Odd-Numbered Exercises” section at the end of this book. This book is very useful for college students who studied Calculus I, and other students who want to review some linear algebra concepts before studying a second course in linear algebra. This book is available online for free in google books and ResearchGate in PDF format under a Creative Commons license.
Mohammed Kaabar
http://www.oercommons.org/courses/a-first-course-in-linear-algebra-study-guide-for-the-undergraduate-linear-algebra-course/view
CreateSpace, Charleston, SC
Taufiq A Gabi
Creative Commons
Exact Trig Values - Hand Trick
Mathematics
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 part we discovered a different method (constructing a table) which you may prefer. Choose whichever method works best for you.
SUBSCRIBE to the FuseSchool YouTube channel for many more educational videos. Our teachers and animators come together to make fun & easy-to-understand videos in Chemistry, Biology, Physics, Maths & ICT.
VISIT us at www.fuseschool.org, where all of our videos are carefully organised into topics and specific orders, and to see what else we have on offer. Comment, like and share with other learners. You can both ask and answer questions, and teachers will get back to you.
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Sofia Nelly
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