Digital library
Textbooks, references and open learning resources.
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Contemporary Mathematics
Donna Kirk · OpenStax · 2023
Contemporary Mathematics is designed to meet the scope and sequence requirements for a liberal arts mathematics course. This resource provides stand-alone sections with a focus on showing relevance in the features as well as the examples, exercises, and exposition. Contemporary Mathematics integrates technology applications, projects, and highlights a diverse group of contributors to mathematics, statistics, and related fields. Print copies of this book will be available for the fall 2023 semester. You can sign up to be notified when print copies are available.
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Technical Mathematics
Morgan Chase · Open Oregon Educational Resources · 2024
This developmental-level mathematics textbook is intended for career-technical students.
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Math in Society: Mathematics for liberal arts majors
Cara Lee · Portland Community College Math Department · 2018
We dedicate this book to our students. May you have greater ease in paying for college and grow your proficiency and confidence in math.
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Advanced Problems in Mathematics: Preparing for University
Stephen Siklos · Open Book Publishers · 2016
This new and expanded edition 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 for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and 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.
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My Math GPS: Elementary Algebra Guided Problem Solving
Jonathan Cornick; Michael Guy; Karan Puri · CUNY Academic Works · 2016
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 Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors.
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Applied Finite Mathematics
Rupinder Sekhon · OpenStax CNX · 2011
Applied Finite Mathematics covers topics including linear equations, matrices, linear programming, the mathematics of finance, sets and counting, probability, Markov chains, and game theory.
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Proofs and Concepts: The Fundamentals of Abstract Mathematics
Dave Morris; Joy Morris · Dave Witte Morris, Joy Morris · 2013
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.
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Discrete Mathematics: An Open Introduction
Oscar Levin · Oscar Levin · 2024
Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math and computer science majors. The book is especially well-suited for courses that incorporate inquiry-based learning. Since Spring 2013, the book has been used as the primary textbook or a supplemental resource at more than 200 colleges and universities around the world (see the partial adoptions list). After many years of development, I am pleased to announce that the 4th edition of Discrete Mathematics: an Open Introduction is now available, here and on Runestone Academy. The new edition brings many improvements and a new organization of content. In particular, the book now starts with logic and proofs, then practices those proofs with graph theory. The second half of the book contains material on counting (with a new "application to probability" section) and sequences. Over the last few years, I have found that students have more success with this arrangement. There is also a stronger emphasis on discrete structures, which should make the book more useful for students in computer science, while still focusing on understanding mathematical concepts essential for math majors and future math teachers.
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Introduction to Mathematical Analysis I
Beatriz Lafferriere; Gerardo Lafferriere; Mau Nam Nguyen · Portland State University Library · 2016
Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs. The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds. The second edition includes a number of improvements based on recommendations from students and colleagues and on our own experience teaching the course over the last several years. In this edition we streamlined the narrative in several sections, added more proofs, many examples worked out in detail, and numerous new exercises. In all we added over 50 examples in the main text and 100 exercises (counting parts).
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Spiral Workbook for Discrete Mathematics
Harris Kwong · Open SUNY · 2015
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.Open SUNY Textbooks is an open access textbook publishing initiative established by State University of New York libraries and supported by SUNY Innovative Instruction Technology Grants. This initiative publishes high-quality, cost-effective course resources by engaging faculty as authors and peer-reviewers, and libraries as publishing service and infrastructure. The pilot launched in 2012, providing an editorial framework and service to authors, students and faculty, and establishing a community of practice among libraries. Participating libraries in the 2012- 2013 pilot include SUNY Geneseo, College at Brockport, College of Environmental Science and Forestry, SUNY Fredonia, Upstate Medical University, and University at Buffalo, with support from other SUNY libraries and SUNY Press. More information can be found at http://textbooks.opensuny.org.
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A Gentle Introduction to the Art of Mathematics
Joseph Fields · Southern Connecticut State University · 2015
This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable. It is written in an informal, conversational style with a large number of interesting examples and exercises, so that a student learns to write proofs while working on engaging problems.
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Fundamentals of Mathematics
Denny Burzynski; Wade Ellis · OpenStax CNX · 2008
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.
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Math in Society
David Lippman · David Lippman · 2017
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 independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Math 107 (Washington State Community Colleges common course number).
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Fundamentals of Math, Physics, and Statistics for Future Transportation Professionals
Anurag Pande; Peyton Ratto; Ahmed Farid · Mavs Open Press · 2024
This textbook and OER material cover tools and basic knowledge required to master the prerequisite essentials of physics, mathematics, and statistics applied in transportation engineering. To our knowledge, no such textbook currently exists to build the KSTs (Knowledge, Skills, Tools) for college freshmen’ remedial courses required by most transportation engineering graduate programs that admit non-engineers (e.g., PHYS 141, MATH 142, STAT 321 at California Polytechnic State University, San Luis Obispo). The textbook modules are intended for students with undergraduate degrees in planning and other less technical fields who are interested in pursuing transportation careers where background engineering knowledge is required. This textbook is a product of the grant OERTransport: Enabling Transportation Planning Professional Advancement awarded to the University of Texas-Arlington (UTA) in consortium with California Polytechnic State University (Cal Poly) and the University of South Florida (USF). It was developed under an Open Textbooks Pilot grant from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education. However, its contents do not necessarily represent the policy of the Department of Education, and no endorsement by the Federal Government should be assumed
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The Academic Language of Mathematics
Costas Loizou; Deak Kirkham; Shuwei Chen · University of Leeds Open Books · 2026
The Academic Language of Mathematics is an eight-chapter, open-access textbook that helps any student studying mathematics as part of their degree to understand mathematical terminology and communicate mathematical topics clearly in English. Developed through collaboration between a mathematics lecturer at the University of Leeds, an English for Academic Purposes lecturer at the University of Leeds and a mathematics lecturer at Southwest Jiaotong University, it integrates core mathematical content with systematic work on vocabulary, structures and text types, with particular support for students in English‑medium instruction and international STEM programmes.
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Mathematics Methods for Early Childhood
Janet Stramel · Fort Hays State University · 2021
Welcome to Early Childhood Mathematics! This course satisfies the Early Childhood Unified requirements in the state of Kansas for a teaching license Birth to Grade 3. Most people agree that early childhood includes the period from infancy until eight years of age, characterized by rapid and complex growth in physical, cognitive, and social domains. Math skills must be taught in early childhood. Children should be provided a foundation to succeed in elementary school and beyond. Teachers should focus lessons in early childhood around the basic skills that will help to advance future mathematics. From preschool to the end of elementary school, children are setting the foundation for future life skills. Learning mathematics is “a ‘natural’ and developmentally appropriate activity for young children” (Ginsberg, Lee, and Boyd, 2008). Through their everyday interactions with the world, many children develop informal concepts about space, quantity, size, patterns, and operations. Unfortunately, not all children have the same opportunities to build these informal and foundational concepts of mathematics in their day-to-day lives (Sherman-LeVos, 2010). Young children are naturally curious, and the best time to begin mathematics is at a time while the young child’s brain is rapidly developing. Mathematics in early childhood helps children develop critical thinking and reasoning skills early on and it’s the key to the foundation for success in their formal schooling years.
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Teaching Math for Emergent Bilinguals: Building on Culture, Language, and Identity
Ji-Yeong I; Ricardo Martinez · Iowa State University · 2020
This book is designed for pre-service/in-service teachers and others who will work or work with K–12 students who have linguistically and culturally diverse backgrounds, especially students of other languages (English language learners/Emergent bilingual/multilingual). The core concept of this course is helping teachers understand the needs of various Emergent Bilinguals (a.k.a. English language learners (ELLs)/English Learners (ELs), learn to use their language and culture as a resource in mathematics classrooms and implement research-based instructional strategies that are effective to teach mathematics for Emergent Bilinguals.
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Mathematics for Elementary Teachers
Michelle Manes · University of Hawaii Manoa · 2017
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 exploring unfamiliar mathematical situations.The primary goal of this book is to help you learn to think like a mathematician in some very specific ways. You will:• Make sense of problems and persevere in solving them. You will develop and demonstrate this skill by working on difficult problems, making incremental progress, and revising solutions to problems as you learn more.• Reason abstractly and quantitatively. You will demonstrate this skill by learning to represent situations using mathematical notation (abstraction) as well as creating and testing examples (making situations more concrete).• Construct viable arguments and critique the reasoning of others. You will be expected to create both written and verbal explanations for your solutions to problems. The most important questions in this class are “Why?” and “How do you know you're right?” Practice asking these questions of yourself, of your professor, and of your fellow students.Throughout the book, you will learn how to learn mathematics on you own by reading, working on problems, and making sense of new ideas on your own and in collaboration with other students in the class.
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Contemporary Mathematics
Donna Kirk; Barbara Boschmans; Brian Beaudrie; Matthew Cathey · OpenStax, Rice University
Contemporary Mathematics is designed to meet the scope and sequence requirements for a liberal arts mathematics course. This resource provides stand-alone sections with a focus on showing relevance in the features as well as the examples, exercises, and exposition. Contemporary Mathematics integrates technology applications, projects, and highlights a diverse group of contributors to mathematics, statistics, and related fields.
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Beginning Algebra
Lumen Learning
This text builds concepts and skills in preparation for student success in subsequent college math courses. Course content includes basic solving equations & inequalities, graphing, solving systems of equations & inequalities, exponents, polynomials, factoring, rational expressions, roots, and rational exponents. With an OER text, aligned OER videos, complete slides, lecture notes, and complete online assessments, this title is a great low-cost alternative to traditional publisher materials.