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The Basics of General, Organic, and Biological Chemistry
David Ball; John Hill; Rhonda Scott · Saylor Foundation · 2011
The Basics of General, Organic, and Biological Chemistry by David W. Ball, John W. Hill, and Rhonda J. Scott is for the one-semester General, Organic and Biological Chemistry course. The authors designed this textbook from the ground up to meet the needs of a one-semester course. It is 20 chapters in length and approximately 350-400 pages; just the right breadth and depth for instructors to teach and students to grasp. In addition, The Basics of General, Organic, and Biological Chemistry is written not by one chemist, but THREE chemistry professors with specific, complimentary research and teaching areas. David W. Ball's specialty is physical chemistry, John W. Hill's is organic chemistry, and finally, Rhonda J. Scott's background is in enzyme and peptide chemistry. These three authors have the expertise to identify and present only the most important material for students to learn in the GOB Chemistry course. These experienced authors have ensured their text has ample in-text examples, and ”Test Yourself“ questions following the examples so students can immediately check their comprehension. The end-of-chapter exercises will be paired, with one answered in the back of the text so homework can easily be assigned and self-checked. The Basics of General, Organic, and Biological Chemistry by David W. Ball, John W. Hill, and Rhonda J. Scott is the right text for you and your students if you are looking for a GOB textbook with just the right amount of coverage without overdoing the concepts and overwhelming your students.
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Community and Public Health Nursing: A Call to Action
Andrea Reed; Beth Tremblay; Chloe Gross; Felisa Smith · Virginia's Academic Library Consortium (VIVA) · 2024
Community and Public Health Nursing: A Call to Action is a primer exploring the diverse roles of community and public health nurses through a social justice lens. Students will gain the fundamental knowledge and skills to work with community members and other stakeholders to promote health and well-being and to prevent disease. This textbook examines key issues such as health disparities, access to care, cultural competence, and the impact of social determinants on public health outcomes. Students will gain knowledge, practical skills, and insight into how nurses can improve community health, advocate for health-related policies, and promote health equity at the individual through systemic levels. The textbook also maps the content to the AACN New Essentials for Baccalaureate Nursing Education. The book is accompanied by a comprehensive Instructor’s Guide designed to support educators in meeting educational goals and developing competencies. The guide offers practical teaching strategies, such as role-playing communication exercises and simulation activities; suggests clinical activities to facilitate deeper understanding and classroom engagement; and includes NCLEX-style practice questions to reinforce key concepts, test critical thinking skills, and provide students valuable practice preparing for the NCLEX exam.
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Human Anatomy and Physiology Laboratory Manual: Understanding How Structure Determines Function
Maria Carles · ROTEL · 2024
This lab manual introduces students to Human Anatomy and Physiology concepts. The laboratory exercises contain applied activities and experiments to help students visualize anatomical structures and relate them to specific functions and the complex physiological events that allow us to maintain homeostasis.
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Tea Time Linear Algebra Explorations in Mathematics
Leon Brin · Leon Q. Brin · 2022
This creation is an all-purpose open source textbook for linear algebra classes of all ilks. Inside you will find a complete and engaging introduction to linear algebra, making it a perfect primary resource for classroom study. Take a ride through the landscape of linear algebra from basic mechanics through inner product spaces. 386 pages Over 1000 exercises with over 200 detailed solutions and hundreds more answers Over 250 illustrations Nearly 150 live SageMathCell links Open source Now with online homework and course management at MyOpenMath! Presented in a conversational style with plenty of motivation, illustrations, applications, and theory, this text should be a comfortable read for most beginning mathematicians. Readers and instructors alike will appreciate the numerous detailed exercise solutions accompanying each section. Examine the distribution of bicycles in the Capital Bikeshare system, model an un-preheated oven baking brownies, reproduce sounds via Fourier series, explore reptiles like the one decorating this cover, and more. Read proofs of the rank and nullity theorem, the determinant expansion formula, existence and uniqueness of solutions of linear systems and others. It's all here in Tea Time Linear Algebra.
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Multivariable Calculus
Don Shimamoto · Don Shimamoto · 2019
This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and finally the general case of vector-valued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required.
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An Introduction to the Theory of Numbers
Leo Moser · The Trillia Group · 2011
This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text.
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Introduction to Financial Mathematics Concepts and Computational Methods
Arash Fahim · Florida State University · 2019
Introduction to Financial Mathematics: Concepts and Computational Methods serves as a primer in financial mathematics with a focus on conceptual understanding of models and problem solving. It includes the mathematical background needed for risk management, such as probability theory, optimization, and the like. The goal of the book is to expose the reader to a wide range of basic problems, some of which emphasize analytic ability, some requiring programming techniques and others focusing on statistical data analysis. In addition, it covers some areas which are outside the scope of mainstream financial mathematics textbooks. For example, it presents marginal account setting by the CCP and systemic risk, and a brief overview of the model risk. Inline exercises and examples are included to help students prepare for exams on this book.
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Mathematical Analysis I
Elias Zakon · The Trillia Group · 2004
This award-winning text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material. For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text.
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Business Math: A Step-by-Step Handbook
Jean-Paul Olivier · Lyryx · 2023
Business Mathematics was written to meet the needs of a twenty-first century student. It takes a systematic approach to helping students learn how to think and centers on a structured process termed the PUPP Model (Plan, Understand, Perform, and Present). This process is found throughout the text and in every guided example to help students develop a step-by-step problem-solving approach. This textbook simplifies and integrates annuity types and variable calculations, utilizes relevant algebraic symbols, and is integrated with the Texas Instruments BAII+ calculator. It also contains structured exercises, annotated and detailed formulas, and relevant personal and professional applications in discussion, guided examples, case studies, and even homework questions.
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Representation Theory
Jan Grabowski · Open Book Publishers · 2025
This volume offers a fresh and modern introduction to one of abstract algebra’s key topics. Guiding readers through the transition between structure theory and representation theory, this textbook explores how algebraic objects like groups and rings act as symmetries of other structures. Using the accessible yet powerful language of category theory, the book reimagines standard approaches to topics such as modules and algebras in a way that unlocks modern treatments of more advanced topics such as quiver representations and even representations of Hopf algebras and categories. Aimed at undergraduate students with prior exposure to linear algebra and basic group theory, the book introduces categories early and uses them throughout, providing a cohesive framework that mirrors current mathematical research. Though technically sophisticated, it also includes examples and exercises designed to develop intuition and understanding. Grabowski’s inclusion of computational tools such as SageMath offers a valuable and traditionally underdeveloped bridge between abstract theory and hands-on exploration. This is a uniquely valuable guide for students ready to stretch their understanding of the subject’s conceptual depth and evolving frontiers.
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Integral Calculus with Applications to Life Sciences
Paul Tsopméné · University of British Columbia Library · 2025
Integral Calculus with Applications to Life Sciences is an open educational resource (OER) that covers an unusually broad range of topics—including integration, infinite series, differential equations, linear algebra, probability, and statistics—rarely found in a single textbook. Each section begins with clear learning outcomes and a motivational paragraph, often tied to applications in the life sciences, helping students see the immediate relevance of what they learn. Examples are worked out in full detail. Every time a calculus or algebraic rule is applied, it is explicitly stated at the point of use. Rather than isolating algebra review in a preliminary chapter, this text integrates algebra throughout, allowing students to reinforce foundational skills while learning new material. This approach is especially supportive for students who may struggle with algebra. Practice problems with complete solutions follow each example, and most sections end with an application to biology, medicine, or related fields. The exercise sections include not only standard questions but also critical thinking problems such as finding errors in worked solutions, constructing counterexamples, and solving real-world problems. The text includes final answers for all exercises at the back. Hyperlinks allow students to jump seamlessly between exercises and final answers. By combining clarity, rigor, accessibility, and real-world relevance, one of the main goals of this OER is to help students not only to succeed in calculus but also to appreciate its power in understanding the living world.
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Linear Algebra Done Right
Sheldon Axler · Springer · 2024
Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. The text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.
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Geometry with an Introduction to Cosmic Topology
Michael Hitchman · Michael P. Hitchman · 2020
Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe. The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits. Geometry is suitable for a semester course in non-Euclidean geometry or as a guide to independent study, with over 200 exercises and several essays on topics including the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe.
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Counting Rocks! An Introduction to Combinatorics
Henry Adams; Kelly Emmrich; Maria Gillespie; Shannon Golden · Henry Adams, Rachel Pries, and Maria Gillespie · 2023
This textbook, Counting Rocks!, is the written component of an interactive introduction to combinatorics at the undergradaute level. Throughout the text, we link to videos where we describe the material and provide examples; see the Youtube playlist on the Colorado State University (CSU) Mathematics YouTube channel. The major topics in this text are counting problems (Chapters 1-4), proof techniques (Chapter 5), recurrence relations and generating functions (Chapters 6-7), and graph theory (Chapters 8-12). The material and the problems we include are standard for an undergraduate combinatorics course. In this text, one of our goals was to describe the mathematical structures underlying problems in combinatorics. For example, we separate the description of sequences, permutations, sets and multisets in Chapter 3. In addition to the videos, we would like to highlight some other features of this book. Most chapters contain an investigation section, where students are led through a series of deeper problems on a topic. In several sections, we show students how to use the free online computing software SAGE in order to solve problems; this is especially useful for the problems on recurrence relations. We have included many helpful figures throughout the text, and we end each chapter (and many of the sections) with a list of exercises of varying difficulty.
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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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Numerical Methods for Ordinary Differential Equations
Kees Vuik; Fred Vermolen; Martin van Gijzen · TU Delft Open · 2023
In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize the aspects that play an important role in practical problems. We confine ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation. The techniques discussed in the intro-ductory chapters, for instance interpolation, numerical quadrature and the solution to nonlinear equations, may also be used outside the context of differential equations. They have been in-cluded to make the book self-contained as far as the numerical aspects are concerned. Chapters, sections and exercises marked with a * are not part of the Delft Institutional Package. The numerical examples in this book were implemented in Matlab, but also Python or any other programming language could be used. A list of references to background knowledge and related literature can be found at the end of this book. Extra information about this course can be found at http://NMODE.ewi.tudelft.nl, among which old exams, answers to the exercises, and a link to an online education platform. We thank Matthias Moller for his thorough reading of the draft of this book and his helpful suggestions.
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Elementary Calculus
Michael Corral · Michael Corral · 2020
This textbook covers calculus of a single variable, suitable for a year-long (or two-semester) course. Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II. The book is designed for students who have completed courses in high-school algebra, geometry, and trigonometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but the old idea of an infinitesimal is resurrected, owing to its usefulness (especially in the sciences). There are 943 exercises in the book, with answers and hints to selected exercises.
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Introduction to Modern Statistics
Mine Çetinkaya-Rundel; Jo Hardin · OpenIntro · 2024
Introduction to Modern Statistics is a re-imagining of a previous title, Introduction to Statistics with Randomization and Simulation. The new book puts a heavy emphasis on exploratory data analysis (specifically exploring multivariate relationships using visualization, summarization, and descriptive models) and provides a thorough discussion of simulation-based inference using randomization and bootstrapping, followed by a presentation of the related Central Limit Theorem based approaches. The second edition of IMS has updated datasets, additional exercises, a new application for chapter 3, and updated text and code to reflect changes in best practices. You can access the full PDF by clicking the Read Free Sample button at the PDF link.
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Intermediate Algebra
Lynn Marecek; Andrea Mathis · OpenStax · 2017
Intermediate Algebra 2e is designed to meet the scope and sequence requirements of a one-semester intermediate algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. The material is presented as a sequence of clear steps, building on concepts presented in prealgebra and elementary algebra courses. The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty.
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Elementary College Geometry
Henry Africk · CUNY Academic Works · 2021
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.