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Learning Statistics with jamovi: A Tutorial for Beginners in Statistical Analysis
Danielle Navarro; David Foxcroft · Open Book Publishers · 2025
Based on Danielle Navarro’s widely acclaimed and prize-winning book Learning Statistics with R, this elegantly designed textbook offers undergraduate students a thorough and accessible introduction to jamovi, as well as how to get to grips with statistics and data manipulation. Lucid and easy to understand, Learning Statistics with jamovi covers the analysis of contingency tables, t-tests, correlation, regression, ANOVA and factor analysis, while also giving students a firm grounding in descriptive statistics and graphing. It includes learning aids for applying statistical principles using the jamovi interface, as well as embedded data files to accompany the book, and comprehensive chapters on probability theory, sampling and estimation, and null hypothesis testing. Freely available in open access, Learning Statistics with jamovi is an ideal introduction for undergraduate and postgraduate students of psychology, as well as behavioural and health science students and anyone who needs to understand and use statistical analysis in their work.
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Statistics Minus The Math
Nathan Favero · Nathan Favero · 2024
This book was largely adapted from the public domain resource Online Statistics Education: A Multimedia Course of Study (https://onlinestatbook.com Project Leader: David M. Lane, Rice University). A huge thanks to David Lane and his colleagues at Rice University for their creation of this wonderful resource. I use footnotes throughout to indicate precisely where the various sections of each chapter came from. Chapters 11-13 (as well as Section 3.5, Section 4.2.2, most of Section 4.2.3, and Section 9.3.1) were written by me (Nathan). This book is meant to be a free resource and is licensed under CC BY 4.0. You’re welcome to share or adapt it, as long as you provide attribution to any work of mine that you use. This book was made using Quarto and is hosted using GitHub Pages. There are still formatting inconsistencies, and this is ever a work in progress. If you find errors, feel free to reach out (find updated contact info here: https://nathanfavero.com) so I can correct them for the next version I publish.
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A Cool Brisk Walk Through Discrete Mathematics
Stephen Davies · University of Mary Washington · 2023
A Cool Brisk Walk Through Discrete Mathematics - and its companion site "allthemath" - are completely-and-forever-free-and-open-source educational materials dedicated to the mathematics that budding computer science practitioners actually need to know. They feature the fun and addictive teaching of award-winning lecturer Dr. Stephen Davies of the University of Mary Washington in Fredericksburg, Virginia!
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Statistics for Ecologists: A Frequentist and Bayesian Treatment of Modern Regression Models
John Fieberg · University of Minnesota Libraries Publishing · 2024
Ecological data pose many challenges to statistical inference. Most data come from observational studies rather than designed experiments; observational units are frequently sampled repeatedly over time, resulting in multiple, non-independent measurements; response data are often binary (e.g., presence-absence data) or non-negative integers (e.g., counts), and therefore, the data do not fit the standard assumptions of linear regression (Normality, independence, and constant variance). This book will familiarize readers with modern statistical methods that address these complexities using both frequentist and Bayesian frameworks.
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Classical Numerical Methods in Scientific Computing
Jos van Kan; Guus Segal; Fred Vermolen; Hans Kraaijevanger · TU Delft Open · 2023
Partial differential equations are paramount in mathematical modelling with applications in engineering and science. The book starts with a crash course on partial differential equations in order to familiarize the reader with fundamental properties such as existence, uniqueness and possibly existing maximum principles. The main topic of the book entails the description of classical numerical methods that are used to approximate the solution of partial differential equations. The focus is on discretization methods such as the finite difference, finite volume and finite element method. The manuscript also makes a short excursion to the solution of large sets of (non)linear algebraic equations that result after application of discretization method to partial differential equations. The book treats the construction of such discretization methods, as well as some error analysis, where it is noted that the error analysis for the finite element method is merely descriptive, rather than rigorous from a mathematical point of view. The last chapters focus on time integration issues for classical time-dependent partial differential equations. After reading the book, the reader should be able to derive finite element methods, to implement the methods and to judge whether the obtained approximations are consistent with the solution to the partial differential equations. The reader will also obtain these skills for the other classical discretization methods. Acquiring such fundamental knowledge will allow the reader to continue studying more advanced methods like meshfree methods, discontinuous Galerkin methods and spectral methods for the approximation of solutions to partial differential equations.
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Introducing Mathematical Biology
Alex Best · The University of Sheffield · 2023
Mathematical modelling plays an increasingly important role in almost any area of life sciences, and this interactive textbook focuses on the areas of population ecology, infectious diseases, immunology and cell dynamics, gene networks and pharmacokinetics. It is aimed at anyone who is interested in learning about how to model biological systems, including undergraduate and postgraduate mathematics students who have not studied mathematical biology before, life-sciences students with an interest in modelling, and post-16 mathematics students interested in university-level material. Some mathematical knowledge is assumed, and the mathematical models used are all in the form of ordinary differential equations.
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An Intuitive, Interactive, Introduction to Biostatistics
Caitlin Ward; Collin Nolte · University of Iowa · 2023
"An Intuitive, Interactive Introduction to Biostatistics" is an introductory statistics textbook oriented towards towards undergraduate students in the health sciences. While covering the breadth of material typically presented in a first semester statistics course, including introductions to probability and distributions, study design, CLT, hypothesis testing, and inference, IIIB distinguishes itself with its focus on cultivating student intuition through the use of guided questions and interactive simulation-based applets. Written in R, this open-source text has been created with customizability in mind, offering instructors maximal flexibility in arranging and modifying the content.
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COMPUTATIONAL PHYSICS: A Practical Introduction to Computational Physics and Scientific Computing (using C++)
Konstantinosn Anagnostopoulos · National Technical University of Athens · 2016
This book is an introduction to the computational methods used in physics, but also in other scientific fields. It is addressed to an audience that has already been exposed to the introductory level of college physics, usually taught during the first two years of an undergraduate program in science and engineering. It assumes no prior knowledge of numerical analysis, programming or computers and teaches whatever is necessary for the solution of the problems addressed in the text. It can be used as a textbook in introductory computational physics or scientific computing classes. The book starts with very simple problems in particle motion and ends with an in-depth discussion of advanced techniques used in Monte Carlo simulations in statistical mechanics. The level of instruction rises slowly, while discussing problems like the diffusion equation, electrostatics on the plane, quantum mechanics and random walks. All the material can be taught in two semesters, but a selection of topics can form the material of a one semester course. The book aims to provide the students with the background and the experience needed in order to advance to high performance computing projects in science and engineering. It puts emphasis on hands--on programming of numerical code but also on the production, analysis and interpretation of data. But it also tries to keep the students motivated by considering interesting applications in physics, like chaos, quantum mechanics, special relativity and the physics of phase transitions. There is a C++ and a Fortran edition for the core programming. Data analysis is performed using the powerful tools of the GNU/Linux environment. All the necessary software is open source and freely available. The book and the accompanying software are given under a Creative Commons License/GNU public License as a service to the community. It can be used freely as a whole, or any part of it, in any form, by anyone. There is no official distribution of hard copies, b
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Calculus in Context
James Callahan; David Cox; Kenneth Hoffman · Smith College Open Educational Resources: Textbooks · 1994
Designing the curriculum We believe that calculus can be for students what it was for Euler and the Bernoullis: a language and a tool for exploring the whole fabric of science. We also believe that much of the mathematical depth and vitality of calculus lies in connections to other sciences. The mathematical questions that arise are compelling in part because the answers matter to other disciplines. We began our work with a "clean slate," not by asking what parts of the traditional course to include or discard. Our starting points are thus our summary of what calculus is really about. Our curricular goals are what we aim to convey about the subject in the course. Our functional goals describe the attitudes and behaviors we hope our students will adopt in using calculus to approach scientific and mathematical questions. Starting Points Calculus is fundamentally a way of dealing with functional relationships that occur in scientific and mathematical contexts. The techniques of calculus must be subordinate to an overall view of the questions that give rise to these relationships. Technology radically enlarges the range of questions we can explore and the ways we can answer them. Computers and graphing calculators are much more than tools for teaching the traditional calculus. The concept of a dynamical system is central to science. Therefore, differential equations belong at the center of calculus, and technology makes this possible at the introductory level. The process of successive approximation is a key tool of calculus, even when the outcome of the process--the limit--cannot be explicitly given in closed form. Curricular Goals Develop calculus in the context of scientific and mathematical questions. Treat systems of differential equations as fundamental objects of study. Construct and analyze mathematical models. Use the method of successive approximations to define and solve problems. Develop geometric visualization with hand-drawn and computer graphics. Give num
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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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Learning Statistics with R: A tutorial for psychology students and other beginners
Danielle Navarro · Danielle Navarro · 2018
Learning Statistics with R covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software. The book discusses how to get started in R as well as giving an introduction to data manipulation and writing scripts. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, t-tests, ANOVAs and regression. Bayesian statistics are covered at the end of the book.
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Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students
Jason Lachniet · Jason Lachniet · 2017
This brief book provides a noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.
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Linear Algebra with Applications
W. Keith Nicholson · Lyryx · 2023
The aim of this textbook is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work. The content has enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners, whereas Chapters 5–9 contain a second semester course. The textbook is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A).
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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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Precalculus
Thomas Tradler; Holly Carley · CUNY Academic Works · 2015
These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems. This course in precalculus has the overarching theme of “functions.” This means that many of the often more algebraic topics studied in the previous courses are revisited under this new function theoretic point of view. However, in order to keep this text as self contained as possible we always recall all results that are necessary to follow the core of the course even if we assume that the student has familiarity with the formula or topic at hand. After a first introduction to the abstract notion of a function, we study polynomials, rational functions, exponential functions, logarithmic functions, and trigonometric functions with the function viewpoint. Throughout, we will always place particular importance to the corresponding graph of the discussed function which will be analyzed with the help of the TI-84 calculator as mentioned above. These are in fact the topics of the first four (of the five) parts of this precalculus course. In the fifth and last part of the book, we deviate from the above theme and collect more algebraically oriented topics that will be needed in calculus or other advanced mathematics courses or even other science courses. This part includes a
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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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Abstract Algebra: Theory and Applications
Thomas Judson · University of Puget Sound · 2016
This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly. Until recently most abstract algebra texts included few if any applications. However, one of the major problems in teaching an abstract algebra course is that for many students it is their first encounter with an environment that requires them to do rigorous proofs. Such students often find it hard to see the use of learning to prove theorems and propositions; applied examples help the instructor provide motivation. This text contains more material than can possibly be covered in a single semester. Certainly there is adequate material for a two-semester course, and perhaps more; however, for a one-semester course it would be quite easy to omit selected chapters and still have a useful text. The order of presentation of topics is standard: groups, then rings, and finally fields. Emphasis can be placed either on theory or on applications. A typical one-semester course might cover groups and rings while briefly touching on field theory, using Chapters 1 through 6, 9, 10, 11, 13 (the first part), 16, 17, 18 (the first part), 20, and 21. Parts of these chapters could be deleted and applications substituted according to the interests of the students and the instructor. A two-semester course emphasizing theory might cover Chapters 1 through 6, 9, 10, 11, 13
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A First Course in Linear Algebra
Ken Kuttler · Lyryx · 2023
This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra. All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text. Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.
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Introductory Statistics
Barbara Illowsky; Susan Dean; Daniel Birmajer; Bryan Blount · OpenStax · 2023
Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others. The material supports students with conceptual narratives, detailed step-by-step examples, and a wealth of illustrations, as well as collaborative exercises, technology integration problems, and statistics labs. The text assumes some knowledge of intermediate algebra, and includes thousands of problems and exercises that offer instructors and students ample opportunity to explore and reinforce useful statistical skills.
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Introduction to Real Analysis
William Trench · A.T. Still University · 2013
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.