Digital library
Textbooks, references and open learning resources.
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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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Advanced High School Statistics
David Diez; Christopher Barr; Mine Çetinkaya-Rundel; Leah Dorazio · OpenIntro · 2019
We hope readers will take away three ideas from this book in addition to forming a foundationof statistical thinking and methods. (1) Statistics is an applied field with a wide range of practical applications. (2) You don't have to be a math guru to learn from real, interesting data. (3) Data are messy, and statistical tools are imperfect. But, when you understand the strengths and weaknesses of these tools, you can use them to learn about the real world. Textbook overviewThe chapters of this book are as follows: 1. Data collection. Data structures, variables, and basic data collection techniques. 2. Summarizing data. Data summaries and graphics. 3. Probability. The basic principles of probability. 4. Distributions of random variables. Introduction to key distributions, and how the normal model applies to the sample mean and sample proportion. 5. Foundation for inference. General ideas for statistical inference in the context of estimating the population proportion. 6. Inference for categorical data. Inference for proportions using the normal and chisquare distributions. 7. Inference for numerical data. Inference for one or two sample means using the t distribution, and comparisons of many means using ANOVA. 8. Introduction to linear regression. An introduction to regression with two variables. Instructions are also provided in several sections for using Casio and TI calculators.
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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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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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A Primer of Real Analysis
Dan Sloughter · Dan Sloughter · 2009
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.
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Introduction to Statistics
David Lane · David Lane · 2003
Introduction to Statistics is a resource for learning and teaching introductory statistics. This work is in the public domain. Therefore, it can be copied and reproduced without limitation. However, we would appreciate a citation where possible. Please cite as: Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University. Instructor's manual, PowerPoint Slides, and additional questions are available.
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Statistical Inference For Everyone
Brian Blais · Brian Blais · 2017
This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a course. It is freely available under the Creative Commons License, and includes a software library in Python for making some of the calculations and visualizations easier.
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Introductory Business Statistics
Thomas Tiemann · BCcampus · 2010
The book "Introductory Business Statistics" by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions. The author covers topics including descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. Using real-world examples throughout the text, the author hopes to help students understand how statistics works, not just how to "get the right number."
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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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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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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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A Computational Introduction to Number Theory and Algebra
Victor Shoup · Cambridge University Press · 2009
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 generali
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Combinatorics Through Guided Discovery
Kenneth Bogart · Kenneth P. Bogart · 2004
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 consists 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. There are problems that some people will solve quickly, and there are problems that will take days of thought for everyone. Probably the best way to use this book is to work on a problem until you feel you are not making progress and then go on to the next one. Think about the problem you couldn't get as you do other things. The next chance you get, discuss the problem you are stymied on with other members of the class. Often you will all feel you've hit dead ends, but when you begin comparing notes and listening carefully to each other, you will see more than one approach to the problem and be able to make some progress. In fact, after comparing notes you may realize that there is more than one way to interpret the problem. In this case your first step should be to think together about what the problem is actually asking you to do. You may have learned in school that for every problem you are given, there is a method that has already been taught to you, and you are supposed to figure out which method applies and apply it. That is not the case here. Based on some simplified examples, you will discover the method for yourself. Later on, you may recognize a pattern that suggests you should try to use this metho
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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.
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Introductory Statistics
Douglas Shafer; Zhiyi Zhang · Saylor Foundation · 2012
In many introductory level courses today, teachers are challenged with the task of fitting in all of the core concepts of the course in a limited period of time. The Introductory Statistics teacher is no stranger to this challenge. To add to the difficulty, many textbooks contain an overabundance of material, which not only results in the need for further streamlining, but also in intimidated students. Shafer and Zhang wrote Introductory Statistics by using their vast teaching experience to present a complete look at introductory statistics topics while keeping in mind a realistic expectation with respect to course duration and students' maturity level. Over time the core content of this course has developed into a well-defined body of material that is substantial for a one-semester course. Shafer and Zhang believe that the students in this course are best served by a focus on that core material and not by an exposure to a plethora of peripheral topics. Therefore in writing Introduction to Statistics they have sought to present only the core concepts and use a wide-ranging set of exercises for each concept to drive comprehension. As a result Introduction to Statistics is a smaller and less intimidating textbook that trades some extended and unnecessary topics for a better-focused presentation of the central material. You will not only appreciate the depth and breadth of exercises in Introduction to Statistics, but you will also like the close attention to detail that Shafer and Zhang have paid to the student and instructor solutions manuals. This is one of few books on the market where the textbook authors have written the solutions manuals to maintain the integrity of the material. In addition, in order to facilitate the use of technology with the book the authors included “large data set exercises,” where appropriate, that refer to large data sets that are available on the web, and for which use of statistical software is necessary.
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Basic Analysis: Introduction to Real Analysis
Jirí Lebl · Jirí Lebl · 2016
This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.
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OpenIntro Statistics
David Diez; Christopher Barr; Mine Cetinkaya-Rundel · OpenIntro · 2019
OpenIntro Statistics covers a first course in statistics, providing a rigorous introduction to appliedstatistics that is clear, concise, and accessible. This book was written with the undergraduate levelin mind, but it’s also popular in high schools and graduate courses.We hope readers will take away three ideas from this book in addition to forming a foundationof statistical thinking and methods. • Statistics is an applied field with a wide range of practical applications.• You don’t have to be a math guru to learn from real, interesting data.• Data are messy, and statistical tools are imperfect. But, when you understand the strengthsand weaknesses of these tools, you can use them to learn about the world.
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Book of Proof
Richard Hammack · Richard Hammack · 2018
This is a book about how to prove theorems. Until this point in your education, you may have regarded mathematics primarily as a computational discipline. You have learned to solve equations, compute derivatives and integrals, multiply matrices and find determinants; and you have seen how these things can answer practical questions about the real world. In this setting, your primary goal in using mathematics has been to compute answers. But there is another approach to mathematics that is more theoretical than computational. In this approach, the primary goal is to understand mathematical structures, to prove mathematical statements, and even to invent or discover new mathematical theorems and theories. The mathematical techniques and procedures that you have learned and used up until now have their origins in this theoretical side of mathematics. For example, in computing the area under a curve, you use the fundamental theorem of calculus. It is because this theorem is true that your answer is correct. However, in your calculus class you were probably far more concerned with how that theorem could be applied than in understanding why it is true. But how do we know it is true? How can we convince ourselves or others of its validity? Questions of this nature belong to the theoretical realm of mathematics. This book is an introduction to that realm. This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems,explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics. This text has been used in classes at: Virginia Commonwealth University, Lebanon Valley College, University of California - San Diego, Colorado State University, Westminster College, South Dakota State University, PTEK College - Brunei,
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Ethics in Law Enforcement
Steve McCartney; Rick Parent · BCcampus · 2015
In this book, you will examine the moral and ethical issues that exist within law enforcement. This book will also familiarize you with the basic history, principles, and theories of ethics. These concepts will then be applied to the major components of the criminal justice system: policing, the courts, and corrections. Discussion will focus on personal values, individual responsibility, decision making, discretion, and the structure of accountability. Specific topics covered will include core values, codes of conduct, ethical dilemmas, organizational consequences, liability, and the importance of critical thinking. By the end of this book, you will be able to distinguish and critically debate contemporary ethical issues in law enforcement.
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Sources of American Law: An Introduction to Legal Research
Beau Steenken; Tina Brooks · CALI's eLangdell® Press · 2024
At its most basic definition the practice of law comprises conducting research to find relevant rules of law and then applying those rules to the specific set of circumstances faced by a client. However, in American law, the legal rules to be applied derive from myriad sources, complicating the process and making legal research different from other sorts of research. This text introduces first-year law students to the new kind of research required to study and to practice law. It seeks to demystify the art of legal research by following a “Source and Process” approach. First, the text introduces students to the major sources of American law and describes the forms the various authorities traditionally took in print. After establishing this base, the text proceeds to instruct students on the methods they will most likely use in practice, namely electronic research techniques and the consultation of secondary sources. Sources of Law incorporates screencasts currently hosted on YouTube that actively demonstrate the processes described in the static text. Finally, the text illustrates how the different pieces come together in the legal research process. Sources of Law focuses on realistic goals for 1Ls to learn in a relatively small amount of instruction time, and so focuses mainly on the basics. It does introduce some advanced material so that 1Ls can recognize pieces of information they may encounter in research, but it does not fully cover researching materials outside the scope of the traditional 1L course. As such, it is best-suited for introductory legal research courses for 1Ls. What's New in the Eighth Edition: The Eighth Edition primarily expands Chapter 9’s discussion of the research process to compare currently available legal generative AI tools to previously existing research tools such as secondary sources and electronic citators. That expansion also addresses some of the AI tools’ limitations and further discusses how thoughtful evaluation of available re