Euclidean plane and its relatives
(View Complete Item Description)This book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalistic.
Material Type: Textbook
All resources in VIVA Curation October 2020
College Algebra & Trigonometry
(View Complete Item Description)This College Algebra text will cover a combination of classical algebra and analytic geometry, with an introduction to the transcendental exponential and logarithmic functions. If mathematics is the language of science, then algebra is the grammar of that language. Like grammar, algebra provides a structure to mathematical notation, in addition to its uses in problem solving and its ability to change the appearance of an expression without changing the value.
Material Type: Textbook
Introduction to Axiomatic Geometry
(View Complete Item Description)This book presents Euclidean Geometry and was designed for a one-semester course preparing junior and senior level college students to teach high school Geometry. The book could also serve as a text for a junior level Introduction to Proofs course.
Material Type: Textbook
Brief Calculus
(View Complete Item Description)This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all the end-of-chapter problems. For a more traditional text designed for classroom use, see Fundamentals of Calculus (http://www.lightandmatter.com/fund/). The focus is mainly on integration and differentiation of functions of a single variable, although iterated integrals are discussed. Infinitesimals are used when appropriate, and are treated more rigorously than in old books like Thompson's Calculus Made Easy, but in less detail than in Keisler's Elementary Calculus: An Approach Using Infinitesimals. Numerical examples are given using the open-source computer algebra system Yacas, and Yacas is also used sometimes to cut down on the drudgery of symbolic techniques such as partial fractions. Proofs are given for all important results, but are often relegated to the back of the book, and the emphasis is on teaching the techniques of calculus rather than on abstract results.
Material Type: Textbook
Abstract Algebra: Theory and Applications
(View Complete Item Description)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.
Material Type: Textbook
Introductory Statistics
(View Complete Item Description)Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs.
Material Type: Textbook
City Life - Inquiry and Problem Solving Exercise
(View Complete Item Description)Living in a big city like New York can be very challenging. City planning is an interdisciplinary enterprise where social scientists, humanists, psychologists, scientists, statisticians, citizens, politicians, etc. come together to offer solutions to improve quality of life in the city. To find such solutions, these people need clear and reliable (qualitative and quantitative) information about specific challenges that residents and visitors face For the variety of stakeholders in the city, many different things might be considered worthy of study, depending on their interests and needs regarding, e.g., employment, financial status, family size, healthcare, mobility, and education. For example, do you know whether your neighborhood issufficiently protected from a fire? What about other neighborhoods in the city? To what extent does a CUNY degree help a person gain employment in the City? In which ways do race or gender or sexual preference play a role in how people experience city life? Can these be quantified in dollar terms? Once you have identified a problem, write an essay that describes a question about city life that you believe is worthy of a statistical study.
Material Type: Textbook
WeBWorK Problems for OpenStax Introductory Statistics
(View Complete Item Description)These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform and correspond to chapters in OpenStax Introductory Statistics. They were created through a Round Eight Textbook Transformation Grant.
Material Type: Interactive
Think Bayes: Bayesian Statistics Made Simple
(View Complete Item Description)The book is appropriately comprehensive, covering the basics as well as interesting and important applications of Bayesian methods.
Material Type: Textbook
Lies, Damned Lies, or Statistics: How to Tell the Truth with Statistics
(View Complete Item Description)This is a first draft of a free (as in speech, not as in beer, [Sta02]) (although it is free as in beer as well) textbook for a one-semester, undergraduate statistics course. It was used for Math 156 at Colorado State University–Pueblo in the spring semester of 2017.
Material Type: Textbook
Introduction to Statistics
(View Complete Item Description)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.
Material Type: Textbook
Statistical Inference For Everyone
(View Complete Item Description)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.
Material Type: Textbook
Statistical Thinking for the 21st Century
(View Complete Item Description)Statistical thinking is a way of understanding a complex world by describing it in relatively simple terms that nonetheless capture essential aspects of its structure, and that also provide us some idea of how uncertain we are about our knowledge. The foundations of statistical thinking come primarily from mathematics and statistics, but also from computer science, psychology, and other fields of study.
Material Type: Textbook
Discrete Mathematics: An Open Introduction
(View Complete Item Description)Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring 2013, and have been used by other instructors as a free additional resource. Since then it has been used as the primary text for this course at UNC, as well as at other institutions.
Material Type: Textbook
Applied Discrete Structures
(View Complete Item Description)The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text.
Material Type: Textbook
Measure, Integration & Real Analysis
(View Complete Item Description)This book seeks to provide students with a deep understanding of the definitions, examples, theorems, and proofs related to measure, integration, and real analysis. The content and level of this book fit well with the first-year graduate course on these topics at most American universities. This textbook features a reader-friendly style and format that will appeal to today's students.
Material Type: Textbook
Solving Linear First-Order Differential Equations Bernoulli's (Almost) Variation of Parameters Method
(View Complete Item Description)Course material on solving linear first-order differential equations.
Material Type: Reading