# 35 Mathematics & Statistics

#### Linear Algebra

### Linear Algebra with Applications: Lyryx

The first version of this textbook was published in 1986 as a traditional textbook. The current version from 2018 was published as an open educational resource for a traditional or advanced introduction to the topics within linear algebra.

**Includes**: Instructor resources: solution manual to exercises, and lecture slides.

*May suit: *MATH 1B03/1ZC3.

### Linear Algebra

This textbook has been positively reviewed by four math professors from American universities and the Mathematical Association of America.

**Includes**: Exercises, solutions, a lab manual, lecture slides, and includes applications of linear algebra.

*May suit: *MATH 1B03/1ZC3.

#### Calculus for Life Sciences

### Differential Calculus for the Life Sciences

This textbook was written by a math professor at the University of British Columbia and is currently used as a textbook for introductory calculus courses for life sciences undergraduates.

**Includes**: Exercises and solutions to selected problems.

*May suit: *MATH 1LS3/1LT3.

### Calculus for the Life Sciences: A Modelling Approach Volume 1

This textbook was written by two professors at Iowa State University with the goal introducing students to scientific modeling. This course aims to teach students the necessary skills and concepts from a traditional physical sciences course, while explaining the applications of calculus to the life sciences.

**Includes**: Exercises, solutions to select problems, and MATLAB exercises.

*May suit: *MATH 1LS3/1LT3.

#### Calculus

### Calculus: OpenStax Volumes 1-3

Volume 1 concepts: functions, limits, derivatives, and integration

Volume 2 concepts: integration, differential equations, sequences and series, and parametric equations and polar coordinates

Volume 3 concepts: parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations

**Includes**: Exercises and answers. Volume 1 has been faculty-reviewed, adopted, is accessible, and has ancillary resources. Volume 2 has been adopted, has ancillary resources, and is accessible. Volume 3 is accessible and has ancillary resources. Adopt and adapt these volumes at the links above on Volumes 1, 2, and 3, respectively.

*May suit: *MATH 1A03/1AA3, 1X03/1XX3, 1ZA3/1ZB3, 1M03 and ISCI 1A24.

### Community Calculus (Single, Multivariable)

This online compilation of four calculus textbooks is frequently updated and has been used in courses. It has been positively reviewed by the Mathematical Association of America. It also covers early and late transcendentals.

**Includes**: Exercises, solutions, and WeBWorK problem sets.

*May suit: *MATH 1A03/1AA3, 1X03/1XX3, 1ZA3/1ZB3, 1M03 and ISCI 1A24.

### APEX Calculus

This text, or portions of it, has been adopted at a considerable number of American institutions to teach calculus, according to their website. These institutions include the Virginia Military Institute, where the author is an associate professor of mathematics.

**Includes**: Interactive graphics, exercises and solutions.

*May suit: *MATH 1A03/1AA3, 1X03/1XX3, 1ZA3/1ZB3, 1M03 and ISCI 1A24.

### Contemporary Calculus

This textbook was created as part of the Washington State Colleges’ Open Course Library Project, which received funding through the Gates Foundation. This text has been used by thousands of students within Washington State and was developed by a professor at Bellevue College.

**Includes**: Exercises, solutions to odd-numbered problems, and other resources.

*May suit: *MATH 1A03/1AA3, 1X03/1XX3, 1ZA3/1ZB3, 1M03 and ISCI 1A24.

### Calculus

Originally published through traditional means, this textbook is now available as an open educational resource. This text includes single and multivariable calculus and was written by a professor of mathematics at the Massachusetts Institute of Technology.

**Includes**: An instructor’s manual, a student study guide with exercises and select solutions, and links to a calculus video series by the author.

*May suit: *MATH 1A03/1AA3, 1X03/1XX3, 1ZA3/1ZB3, 1M03 and ISCI 1A24.

#### Statistics

### Introductory Statistics: Saylor

This peer-reviewed resource introduces statistical concepts, including: descriptive statistics, basic concepts of probability, discrete random variables, continuous random variables, sampling distributions, estimation, testing hypotheses, two-sample problems, correlation and regression, and chi-square and f-tests.

**Includes**: Exercises and answers.

*May suit: *STAT 2B03.

### Precalculus

*Precalculus* is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives and includes worked examples that demonstrate problem-solving approaches in an accessible way.

**Includes**: Chapter reviews, review exercises, practice tests and instructor resources (PowerPoint slides and solution manual).

*May suit: *MATH 1K03/1F03.

### Fundamentals of Business Mathematics

*Business Math 1* is aimed at university business students as an introduction to the mathematics required for the field of business. This textbook covers the fundamentals of business precalculus, finance, as well as the applications to general business management, human resources and the economy, marketing and accounting.

**Includes**: Examples, in-chapter exercises and key takeaways.

*May suit: *MATH 1MM3.

### Linear Algebra with Applications

*Linear Algebra with Applications* by W. Keith Nicholson, traditionally published for many years is now being released as an open educational resource and part of Lyryx with Open Texts! Supporting today’s students and instructors requires much more than a textbook, which is why Dr. Nicholson opted to work with Lyryx Learning.

Overall, the aim of the 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.

**Includes**: Summaries, examples, supplementary exercises and instructor resources (solution manual to exercises and lecture slides).

*May suit: *MATH 1B03/1ZC3.

### Introductory Statistics

*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.

**Includes**: Examples, in-chapter exercises, summaries, practice/homework questions, collaborative exercises, technology integration questions, statistics labs and instructor resources (PowerPoint slides and solution manual).

*May suit: *STATS 1LL3/2B03.

### 3D Interactive Plots for Multivariate Calculus

An open textbook created to improve both teaching and learning vital concepts and techniques in multivariable calculus, one of the fundamental courses across the undergraduate curriculum in science and engineering. The goals of this resource are to help learners develop their geometric intuition about abstract and complex mathematical concepts (e.g., partial derivatives, multiple integrals, vector fields), and train them to make connections between concepts visually (e.g., connecting “vectors” in mathematics with “magnitude” and “direction” in physics) in order to more fully understand engineering, physics and mathematical problems (e.g., differential equations) in their subsequent STEM coursework.

**Includes**: Interactive 3D graphs and self-checking questions with answers.

*May suit: *MATH 1AA3/1LT3/1XX3/1ZB3.

### Mathematics LibreTexts

A collection of open textbooks, assignments, and other educational resources on mathematical subjects.

### Statistics LibreTexts

A collection of open textbooks, assignments, and other educational resources on statistics.

### Book of Proof (Third Edition)

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 mathematic.

**Includes**: Video lectures, sample tests, examples (with solutions) and exercises.

*May suit: *MATH 1XA3.

### Applied Discrete Structures

An open content discrete mathematics textbook in three form factors.

**Includes**: Examples, exercises, and videos.

*May suit: *MATH 1B03/1ZC3/1LS3 and COMPSCI 1DM3.

### Calculus for the Life Sciences: A Modeling Approach Volume 2

In this textbook, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus.

**Includes**: Examples, and end-of-section exercises (with suggested solutions).

*May suit: *MATH 1LT3.

### Discrete Mathematics – An Open Introduction (3rd Edition)

*Discrete Mathematics: An Open Introduction* is a free, open source textbook appropriate for a first or second year undergraduate course for math majors. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado, and now contains a number of features that should support its use as a primary textbook. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way, proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.

**Includes**: Investigate activities, examples (with solutions), exercises (with solutions), summaries and instructor resources available upon request. Email oscar.levin@unco.edu for access to instructor resources.

*May suit: *MATH 1B03/1ZC3/1LS3, COMPSCI 1DM3, SFWRENG 2DM3/2FA3, and ENGTECH 3DM3.

### Matrix Algebra with Computational Applications

*Matrix Algebra with Computational Applications* is a collection of Open Educational Resource (OER) materials designed to introduce students to the use of Linear Algebra to solve real-world problems. Students need to have strong Python programming skills. Students will leverage these coding skills to write programs that use Linear Algebra to solve science and engineering problems.

**Includes**: In-class assignment, pre-class assignment, videos and examples.

*May suit:* MATH 1B03/1ZC3.

### CLP Calculus Textbooks

A collection of calculus textbooks and problem books developed by the University of British Columbia. The textbooks and problem books cover differential calculus, integral calculus, multivariable calculus, and vector calculus.

**Includes**: Exercises (of 3 stages), examples and instructor resources (lecture slides).

*May suit:* MATH 1LS3/1LT3, 1A03/1AA3, 1ZA3/1ZB3/1ZB3.

### Probability and Statistics – The Science of Uncertainty (Second Edition)

This book is an introductory text on probability and statistics, targeting students who have studied one year of calculus at the university level and are seeking an introduction to probability and statistics with mathematical content. Where possible, we provide mathematical details, and it is expected that students are seeking to gain some mastery over these, as well as to learn how to conduct data analyses. All the usual methodologies covered in a typical introductory course are introduced, as well as some of the theory that serves as their justification.

**Includes**: Examples, exercises, problems, challenges, discussion topics, summaries, computer exercises, computer problems, answers to odd-numbered exercises and an instructor solution manual.

*May suit: *STATS 2D03.

### Learn Statistics with R

*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.

**Includes**: Examples, summaries and data sets.

*May suit: *STATS 2B03, PNB 2XE3/3XE3, ARTSSCI 2R03, COMMERCE 2QA3, EARTHSC 2MB3, ECON 2B03, ENVIRSC 2MB3, GEOG 2MB3, and HTH SCI 2A03/2GG3.

### Active Calculus

*Active Prelude to Calculus*, *Active Calculus*, and* Active Calculus Multivariable* are free, open-source texts designed for a more active learning experience for students. Every section of each text has engaging activities for students to complete before and during class, as well as exercises that challenge students to connect and assimilate core concepts.

**Includes**: Examples, activities (with answers), interactive graphs, summaries, exercises (with answers) and lab manual.

*May suit: *MATH 1M03, 1LS3/1LT3, 1A03/1AA3, 1X03/1XX3, 1ZA3/1ZB3, 2X03/2XX3, 2Z03/2ZZ3 and ISCI 1A24.

### A Friendly Introduction to Mathematical Logic

At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary’s user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study.

**Includes**: Examples and exercises.

*May suit: *MATH 3GR3/4L03/4LT3.

### Math in Society

*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 quantitative literacy 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.

The HTML version can be accessed at https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_in_Society_(Lippman).

**Includes**: Examples, Try it now activities (with answers), exercises, solutions to selected exercises and video playlist.

*May suit: *MATH 1MM3.

### Number Theory: In Context and Interactive

*Number Theory: In Context and Interactive* is a free textbook for an upper-level number theory course, with a clear vision to expose students to the connections to all areas of mathematics. There are many exercises, both proof-based and computational, and nearly every concept can be visualized or experimented with using the open source mathematics software SageMath.

**Includes**: Exercises, examples and questions.

*May suit:* MATH 3H03.