Search
Filters ▾
External
Teaching Mathematics at Secondary Level
Tony Gardiner · Open Book Publishers · 2016
Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles and concepts that need to be borne in mind by all teachers and textbook authors—but which are little appreciated in the UK at present. This study is aimed at anyone who would like to think more deeply about the discipline of ‘elementary mathematics’, in England and Wales and anywhere else. By analysing and supplementing the current curriculum, Teaching Mathematics provides food for thought for all those involved in school mathematics, whether as aspiring teachers or as experienced professionals. It challenges us all to reflect upon what it is that makes secondary school mathematics educationally, culturally, and socially important.
External
The Essence of Mathematics Through Elementary Problems
Alexandre Borovik; Tony Gardiner · Open Book Publishers · 2019
It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside. The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline. The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works.
External
Fundamentals of Matrix Algebra
Gregory Hartman · APEX Calculus · 2011
A college (or advanced high school) level text dealing with the basic principles of matrix and linear algebra. It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations. Numerous examples are given within the easy to read text. This third edition corrects several errors in the text and updates the font faces.
External
APEX PreCalculus
Amy Chapman; Meagan Herald; Jessica Libertini · APEX Calculus · 2017
This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.
External
Open Resources for Community College Algebra
Portland Community College Faculty · Portland Community College · 2018
Open Resources for Community College Algebra (ORCCA) is an open-source, openly-licensed textbook package (eBook, print, and online homework) for basic and intermediate algebra. At Portland Community College, Part 1 is used in MTH 60, Part 2 is used in MTH 65, and Part 3 is used in MTH 95.
External
College Algebra & Trigonometry
Richard Beveridge · Richard W. Beveridge · 2018
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.
External
Mathematics for Biomedical Physics
Jogindra Wadehra · Wayne State University Library System · 2022
Mathematics for Biomedical Physics is an open access peer-reviewed textbook geared to introduce several mathematical topics at the rudimentary level so that students can appreciate the applications of mathematics to the interdisciplinary field of biomedical physics. Most of the topics are presented in their simplest but rigorous form so that students can easily understand the advanced form of these topics when the need arises. Several end-of-chapter problems and chapter examples relate the applications of mathematics to biomedical physics. After mastering the topics of this book, students would be ready to embark on quantitative thinking in various topics of biology and medicine
External
Statistical Thinking for the 21st Century
Russell Poldrack · Russell Poldrack · 2018
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.
External
You're Smarter Than You Think: Statistics
Safaa Dabagh · Safaa Dabagh · 2026
You're Smarter Than You Think: Statistics is a free, openly licensed introduction to statistics written for community college students and designed from the ground up for neurodivergent and anxious learners. Every section follows the same six-step rhythm (Read This First, Let's Talk About It, Now We Name It, Watch It Work, Your Turn, Check Your Voice), and every chapter opens with a Math Skills warm-up so a missing arithmetic step never derails a big idea. The book is organized around the student learning outcomes shared by community college statistics courses: describing data, estimating with confidence, and testing claims. It covers data and sampling, graphs, center and spread, probability, distributions, the Central Limit Theorem, confidence intervals, hypothesis testing, two-sample tests, ANOVA, chi-square, and regression. Four free Technology Companions (R and RStudio, jamovi, StatCrunch, and the TI-84) carry every method into whatever software a course uses, each keyed chapter by chapter and packaged with ready-made datasets. Graphs, printable work space, answer keys, per-part formula sheets, and a cumulative final-exam prep are included throughout.
External
Python for Introductory Statistics
Simon Aman · City Colleges of Chicago · 2021
The purpose of this material is to provide an overview of the free programming language, Python, and a few of its software libraries that are most useful for improving Introductory Statistics students' learning and for providing an alternative statistical software package for those who perform statistical data analysis and plotting. This material, along with the companion workbook and a free web-based Python platform, could easily replace the use of other software packages and calculators in an Introductory Statistics course. Part I, Sections 1 to 4, covers the basics of the Python programming language. Part II, Sections 5 to 13, focuses on Python for introductory statistics, and Part III, Section 14, covers selected advanced statistics topics in Python. Additionally, there are demo video links accompanying key steps for further instruction. No prior programming knowledge is required or assumed.
External
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.
External
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.
External
A Contemporary Approach to Research and Statistics in Psychology
Klaire Somoray · Council of Australian University Librarians · 2023
This book is designed as a short and introductory resource specifically aimed to help students grasp key concepts typically found in undergraduate psychology statistics subjects. It was initially developed for online and intensive programs, which are becoming increasingly popular in psychology education. The book utilises jamovi, a free and open-source statistical software. This peer reviewed book is completely free to download, use, and adapt and it is released using the CC BY-NC 4.0 licence.
External
Functions, Trigonometry, and Systems of Equations
Vanessa Coffelt · Texas A&M University · 2025
This is the second edition of a Precalculus textbook designed specifically for Math 150: Functions, Trigonometry, and Systems of Equations at Texas A&M University.
External
Significant Statistics
John Russell · Virginia Tech Publishing · 2025
Significant Statistics: An Introduction to Statistics is intended for students enrolled in a one-semester introduction to statistics course who are not mathematics or engineering majors. It focuses on the interpretation of statistical results, especially in real world settings, and assumes that students have an understanding of intermediate algebra. In addition to end of section practice and homework sets, examples of each topic are explained step-by-step throughout the text and followed by a 'Your Turn' problem that is designed as extra practice for students. Significant Statistics: An Introduction to Statistics was adapted from content published by OpenStax including Introductory Statistics, OpenIntro Statistics, and Introductory Statistics for the Life and Biomedical Sciences. John Morgan Russell reorganized the existing content and added new content where necessary. Instructors reviewing, adopting, or adapting this textbook: please help us understand your use by filling out this form: https://bit.ly/stat-interest.
External
Mathematical Reasoning and Investigation
Simon James; Chris Rawson; Erin Cheffers · Deakin University · 2023
Mathematical Reasoning and Investigation is designed to help you develop the ability to use mathematics to solve the kinds of problems that don't come with answers in the back of the book. We like to think of it as a mathematics book for people who think they're not good at mathematics. The work will be useful for anyone wanting to develop their own skills in reasoning and problem solving using mathematics, and for teachers and preservice teachers hoping to help their students to develop these same skills.
External
Statistics with JASP: First Steps for Psychology Students
Rebecca Denniss; Stanislava Naneva · University of Sheffield · 2025
New to statistics software? This guide is designed just for you. Whether you are studying psychology or any subject that involves analysing data, this easy-to-follow introduction to JASP will help you get to grips with the basics—no previous experience needed. Originally written for first-year psychology students at the University of Sheffield, it walks you through everything from entering data and adjusting settings to running t-tests, correlations, and chi-square analyses. With clear explanations, practical tips, and helpful screenshots, this guide makes learning JASP simple and stress-free.
External
Quantitative Problem Solving in Natural Resources
Pete Moore · Iowa State University Digital Press · 2025
This book is a collection of resources focused on solving quantitative problems that non-mathematicians interested in biology and environmental sciences may find compelling. It is not intended as a guide to be followed through a series of skills, but rather as a resource to support the problem-solving process and help lower conceptual and computational barriers along the way.
External
MGF 1131: Mathematics in Context
Allison Godwin · LibreTexts · 2024
Textbook used by students in MGF 1131 at Northwest Florida State College.
External
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.