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.
Ensuring academic integrity in mathematical tasks presents a unique challenge, for university students and for their assessors, and one that hitherto has been under-examined. Drawing on her twenty years of experience in mathematics education, the recent academic integrity research literature, and on what students say about why misconduct occurs, the author examines this issue head-on.
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.
Publisher:
Council of Australian University Librarians
License:
CC BY-NC
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.
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.
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.
Business Mathematics was written to meet the needs of a twenty-first century student. It takes a systematic approach to helping students learn how to think and centers on a structured process termed the PUPP Model (Plan, Understand, Perform, and Present). This process is found throughout the text and in every guided example to help students develop a step-by-step problem-solving approach.
This version of YAINTT has a particular emphasis on connections to cryptology. The cryptologic material appears in Chapter 4 and §§5.5 and 5.6, arising naturally (I hope) out of the ambient number theory. The main cryptologic applications – being the RSA cryptosystem, Diffie-Hellman key exchange, and the ElGamal cryptosystem – come out so naturally from considerations of Euler’s Theorem, primitive roots, and indices that it renders quite ironic G.H. Hardy’s assertion [Har05] of the purity and eternal inapplicability of number theory. Note, however, that once we broach the subject of these cryptologic algorithms, we take the time to make careful definitions for many cryptological concepts and to develop some related ideas of cryptology which have much more tenuous connections to the topic of number theory. This material therefore has something of a different flavor from the rest of the text – as is true of all scholarly work in cryptology (indeed, perhaps in all of computer science), which is clearly a discipline with a different culture from that of “pure”mathematics. Obviously, these sections could be skipped by an uninterested reader, or remixed away by an instructor for her own particular class approach.
First Semester in Numerical Analysis with Julia presents the theory and methods, together with the implementation of the algorithms using the Julia programming language (version 1.1.0). The book covers computer arithmetic, root-finding, numerical quadrature and differentiation, and approximation theory. The reader is expected to have studied calculus and linear algebra. Some familiarity with a programming language is beneficial, but not required. The programming language Julia will be introduced in the book. The simplicity of Julia allows bypassing the pseudocode and writing a computer code directly after the description of a method while minimizing the distraction the presentation of a computer code might cause to the flow of the main narrative.
This is a free textbook teaching introductory statistics for undergraduates in Psychology. This textbook is part of a larger OER course package for teaching undergraduate statistics in Psychology, including this textbook, a lab manual, and a course website. All of the materials are free and copiable, with source code maintained in Github repositories.
