The goal of this book is to provide a basic understanding of mathematics at an intro to college level. The book is designed to go along with a course of Intro to College Math for those pursuing Nursing AAS or similar programs. It is also designed as a refresher for adult students going back into the classroom. The course is divided into four main sections: Arithmetic, Geometry, Algebra, and Statistics/Probability. This book is an expanded form of my lecture notes and includes extra explanations, examples, and practice. Solutions to practice sets are at the back of the book.

"Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.

This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. 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. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions.

The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.

Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course.This book is an open textbook; it can be read free online at http://www.opentextbookstore.com/mathinsociety/. Editable versions of the chapters are available as well.

Contents: A workbook containing 30 days of basic review exercises in preparation for college mathematics. Each daily section contains a short exercise set covering basic skills necessary to perform well in an introductory college math course. Focus has been placed on those skills which are difficult to retain without continued practice. The exercise collection in Part I is designed for skill enhancement in mathematics skills such as factoring, solving equations, understanding and using function notation, working with exponents and radicals, etc. Rather than being all-inclusive, the work strives to provide continued practice in the most fundamental skills necessary for successful college work. Daily work notes are provided in Part II that speak directly to the pertinent aspects of each day's exercise set. Brief and to the point, with examples when needed for clarity, these work notes add an extra dimension to help students stay on track and progress through the exercise sets. Part III contains a complete answer set. College students and their parents frequently discover that lack of college mathematical readiness requires an extra semester or even a year of college in order to earn a desired degree. A trend at colleges to attempt to remedy this situation is to offer on-campus "summer bridge" or "math boot camp" programs for entering students to alleviate this shortcoming. While effective, these programs are time-consuming and prohibitively costly for many students. In a similarly-designed approach, this workbook provides a cost-effective, self-study method to help students to stay current in mathematics and be prepared to "hit the ground running" when entering college. It is a worthy approach to help you or your child realize a successful start to a college career.

Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.

Accessible to all students with a sound background in high school mathematics, A Concise Introduction to Pure Mathematics, Fourth Edition presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually encountered at this level, such as the theory of solving cubic equations; Euler’s formula for the numbers of corners, edges, and faces of a solid object and the five Platonic solids; the use of prime numbers to encode and decode secret information; the theory of how to compare the sizes of two infinite sets; and the rigorous theory of limits and continuous functions. New to the Fourth Edition Two new chapters that serve as an introduction to abstract algebra via the theory of groups, covering abstract reasoning as well as many examples and applications New material on inequalities, counting methods, the inclusion-exclusion principle, and Euler’s phi function Numerous new exercises, with solutions to the odd-numbered ones Through careful explanations and examples, this popular textbook illustrates the power and beauty of basic mathematical concepts in number theory, discrete mathematics, analysis, and abstract algebra. Written in a rigorous yet accessible style, it continues to provide a robust bridge between high school and higher-level mathematics, enabling students to study more advanced courses in abstract algebra and analysis.