Introductory College Mathematics

Introductory College Mathematics: With Linear Algebra and Finite Mathematics is an introduction to college mathematics, with emphasis on linear algebra and finite mathematics. It aims to provide a working knowledge of basic functions (polynomial, rational, exponential, logarithmic, and trigonometric); graphing techniques and the numerical aspects and applications of functions; two- and three-dimensional vector methods; the fundamental ideas of linear algebra; and complex numbers, elementary combinatorics, the binomial theorem, and mathematical induction. Comprised of 15 chapters, this book begins with a discussion on functions and graphs, paying particular attention to quantities measured in the real number system. The next chapter deals with linear and quadratic functions as well as some of their applications. Tips on graphing are offered. Subsequent chapters focus on polynomial functions, along with graphs of factored polynomials; rational functions; exponential and logarithm functions; and trigonometric functions. Identities and inverse functions, vectors and matrices, and trigonometry are also explored, together with complex numbers, linear transformations, and the geometry of space. The book concludes by considering finite mathematics, with particular reference to mathematical induction and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

Intended to improve mathematics education at two-year colleges and other institutions offering lower division courses as well as to encourage more students to study mathematics, this publication presents the American Mathematical Association of Two-Year Colleges' (AMATYC's) standards for revitalizing the pre-calculus mathematics curriculum and stimulating changes in instructional methods. Following introductory sections, chapter 1 describes the goals and basic principles underlying the document, while chapter 2 presents standards for introductory college mathematics including seven standards related to intellectual development, seven related to curriculum content, and five related to pedagogy. This chapter also provides charts of guidelines for achieving the standards. Chapter 3 addresses issues of content and pedagogy related to the interpretation of the standards in the areas of mathematics foundation-building courses, technical programs, mathematics-intensive programs, liberal arts programs, and programs for prospective teachers. Chapter 4 reviews implications of the standards for faculty development and other departmental considerations; advising and placement; laboratory and learning center facilities; the use of technology; assessment of student outcomes; program evaluation; and articulation with high schools, other colleges and universities, and employers. Finally, chapter 5 covers implementation, including institutional recommendations, the role of professional organizations, proposed regional workshops, and the development of materials, while chapter 6 provides concluding remarks. (Contains 78 references.) (Sample math problems based on the standards are appended.) (KP)

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.