Basic Concepts of Mathematics
This book helps the student complete the transition from purely manipulative to rigorous mathematics. The clear exposition covers many topics that are assumed by later courses but are often not covered with any depth or organization: basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers (including consequences of the completeness axiom), fields, and basic properties of n-dimensional Euclidean spaces.
An Introduction to the Theory of Numbers
This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercis
NIST Metric Information and Conversions
This site provides background on the metric system and exercises to help students learn to think metric. It includes metric units and sports, metric activities associated with the Wright Brothers' flight experiments, and conversion tables for length, area, temperature, and volume.
Algebra
InterMath is a professional development effort designed to support teachers in becoming better mathematics educators. It focuses on building teachers' mathematical content knowledge through mathematical investigations that are supported by technology. InterMath includes a workshop component and materials to support instructors. For each of the following problems, consider how you would pose the same problem to your students. Would the wording need to change? Would you need to include more pictur
Topics in Calculus
This page emphasizes the practical concepts of calculus, and is intended to provide a new context for the student already familiar with much of the material. The emphasis is on how calculus can actually be used outside of the classroom, and how the language of calculus is important in many other disciplines. It features articles for download, on topics from exponential growth and decay to discontinuities, vector fields and differential equations. All of the articles include extensive notes, exam
Calculus without Limits (Lecture Notes for Applied Calculus)
This book introduces differentiability as a local property without using limits. The philosophy behind this idea is that limits are the a big stumbling block for most students who see calculus for the first time, and they take up a substantial part of the first semester.
A Summary of Calculus
This book includes notes to summarize Calculus.
Money Math: Lessons for Life
In these four lessons students learn: 1. How saving helps people become wealthy. They develop "rules to become a millionaire" as they work through a series of exercises, learning that it is important to: save early and often, save as much as possible, earn compound interest, try to earn a high interest rate, leave deposits and interest earned in the account as long as possible, and choose accounts for which interest is compounded often. This lesson assumes that students have worked with percents
Introduction to Economic Analysis
This book presents introductory economics ("principles") material using standard mathematical tools, including calculus. It is designed for a relatively sophisticated undergraduate who has not taken a basic university course in economics. It also contains the standard intermediate microeconomics material. 328 page pdf.
Calculus on the Web
COW is an internet utility for learning and practicing calculus. The principal purpose of COW is to provide you, the student or interested user, with the opportunity to learn and practice problems in calculus (and in the future other topics in mathematics) in a friendly environment via the internet. The most important feature of the COW is that you get to know whether your answer is correct almost immediately. It is as if you had a tutor looking over your shoulder and helping you along as you wo
From Algorithms to Z-Scores: Probabilistic and Statistical Modeling in Computer Science
The materials here form a textbook for a course in mathematical probability and statistics for computer science students. Computer science examples are used throughout, in areas such as: computer networks; data and text mining; computer security; remote sensing; computer performance evaluation; software engineering; data management; etc.
Elementary Linear Algebra & Solutions to Elementary Linear Algebra
This book is an introduction to linear algebra, based on lectures given by me over 17 years, in the (now defunct) first year course MP103 at the University of Queensland.
Calculus (CA Textbook)
This Internet resource provides introductory information, concept or skill development in Mathematics for grade 9, 10, 11, and 12 students who are at grade level in a single student situation. This text was initially written by David Guichard. The single variable material (not including infinite series) was originally a modification and expansion of notes written by Neal Koblitz at the University of Washington, who generously gave permission to use, modify, and distribute his work. New material
Whitman Calculus
This calculus book covers a fairly standard course sequence: single variable calculus, infinite series, and multivariable calculus. There is no chapter on differential equations.
Introduction to Probability
This is an introductory probability book. This book emphasizes the use of computing to simulate experiments and make computations.
Elements of Abstract and Linear Algebra
This is a foundational textbook on abstract algebra with emphasis on linear algebra.
Introductory Statistics: Concepts, Models, and Applications
The book, Introductory Statistics: Concepts, Models, and Applications, presented in the following pages represents over twenty years of experience in teaching the material contained therein. The high price of textbooks and a desire to customize course material for my own needs caused me to write this material. This Web text and associated exercises is a continuing project. Check back often for updates.
forall x: Introductory Textbook in Formal Logic
This book is an introduction to sentential logic and first-order predicate logic with identity, logical systems that significantly influenced twentieth-century analytic philosophy. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading.
A First Course in Complex Analysis
These are the lecture notes of a one-semester undergraduate course which we taught at SUNY Binghamton. For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated "from scratch." This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.
Mathematics Under the Microscope
This book inevitably asks the question "How does the mathematical brain work?" The author tries to reflect on the explosive development of mathematical cognition, an emerging branch of neurophysiology which purports to locate structures and processes in the human brain responsible for mathematical thinking. PDF file.
