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There are 24 chapters in Understanding Mathematics: From Counting to Calculus . Some of the chapter titles are "Addition and Subtraction," "Fractions," and "Negative Numbers" (in the Elementary Mathematics section), "Functions," "Geometry," and "Trigonometry" (in the Intermediate Mathematics section), and "Logarithms," "The Derivative," and "The Integral" (in the Advanced Mathematics Section). Each of the 24 chapters is further broken down into short sections, and each section includes easy-to-understand explanations of the concept being presented, along with several examples. The examples are taught step by step, so the concepts are covered thoroughly. In Math Problems and Solutions Guide, there are several problems for the student to work, and these problems correspond to the sections in Understanding Mathematics: From Counting to Calculus.
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Topics include such things as fair division, time travel, maze threading, logic puzzles and paradoxes, famous math problems and solutions, cryptarithmetic puzzles, how to use and misuse maps, mathematical humor, symmetry and coloring as problem-solving strategies, error-correcting codes, some transfinite arithmetic, and topology of compact surfaces.
Understanding Mathematics: From Counting to Calculus can be used by nearly anyone since it covers all math topics from 1 st grade through college. It can be used as a supplement to another math program or as a refresher course for parents, and it can be used by itself as a math course if you add in the companion book, Math Problems and Solutions Guide. This book contains over 10,000 problems and solutions.