homepage: Dr. Carol JV Fisher Burns

title graphic image:  One Mathematical Cat, Please! an animated mathematical cat
animated gif
by Robin Senseney,
MHS Class of 2006

BY
CAROL J.V. FISHER

Ideas for anyone, grade 7 and up,
who wants to understand mathematics

You're about to learn that
x (“ex”) is to mathematics as “cat” is to English.
The hope is that the next time you find yourself faced with x,
you'll think:

One Mathematical Cat, Please!

and laugh a bit...
making mathematics a little less stressful,
and a little more fun.

for J
who wants me to say everything
first

copyright 1998 Carol J.V. Fisher


For a review of this book, click here!

This is not a true “web book”. The book contains lots of mathematics, and at the time I put this online, mathematical typesetting was not well supported on the web. The original book is typeset using TeX (the technical typesetting language used by the mathematical community), and I created “snapshots” of each page. To view and print these “snapshots”, you'll need the ability to work with portable document format (pdf) file types: Adobe Acrobat Reader is free and available for download at
http://www.adobe.com/products/acrobat/readstep2.html


NOTE:
This ‘original cat book’ (below) was filled out to become an entire First Course in Algebra.
If you go through that entire Algebra I course,
then you're guaranteed to get everything from the book below—plus lots more!

However, if you're trying to use my higher-level materials (e.g., Geometry or Algebra II)
without having gone through the Algebra I course,
then I highly recommend that you read this original cat book.

TABLE OF CONTENTS

Introduction

Brief Table of Ideas, Symbols, and Notation

English versus Mathematics
This diagram summarizes the language ideas discussed in the first section, The Language of Mathematics.

Table of Contents
This is a printable version of the Table of Contents, with page numbers.

  1. THE LANGUAGE OF MATHEMATICS (pages 1–10)
    expressions versus sentences; sentences have verbs and state a complete thought; conventions; definitions; simplifying an expression; connectives
    Solutions to Exercises: Chapter 1

  2. THE REAL NUMBERS (pages 13–22)
    the real numbers and where they live; living to the right or left of zero; size (distance from zero) versus order (left/right positioning); opposites; integers; averaging
    Solutions to Exercises: Chapter 2

  3. MATHEMATICIANS ARE FOND OF COLLECTIONS (pages 26–37)
    introduction to sets; membership in a set; finite versus infinite sets; notation used in connection with sets; the idea of "infinity"; interval notation
    Solutions to Exercises: Chapter 3

  4. HOLDING THIS, HOLDING THAT (pages 40–55)
    letters used to represent other objects—variables; variables "hold" objects; variables are used to state a general principle, represent a sequence of operations, represent an "unknown" quantity; solving a sentence
    Solutions to Exercises: Chapter 4

  5. I LIVE TWO BLOCKS WEST OF YOU (pages 58–71)
    order properties of the real numbers—position of one number relative to another; mathematical sentences used to describe order relationships; the phrases "greatest," "least," "at least," "at most"; describing a whole class of sentences in one fell swoop; equations versus inequalities; solution of a sentence in one variable; graph of a sentence; reading a sentence backwards
    Solutions to Exercises: Chapter 5

  6. NUMBERS HAVE LOTS OF DIFFERENT NAMES! (pages 75–91)
    different names can reveal various properties that a number has; theorems are to a mathematician as tools are to a carpenter; the power of adding zero and multiplying by one; simplifying an expression versus solving a sentence; unit conversion
    Solutions to Exercises: Chapter 6

  7. THESE SENTENCES CERTAINLY LOOK DIFFERENT (pages 94–109)
    comparing expressions versus comparing sentences; equality of expressions versus equivalence of sentences; connectives; truth tables; synonyms for "is equivalent to"; the mathematical words "and" and "or"
    Solutions to Exercises: Chapter 7

  8. TRANSFORMING TOOL #1 (the Addition Property of Equality) (pages 112–125)
    the Addition Property of Equality; facts versus commands; "for all" sentences; translating a theorem; preferred formats for solving a sentence; why the Addition Property of Equality is true; preferred format for checking solutions
    Solutions to Exercises: Chapter 8

  9. TRANSFORMING TOOL #2 (the Multiplication Property of Equality) (pages 128–138)
    the Multiplication Property of Equality; what goes wrong with multiplying by zero; undoing the last operation first; why the Multiplication Property of Equality is true
    Solutions to Exercises: Chapter 9

INDEX

SAMPLE QUIZZES:
Students at Miss Hall's School were given the following quizzes, to test their understanding of each chapter.