# THE MATHEMATICAL WORKS OF Dr. G.

This site contains information for all of

Dr. Chuck Garner’s mathematics teaching and his mathematics books, including the new book Discrete Mathematics.

Scroll down for information on the books.

Click the menu items above for information on the courses.

# WELCOME!

I am Chuck Garner and I teach mathematics at Rockdale Magnet School for Science and Technology in Conyers, Georgia. This site is the portal to access classroom pages for the mathematics classes I teach, and much more.

I am the sponsor of the award-winning Rockdale Magnet Math Team, the director of the popular Rockdale Mathematics Competition, and author of a number of books (featured below).

# AP Precalculus: The Teacher'sCompendium

NEW! Published May 2024

This 468-page book is a collection of lessons and activities for every topic in the AP Precalculus course that will be assessed on the AP exam. Each lesson or activity comes with full solutions, a homework assignment with solutions, sample multiple choice items, and the author’s reflection on teaching the lesson or facilitating the activity. This compendium also includes a sample unit test for each of the 3 units, a detailed assessment writing guide, and sample pacing for 4 different school calendars. This book provides a complete curriculum for the entire school year!

Also available is a Student Edition that includes only the lessons, activities, and homework.

## MASTERING COMPETITION MATHEMATICSVolume 1: Functions& Polynomials

NEW! Published May 2024!

This is the first volume in a series that prepares middle and high school students for any mathematics competition. The problems contained in the book are curated from actual competition problems from various high school mathematics tournaments in Georgia from the years 1987 to 2020. Each chapter includes expository remarks, important problem-solving techniques, theorems, and formulas, with examples and exercises. These are followed by extensive problems sets in each chapter, divided into Junior Varsity and Varsity problems. Full solutions to all problems are included.

*Volume 1: Functions & Polynomials*includes 1519 problems in six chapters: Chapter 1, Polynomials; Chapter 2, Functions; Chapter 3, Logarithms and Exponentials; Chapter 4, Complex Numbers; Chapter 5, Inequalities; and Chapter 6, Analytic Geometry. Chapters 7 through 12 contain solutions to the problems.

Paperback, 7.44 in by 9.68 inches, 553 pages, $68

##### Preview *Discrete Mathematics*

Download a pdf of the Contents, Preface, and selected sections of the textbook.

Preview## DISCRETE MATHEMATICS

A Gateway to the Mathematical Garden

**PUBLISHED JULY 2023**

*Discrete Mathematics: A Gateway to the Mathematical Garden*, is an introduction to finite and discrete mathematics. This book includes all the important and foundational mathematics to support the student learning finite mathematics for the first time: logic, set theory, number theory, proofs, combinatorics, and graph theory. The exposition helps the student-reader learn to think logically and reasonably about mathematical structures.

Discussions of cryptology, computer science, machine-readable codes, and operations research are used to give the student a sense of how the mathematics is applied. Throughout the book, examples illustrate the material and provide insight into the mathematical theory. The book is essentially self-contained. There are very few prerequistes aside from some mathematical maturity and familiarity with algebra.

Problems to help the student master the concepts are included at the end of each section. Each chapter concludes with a set of supplementary problems and a set of sample test questions.

This is also the only textbook written to align specifically with the Georgia Department of Education standards for Advanced Finite Mathematics course.

Click the image of the book cover above to make your purchase from Lulu.com.

Click the image above to make your purchase from Lulu.com.

##### Preview *Calculus: Dynamic Mathematics*

Download a pdf of the Contents, Preface, and selected sections of the textbook.

Preview## CALCULUS: DYNAMIC MATHEMATICS

Single and Multivariable

**Fourth Edition**

*Calculus: Dynamic Mathematics, Single and Multivariable*presents, in just under 700 pages, a complete calculus course for high school students. There are two big changes in the fourth edition. One change is the size: instead of a 6 inch by 9 inch book, this edition is 7 inches by 10 inches. The second is that the new edition is printed in color. Color is used to highlight important ideas and examples, and all the figures and graphs were redrawn to use color.

The thread that runs through the book is a justification of why we need calculus. The book begins with attempts to make predictions based on rates of change, and from there the idea of the derivative is developed. The initial attempts at using tables of data, graphs, and algebraic processes show the limitations of using rates of change without calculus. This gives the student a reason for knowing and studying limits and derivatives. Similarly, notions of area approximations are used to develop the idea of the definite integral, and notions of polynomial approximations stimulate the need for convergence tests of infinite series.

Concepts of linear algebra are introduced before any multivariable calculus concepts. The ideas of determinants, eigenvalues, and matrices justify some techniques in multivariable calculus, such as the Jacobian, the Lagrange multiplier, predator-prey differential equations, and substitution of variables in double integrals. Rather than rules being given without a reason why the rule exsits, everything is justified and all concepts are explained at the level of a senior high school student. These justifications sometimes appear in the text as inductive arguments, or more often as formal proofs.

Answers to nearly all the problems appear in the back of the book, as well as a list of useful formulas and an index.

## CALCULUS: DYNAMIC MATHEMATICS

For AB, For BC, For Multivariable

Fourth Editions - Approved textbook for the AP Course Audit

These three books are versions of Calculus: Dynamic Mathematics, Single and Multivariable specifically for students in

AP Calculus AB, AP Calculus BC, or a post-AP Multivariable Calculus course.

Calculus: Dynamic Mathematics, For AB, is adapted and excerpted from the first 7 chapters of the

*Single and Multivariable*book to meet the needs of students enrolled in AP Calculus AB. To make this a more lively calculus course, some topics not found in the AP Calculus AB curriculum are included: Euler's method, the shell method for volumes of solids of revolution, and the use of the differential to make approximations.##### Preview *Calculus: Dynamic Mathematics,For AB*

Download a pdf of the Contents, Preface, and selected textbook sections.

PreviewCalculus: Dynamic Mathematics, For BC, is the first 9 chapters of the Single and Multivariable book. This is designed to meet the needs of students enrolled in AP Calculus BC. To make this a more comprehensive calculus course, some topics not found in the AP Calculus BC curriculum are included: hyperbolic functions, the shell method and the surface area of a solid of revolution, and the root test for convergence of infinite series. This book is approved by College Board for the AP Course Audit!

##### Preview *Calculus: Dynamic Mathematics,For BC*

Download a pdf of the Contents, Preface, and selected textbook sections.

PreviewCalculus: Dynamic Mathematics, For Multivariable is the last 4 chapters of the Single and Multivariable book. This presents a complete multivariable calculus course in four major areas: linear algebra, partial derivatives, multiple integrals, and line and surface integrals. There is also a short concluding chapter on some aspects of differential equations. It is assumed that students have had a prerequisite single-variable calculus course, such as AP Calculus BC.

##### Preview *Calculus: Dynamic Mathematics, For Multivariable*

Download a pdf of the Contents, Preface, and selected textbook sections.

Preview#### Are you interested in a Teacher’s Guide and Solutions Manual?

You have to be a teacher or educator to get one! If you are, then send an email to cgarner at gctm dot org, with the subject “Teacher’s Guide”. The body of the email should include which Teacher’s Guide you want, your name, your school or other institution of learning, and the location (city, state) of your school or other institution of learning. Once your information is verified (that is, once I know you are a teacher and not a student trying to get your grubby little hands on the solutions to those tricky, tricky problems), then I will send you a link to purchase a print copy of the book. A pdf version is not, and never will be, available. Thanks!

## FIVE WEEKS TO A FIVE:

Preparation for the AP Calculus Exam

Click the image above to make your purchase from Lulu.com.

An AP Calculus Exam Preparation Book, in both AB and BC versions. Each book features 12 Lessons which provide focused review of every topic assessed on the AP Exam. Each Lesson includes 15 multiple-choice problems and 2 free-response problems in the style of the AP Exam.

Also included are FOUR full-length practice AP Calculus AB Exams in the AB Book, and four full-length AP Calculus BC Exams in the BC Book.

All the problems are new and none are found in any of my other books!

A complete

*Solutions Manual*is also available for each of Preparation Book: Click the image above to make your purchase from Lulu.com.

## The AP CALCULUS PROBLEM BOOK

**Now in its Fifth Edition**

This is the latest edition of the book hated by high school calculus students everywhere:

*The AP Calculus Problem Book*! This edition contains over 3000 problems! Yes, that’s three-thousand problems -- 50% more than the previous edition, which has been pirated and is available on the web at many different websites for free.The book also contains two practice end-of-chapter tests for each chapter, extra review problems, calculus labs, and answers to nearly all the problems. The free-response questions which appear in each end-of-chapter test have AP-style Scoring Guidelines in the back of the book as well.

##### Preview the*AP Calculus Problem Book*

*AP Calculus Problem Book*

Download a pdf of the Contents, Preface, and eight sample pages

PreviewThe two volumes together comprise a complete course in single and multivariable calculus.

## A YOUNG PERSON'S GUIDE TO

COMPETITION MATHEMATICS

This book is a joint effort between Debbie Poss, Don Slater, and myself. This book collects 10 year’s worth of wonderful problems from the annual Lassiter High School Math Tournament. The problems are arranged by topic, so students can learn from the book as well as using it for practice math tournament problems. Each chapter is devoted to one topic: Included are example problems, practice problems, full solutions, and explanatory remarks. Important formulas, methods, and techniques are presented, and proofs of theorems are included where they would be instructive.

##### Preview A Young Person's Guide to Competition Mathematics

Download a pdf of the Contents, Preface, and the entire first chapter.

Preview## The ROCKDALE MATHEMATICS

COMPETITION PROBLEM BOOK

This new edition of the book collects the competition papers from the 2007 through 2024 Rockdale Mathematics Competition. All problems from the middle school, junior varsity, and varsity levels are included, as well as full solutions to all problems. The Rockdale Mathematics Competition is structured like ARML, with a Team, Power, Relay, and Individual Round at each level. An Index and a list of award winners is included.

##### Preview The Rockdale Mathematics Competition Problem Book.

Download a pdf of the Contents, Preface, and an excerpt of the fourth chapter.

Preview# The GCTM STATE MATHEMATICSTOURNAMENT PROBLEM BOOKS

**The Georgia Council of Teachers of Mathematics sponsors Georgia's State Math Tournament Championship each year. All the problems, with complete solutions, are collected in seven volumes.**

They are also available as PDFs: Volumes 3 through 7 are $20; Volume 2 is $15; Volume 1 is FREE. (If you would like a preview, download the pdf of Volume 1.)

Clicking or tapping the cover image takes you to Lulu.com to purchase the print book; the PDF link is under the image.

All profits go to GCTM to support the State Math Tournament.