# Summer Courses

## Summer 2020

#### Geometry | Algebra | Euclid for Parents | The Intellectual Life

## Geometry: Introduction to Euclid

*9-12 Grade* :: *Online Class* :: Tutor – Daniel Maycock

During this 6-week seminar, we’ll take a close look at Book I of the *Elements*, in which Euclid lays out the foundation of his geometry. Book I lays out the fundamentals of high school geometry and covers 1) principles of proof, 2) constructions, 3) theorems, 4) triangles, 5) parallelism, 6) parallelograms, and 7) squares. We reach the climax of Book I during our last class, when we examine Euclid’s proof of the Pythagorean theorem.

This workshop is a great introduction to geometry and deductive logic and has no mathematical prerequisites. You may also consider counting this workshop as an addition to your students regular math for an Honors designation. Suggested weight: 1/4 credit. (See your state’s regulations, etc.)

**Required materials**

- Euclid’s
*Elements*(preferably the Green Lion Press edition) - Notebook (plain paper), pencil, compass

**Online Class:** 15 Seats available

**Schedule**

- Mondays & Wednesdays 1-2:30pm (EST)
- June 22 – July 29

**Cost: $105 ***(books & materials not included)*

## Algebra: Diophantus

*9-12 Grade* :: *Online class *:: Tutor – Daniel Maycock

This 6-week course is an exploration into a fascinating world of rhetorical algebra through the work of Diophantus of Alexandria. Diophantus was a Greek mathematician who lived some time between the 3rd and 4th century A.D. Although he is often called “The Father of Algebra,” his work is almost entirely absent from modern high school math curricula. Diophantus is ignored for two reasons: his work is difficult to understand and roughly corresponds to what is typically studied in Algebra 1. There are easier ways to study Algebra 1, but there may be no better way to study the relationship between ratio and equation.

Perhaps the greatest benefit of studying Diophantus is that students will learn to read and understand word problems. Word problems are a bane to many students, but Diophantus, lacking the efficiency of modern algebraic notation, wrote his problems almost entirely in words rather than symbols. Thus, once a student learns to work through problems in Diophantus’ “rhetorical algebra” traditional word problems will no longer be perplexing, and students will have learned invaluable skills of mathematical analysis.

It’s easy to understate the importance of Diophantus in the history of mathematics. Viete’s *Five Books of Zetetica* are an algebraic expansion of Diophantus’ Arithmetica. Even the mathematical giants like Euler and Fermat were intrigued by Diophantus problems and wrote a great deal about them.

This course seeks to introduce students to this important and overlooked mathematician while making Diophantus’ *Arithmetica* accessible to high school students.

*Note: Although the algebra itself is not more difficult than what is studied in Algebra 1, students must be prepared to read problems that appear more difficult than they are. This requires patience and the understanding that grasping these problem will take more time than grasping problems presented in Algebra textbooks.*

Suggested weight: 1/4 credit. (See your state’s regulations, etc.)

**Required materials:**

*Diophantus of Alexandria*by T. L. Heath (This text contains a translation of the*Arithmetica*that will serve as our primary text. )*Classical Mathematics: Diophantine Algebra*by Daniel Maycock- Euclid’s
*Elements*(preferably the Green Lion Press edition) - Mathematics for the Nonmathematician by Morris Kline
- Notebook

**Online Class:** 15 Seats available

**Schedule**

- Tuesdays & Thursdays 1-2:30pm (EST)
- June 23 – July 30

**Cost: ****$105 ***(books & materials not included)*

~~Euclid for Parents~~

This course is no longer available for summer 2020. If you are interested in this course for next year, please send me an email at *help@polymathclassical.com* and ask to be added to my email list. I send out updates a few times per year to announce my projects and upcoming seminars. Thank you!

*-Daniel Maycock*

*Adult* :: *Online* *Class* :: Tutor – Daniel Maycock

~~This 6-week course covers the first book of Euclid’s ~~~~Elements~~~~ with a special focus on how to use and teach ~~~~Classical Math ONE~~~~. During the course, we will explore the foundation of Euclid’s geometry while considering its relationship to contemporary high school mathematics. Special emphasis will be placed on teaching and study techniques, and each participant will receive a digital copy of our ~~~~Guidebook to Euclid’s ~~~~Elements~~~~: Book 1~~~~ with the accompanying Answer Key (this guidebook is something of a miniature version of ~~~~Classical Math ONE~~~~).~~

**Required materials**

- Euclid’s
*Elements*(Green Lion Press or Dover) - Notebook (plain paper), pencil, compass

**Online Class: **15 Seats available

**Schedule**

- Mondays & Wednesdays 3-4:30pm (EST)
- June 22 – July 29

**Cost: ****$105 ***(books & materials not included)*

## The Intellectual Life

*Adult *::* Online class hosted by Memoria Press *:: Tutor – Daniel Maycock ::

A.G. Sertillanges first wrote *The Intellectual Life* in 1920 as an aid for those called by God to be scholars. In this book, he presents the trials and joys of intellectual work along with the virtues and daily practices necessary to succeed. Sertillanges also reminds us what true success looks like: a life lived in willful obedience to God. Thus,* The Intellectual Life* deals not only with practical questions of how to organize ideas and time, but also tackles questions of sin, falsehood, and living a well-balanced life dedicated to discovering and sharing truth.

**Required Materials**

*The Intellectual Life*by A. G. Sertillanges

**Online Class:** 15 Seats Available

**Schedule**

- Fridays 1:00 – 3:00pm
- June 26 – July 31

**Cost: $105**

## REGISTER

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