## Summer 2023

*Summer 2024 seminar listings will be posted Feb 2024.*

*Send Daniel an email at daniel@polymathclassical.com to be added to our email list, and you’ll get an email when the 2024 seminar listings go up.*

#### Seminars

### Geometry: Introduction to Euclid / Euclid for Parents

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

*(**This is a combined class for both high-school students and parents.)*

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 aside from Pre-Algebra. 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

- Limited to 15 seats

#### Schedule

- Tuesdays & Thursdays 10 – 11:30am (Eastern Time)
- June 20 – Aug 3 (
*no class on July 4, 11, 13*)

#### Cost

**$150***(books & materials not included)*

Register using the payment link below. After we receive your payment, Daniel will follow-up with you by email, so please make sure to provide a current email address when checking out. Thank you!

Each seminar has a 4-student minimum. If, 2 weeks before the start date, a seminar has fewer than 4 enlisted students, the seminar will be canceled and registration fees refunded.

*Classes are held on Zoom.*

#### Requirements

Any reasonably modern computer running MacOS, Windows, Linux.

Android and iOS devices are also supported, but not recommended.

### Diophantine Algebra

*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

- Limited to 15 seats

#### Schedule

- Tuesdays & Thursdays 1-2:30pm (Eastern Time)
- June 20 – Aug 3 (
*no class on July 4, 11, 13*)

#### Cost

**$150***(books & materials not included)*

Register by paying using the payment button below. After we receive your payment, Daniel will follow-up with you by email, so please make sure to provide a current email address when checking out. Thank you!

Each seminar has a 4-student minimum. If, 2 weeks before the start date, a seminar has fewer than 4 enlisted students, the seminar will be canceled and registration fees refunded.

*Classes are on Zoom.*

#### Requirements

Any reasonably modern computer running MacOS, Windows, Linux.

Android and iOS devices are also supported, but not recommended.