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)