Classical Mathematical Community: Materials

The canon of world class literature is well-known and well-taught. Less so the canon of great mathematical writing. So our initial project is one of textual archaeology, similar to the project of the first humanists. This page is a list of primary sources and secondary materials that support them.

Euclid's Elements

Euclid's Elements: All 13 Books in One Volume

Dana Densmore (Editor), T.L. Heath (Translation)

This is the edition we use at Ad Fontes for our Geometry course. We issue it to the students to keep so they can write in it and use it in their Algebra II course.

Amazon

D.E. Joyce's Euclid Website

D.E. Joyce, Editor (Clark University)

This website contains the full text of Euclid's Elements along with interpretive notes written by Joyce. It's a great source for when you need to look up a particular proposition to make sense of an argument your students are making.

Joyce's Website

Byrne's Euclid Website

Oliver Byrne (Surveyor of Her Majesty's Settlements in the Falkland Islands)

Euclid, but with pictures!

Byrne's Euclid Website

Nicomachus's Arithmetic

Diophantus's Arithemtic

Heath's Translation of Diophantus's Arithmetic

Sir Thomas L. Heath (Trinity College)

This is a scholarly edition of Diophantus with significant introductory material. It also includes a good translation of all of Diophantus's arguments, great fodder for teaching Arithmetic. I've gradually been annotating Diophantus's arguments for use with students.

Amazon Annotated Arguments (PDF)

Modern Sources and Papers

Patterns of Mathematical Argument

William Carey (Ad Fontes Academy)

This is a collection of discussion problems combined with a description of how I use them in my classroom. It's meant as an introduction for a teacher who's exploring teaching math as one of the humanities. What I've posted here is mostly the student facing part of the text. I've included two of the twelve problems fully. So as not to lead my students into temptation, I haven't posted the full teacher's edition, which explains in great detail how I use each of these problems and what you can expect from them. If you'd like that, shoot me an e-mail and I'll pass it along.

Patterns of Mathematical Argument (PDF)

Recounting the Rationals

Neil Calkin (Clemson University), Herbert Wilf (University of Pennsylvania)

This short paper in number theory offers a variety of mathematical arguments. It includes proof by contradiction, by induction, and a nice variety of pattern making and finding. It makes a nice introduction to modern mathematical writing. And it's short!

Recounting the Rationals (PDF) Supporting Materials (Zip Archive)

Arithmetic

Paul Lockhart (Saint Ann's School, Brooklyn)

This is a delightful book by Paul Lockhart that explores how number systems work. Accessible to anyone, particularly good for parents who consider themselves "not-math-people".

Amazon

Measurement

Paul Lockhart (Saint Ann's School, Brooklyn)

Another classic by Paul Lockhart that develops calculus in an intuitive and narrative way. This is a gold mine for good discussion problems. Lockhart peppers his narrative with questions (and no answers!) that prompt good mathematical conversation. I give this as the book award for Pre-Calculus every year.

Amazon