# HISTORY OF MATHEMATICS

## About the course

I designed, developed, and authored this course which was first taught during the 03-04 school year. The rationale for this course was simple: offer the magnet school students a math class that was not as intense as AP Calculus; that serves as an introduction to higher-level mathematics; and that my students (who will mostly be engineers, chemists, or biologists) will probably not ever repeat in college. Having had an unbridled interest in the history of mathematics for over 20 years, I knew I could create a course in the history of mathematics that met all the criteria.

When the course was originally accepted to be included on the state list of courses, I wrote all the QCC objectives for it. With the advent of the Georgia Performance Standards, I was required to write standards for the course so it could still be offered. These standards are posted here.

Originally a year-long course, it is now a semester course.

## The textbooks

The course topical outline was greatly influenced by Howard Eves’ two books Great Moments in Mathematics, although these books have never served as the course textbooks.

Originally I used the amazing textbook, The History of Mathematics: an Introduction, second edition, by Victor Katz. This is a fantastic scholarly work with lots of interesting problems. This was supplemented by The History of Mathematics: a Reader by John Fauvel and Jeremy Gray. The Reader contains excerpts of notable mathematics works (Newton’s “Algebra”, Gauss’ mathematical diaries, the introduction to Euler’s textbooks, etc.) which brings more life to the famous mathematicians and their works.

Unfortunately, as Katz’s book was not designed for the punishment of high school students, the books fell apart. After six years of holding the books together with tape, they were finally beyond saving. I took the opportunity to try a new textbook,

Math Through the Ages: a Gentle History for Teachers and Others, expanded 2nd edition, by William Berlinghoff and Fernando Gouvea. This is an easier read than Katz’s book, and offers projects and research paper ideas ideally suited for my students. (I no longer use The Reader since our copies are worn and the book is out-of-print.)

## The syllabus

The course syllabus is different from the other syllabi I write. Since the concept and content of the course was influenced by Eves’ books, I pick and choose sections, chapters, and readings from Math Through the Ages. These readings are often supplemented by photocopies of articles, webpages, a few pages from Katz’s book, or other sources.

I have taught this course every year since the 03-04 school year (with the sole exceptions of the 11-12 school year and the 19-20 school year).

## Course resources

At the beginning of each week, I give out a problem set that is then due seven days later. I used to call these “Weekenders” since students waited until the weekend to work on them. However, students actually waited until the last possible moment to complete these, so I now call them “Last-Minute Problems”. The majority of these problems come from Great Moments in Mathematics, from Eves’ textbook An Introduction to the History of Mathematics, sixth edition, or from William Dunham’s problem set which goes with his fabulous book, Journey Through Genius.

I re-worked my presentations and lesson plans for this course during the latter half of 2020. I was inspired to do so through reading John Stillwell’s book Yearning for the Impossible, and a re-watching of James Burke’s great 10-part documentary series The Day the Universe Changed. I added new lectures concerning the development of projective geometry through perspective, and extended lectures on Gauss, quaternions, and Cantor.

The general tone of the lectures has changed as well. Instead of disconnected, stand-alone lectures, I have attempted to craft a narrative that joins many lectures together.

Below are the presentation slides for the lectures in the first half of the course, all in pdf format.

13 The Blockhead

14 A New Viewpoint

15 From a Different Perspective

At the top of the page is the result of a research project given over nine academic years. Students were challenged to write a one-page paper summarizing the life and achievements of a mathematician. These were submitted in Word, converted to LaTeX, and the book above was created. I was so pleased with the work of the students that a book was created and each student in the class was given a copy. I never imagined this book would eventually swell to over 300 pages! Enjoy!