Algebra was an Arabic synthesis of the algorithmic tradition of Indian mathematics and the geometric, proof-based tradition of the Greeks. Following the devastating Siege of Baghdad in 1258, this unified tradition survived in monasteries in northern Europe. The pages of knotted ornament in these monks’ illuminated manuscripts are among the most complex works of abstract decoration ever produced, and are rooted not in classical, Christian, or Arabic but rather Celtic tradition. In this course we will study the ongoing synthesis of these juxtaposed traditions, algebra and knots.
Folio 94 (verso) of the Lindisfarne Gospels
Music from The Harp of New Albion (1986) by Terry Riley
Folio 94 (verso) of the Lindisfarne Gospels by Eadfrith (ca. 700)

An Introduction to Knot Theory (110.431) Spring 2015

Instructor:Carl McTague
Lectures:MW 3–4:15pm in Krieger 304
Office Hours:T 3–4pm in Krieger 212
TA:Cong Ma
Text:Colin Adams, The Knot Book, American Mathematical Society, 2004 (Amazon)

Homework

Due
9 Feb: §1.1: 1.2, 1.4, 1.5, 1.6, 1.7.
§1.2: 1.8.
§1.3: 1.10, 1.11.
§1.4: 1.13, 1.15, 1.16, 1.17, 1.19.
§1.5: 1.21, 1.23, 1.25, 1.27, 1.29.
23 Feb: §2.2: 2.2, 2.3, 2.5, 2.7, 2.9.
§2.3: 2.10, 2.11, 2.12, 2.13, 2.14, 2.16
§2.4: 2.28, 2.29, 2.30
2 Mar: §3.1: 3.4, 3.5, 3.6, 3.9.
§3.2: 3.11, 3.12.
§3.3: 3.15.
23 Mar: §4.1: 4.2–4.12.
§4.2: 4.13–4.17.
§4.3: 4.19, 4.20, 4.22, 4.23, 4.25–4.29.
20 Apr: §5.1: 5.2, 5.4, 5.6, 5.8.
§5.2: 5.13, 5.14.
§5.4: 5.16, 5.18, 5.19, 5.20, 5.23, 5.24.b, 5.26, 5.27.
29 Apr: §6.1: 6.1, 6.2, 6.4, 6.5.
§6.2: 6.9–13.
§6.3: 6.14–21.
§6.4: 6.22–26.

Copyright © 2015 by Carl McTague