Reading materials and handouts

Studying and doing mathematics:

Materials supplementing the lectures:

Exam review materials:

Homework guidelines

How to study mathematics (shorter version)

How to study mathematics (longer version)

Here is an article on the history of group theory. And here is an article of the history of algebra, including the explanation of the etymology of the word algebra.

During our first class, we talked about symmetries of the square. Here is a more complete story. And here is the same story, but for an equilateral triangle.

Here is more on the symmetric group (with cool pictures).

Here is an article on the history of Lagrange’s Theorem. And this page lists some of its important consequences.

Here is an article about the classification of finite simple groups. And here is another. One of the groups in the classification is the monster group which we mentioned in class.

Here is an article on what being well-defined means. We've been encountering this notion in various contexts lately.

Here is an article about the significance of the quaternion group in physics.

We briefly mentioned Galois Theory in one class; here is a biography of Évariste Galois.

Here is an article about geometric group theory, a cool field of math where algebra and geometry come together. And here is an article about algebraic topology, another cool place where a kind of geometry called topology (that studies geometric objects but allows deformations) and algebra intersect.

First exam review (includes practice problems)

Second exam review (includes practice problems)

Final exam review (includes practice problems)