Theorems:

There are two types of theorems: The first consists of theorems whose proofs are intricate and the student is expected to be able to state them and apply them, but is not expected to prove them. The second type consists of theorems which the student is expected to know how to prove. In the first type are: Van Kampen's Theorem, the existence of a universal cover, the excision property of singular homology theory, the isomorphism of singular and cellular homology. In the second type are: Lifting theorems for covering spaces, calculation of the fundamental group of the circle, the Mayer-Vietoris sequence, the Euler-Poincare formula, the Brouwer fixed point theorem.

Parts b and c are normally covered in detail in Math 114. Part a is often covered in Math 74; it can also be learned by reading independently under the direction of the student's committee.