Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
Search by ISBN on Amazon: 9780131816299
Prerequisites:
Suggested Schedule:
Lecture(s) 
Sections 
Comments/Topics 
1 
12 
Topological Spaces 
2 
13 
Basis for a Topology 
3 
13 
Basis for a Topology 
4 
14 
The Order Topology 
5 
15 
The Product Topology 
6 
16 
The Subspace Topology 
7 
17 
Closed Sets and Limit Points 
8 
17 
Closed Sets and Limit Points (cont’d) 
9 
18 
Continuous Functions 
10 
18 
Continuous Functions (cont’d) 
11 
19 
Continuous Functions (cont’d) 
12 
20 
The Metric Topology 
13 
21 
The Metric Topology (cont’d) 
14 
21 
The Metric Topology (cont’d) 
15 
22 
The Quotient Topology 
16 
23 
Connected Spaces 
17 
24 
Connected Spaces of the Real Line 
18 
26 
Compact Spaces 
10 
26 
Compact Spaces (cont’d) 
20 
27 
Compact Subspaces of the Real Line 
21 
30 
The Countability Axioms 
22 
31 
The Separation Axioms 
23 
31 
The Separation Axioms (cont’d) 
24 
32 
Normal Spaces 
25 
33, 34 
The Urysohn Lemma & The Urysohn Metrization Theory 
26 
50 
An Introduction to Dimension Theory 
27 
Review 

28 
Review 

29 
Final Exam 
Additional Notes:
Learning Goals:
Mastery of this course gives students preparation for graduate school in mathematics or related areas. Or otherwise, they learn some of the most abstract ideas in the undergraduate mathematics curriculum. They also gain further experience with proofbased mathematics.
Assessment: