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.

MAT 147: Topology
Approved: 2004-12-01 (revised 2013-06-01, G. Kuperberg)

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Topology, 2nd Edition by James Munkres; Pearson Publishing; $94.00.
Search by ISBN on Amazon: 978-0131816299

Prerequisites:

Completion of courses MAT 67 and MAT 125A.

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:

Additional Topics: Section 48—Baire Spaces; Section 49—A Nowhere—Differentiable Function; Section 50—An Introduction to Dimension Theory

Learning Goals:

The goal of Math 147 is to show students the modern topic of topology as it was developed in the early 20th century. It is an essential topic for students who wish to pursue mathematics further, because topology is important across almost all of modern mathematics. Students see a host of abstract new definitions that are not quite geometry, but rather a fellow traveller of geometry. They learn to write proofs and reason in this modern, geometric setting.

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 proof-based mathematics.

Assessment:

Weekly homework, midterms, and a final exam.