Math 109a
Geometry and Topology
Fall 2011-12
MWF 10:00 AM, 159 Sloan
Course Description | Policies | Textbooks | Lecture Notes | Handouts | Homework | Sections

Instructor: Susama Agarwala, Sloan 276, 626-395-4347,
Office Hours: 
Mondays, 3 pm - 5 pm or by appointment

Grader: Edward Fan, Sloan 155,
Office Hours:  Tuesdays 7-8 pm



Instructor office hours for the week of September 3 moved to Tuesday September 4, 1-3 pm.

Midterm due date: Wednessday Oct 26

On the week of the 17th, I will spend October 19th answering any questions on the point set topology material we have covered. If there are more questions than class time allows, I will continue answering questions after class or by appointment. If there are not many questions, I will start on Homotopy theory.

In homework 3, problem 1, the space X is the disjoint union of two copies of the real line, and the topology is defined accordingly.

OCT 21, 3:15 PM. MIDTERM CORRECTION! Problem 3 on the midterm has been updated. Please make sure you have printed a recent version.

Nov 22 Homework 8 Due on Friday Dec 2

Nov 30 Review session in class on Friday, December 2. Please e-mail me any exercises that you want me to do in class by Thursday 5 pm.


Course Description

Math 109a is the first course in the math 109 sequence, Introduction to Geometry and Topology. In the first part of the course, we will develop ideas from general topology. This will include the definition of topological spaces and basic examples and constructions. We will study properties of spaces including connectedness and compactness, and we will briefly discuss the difficulties that can arise in general topological spaces.
In the remainder of the course, we will introduce some invariants from algebraic topology, including the fundamental group of a space and the homology groups of a space. We will discuss some preliminary concepts from group theory, including group presentations, and prove Van Kampen's theorem, which makes it possible to compute fundamental groups. We will study the simplicial and singular versions of homology theory. We will consider many examples.


Prerequisites: Ma 2 or equivalent, and Ma 108 must be taken previously or concurrently.
Grading Policy: Class participation 10%, homework 30%, midterm 30% and final exam 30 %. The class participation grade includes but is not limited to attendance, questions asked in class, outside of class, or in TA and instructors office hours.
Homework Policy: Homework is due at 1 p.m. sharp on Wednesdays, in the box for Ma 109 in the hallway outside the math office (Sloan 253). Each student is allowed one late homework, at the instructor's discretion. The instructor should be notified of the extension request at least 24 hours before the homework is due.


We will use "Topology" , James Munkres, Prentice-Hall, 2000. as a reference for the first part of the course. We will use Hatcher's "Algebraic Topology" (available at the author's webpage) as the textbook for the material in the second part of the course.

Lecture Notes

Date Description
Sept 26 Topologies, limits, examples Sections 12-18 (M)
Oct 3 Product, Metric, Quotient Topology; Seperability and Countability Axioms. Sections 19-22; 30-31 (M)
Oct 10 Connectedness and Compactness Chapter 3 (M)
Oct 21 Chaper 0: Cell Complexes, Appendix pp. 519-522 (H)
Oct 24 Chaper 0 (H) Section 51, 55 (M)
Oct 24 Chaper 1.1 (H) Section 52, 54 (M)


Date Description


Due Date Homework  Solutions
October 5, 2011 Homework 1 Solution
October 12, 2011 Homework 2 Solution
October 19, 2011 Homework 3 Solution
October 26 Midterm  
November 2, 2011 Homework 4 Solution
November 9, 2011 Homework 5 Solution
November 16, 2011 Homework 6 Solution
November 23, 2011 Homework 7 Solution
December 2, 2011 Homework 8 Solution
December 7, 2011 Final Solution

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