Math 147: Topology

Spring 2013

Overview

This is an Inquiry Based Learning (IBL) course in Topology, covering geometric topology and the fundamental group. There is no text; indeed, it is the goal of the course for each student to write their own text in topology, using the IBL guide written by Francis Su.

Instructors

Dagan Karp
1267 Olin
Office hours: Tue 1:30-2:30 p.m., and open door

Course Format

The course "text" contains theorems, definitions and examples. The goal of each student is to prove all the theorems outside of class with the collaboration of classmates and instructor advice.

In class, students will take turns presenting proofs, while the other students determine if the proof is correct.

Text

We will follow the IBL topology notes of Francis Su, available in Sakai (linked below). You are forbidden from consulting any other Topology text during the course of the semester. The goal is to create and discover all proofs yourself or in collaboration with other students in the class (and hints from me).

Grading

Homework 25%
Class participation and presentations 25%
Final Exam 25%
Notebook and its theorems 25%

Required Materials

A loose leaf binder is required; this is to contain all written theorems and proofs. Also, you need a pack of white index cards, to be brought to class every day. These will be used to provide feedback on other students' presentations.

Homework

Between classes, you are expected to write up any theorems that you prove. These should be placed in your binder. I will inspect these from time to time, and they will be used in evaluating grades. The goal is for this binder to become your own text in Topology written throughout the semester.

Tutoring

Olivia Beckwith is generously serving as grader and tutor for this course. Her tutoring hours are Tuesdays, 7-9pm, in Platt.

Exams

There will be one final exam (and no midterm).

Sakai

We will use our Sakai site fairly heavily in conjunction with this class. In particular, you will find there in Course Resources, some history of IBL and the Moore method, and the course guide, which is written by Francis Su, and only intended for HMC distribution.

LaTeX

You are required to LaTeX your work, aside from diagrams, which may be hand drawn.

Disabilities

Students who need disability-related accommodations are encouraged to discuss this with the instructor as soon as possible.

Homework Assignments

  • HW #1. Due Wednesday, Jan 30.

    # 1.1, 2.17, 2.26, 3.2, 3.12.
    Read up to, and including, Section 3.3.

  • HW #2. Due Wednesday, Feb 6.

    # 3.13, 3.19, 3.21, 4.4, 4.23.
    Read up to, and including, Section 4.4.

  • HW #3. Due Wednesday, Feb 13.

    # 4.36, 5.2, 5.6, 5.9 (only show R_LL is normal for now), 5.10.
    Read up to, and including, Chapter 5.

  • HW #4. Due Wednesday, Feb 20.

    # 5.13, 6.16, 6.23, 7.1 (1 => 3 only), 7.7
    Read up to, and including, Section 7.1.

  • HW #5. Due Wednesday, Feb 27.

    # 7.14, 7.40, 7.42
    Read up to, and including, Section 7.5.

    HAND IN your NOTEBOOKS for evaluation! (The notebooks will go to me, and the assignment to the grader.)

      I will look over the notebooks and evaluate them based on the following criteria: content [10 pts] and organization [10 pts]. The folder should be made in such a way that, in 10 years, you can pull it off your shelf and understand what you did in class! For more details on my grading rubric:

      Content:
      10 pts = all theorems are written out carefully.
      7-9 pts = all theorems written out or sketched
      6 pts or less = various kinds of incompleteness

      Organization:
      10 pts = folder neatly organized, with notes, theorems, HW's separated by sections, and the Progress Sheet on top (with a completely updated list of theorems presented, proved, learned in class, etc.)
      7-9 pts = less neatly organized
      6 pts or less = sections missing, folder not neat

  • HW #6. Due Wednesday, Mar 6.

    # 7.23, 7.27, 7.28, 7.31, 7.44

  • HW #7. Due Wednesday, Mar 13.

    # 7.19, 7.21, 7.43, 8.1 (1) => (2), 8.1 (1) <=> (3)

  • No homework due Wednesday, Mar 20.

    SPRING BREAK

  • HW #8. Due Wednesday, Mar 27.

    # 8.4, 8.9, 8.12, 8.29, 8.31
    Read up to, and including, Section 8.3.

  • HW #9. Due Wednesday, Apr 3.

    # 8.34, 8.37, 9.6, 9.7 (4) => (1), 9.7 (3) => (4)
    Read up to, and including, Section 9.1.

  • HW #10. Due Wednesday, Apr 10.

    # 10.1, 10.3, 10.6, 10.7, 10.8.1
    Read up to, and including, Section 10.2.

  • HW #11. Due Wednesday, Apr 17.

    # 12.5, 12.9 1-4, 12.9 5-9, 12.12 1 and 2, 12.12 3 and 4
    Read up to, and including, Section 12.2.

  • HW #12. Due Wednesday, Apr 24.

    # 12.16, 12.26, 12.31, 12.33, 12.43
    Read up to, and including, Section 12.4.

    Note: For groups A and B, A*B is the free product of A and B. Since this material is assumed as background and is not included in the course text, feel free to read elsewhere about free products.

  • Due Wednesday, May 1.

    Notebooks Due!!
    Turn in your notebooks, keeping in mind the above guidelines.

  • Due Friday May 10 or Monday May 13.

    Final Exam
    Available from the mathematics department office on Friday May 3. Seniors due 5/10 at 3pm, others 5/13 at 3pm.