M375T Spring 2020
This schedule is tentative.


Week
 Dates
 Daily schedule
Homework
1
 Jan 20-24
 Plan for the week: We'll go over the syllabus, I'll give an overview of the course and we'll cover 1.1-1.4 from the textbook. (We actually covered 1.1-1.2 and maybe half of 1.3. )

Key Concepts: orbits, fixed points, periodic points, stable sets, phase portraits, graphical analysis, types of periodic points (hyperbolic, attracting, repelling, etc), local stable/unstable sets.

Extras:
(1) Using the contraction mapping theorem to solve differential equations (Picard iteration) and find roots of polynomials (Newton's method)
 
Mon: Martin Luther King III day. No class.
Tues: Our first class day.
Thurs:
Fri: Last day of official add/drop period. 		Homework #1

1.2: 1, 2
1.3: 3, 4, 6, 8, 10.
1.4: 1, 2, 3

Due: Thurs Jan 30
2
 Jan 27-
Jan 31
 Plan for the week: We'll cover 1.3-1.6 from the textbook. (We actually covered 1.3-1.5)
 
Key Concepts: types of periodic points (hyperbolic, attracting, repelling, etc), local stable/unstable sets, the quadratic family, Cantor sets, hyperbolic sets, symbolic dynamics.

Extras:
(1) For any compact subset X of R^n, there exists a surjective continuous map Cantor -> X.
(2) The Cantor set is the unique compact, totally disconnected, perfect metrizable space up to homeomorphism.
(3) The shift space is homeomorphic to the Cantor set.

Tues: Office hours 11-12:30 in RLM 9.154 (with Lewis Bowen).
Wed: Office hours 1-2pm in RLM 12.120 (with Frank Lin).
Thurs: Homework 1 due.
Fri: office hours 11-12noon in RLM 9.154 (with Lewis Bowen). 		Homework #2


1.5: 2, 3, 4, 6
1.6: 2, 4, 6.


Due: Fri Feb 7
3
Feb
3-7
 Plan for the week: We'll cover 1.5-1.8 from the textbook. Homework #2 will be due on Friday (online). Of course, you can turn it in early. Homework #2 has changed (you no longer have to do problems from 1.7). (We actually covered 1.5- 1.7)
 
Key Concepts:  the quadratic family, Cantor sets, hyperbolic sets, symbolic dynamics, topological conjugacy, topological transitivity, sensitive dependence on initial conditions, chaotic maps, C^r distance, C^r structural stability, fundamental domain.

Extras (topics we covered that aren't in the book):
(1) Baire category theorem and topological transitivity.

Tues: Office hours 11-12:30 in RLM 9.154 (with Lewis Bowen).
Wed: Last day to drop a class for a possible refund.
Thurs: Office hours 11-12:30 in RLM 9.154 (with Lewis Bowen).
Fri: Homework 2 due.  office hours 11-12noon in RLM 9.154 (with Lewis Bowen). 		Homework #3


1.7: 1, 2, 3
1.8: 1, 4
1.9: 2, 3.

Due: Fri Feb 14.
4
 Feb 10-14
 Plan for the week: We'll review a bit and cover 1.8-1.9 from the textbook.

Key Concepts:  topological transitivity, sensitive dependence on initial conditions, chaotic maps, C^r distance, C^r structural stability, fundamental domain.

Homework #3: (1.7) 1, 2, 3; (1.8) 1, 4; (1.9) 2, 3. Due Friday Feb 14.

Tues: Office hours 11-12:30 in RLM 9.154 (with Lewis Bowen).
Wed: Office hours 1-2pm in RLM 12.120 (with Frank Lin).
Thurs:
Fri: Homework 3 due.  office hours 9-10am in RLM 9.154 (with Lewis Bowen).
5
 Feb 17-21
 Tues: Early voting begins (for the primaries)

Thurs: I will hand out exam 1.
6
 Feb 24-
Feb 28
 Tues: Exam 1 is due.

Thurs:
7
 Mar 2-6
 Tues: Voting Day.

Thurs:
8
 Mar 9-13
 Tues:

Thurs:
9
 Mar 16-20
 Spring Break (no class)
10
 Mar 23-27
 Tues:

Thurs:

11
 Mar 30 - Apr 3
 Tues:

Thurs: I will hand out exam 2. If you would like expedited grading, please let me know and turn your exam in early.
12
 April 6-10
 Mon: Last day an undergraduate student may, with the dean’s approval, withdraw from the University or drop a class except for urgent and substantiated, nonacademic reasons. Last day an undergraduate student may change registration in a class to or from the pass/fail basis

Tues: Exam 2 is due.

Thurs:
13
 April 13-17
 Tues:

Thurs:
14
 April 20-24
 Tues:

Thurs:
15
 April 27-May 1
 Tues:

Thurs:
16
 May 4-8
 Tues:

Thurs: last class day.

17
 May 11-15
 Tues:

Thurs:

Fri:
18
 May
18-22
 Tues May 19: Final exam from 9am-12noon.