Math 0540: Honors linear algebra, Fall 2015
MWF 2-3 Smith-Buonanno Hall 201 (NOTE ROOM CHANGE)

Instructor: Melody Chan
office: 311 Kassar House
email: melody_chan+0540@brown.edu
course website: http://www.math.brown.edu/~mtchan/2015Fall_0540.html
office hours: Mondays 1-2, Wednesdays 10:30-12, and by appointment
TA: Claire Frechette
TA office hour: Tuesdays 4-4:50 Barus and Holley 153
graders: Claire Frechette and Kavi Duvvoori

Course description

This is a one-semester honors undergraduate course in linear algebra, the study of vector spaces and linear maps. It will be a fast-paced course, encompassing a theoretical and rigorous treatment of linear algebra. I will expect plenty of work outside of class from you, including homework assigned at the end of every class, and due once a week. I expect the course to be challenging and it is important that you do not fall behind. In return, I hope that your hard work will be rewarded with a good understanding of an interesting and important topic, and a taste of rigorous mathematical thinking and proof.

If you are unsure about whether to take this course, please feel free to discuss it with me.

Topics

Vector spaces and linear maps. Eigenvalues, eigenvectors, invariant subspaces. Inner product spaces, operators on inner product spaces. Trace and determinant. Additional topics, time permitting.

Required textbook

Axler, Linear algebra done right, 3rd ed, Springer, 2015.
This book is available on SpringerLink to students with a Brown ID here as a free PDF.
You can also follow that link to order your own copy for $24.99.
It's also available at the bookstore for $59.99 new.
Make sure you get the newest edition (3rd edition).

Supplementary textbook

Treil, Linear algebra done wrong. Click here to download a free PDF copy of this book. We will be covering Chapter 3 on determinants.

Important dates

First hour exam: Friday October 9
Second hour exam: Monday November 9
Final exam: December 21, 9AM

Homework

Homework will be assigned every class and will be due every Wednesday. Staple all your homework together and make sure it is organized and legible. Late homework will not be accepted. However, I will drop your lowest homework score.

Class Date Reading Homework assigned Homework due
1 Wed Sept 9 p. 1-10 p. 11 #1,2,12,13, A1 Wed Sept 16
2 Fri Sept 11 p. 12-24 p. 24 #1,7,8,11,20 Wed Sept 16
3 Mon Sept 14 p. 27-36 p. 37 #1,3,10,16 Wed Sept 16
4 Wed Sept 16 p. 39-42 p. 43 #4, 5, 8 Wed Sept 23
5 Fri Sept 18 p. 44-47, 51-53 p. 48 #1, 6, 12 Wed Sept 23
6 Mon Sept 21 p. 54-57, 59-62 #A2, p. 57 #4, p. 67 #1, 2 Wed Sept 23
7 Wed Sept 23 p. 63-64 p. 67 #9, 10, #A3 Wed Sept 30
8 Fri Sept 25 p. 65-66, 70-72 p. 67 #20, #A4, #A5 Wed Sept 30
9 Mon Sept 28 p. 72-78 #A6, #A7 Wed Sept 30
10 Wed Sept 30 p. 80-83, 86-88 p. 89 #9, 10, 16, 18, 20 Wed Oct 7
11 Fri Oct 2 p. 91-92, 95-96 p. 98 #1 Wed Oct 14
12 Mon Oct 5 p. 96-98 p. 100 #14, 18 Wed Oct 14
13 Wed Oct 7 p. 120-123 -- --
14 Fri Oct 9 Exam 1. Solutions Covers all homework, class material,
and reading from Classes 1-10		 --
15 Wed Oct 14 p. 124-128, 131-133 p. 129 #6, p. 139 #6 Wed Oct 21
16 Fri Oct 16 p. 134-138, 143-145 p. 139 #8, 9, 14, p. 161 #16 (part (e) is optional) Wed Oct 21
17 Mon Oct 19 p. 146-152 p. 153 #1(a), 3, 4 Wed Oct 21
18 Wed Oct 21 p. 155-160 p. 153 #9, p. 160 #1, 2, 7 Wed Oct 28
19 Fri Oct 23 Treil's book p. 75-79 Treil p. 85 #3.1, 3.2, 3.3 and A8 Wed Oct 28
20 Mon Oct 26 Treil's book p. 40-45, 79-82 A9 Wed Oct 28
21 Wed Oct 28 Treil's book p. 82-85 Treil p. 85 3.4, 3.5, 3.7 Wed Nov 4
22 Fri Oct 30 Treil's book p. 86-89 Treil p. 89 4.1, 4.2, 4.3, 4.4, p.96 7.1 Wed Nov 4
23 Mon Nov 2 Treil's book p. 90-94 Treil p. 95 5.4, 5.5, p. 97 7.5 Wed Nov 4
24 Wed Nov 4 back to Axler, p. 164-169 Axler p. 175 #4, 8, 13 Wed Nov 11
25 Fri Nov 6 p. 169-174 p. 175 #10, 22 Wed Nov 11
26 Mon Nov 9 Exam 2. Solutions Covers all homework, class material,
and reading from Classes 1-23		 --
27 Wed Nov 11 p. 180-184 A10, A11, p. 190 #5 Wed Nov 18
28 Fri Nov 13 p. 185-189 p. 190 #6, 7 Wed Nov 18
29 Mon Nov 16 Class cancelled. Please attend this -- --
30 Wed Nov 18 p. 193-196 p. 201 #1, 3, 14 Wed Dec 2
31 Fri Nov 20 p. 197-200 p. 201 # 11, 12 Wed Dec 2
32 Mon Nov 23 p. 203-208 p. 214 # 1, 2, 6 Wed Dec 2
33 Mon Nov 30 p. 207-214 A12 Wed Dec 2
34 Wed Dec 2 p. 217-222 p. 223 #1, 2, 9 Wed Dec 9
35 Fri Dec 4 p. 225-230, 233-235 A13, p. 231 #5, 6, p. 238 #7 Wed Dec 9
36 Mon Dec 7 p. 236-238, ATLA p. 5-6 p. 238 #5, 18 Wed Dec 9
37 Wed Dec 9 ATLA p. 6-13 (optional, ungraded) ATLA p. 13 C.1, C.2, C.5 --

Finals week schedule


Wednesday December 16, 2-3pm, extra office hour, Kassar 311.

Thursday December 17, 7-8pm, extra TA office hour, Smith Buonnano 201.
You can pick up any remaining homework at this office hour.
The room is reserved for longer so that you can stay and study if you want.

Sunday, December 20, 7pm-9pm or later, extra office hour, Smith Buonnano 201.
You can pick up any remaining homework at this office hour.
The room is reserved for longer so that you can stay and study if you want.

Monday, December 21, 9am-noon, Final Exam, Smith Buonnano 106.
The final exam is comprehensive and covers all reading, class material, and homework for the course.


Getting extra help

Please come to my office hours, Monday 1-2, Wednesday 10:30-12, Kassar 311.

TA Office Hour: Tuesdays 4-4:50, Barus and Holley 153.

Please check out the Math Resource Center. There are drop-in hours most Mondays through Thursdays 8-10pm in Foxboro Auditorium, Kassar House.

You can also request private tutoring through the math department by contacting Audrey Aguiar.

Grades

Homework (15%), two one hour exams (20% + 25%), final exam (40%).

Collaboration

You are welcome to collaborate with other students in the class on your homework. You are required to write up your solutions separately and write the names of the students with whom you worked on the assignment. (You may only use the Internet as a general reference, at the level of generality of Wikipedia.)

Accommodations for students with disabilities

Any student with a documented disability is welcome to contact me as early in the semester as possible so that we may arrange reasonable accommodations. As part of this process, please be in touch with Student and Employee Accessibility Services by calling 401-863-9588 or online at
http://brown.edu/Student_Services/Office_of_Student_Life/seas/index.html