**MATH 52: LINEAR ALGEBRA**

**Barus-Holley 155, M-W-F 2:00 - 2:50pm**

Professor Steven Miller (sjmiller@math.brown.edu), Kassar House, Room 217, 863-7961

FINAL EXAM: DEC 17th, 2:00-5:00pm

FREE TUTORING: Math Resource Center

**COURSE DESCRIPTION:** Vector spaces, linear
transformations, matrices, systems of linear equations, bases, projections,
rotations, determinants, and inner products. Applications may include
differential equations, difference equations, least squares approximations, and
models in economics and in biological and physical sciences. MA 52 or MA 54 is a
prerequisite for all 100-level courses in Mathematics except MA 126.
Prerequisite: MA 10, MA 17, or MA 19. May not be taken in addition to MA 54.

We will cover most of the first six chapters of Gilbert Strang's
*Introduction to Linear Algebra, *as well as a few additional topics
such as linear programming and best fit approximations. Much emphasis will be
placed on efficient algorithms. *Please read the relevant sections before
class.*

**GRADING / HOMEWORK: **Homework 10%, Midterm 1 25%, Midterm
2 25%, Final 40%. Homework is to be handed in on time, stapled and legible.
Late, messy or unstapled homework will not be graded. I encourage you to work in
small groups, but everyone must submit their own homework assignment.

**EXAM DATES: First Midterm will be Monday, October 4th;
Second
Midterm will be Monday, November 15th (note the time change from Wed, Nov 10th). These dates may change; if so,
announcements will be made in class and on the web page.**

I've written over the years some notes for linear algebra. These are meant
to supplement the coursebook, not to replace it: **
NOTES ON LINEAR ALGEBRA. **
You can also check out the
webpage for the other
section of Math 52.

**HOMEWORK**

**Week One (9/8 - 9/10): **

**Read:**
Sections 1.1, 1.2, 2.1, 2.2, 2.3, 2.4

**HW: Due Monday 9/13:**
Page 17: #3, #8; Page 31: #19, #20, #29; Page 41, #12

**Week Two (9/13 - 9/17): **

**Read:**
Sections 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7

**HW: Due Monday 9/20:**
Page 41, #25; Page 50, #3, #15, #20, Page 60: #1ac, #5, #11ab, $14ab, Page 73:
#9, #24 (just the first A); Page 84: #1.

**Week Three (9/20 - 9/24): **

**Read:**
Sections 3.1, 3.2, 3.3

**HW: Due Monday 9/27:**
Page 108: #10, #17, #18, #20a, #26; Page 118: #1a, #9, #10, #21, #23, #30.

**Week Four (9/20 - 10/4): **

**Read:**
Sections 3.3, 3.4, 3.5

**HW: Due Monday 10/4:**
Study for in-class exam (Mon, Oct 4th); Page 119: #1ab (in addition to finding the free variables and the pivot
variables, find the nullspace of A, the column space of A and the row space of
A); Page 129: #8 (only find the special solutions to Rx = 0; do not solve y^T R
= 0).

**Week Five (10/1 - 10/5): **

**Read:**
Sections 3.3, 3.4, 3.5

**HW: Due Wednesday 10/13: **
Page 129: #12ab, #14 (you do not need to do #13, but you will need its result),
#15; Page 140: #33; Page 150: #1, #2, #11, #17abc, #25, #27.

**Week Six (10/11 - 10/15): **

**Read:**
Sections 4.1, 4.2

**HW: Due Monday 10/18: **
Page 161: #2, #13, #28 (just do for B, not for C); Page 171: #8, #17; Page 181:
#1a, #3a

**Week Seven (10/18 - 10/22): **

**Read:**
Sections 4.4, 5.1, 5.2

**HW: Due Monday 10/25: **Page 203: #5, #9, #20, and apply Gram-Schmidt to
the vectors v_{1} = (1,2,3,0), v_{2} = (1,1,1,1) and v_{3}
= (1,0,-1,1); Page 213: #1, #13 (just do the first matrix), #14; Page 225:
#2, #4.

**Week Eight (10/25 - 10/29): **

**Read:**
Sections 5.2, 5.3, 6.1

**HW: Due Monday 11/1: **Page 203: #10a (and find the matrix that projects
onto **a** and **b**), #11; Page 214: #17; Page 225: #10, #11, #19,
#29; Page 240: #1b, #6, #13

**Week Nine (11/1 - 11/5): **

**Read:**
Sections 6.1, 6.2, 6.3; **EXAM MONDAY,
NOVEMBER 15th (IN CLASS EXAM)**

**HW: Due Monday 11/8: **Page 253: #2, #3, #14, #27 (just for A), #32; Page
266: #1, #4, #5.

**Week Ten (11/8 - 11/12): **

**Read:**
Sections 6.4, 6.5; **EXAM MONDAY,
NOVEMBER 15th (IN CLASS EXAM)**

**HW: Due Monday 11/15: **Page 266: #7, #19, #23, #28; Page 290: #5, #6, #8.

**Week Eleven (11/15 - 11/19): **

**Read:**
Sections 6.5, 6.6, 6.3

**HW: Due Monday 11/22: **Page 302: #7, #14, #21, #24 (also find the angle of
rotation), #28; Page 310: #1, #17

**Week Twelve (11/22 - 11/22): **

**Read:**
Sections 6.3, 4.3

**HW: **Read 6.3, 4.3; review material from course. I've written some
supplementary notes, which are available HERE. We
have covered everything except the stuff on Jordan Canonical Form.

**Week Thirteen (11/29 - 12/3): **

**Read:**
Review course notes for exam, final

**HW: **For Wed or Friday, describe in as much detail as possible the
eigenvalues for Markov matrices (columns sum to 1, each entry is between 0 and
1). Practice Exam (computational, can only help you) is THIS THURSDAY in BH-141
(couldn't get 155) from 6-7pm. You have from 6-6:30 or 6:40 to take the exam,
and then we'll grade it immediately after. If you cannot make this time on
Thursday, email me.