Math 250: Introduction to Linear Algebra


Instructor: Joseph Palmer
Email: j.palmer at rutgers.edu
Syllabus: link
Textbook: Elementary Linear Algebra by Spence, Insel & Friedberg. Either the "2nd edition" (ISBN 0-13-187141-2) or the "classic 2nd edition" (ISBN 0-13-468947-X)

Section B1: Mon, Tue, Wed, Thurs 10:10 - 12:10 in Hill 423 (starting May 28th)
Section B2: Mon, Tue, Wed, Thurs 12:20 - 2:20 in SEC 206 (starting May 28th)
Office Hours: Tuesday 9-10am and Wednesday 2:30-3:30pm (in my office, Hill 340)

Sakai: You can check your grades in this course with sakai. Please let me know as early as possible if you think there is an error on the sakai gradebook.

About this course:

This course is an introduction to linear algebra for students who haven't seen it before. It is not a proof-based course, but there will be some time spent on trying to understand the tools/techniques that we use. We will cover the following six general topics:

Grade Breakdown:

15% Quizzes
15% Homework
30% Midterm
40% Final Exam

Warning about summer courses:

Even though we only have six weeks for this course we will still cover all of the topics that are covered when this course is taught in the fall or spring. This means we will have to move relatively quickly, and these six weeks will have to be rather intense. Think of it this way: we are meeting around 9 hours a week for lecture, which is three times as much as this course meets during the usual semester - which means that you should be spending three times the usual amount of time working/studying for this course outside of lectures each week. It's a lot of work, but you will learn a lot of linear algebra in just six weeks so it will be worth it!

Quizzes:

There will be approximately one short quiz at the beginning of each class. It will be about 10 minutes and will cover the most fundamental and basic ideas from the previous lecture.

Homework:

Your homework assignments will be posted here throughout the semester. To keep up with the quick pace of a summer course there will be an assignment due 1-2 times per week.

The homework is to be turned in either as a scanned pdf or photos (pdf prefered) using the "Assignments" tool in sakai, and is due at noon each day that it is due.


Homework Assignments:

The problems in parenthesis are optional (not to be turned in). These assignments (without the optional problems) can be found on sakai as well.

Homework 1 (due Tuesday, June 4th at noon):
Section 1.1: 4, 18, 26, 27, 37, 38, 41, 46, 56, 71, 75, (79)
Section 1.2: 1, 5, 7, 10, 17, 29, 35, 45, 47, 53, 59, 62, (68, 76), 78
Section 1.3: 4, 5, 7, 9, 23, 41, 43, 47, 55, 57, 58, 64, 65, 70, 72, (81)
Section 1.4: 1, 5, 11, 17, 27, 35, 37, 53, 54, 58, 62, 64, 65, 70, 71, 74, 75, 77, 78, 81, 87, (88, 89)

Homework 2 (due Tuesday, June 11th at noon):
Section 1.6: 2, 3, 17, 23, 25, 29, 39, 45, 47, 49, 51, 55, 58, 60, 63, 65, (72)
Section 1.7: 1, 5, 14, 15, 19, 23, 39, 63, 65, 68, 71, 72, 81, (87, 89)
Section 2.1: 7, 9, 11, 27, 29, 34, 36, 38, 41, 46, 47, 49
Section 2.3: 1, 9, 11, 17, 19, 23, 25, 31, 33, 34, 35, 36, 42, 44, 46, 54, (59, 61), 67, 71, (83)
Section 2.4: 1, 7, 9, 27, 35, 36, 37, 38, 39, 40, 41, 48, 64
Section 2.5: 3, 9
Section 2.6: 1, 5, 9, 13, 33, 34, 41, 42, (43, 44, 45)

Homework 3 (due Thursday, June 13th at noon):
Section 3.1: 1, 9, 14, 21, 23, 29, 37, 43, 45, 49, 52, 54, 55, 56, 60, 62
Section 3.2: 13, 27, 39, 40, 41, 42, 43, 44, 48, 49, 51, 55, 56, 57, 67, 69, 70, 71, 72, (73, 74)

Homework 4 (due Thursday, June 20th):
Section 4.1: 1, 9, 11, 19, 21, 27, 29, 43, 44, 45, 46, 47, 48, 49, 50, 51, 57, 67, 72, (73, 74), 78, 81, 83
Section 4.2: 3, 7, 19, 21, 25, 27, 33, 34, 35, 36, 37, 38, 39, 40, (41-50), 53, 54, 59, 65
Section 4.3: 1, 3, 5, 7, 9, 15, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 59, 60, 63, 69, 73, (74), 75, (76, 77, 78), 83

Homework 5 (due Tuesday, June 25th):
Section 5.1: 3, 7, 13, 23, 41, 42, 43, 44, 46, 50, 51, 55, 56, 57, 58, 59, 60, 63, 66, (68), 72
Section 5.2: 1, 5, (9, 11), 13, 19, 21, 41, 53, 54, 55, 56, 57, 58, 59, 64, 65, 77, (79, 81), 85, 86
Section 5.3: 3, 7, 11, 15, 17, 19, 29, 30, 34, 35, 36, 37, 38, 39, 40, 49, 51, 55, 57, 73, (77, 78, 81, 82), 83
Section 5.5: 73, 79

Homework 6 (due Tuesday, July 2nd):
Section 6.1: 3, 7, 11, 13, 15, 17, 29, 37, 43, 49, 51, 53, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 76, 95, 97
Section 6.2: 1, 3, 7, 9, 13, 17, 21, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, (53)
Section 6.3: 1, 5, 9, 11, (17, 19), 21, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, (44-56), 59, 61
Section 6.4: 1, 3, 16, 17, 28, 29, 30, 31
Section 6.5: 3, 5, 7, 17, 21, 22, 23, 24, 25, 26, 27, 28, 29
Section 6.6: (3, 5, 15, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 35)
(Notice all problems from section 6.6 are optional, they are to help study for the final but you don't have to turn them in)

Tentative Schedule:

This will be updated throughout the semester to stay as accurate as possible.

           Date       Sections       Topics Homework due
1: T 5/28 1.1, 1.2 Matrices and linear systems ---
2: W 5/29 1.3, 1.4 Gaussian Elimination, Rank/Nullity, Span ---
3: Th 5/30 1.4, 1.6 Rank/Nullity, Span ---
 
4: M 6/3 1.7 Linear dependence/independence ---
5: T 6/4 2.1, 2.3 Matrix algebra, inverses HW1
6: W 6/5 2.4 More inverses ---
7: Th 6/6 2.5, 2.6 Block matrices, LU decomposition ---
 
8: M 6/10 3.1, 3.2 Determinants ---
9: T 6/11 4.1 Subspaces HW2
10: W 6/12 4.2, (4.3) Basis and dimension ---
11: Th 6/13 4.3 Column/null/row space HW3
 
  M 6/17 - Midterm (Chapters 1-4) ---
12: T 6/18 5.1, 5.2 Eigenvalues/vectors, char poly ---
13: W 6/19 5.2, 5.3 the characteristic polynomial ---
14: Th 6/20 5.3, 5.5 Diagonalization HW4
 
15: M 6/24 6.1, 6.2 Projection onto a line, Orthogonal sets ---
16: T 6/25 6.2, 6.3 Orthogonal sets HW5
17: W 6/26 6.3, 6.4 Gram-Schmidt, Orthog proj, Least squares ---
18: Th 6/27 6.5 Orthogonal matrices, diagonalization ---
 
19: M 7/1 6.5, 6.6 Orthogonal matrices, diagonalization ---
20: T 7/2 6.6 Spectral theorem HW6
  W 7/3 - Final Exam (12:30-3:30 in SEC 208) ---