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)

Schedule: MWF 6-8:45pm in SEC-211 (starting May 30th)
Office Hours: 1-3pm Wednesdays and Fridays (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:

30% Homework and quizzes
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!

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 6pm (the start of class time) each day that it is due.
Homework Assignments:

The problems in parenthesis are optional (not to be turned in)

Homework 1 (due Wednesday, June 6th):
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)
Section 1.6: 2, 3, 17, 23, 25, 29, 39, 45, 47, 49, 51, 55, 58, 60, 63, 65, (72)

Homework 2 (due Monday, June 11th):
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)

Homework 3 (due Friday, June 15th):
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)
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 Friday, June 22nd):
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 Wednesday, June 27th):
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 3rd):
NOTICE DUE ON TUESDAY!

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

Tentative Schedule:

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

           Date       Sections       Topics Homework due
1: W 5/30 1.1-1.3 Matrices and linear systems ---
2: F 6/1 1.4, 1.6 Gaussian Elimination, Rank/Nullity, Span ---
 
3: M 6/4 1.7, 2.1 Linear dependence/independence, homogenous systems ---
4: W 6/6 2.1, 2.3 Matrix algebra, invertability HW1
5: F 6/8 2.4 - 2.6 Inverses, LU decomposition ---
 
6: M 6/11 3.1, 3.2 Determinants HW2
7: W 6/13 4.1, 4.2 Subspaces, Basis and dimension ---
8: F 6/15 4.3 Column/null/row space (and review/catch up) HW3
 
  M 6/18 - Midterm (Chapters 1-4) ---
9:W 6/20 5.1, 5.2 Eigenvalues/vectors, the characteristic polynomial ---
10:F 6/22 5.3, 5.5 Diagonalization HW4
 
11:M 6/25 6.1, 6.2 Projection onto a line, Orthogonal sets ---
12:W 6/27 6.3, 6.4 Gram-Schmidt, Orthogonal projection, Least squares HW5
13:F 6/29 6.5, 6.6 Orthogonal matrices, diagonalization ---
 
14:M 7/2 - Catch up and review HW6 (due Tuesday)
  W 7/4 No class (holiday)
  F 7/6 - Final Exam (usual room and time) ---