This page is http://www.math.columbia.edu/~bayer/S07/LinearAlgebra
Dave Bayer (x42643, 426 Mathematics,
http://www.math.columbia.edu/~bayer)
Bulletin page |
Directory of Classes :
Mathematics
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Student Services Online
For correspondence concerning this course, please use the email address bayer@math.columbia.edu with a subject that includes the text [MATH V2010: Linear Algebra]
Including our final, there will be a total of four exams that count toward the course grade.
Test | Day | Date | Time | Points |
Exam 1 | Tuesday | February 13 | in class | 25 |
Exam 2 | Tuesday | March 20 | in class | 25 |
Exam 3 | Tuesday | April 17 | in class | 25 |
Final | Thursday | May 10 | 9:00am - Noon | 25 |
These dates do not coincide with any religious holiday which causes suspension of
New York City's alternate side parking regulations; see
NYC Parking Calendar.
Please discuss other conflicts with me well in advance of the exam in question.
Master University Examination Schedule
University Academic Calendar
Elementary Linear Algebra: A Matrix Approach,
by Lawrence E. Spence, Arnold J. Insel, and Stephen H. Friedberg, .
Prentice Hall, 2000.
ISBN-10: 0137167229, ISBN-13: 9780137167227.
University bookstore ($125) or
AddALL ($43 and up).
This is our primary text. All exercises and section numbers listed below are from this text.
Linear Algebra, by Dave Bayer, Projective Press, 2007.
This text is available online. It is a draft in progress, supplementing my lectures. It is aimed at math majors planning to continue with the Modern Algebra sequence, but other students may also find it useful.
We are using a new textbook, and I only recently adopted an exam schedule of four exams, so the exams from previous semesters will not match our schedule.
The following chart gives a rough indication of which old exam questions to study for each of our current exams: Exam Chart
Our four exams will consist of a total of twenty exam questions over the course of the semester, each graded on a scale of 0 to 5. These are relative scores; I sort the entire class into six piles according to the answers for a particular problem, with the stronger answers receiving higher scores.
With rare exceptions, it is not possible to get a higher score than 3 for any wrong answer, no matter how inconsequential the arithmetic error leading to the wrong answer. It is possible to check the answer for every test question, and I am implicitly testing your ability to check the answer. With a deep understanding of linear algebra, one can look at any exam problem and see several different ways to tell that the answer is unquestionably correct. I am testing for this understanding.
Exercises are not collected. Below, I am listing all exercises that you certainly should be able to solve. Use your judgment in deciding which exercises to actually work. It is a good idea to work as many exercises as you can find time to solve; your goal is to achieve fluency, so that you can complete exams comfortably in the time allowed.
You are also invited to look at the more advanced exercises that are not listed.
Section | Exercises |
1.1 Matrices and Vectors | 1-16 |
1.2 Linear Combinations, Matrix-Vector Products, and Special Matrices | 1-32 |
1.3 Systems of Linear Equations | 1-38 |
1.4 Gaussian Elimination | 1-32 |
1.6 The Span of a Set of Vectors | 1-36 |
1.7 Linear Dependence and Linear Independence | 1-34 |
2.1 Matrix Multiplication | 1-21 |
2.3 Invertibility and Elementary Matrices | 1-16 |
2.4 The Inverse of a Matrix | 1-22 |
2.6 Linear Transformations and Matrices | 1-34 |
2.7 Composition and Invertibility of Linear Transformations | 1-58 |
Exam 1 | |
3.1 Cofactor Expansion | 1-40 |
3.2 Properties of Determinants | 1-36 |
4.1 Subspaces | 1-50 |
4.2 Basis and Dimension | 1-34 |
4.3 The Dimension of Subspaces Associated with a Matrix | 1-34 |
4.4 Coordinate Systems | 1-24 |
4.5 Matrix Representations of Linear Operations | 1-30 |
5.1 Eigenvalues and Eigenvectors | 1-36 |
5.2 The characteristic Polynomial | 1-54 |
Exam 2 | |
5.3 Diagonalization of Matrices | 1-34 |
5.4 Diagonalization of Linear Operators | 1-26 |
6.1 The Geometry of Vectors | 1-29 |
6.2 Orthogonal Vectors | 1-28 |
6.3 Least-Squares Approximation and Orthogonal Matrices and Operators | 1-22 |
6.4 Orthogonal Matrices and Operators | 1-16 |
6.5 Symmetric Matrices | 1-20 |
Exam 3 | |
7.1 Vector Spaces and their Subspaces | 1-11 |
7.2 Dimension and Isomorphism | 1-26 |
7.3 Linear Transformations and Matrix Representations | 1-10 |
7.4 Inner Product Spaces | 1-17 |
Final |
This calendar gives our schedule of classes and exams, and a rough indication of which sections will be covered on which days.
Monday | Tuesday | Wednesday | Thursday | Friday |
15 Jan 06 |
16 1.1, 1.2 |
17 |
18 1.3 |
19 |
22 Jan |
23 1.4 |
24 |
25 1.6, 1.7 |
26 |
29 Jan |
30 2.1, 2.3 |
31 |
1 Feb 2.4 |
2 |
5 Feb |
6 2.6 |
7 |
8 2.7 |
9 |
12 Feb |
13 Exam 1 |
14 |
15 3.1 |
16 |
19 Feb |
20 3.2 |
21 |
22 4.1 |
23 |
26 Feb |
27 4.2, 4.3 |
28 |
1 Mar 4.4, 4.5 |
2 |
5 Mar |
6 5.1 |
7 |
8 5.2 |
9 |
12 Mar |
13 |
14 |
15 |
16 |
19 Mar |
20 Exam 2 |
21 |
22 5.3 |
23 |
26 Mar |
27 5.4 |
28 |
29 6.1 |
30 |
2 Apr |
3 6.2 |
4 |
5 6.3 |
6 |
9 Apr |
10 6.4 |
11 |
12 6.5 |
13 |
16 Apr |
17 Exam 3 |
18 |
19 7.1, 7.2 |
20 |
23 Apr |
24 7.3 |
25 |
26 7.4 |
27 |
30 Apr |
1 May |
2 |
3 |
4 |
7 May |
8 |
9 |
10 FINAL |
11 |