Linear Algebra - Summer 2008

Course: MATH 2010-050 Call # 21169

Time and Place: 1:00-2:30 MTWRF in Room 314 of Gilbreath Hall

Instructor: Dr. Robert Gardner Office Hours: By appointment.

Office: Room 308F of Gilbreath Hall

Phone: 439-6979 (308G Gilbreath), Math Department Office 439-4349

E-Mail: gardnerr@etsu.edu
Class Webpage: www.etsu.edu/math/gardner/2010/silsum08.htm

Text: Linear Algebra, 3rd Edition, by J. Fraleigh and R. Beauregard.

Sample Tests: Copies of old tests, along with solutions, are available through the Sherrod Library. They can be accessed over the internet. Go to the Millennium Library Catalog (http://libraries.etsu.edu/) and click on "Author" tab. Select "ETSU Sherrod Library-Reserves" and enter "gardner" in the "Look for" field. This may return more than one entry ("Gardner, Robert" and simply "Gardner"). Click on the name and this will bring up several files, including the relevant files for this class. In particular, there are copies of old tests in PDF form.

Supplemental "Text": Instructor's Solution Manual, J. Fraleigh and R. Beauregard (a copy will be on reserve in the library). You can download PDF versions of some of the sections of the solutions manual at:

www.etsu.edu/math/gardner/2010/manual1.pdf
www.etsu.edu/math/gardner/2010/manual2.pdf
www.etsu.edu/math/gardner/2010/manual3.pdf

Class Notes: We will use overheads for the bulk of the in-class lectures. Copies of the overheads are available on the web in both PostScript and PDF formats. For details see:

www.etsu.edu/math/gardner/2010/notes.htm.

Prerequisite: A knowledge of differential calculus (such as provided by Calculus 1 or Technical Calculus 1). You will also need to know how to evaluate elementary definite integrals.

Math Lab: The Mathematics Laboratory is located in Room 309 of Warf-Pickle Hall. It is staffed by graduate students. They are there to help you! Hours of operation are Monday-Friday 11:00-4:00. The phone number is 439-7611.

Note. Linear Algebra (or "Matrix Theory") is one of the most useful areas of mathematics. It is applicable in mathematics itself in areas ranging from Calculus and Discrete Math to Functional Analysis. It is applicable in statistics (least-squares methods and transition matrices), biology (population distributions and genetics), physics (theoretical and applied), computer science (in coding theory and cryptography) and almost any other area that uses numbers! We will illustrate some of these applications in this class. We will depend somewhat on technology (such as the TI-89 calculator) for rote computational work (though we will make sure to do several examples of each type of computation by hand, before relying on the technology). A users guide to the TI-89 for linear algebra computations will be given out in class and made available on the web at:

www.etsu.edu/math/gardner/2010/ti89la.pdf and www.etsu.edu/math/gardner/2010/ti89la.ps.
This will allow us to concentrate more on the concepts (i.e. the definitions, theorems, and ideas underlying the material).

Grading: Your grade will be determined by averaging your scores on three tests (T1 - T3) as follows:

Average = (T1 + T2 + T3)/3.
Grades will be assigned based on a 10 point scale with "plus" and "minus" grades being assigned as appropriate.

Important Dates:
Friday, July 11 = Last day to drop without grade of "W".
Friday, July 18 = Test 1 (1.1-1.6, 2.1, 2.2).
Friday, July 25 = LAST DAY TO DROP without dean's approval. Verifiable extenuating circumstances required after this date.
Friday, August 1 = Test 2 (2.3-2.5, 3.1-3.4).
Wednesday, August 6 = Last day to withdraw from the university.
Friday, August 8 = Test 3 (4.1, 4.2, 5.1, 5.2, 6.1, 6.2).

We will follow this tentative outline. Changes to the original schedule are made in red.

DATE
AGENDA
HOMEWORK
MON 7/7
Introduction, 1.1 = Vectors in Euclidean Spaces
1.1 = 1-41 odd
TUE 7/8
1.2 = The Norm and the Dot Product
1.2 = 1-45 odd, 40
TUE 7/8
1.1 (cont.), 1.2 = The Norm and the Dot Product
1.2 = 1-45 odd, 40
WED 7/9
1.3 = Matrices and Their Algebra
1.3 = 1-45 odd
WED 7/9
1.2 (cont.)
-
THR 7/10
1.4 = Solving Systems of Linear Equations
1.4 = 1-51 odd
WED 7/9
1.3 = Matrices and Their Algebra
1.3 = 1-45 odd
FRI 7/11
1.5 = Inverses of Square Matrices
1.5 = 1-37 odd
FRI 7/11
1.3 (cont.), 1.4 = Solving Systems of Linear Equations
1.4 = 1-51 odd
MON 7/14
1.6 = Homogeneous Systems, Subspaces, and Bases
1.6 = 1-47 odd
MON 7/14
1.4 (cont.)
-
TUE 7/15
2.1 = Independence and Dimension
2.1 = 1-37 odd, 28
TUE 7/15
1.5 = Inverses of Square Matrices
1.5 = 1-37 odd
WED 7/16
2.2 = The Rank of a Matrix
2.2 = 1-23 odd
WED 7/16
1.6 = Homogeneous Systems, Subspaces, and Bases
1.6 = 1-47 odd
THR 7/17
Review, 2.3 = Linear Transformations of Euclidean Spaces
2.3 = 1-33 odd
THR 7/17
Review
-
FRI 7/18
Test 1 (1.1-1.6, 2.1, 2.2)
-
FRI 7/18
Test 1 (1.1-1.6)
-
MON 7/21
2.4 = Linear Transformations of the Plane (in brief)
2.4 = 1-15 odd
MON 7/21
2.1 = Independence and Dimension
2.1 = 1-37 odd, 28
TUE 7/22
2.5 = Lines, Planes, and Other Flats
2.5 = 1-13, 21-43 odd
TUE 7/22
2.2 = The Rank of a Matrix
2.2 = 1-23 odd
WED 7/23
3.1 = Vector Spaces
3.1 = 1-29 odd, 18
WED 7/23
2.3 = Linear Transformations of Euclidean Spaces
2.3 = 1-33 odd
THR 7/24
3.2 = Basic Concepts of Vector Spaces
3.2 = 1-47 odd, 26
THR 7/24
2.4 = Linear Transformations of the Plane (in brief)
2.5 = Lines, Planes, and Other Flats
2.5 = 1-13, 21-43 odd
FRI 7/25
3.3 = Coordinatization of Vectors
3.3 = 1-21 odd, 22
FRI 7/25
3.1 = Vector Spaces (Michel Helfgott)
3.1 = 1-29 odd, 18
MON 7/28
3.3 = Coordinatization of Vectors (cont.)
-
MON 7/28
3.2 = Basic Concepts of Vector Spaces
3.2 = 1-47 odd, 26
TUE 7/29
3.4 = Linear Transformations
3.4 = 1-45 odd, 34
TUE 7/29
3.2 (cont.)
-
WED 7/30
Review, 4.1 = Areas, Volumes, and Cross Products
4.1 = 1-59 odd
WED 7/30
3.3 = Coordinatization of Vectors
3.3 = 1-21 odd, 22
THR 7/31
4.2 = The Determinant of a Square Matrix
4.2 = 1-35 odd
THR 7/31
Review
-
FRI 8/1
Test 2 (2.3-2.5, 3.1-3.4)
-
FRI 8/1
Test 2 (2.1-2.5, 3.1, 3.2)
-
MON 8/4
5.1 = Eigenvalues and Eigenvectors
5.2 = Diagonalization
5.1 = 1-41 odd
5.2 = 1-25 odd
MON 8/4
4.1 = Areas, Volumes, and Cross Products
4.2 = The Determinant of a Square Matrix
4.1 = 1-59 odd
4.2 = 1-35 odd
TUE 8/5
5.2 (cont.), 6.1 = Projections
6.1 = 1-39 odd
TUE 8/4
4.2 (cont.), 5.1 = Eigenvalues and Eigenvectors
5.1 = 1-41 odd
WED 8/6
6.2 = The Gram-Schmidt Process
6.2 = 1-35 odd,
not 25g,h, 27
WED 8/6
5.1 (cont.), 5.2 = Diagonalization
5.2 = 1-25 odd
THR 8/7
Review
-
FRI 8/8
Test 3 (4.1, 4.2, 5.1, 5.2, 6.1, 6.2)
-
FRI 8/8
Test 3 (3.3, 4.1, 4.2, 5.1, 5.2)
-
The departmental syllabus for this class also includes sections 3.5 (Inner-Product Spaces), 4.3 (Cramer's Rule), 6.1 (Projections), 6.2 (Gram-Schmidt Process), and 6.3 (Orthogonal Matrices). If time permits, we will also cover these sections.

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