Linear Algebra - Summer 2020

Course: MATH 2010-990 Call # 51405

Time and Place: MTWRF 11:20-12:50, Online through Zoom.

Instructor: Dr. Robert Gardner Office Hours: By appointment ("virtually"), just e-mail.

Office: Room 308F of Gilbreath Hall (but Gilbreath Hall is closed due to the COVID-19 social distancing situation).

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

E-Mail: gardnerr@etsu.edu
Class Webpage: faculty.etsu.edu/gardnerr/2010/silsum20.htm

Assistant: The graduate assistant for this class is Gaffar Solihu. Mr. Solihu will grade the tests and be available online for help through e-mail at solihu@etsu.edu (and also possibly available through Zoom).

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

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 integrals.

Supplemental "Text": Instructor's Solution Manual, J. Fraleigh and R. Beauregard. You can download PDF versions of some of the sections of the solutions manual at:

faculty.etsu.edu/gardnerr/2010/manual1.pdf (1.1-1.6)
faculty.etsu.edu/gardnerr/2010/manual2.pdf (2.1-2.4, 3.1-3.4)
faculty.etsu.edu/gardnerr/2010/manual3.pdf (4.1-4.3, 5.1-5.2)
Beware that the answers presented in the Instructor's Solution Manual are brief and most are not acceptable for full credit as test solutions. Answers to test questions should include full explanations (as given in problems presented in class). For examples, see the sample tests referenced below.

Class Notes: We will use online notes for the bulk of the "in-class" lectures. Copies of the notes are available in PDF format. For details see my Linear Algebra Class Notes Webpage.

Online Videos and the Format of Class: A video has been prepared for each section which we will cover in this class. You should watch the appropriate video before each class meets. During our formal class meetings, I will go through the notes again, but rather quickly since the detailed presentation is in the video. You can feel free to interupt during the lecture and I can address questions then. Since so much time is involved in watching the videos, we will not necessarily hold class for the whole hour and a half. Links to the videos are available in two formats. Links to the versions of the videos as posted on Zoom are on the webpage with Zoom links. Links to the same videos, but posted on the ETSU faculty server, are on the webpage with ETSU server links. The only difference in these videos is that the Zoom videos have a transcript of the video synchonized with the video. The ETSU server videos have the videos in mp4 format with the transcript given separately as a text ("txt") file. Also, the Zoom videos are not under direct control by ETSU and may be deleted at some point in the future. These two webpages also contain links to the class notes.

Sample Tests: Copies of old tests, along with solutions, are available on my Linear Algebra Test Solutions Webpage. The copies of old tests are in PDF form.

Center for Academic Achievement: Due to the COVID-19 concern, the Center for Academic Achievement (CFAA), located in the Sherrod Library, will not be operational during summer 2020. There is the possibility that some graduate students will be available for online tutoring, but nothing like this is yet in place. For more information, call 439-7115 or go to the Center for Academic Achievement webpage.

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; see Sections 1.7 and 6.5), biology (population distributions and genetics; see section 1.7), physics (theoretical and applied; see Section 1.2), computer science (in coding theory and cryptography; see Section 1.8) and almost any other area that uses numbers! We will illustrate some of these applications in this class. It also provides us with many of the concrete examples in some of our other algebra classes (such as Introduction to Modern Algebra 1 and 2, MATH 4127/5127 and 4137/5137). We will depend somewhat on technology 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). It turns out that we only need one numerical procedure ("RREF") and will rely on Wolfram Alpha for computational work. This will allow us to concentrate more on the concepts (i.e. the definitions, theorems, and ideas underlying the material).

ETSU Abstract Algebra Club: If you are a math major, math minor, or just a math fan, then you might consider joining the ETSU Abstract Algebra Club. Abstract algebra is covered in ETSU's Introduction to Modern Algebra (MATH 4127) which is a requirement of all non-statistics-concentration math majors. The ETSU Abstract Algebra club is the world's only abstract algebra (or "modern algebra") club in the world! For details on activities of the club, click on the club logo:

We have t-shirts made with an abstract algebra theme each year. If you are interested, contact Dr. Bob by e-mail and you will be admitted and issued a membership card.

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 on a 3 point subscale so that, for example, a B+ corresponds to a grade of 87%, 88%, and 89%. Solutions to the tests will be posted online (after they are taken, of course):
  1. Test 1 Solutions.
  2. Test 2 Solutions.
  3. Test 3 Solutions.

Homework: Problems for each section covered will be assigned from the textbook. Working these problems is where you will really develop an understanding of the ideas in this class (as is the case in any math class!). These exercises are not directly part of your grade, but they definitely will indirectly determine your grade since the test questions will be based on these exercises. We will work assigned homework problems (as best as we can in the online format) as requested "in class."

Tests: Test will be administered through D2L. You will need access to a scanner or digital camera in order to submit copies of your solutions to the test questions. The tests will be open book and open notes. You are NOT to communicate with anyone else, however (though Mr. Solihu and I will both be available and we will be monitoring things, so you can contact us if you have some technology problems).

Important Dates (for the official university dates, see official ETSU calendar):
Monday, June 8 = First day of class.
Wednesday, June 10 = Last day to register or add without departmental permit.
Sunday, June 14 = Last day to drop without a grade of "W."
Friday, June 19 = Test 1 (1.1-1.6).
Sunday, June 28 = Last day to drop a course with a "W" grade without dean's permission.
Tuesday, June 30 = Test 2 (2.1-2.5, 3.1).
Wednesday, July 8 = Last day to withdraw from the university and last day to drop with dean's approval and extenuating circumstances (by 4:30 pm EST).
Friday, July 10 = Last day of class, Test 3 (3.2, 3.3, 4.1, 4.2, 4.3, 5.1, 5.2).

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

DATE
AGENDA
HOMEWORK
MON 6/8
Introduction, 1.1 = Vectors in Euclidean Spaces
1.1 = 1-41 odd
TUE 6/9
1.1 (cont.), 1.2 = The Norm and the Dot Product
1.2 = 1-43 odd
WED 6/10
1.2 (cont.)
-
THR 6/11
1.3 = Matrices and Their Algebra
1.3 = 1-45 odd
FRI 6/12
1.3 (cont.), 1.4 = Solving Systems of Linear Equations
1.4 = 1-53 odd
MON 6/15
1.4 (cont.)
-
TUE 6/16
1.5 Inverse Matrices
1.5 = 1-37 odd
WED 6/17
1.6 = Homogeneous Systems, Subspaces, and Bases
1.6 = 1-47 odd
THR 6/18
Review
-
FRI 6/19
Test 1 (1.1-1.6)
-
MON 6/22
2.1 = Independence and Dimension
2.1 = 1-37 odd
TUE 6/23
2.2 = The Rank of a Matrix
2.2 = 1-23 odd
WED 6/24
2.3 = Linear Transformations of Euclidean Spaces
2.3 = 1-33 odd (33 is complicated!)
THR 6/25
2.4 = Linear Transformations of the Plane
2.5 = Lines, Planes, and Other Flats
2.4 = 1-21 odd
2.5 = 1-41 odd
FRI 6/26
3.1 = Vector Spaces
3.1 = 1-29 odd
MON 6/29
Review
-
TUE 6/30
Test 2 (2.1-2.5, 3.1)
-
WED 7/1
3.2 = Basic Concepts of Vector Spaces
3.2 = 1-45 odd
THR 7/2
3.3 = Coordinatization of Vectors
3.3 = 1-21 odd
FRI 7/3
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
MON 7/6
4.3 = Computation of Determinants and Cramer's Rule
4.3 = 1-39 odd
TUE 7/7
5.1 = Eigenvalues and Eigenvectors
5.1 = 1-31, 35, 41 odd
THR 7/8
5.1 (cont.), 5.2 = Diagonalization
5.2 = 1-27 odd
WED 7/9
Review
-
FRI 7/10
Test 3 (3.2, 3.3, 4.1, 4.2, 4.3, 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.

Return to Bob Gardner's home page

Last Updated: April 4, 2020