Linear Algebra - Summer 2019

Course: MATH 2010-001 Call # 52539

Time and Place: MTWRF 11:20-12:50, Brown Hall 476

Instructor: Dr. Robert Gardner Office Hours: MTWRF 2:30-3:00 and by appointment.

Office: Room 476 of Brown Hall for Summer Term 1 (traditionally, Room 308F of Gilbreath Hall).

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

E-Mail: gardnerr@etsu.edu
Class Webpage: faculty.etsu.edu/gardnerr/2010/silsum19.htm

Assistant: The graduate assistant for this class is Nesar Ahmed Titu. Mr. Titu will grade the tests and be available in the Center for Academic Achievement for his office hours. He will be in the CFAA Mondays 3:00-5:00, Tuesdays 3:00-5:00, Wednesdays 10:00-1:00 and 3:00-5:00. You can reach him by e-mail at tituna@etsu.edu. Other qualified graduate students will also be available in the CFAA Monday through Thursday from 10:00 to 1:00 and 3:00 to 5:00 (6:00 on Thursdays).

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:

faculty.etsu.edu/gardnerr/2010/notes.htm.

Sample Tests: Copies of old tests, along with solutions, are available online at: http://faculty.etsu.edu/gardnerr/2010/Test Solutions/test-solutions.htm The copies of old tests are in PDF form.

Center for Academic Achievement: Located on the first floor of the Sherrod Library, the Center for Academic Achievement (CFAA) is the place to go for help with writing and speaking, library research, core math and science courses, and other subjects. The center offers tutoring on a walk-in and appointment basis and is open during library hours, including nights and weekends. For more information, call 439-7115 or go to: https://www.etsu.edu/uged/cfaa/.

Attendance Policy: The Department of Mathematics strongly advises students to attend all mathematics classes when physically able. Because there is a positive correlation between attendance and student success in mathematics, the following attendance guidelines will be used in all mathematics courses. Regardless of the reasons for the absences, should a student exceed the following limit, the instructor has the authority to assign a grade of FN or F: For classes scheduled for TR or MW classes or any other 2 day/night classes, 5 absences. Hence, if you miss 5 or more classes, then I have the option (which I may exercise) of assigning you a grade of FN or F, regardless of your performance on the tests.

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 (http://www.wolframalpha.com) 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:

The club will be celebrating the 175th anniversary of the "discovery" of the quaternions by Sir William Rowan Hamilton (1805–1865) during academic 2018-19. We will have t-shirts and lectures celebrating the anniversary. 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. Every class day we will spend time covering some of the assigned homework problems as requested by the class.

Tests and Academic Misconduct: Neither calculators nor access to the internet will be allowed during the taking of tests. As a conseqeunce, you will not be allowed to access your phone or smart watch during the tests. You will not be allowed to stop during a test to go to the bathroom, unless you have presented a medical need beforehand. In the event of suspicious behavior during a test, I will not hesitate to charge you with academic misconduct. When such a charge is lodged, the dean of the College of Arts and Sciences is contacted. Repeated or flagrant academic misconduct violations can lead to suspension and/or expulsion from the university.

Important Dates (for the official university calendar webpage, see http://www.etsu.edu/etsu/academicdates.aspx):
Monday, June 3 = First day of class.
Wednesday, June 5 = Last day to register or add without departmental permit.
Sunday, June 9 = Last day to drop without a grade of "W."
Friday, June 14 = Test 1 (1.1-1.6).
Sunday, June 23 = Last day to drop a course with a "W" grade without dean's permission.
Tuesday, June 25 = Test 2 (2.1-2.5, 3.1).
Wednesday, July 3 = Last day to withdraw from the university and last day to drop with dean's approval and extenuating circumstances (by 4:30 pm EST).
Thursday, July 4 = Independence Day holiday.
Friday, July 5 = Last day of class, Test 3 (3.2, 3.3, 4.1, 4.2, 5.1, 5.2).

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

DATE
AGENDA
HOMEWORK
MON 6/3
Introduction, 1.1 = Vectors in Euclidean Spaces
1.1 = 1-41 odd
TUE 6/4
1.1 (cont.), 1.2 = The Norm and the Dot Product
1.2 = 1-43 odd
WED 6/5
1.2 (cont.)
-
THR 6/5
1.3 = Matrices and Their Algebra
1.3 = 1-45 odd
FRI 6/7
1.3 (cont.), 1.4 = Solving Systems of Linear Equations
1.4 = 1-53 odd
MON 6/10
1.4 (cont.)
-
TUE 6/11
1.5 Inverse Matrices
1.5 = 1-37 odd
WED 6/12
1.6 = Homogeneous Systems, Subspaces, and Bases
1.6 = 1-47 odd
THR 6/13
Review
-
FRI 6/14
Test 1 (1.1-1.6)
-
MON 6/17
2.1 = Independence and Dimension
2.1 = 1-37 odd
TUE 6/18
2.2 = The Rank of a Matrix
2.2 = 1-23 odd
WED 6/19
2.3 = Linear Transformations of Euclidean Spaces
2.3 = 1-33 odd (33 is complicated!)
THR 6/20
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 6/21
3.1 = Vector Spaces
3.1 = 1-29 odd
MON 6/24
Review
-
TUE 6/25
Test 2 (2.1-2.5, 3.1)
-
WED 6/26
3.2 = Basic Concepts of Vector Spaces
3.2 = 1-45 odd
THR 6/27
3.3 = Coordinatization of Vectors
3.3 = 1-21 odd
FRI 7/28
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 7/1
4.2 (cont.), 5.1 = Eigenvalues and Eigenvectors
5.1 = 1-31, 35, 41 odd
TUE 7/2
5.1 (cont.), 5.2 = Diagonalization
5.2 = 1-27 odd
THR 7/3
Review
-
WED 7/4
Independence Day Holiday
-
FRI 7/5
Test 3 (3.2, 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.

Return to Bob Gardner's home page

Last Updated: June 13, 2019