Professor: Peter J. Nyikos
Office: LeConte 406
Email: nyikos @ math.sc.edu
Prerequisite: MATH 241
Office hours when classes are in session [Of course, this excludes Labor Day,
Fall and Thanksgiving breaks,
and announced University closures]:
Monday and Wednesday 10:30 - 11:50 AM and 12:30 - 3:00 PM,
Tuesday and Thursday 1:00 - 3:30 PM.
Also by appointment, and whenever I am in. Exceptions posted on door and announced in advance if possible.
Textbook: Linear Algebra, by Johnson, Riess, and Arnold 5th ed.
The following sections were covered to some extent, some thoroughly:
1.1, 1.2, 1.3; 1.5, 1.6, 1.7; and 1.9
3.2 through 3.7
4.1 through 4.3, 4.8
5.9 applied to 3.7 The last two were only touched upon for enrichment purposes; no testing was done and no practice problems were given.
The final exam for this course is on Thursday, December 13, starting at 9:00 AM. It is cumulative, but special emphasis is given to material not covered on the tests, towards the end of the course. It includes some definitiions (linear combination, linear independence, nonsingular matrix) and parts of Theorem 17 of Section 1.9 and Theorem 2 of Section 3.2. Practice problems are given below for other kinds of questions that may be on the final exam.
Section 1.1 number 3, technique optional
Section 1.2: 31, 37
Section 1.3: 1, 3
Section 1.5: 1(d), 15, 33, 37, 45, 53
Section 1.6: 13, 15, 35. In addition, 43 is very good practice for eigenvalues, eigenvectors, and applications.
Section 1.7: 15, 17, 23
Section 1.9: 13, 19
Section 3.3: 31
Section 3.4: 1, 9(a)(b), 23 (techinique optional on 23)
Section 3.5: Odd-numbered 1 through 13 [only the last one takes more than a few seconds], and 23 and 25.
Section 3.6: 19, 21
Section 3.7: 1, 9, 17; also it is helpful to go over the handout on the extra credit problem 19.
Section 4.1: 1, 9
Section 4.2: 1, 17
Section 4.3: 1, 7
Due to the cancellation of class on Thursday, October 11, when the first test was originally supposed to take place, the test was rescheduled for Tuesday, October 16.
One day on most weeks, except the first two, there was either an extra credit problem to turn in, or a quiz, or a test. The first quiz was on Tuesday, September 4, on Section 1.2.
Learning Outcomes: Students will master concepts and solve problems based upon the topics covered in the course, including the following: solutions of systems of linear equations; Gaussian elimination; matrix multiplication and calculation of inverses; linear transformations and their associated matrices and their geometric interpretations; parametrized solutions to systems of linear equations; vector spaces and subspaces including null spaces and column spaces of matrices; rank and nullity of matrices; bases for, and dimensions of subspaces; determinants, eigenvalues, eigenvectors and the characteristic equation; inner products; orthogonal and orthonormal sets, and the Gram-Schmidt process for producing them; and least squares solutions to data problems.
The grade for the course is primarily based on a combined homework and quiz grade scaled to 100 points, two tests with a maximum of 100 points each, and the final exam of 200 points. It will also take attendance into account in the computer lab, and in borderline cases where classroom attendance is concerned, as long as absences do not exceed 10% and are thus considered excessive.
Only simple calculators (available for $20 or less) are needed for this course, and they will be needed only a small fraction of the time, outside of class. Neither the quizzes, nor the hour tests, nor the final exam will require their use, although they may save some time on a few problems. Programmable calculators are not permitted for quizzes, hour tests, or the final exam.