Syllabus

Pacific Union College

Department of Mathematics

Course : Linear Algebra, MATH 465	Quarter : Spring, 2001
Time : 1:00 - 1:50 pm, M T W Th	Instructor : Steve Waters

Catalog Description: A deeper study than given in MATH 265 (Elementary Linear Algebra), including Jordan form, inner product spaces, quadratic forms, Hamilton-Cayley theorem, and normal operators.
   (Prerequisite: MATH 019, Introductory Algebra )
   A more specific list of topics is included later in this document.

Objectives: The primary objective of this course is to understand thoroughly (with proofs) the basic material on vector spaces, linear transformations and their matrix representations, eigenvalues, and inner products.

Textbook: The textbook for this class is Linear Algebra, 3rd edition, by Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence, published by Prentice Hall (1997).

General Course Policies: I expect you regularly to attend all class meetings. If you must be gone from class for some reason, you are still responsible for all that is done in that meeting.
   There will be a homework assignment due at nearly every class meeting. I strongly encourage you to work with one or more of your classmates on these assignments, but be sure that the paper you turn in is your own composition and reflects your own understanding. To encourage you to stay caught up and to avoid inequities and inefficiencies, assignments will not be accepted late for any reason. If you must be absent from class, it is your responsibility either to hand in your assignment early or to have someone bring it to class for you. If something unexpected occurs and it is impossible for you to get your assignment in on time, you may have it averaged in provided that you inform me of your reason in writing when you return to class. There is however, a maximum of 10% of the work that can be averaged in. To receive full credit on your assignments, you must neatly show all your work -- this means writing full explanations that you will be able to understand without help two or three months in the future .
   There will be a quiz given nearly every week. If you have to be absent on the day of a quiz, you should take that quiz early. If this is impossible, special arrangements may be made to make it up as soon as possible afterwards. Note however that these arrangements will be made only if you have notified me of your circumstances before the quiz is actually given . (You may leave voice mail at 6594 if you wish.)
   The midterm and final tests for this class must be taken at the scheduled times.
   Academic dishonesty will not be tolerated. If you are involved in cheating (or assisting other students in cheating), you should expect severe penalties including possible dismissal from the class with a failing grade. (For more information, refer to the school-wide policy in the catalog.)

Evaluation Procedure : Your overall percentage will be calculated using the following weights: Homework (20%), Quizzes (30%), Midterm (25%), and Final (25%). Your grade will then be determined using the following table.

		B+	84%	C+	70%	D+	53%
A	92%	B	80%	C	65%	D	53%
A-	88%	B-	75%	C-	60%	D-	50%

Available Help : There are many sources for help in this class. My office is in Chan Shun Hall, room 238E. Feel free to drop by during any of the office hours that are posted by the door, or make an appointment for a more convenient time. You also may be amazed at how much understanding you gain for yourself when you work at helping a classmate. Try it!

Schedule for the quarter

Date	Assignment Due	Agenda for Class Meeting
Apr. 2	None	§1.1, 1.2 (vector spaces)
Apr. 3	(H1) p.5:1; p.12: [1-4], 7, 13, 19, 22	§1.3, 1.4a (subspaces, linear combinations)
Apr. 4	(H2) p.19: 5, 8abc, 23, 28; p.31: 3bd, 4bd	§1.4b, 1.5 (span, linear independence)
Apr. 5	(H3) 31: 13; p.38: 4, 5, 7, 9, 10a	§1.6a (bases)
Apr. 9	none	Quiz #1, §1.6b, [1.7] (dimension, infinite bases)
Apr. 10	(H4) p.51: 2b, 3b, 4, 5, 8, 13, 16, 28, 31	§2.1a (linear transformations, range, nullspace)
Apr. 11	none	§2.1b (nullity, rank, dimension thm., T-invariance)
Apr. 12	(H5) p.69: 3, 4, 9cde, 11, 12, 13, 16, 26	§2.2 (matrix representations)
Apr. 16	(H6) p.77: 2be, 4, 5, 14	Quiz #2, §2.3a (composition of transformations)
Apr. 17	none	§2.3b (matrix multiplication, connections)
Apr. 18	(H7) p.89: [2], 4, 10, 12, 15a (for ), 19, 21	§2.4a (invertibility)
Apr. 19	none	§2.4b, 2.5a (isomorphisms, change of coordinates)
Apr. 23	(H8) p.99: 3, 4, 5, 14, 16, 17bc, 18	Quiz #3, §2.5b (similarity)
Apr. 24	(H9) p.107: 2b, 3be, 7, 8, 9	§2.6 (linear functionals, dual spaces)
Apr. 25	(H10) p.114: 3, 6, 9	§3.1, 3.2a (elementary operations, matrix rank)
Apr. 26	(H11) p.142: 2, [3-7]; p.155: 4, 14	§3.2b, 3.3 (matrix inverses, systems of equations)
Apr. 30	(H12) p.155: 5bd, 6bd; p.168: 2bd, 3bd, 4a, 8, 10	Quiz #4, §3.4 (Gaussian elimination)
May 1	(H13) p.184: 4, 5, 8	§4.4 (overview of determinants)
May 2	(H14) p.224: 3be, 4dfh, [5, 6]	Quiz #5, Review
May 3	None	Midterm Test
May 7	None	§5.1a (eigenvalues, eigenvectors, characteristic poly.)
May 8	none	§5.1b, 5.2a (diagonizability)
May 9	(H15) p.247: 2b, 3b, 4, 8, 11, 14, 17	§5.2b (algebraic and geometric multiplicities)
May 10	none	Quiz #6, §5.2c (direct sums, simultaneous diag.)
May 14	(H16) p.268: 2ab, 3b, 7, 8, 12, 17, 22	§5.4a (T-cyclic subspaces)
May 15	none	§5.4b, 6.1a (Cayley-Hamilton thm., inner products)
May 16	(H17) p.309: 2abc, 3, 6bd, 9bd, 10bd, 18, 33, [37, 40]	§6.1b, 6.2a (norm, orthogonality, orthonormality)
May 17	(H18) p.322: 2, 4, 8, 9, 11, 12, 17, 21	Quiz #7, §6.2b (Gram-Schmidt, projections)
May 21	(H19) p.334: 2ac, 12, 17c, 18c	§6.3a (adjoint of a linear operator)
May 22	(H20) p.345: 3ab, 6, 8, 12, 14	§6.3b, 6.4a (least-squares approximation)
May 23	(H21) p.345: 18, 19	§6.4b (normal operators, self-adjoint operators)
May 24	(H22) p.354: 3, 5, 8, 13a, 17	Quiz #8, §6.5a (unitary & orthogonal operators)
May 28	none	Memorial Day
May 29	none	§6.5b (Schur's theorem, rigid motions)
May 30	(H23) p.369: 2bc, 3, 10, 16 (3 by 3), 18, 20	§6.6 (orthogonal projections, spectral theorem)
May 31	(H24) p.379: 2, 3c, 4, 7bfg, 8	Quiz #9, §7.1 (generalized eigenvectors, Jordan bases)
June 4	(H25) p.452: 2b, 3b, 4, 6, [10]	§7.2 (Jordan canonical form)
June 5	(H26) p.466: 2, 3, 4 form only, 5, 14, [19]	§7.3 (minimal polynomial)
June 6	(H27) p.478: 2bd, 3b, 5, 9, something related to 13	§7.4 (rational canonical form)
June 7	(H28) p.502: 2 form only	Quiz #10, Review
June 12	Tuesday, 12:30 pm	Final Examination

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