Class Meeting Times/Room: MWF 1-2, Lopata 323
Textbook: Linear Algebra by K. Hoffman and R. Kunze, 2nd Edition
Strongly Recommended: Scientific Calculator Handling Matrices (TI-82 or better)
Instructor: Edward Wilson
Office/Office Hours: Cupples I, Room 18/MWF 2-3 and by appointment
Office Tel: 935-6729 [leave a voice-mail message if no answer]
E-Mail: enwilson@math.wustl.edu
Description: Math 429 is intended to be a theoretical course in linear algebra. It is presumed that all students have had a course in matrix algebra similar to Math 309, are familiar with row reduction as a computational tool for solving matrix problems, and have been exposed to abstract vector space definitions and a range of applications of matrix algebra. Some of the homework and exam questions will be computational, similar in style to Math 309 exercises; calculators are not only permitted on these types of questions but strongly recommended. The remaining homework and exam questions will be theoretical in nature: prove such and such assuming this and that. A course like Math 310 may be helpful preparation but it is not essential that students have had prior training in how to construct proofs. One of the goals of Math 429 is to develop this skill. Another goal will be to give some insight into why vector spaces arise in so many models of highly complicated phenomena: macroeconomics, quantum mechanics, functioning of the human brain, etc. In all of these models, the total space is huge, possibly infinite dimensional; even so, linear algebra reasoning is a common denominator.
The primary decomposition theorem (Chapter 6), Jordan form theorem (Chapter 7), and Spectral Theorem (Chapter 9) are the most important results discussed in Math 429. Chapters 1-5 lead up to these crucial tools. Along the way, all of the algebraic structures to be studied in more depth in Math 430 will be introduced.
Exam Dates:
In Class Exam ---- Monday, Sept. 27
First Take-home Exam ---- Handed out Nov. 12, Due Monday, Nov. 15
Second Take-home Exam ---- Done over 3 days in the period Dec. 8-17
Homework: Homework will be assigned each Friday to be turned in the following Friday. Homework will usually be discussed on the day that it is due. Late homework will not generally be accepted. It is anticipated that there will be 12 homework assignments over the course of the semester. Students are encouraged to talk with one another and/or seek help from other sources in doing their homework assignments. However, each student should write up her/his own assignment and should acknowledge any sources of help. In cases where solutions are essentially identical and there is no acknowledgment of cooperation, total available credit may be divided among the collaborators.
Ground Rules for Take-Home Exams: Consult only the textbook, course notes, and old homework solutions. Do not consult other books and do not discuss the problems with anyone. If stumped on how to proceed, send an e-mail note to the instructor asking for a hint. Violation of these rules will be considered a very serious breach of academic integrity with evidence of the violation forwarded to the Arts and Sciences Academic Integrity Committee for adjudication.
Make-ups: Exam make-ups will be arranged for those obliged to miss an exam for legitimate reasons (illness, religious observations, etc.). In each case, documentation must be provided, e.g. a note from the Health Service, DeanÆs Office, or a personal physician. Late homework will be accepted without penalty for those obliged to miss a substantial number of classes because of illness or another legitimate excuse.
Grading Policy: There will be a maximum of 30 points awarded throughout the semester with homework accounting for 6 points, the in-class exam another 6 points, and each of the two take-home exams 9 points. From time to time, extra credit homework problems will be mentioned. The grading of extra credit problems will be very generous with up to the same amount of credit as an entire regular assignment awarded for essentially correct solutions of problems considered difficult.. The following conversion table will assign final course grades:
Range for Total Number T of Points Course Grade
25 < T < 30
A
20 < T < 25
B
15 < T < 20
C
T slightly < 15
D
T signficantly < 15
NCR
This policy is worth a bit of pondering. It seems to say homework is only worth 20% and exams 80%. ThatÆs a deceptive reading. Extra credit homework problems can appreciably enhance the homework portion. Also, exam scores are apt to be much lower than homework scores. With a homework total around 6, one would only have to do slightly more than half the exam problems to earn a B. On the other hand, with little or no homework, the same exam performance would put someone dangerously close to failing the course. The moral is the usual one for math courses: do the homework.
Outline of Anticipated Course Pace and Topics Covered:
Sections Covered Topics Discussed Target Date for Completion
1.1 - 1.6
Set Notations, Fields, Matrix Review
Sept. 3
2.1 - 3.4
Vector Spaces, Bases, Linear Transformations
Sept. 24
(little attention paid to linear functionals)
4.1 - 5.4
Polynomials and Determinants
(skipping the sections on multilinear algebra)
Oct. 14
6.1 - 6.8, 7.3
Primary Decomposition Theorem and Jordan Form
Nov. 12
(skipping the rational form theorem)
8.1 - 9.6
Inner Product Spaces and Operators Upon Them
Dec 5
(weÆll do as much of this material as time permits)