Welcome to Tom Roby's Math 3100 homepage! (Spring 2000)

(last updated: 11 May 2000)

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Class Information

COORDINATES: Lectures meet Tues/Thur. 2:00--3:50 (#12036 01) in Sci Science 213.

TEXT: Friedberg, Insel, & Spence Linear Algebra (3rd Edition) (Prentice Hall).

PREREQUISITES: To take this course, you MUST have a good understanding of the material covered in 2101 (Elements of Linear Algebra) . I will expect you to review this material on your own time, if necessary. If it's been a while since you took linear algebra, then please dust off your old book and notes and start reviewing ASAP.

WEB RESOURCE: http://seki.csuhayward.edu/3100.html will be my Math 3100 homepage. It will include a copy of the syllabus and list of homework assignments. I will keep this updated throughout the quarter.

GRADING: Your grade will be based on two exams, weekly quizzes, homework, participation and a portfolio of your work.

The breakdown of points is:

Midterm Final Quizzes Homework Participation Portfolio
25% 25% 20% 10% 10% 10%

LEARNING: The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Come to class prepared with questions. Don't hesitate to seek help from other students. Sometimes the point of view of someone who has just figured something out can be the most helpful.

Please read the sections from the book listed before the date of the first lecture on that material. To encourage this, I will give credit for emailing me with questions and statements about the assigned reading (see "Participation" below).

HOMEWORK: Homework will be given for each lecture, and all the homework assigned the previous week will be due the following Thursday. Please attempt all the problems by Tuesday, so that you can ask any questions you may have in class then. Except for routine computations, you should always give reasons to support your work and explain what you're doing. Not all the problems will be graded, but only a small subset. Please write your solutions carefully.

You do not need to hand in the answers to question I've included in [square brackets], but you should do them to prepare for...

QUIZZES: There will be a short quiz at the end of class each Tuesday on the previous week's material. I will try to be very specific about what you should know. Generally they will be very similar to the easier problems I assign in [square brackets], and to the examples given in the reading.

MIDTERM: Thursday, 27 April 2000 in class, Rearrange your schedule NOW if necessary.

FINAL: Thursday, 8 June 2000 in class, Rearrange your schedule NOW if necessary.

PARTICIPATION: I expect you to generally show up prepared for class and willing to work. Please read the section(s) to be covered by the day before class, and send email to 3100@seki.mcs.csuhayward.edu with at least five (5) statements or questions about the reading. This will help me focus classtime where you need it most. The questions can be anything from "What does the following sentence from the text mean..." to "Why is it important that the derivative measures the slope?" But please be as clear as possible about where the confusion is. Questions like "What's a vector space?" or "What does linear independence mean?" by themselves suggest to me that you haven't yet done the reading. A question like, "I'm not sure I understand linear dependence. If I have two vectors where one is a multiple of another, then I understand they are linearly dependent. But how could I have three vectors that are linearly dependent unless one is a multiple of another?" If you don't have any questions, then come up with five sentences that describe the main points of the reading. Twelve such emails over the course of the quarter will count as full credit. (Note that it doesn't apply to Review or Test Days.)

PORTFOLIO: Please organize your work neatly in some sort of binder (e.g., 3-ring), so that you can refer to all your classnotes, homework assignments, quizzes, exams, handouts, and emails on the reading. I will check them at the end of the term. This will not only help you during the class, but also later when you want to recall something you learned but can't quite remember. It gives you a permanent record of what you learned even if you sell your book.

TECHNOLOGY Many computations in linear algebra are tedious to do by hand, especially in large examples. In practice one uses software to do the computations in all but small examples. I will expect you to know how these computations work and be able to do them in small, simple cases. For larger ones you'll need either a calculator that does matrix computations (such as the TI-86, TI-89, or TI-92), or a computer program (such as Maple, Mathematica, or Matlab). We may spend a small amount of classtime on how these work on a TI-86, but mostly I expect you will read the manual that comes with whatever calculator or software package you choose.

MATERIAL: Linear algebra is one of the most beautiful, useful, and important subjects in the undergraduate curriculum. It extends greatly the subject of solving systems of linear equations that is covered in high-school algebra. The power of abstraction becomes apparent in the many applications of the theory. Linear algebra is a basic tool for differential equations, Fourier analysis, statistics, graph theory, discrete math, and most higher level courses in mathematics. It also has applications in all the sciences, social studies, and statistics. In 3100 we will gain a deeper level of understanding than 2101.


Section: Topic Lect. Date Homework problems Due
§ 1.1 Introduction 3/28 T [#1--4] 4/4
§ 1.2 Vector Spaces 3/28 T [#1--4,14,15,20] #10,16--19 4/6
§ 1.3 Subspaces 3/28 T [#1--5] #12,13 4/6
§ 1.4 Linear Combinations 3/30 R [#1--4] #6,9,11 4/6
§ 1.5 Linear (In)Dependence 3/30 R [#1,2,4,5] #6,7,12,14 4/6
§ 1.6 Bases and Dimension 4/4 T [#1--5] #8,11,13--17,25 4/18 T
§ 2.1 Linear Transformations 4/6 R [#1,2,4,5] 11,12,14,16,17,[22--24],25,26 4/18 T
§ 2.2 Matrix Representations of LT 4/11 T #7,8,10 4/20
§ 2.3 Compositions of LT 4/18 T #8,10,12,16 (NOT 14) 4/27 T
§ 2.4 Invertibility 4.18 T [#7,8,18] #15,16 4/27
§ 2.5 Change of Coordinates 4/20 T [#1--3] #4,8,9 4/27
§ 3.1 Elementary Operations 5/2 T [#1--3] #5 5/11 R
REVIEW FOR MIDTERM 4/25 T (Attempt Practice Midterm by today) .
§ 3.2 Rank & Inverse 5/2 T [#1--3,12] #5bdfh, 6bf,11,16 5/11
§ 3.3 Linear Systems (Theory) 5/2 T [#1--3] 4,7bd,8,10 5/11
§ 3.4 Linear Systems (Computation) 5/4 R [#1] 2bdf, 4b,5 (+some via calculator) 5/11
§ 4.4 Determinants 5/11 R [#1--2] 3be,4bdfg,5,6 5/18
§ 5.1 Eigenvalues & Eigenvectors 5/11 R [1,2ac] #3b,9,11,14,15 5/18
§ 5.2 Diagonalizability 5/16 T [#1,2beg] #2f,3ab,10,16a,17 5/30 T
§ 5.4 Cayley-Hamilton Thm. 5/18 R [#1,2,3] #10,11,17,19,21 5/30 T
§ 6.1 Inner Products 5/18 R [#1,2,3] #4,8,12,16,17,20(a) 5/30 T
§ 6.2 Gram-Schmidt 5/23 T [#1,2,5] #3,10,13,14,15,16 6/1
§ 6.3 Adjoints 5/23 T [#1,2ac] #9,11,12,14,16 6/1
§ 6.4 Normal & Self-Adjoint Ops. 5/30 T [#1,2,6] #3,8,12,13a,14a Never
§ 6.5 Unitary & Orthogonal Ops 5/30 T [#1,2] #9,11,16 Never
§ 6.6 Spectral Theorem 5/30 T [#1,2,3ad] #3c,6,10 Never

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