*
*

- send me email:
- Homepage: http://seki.csuhayward.edu
- Office: South Science 429d, phone: 510-885-2691

- Office hours: Tuesday/Thursday 4:00--4:45; Thursday 6:00--7:30p.m. and by appointment. Please come to scheduled office hours if possible. I'm happy to answer questions anytime by email, which I check frequently.

* 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 | |

NO CLASS OR OFFICE HOURS: 4/13 R | ||||
---|---|---|---|---|

§ 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) | . | |

MIDTERM EXAM: 4/27 R | ||||

§ 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 | |

NO CLASS OR OFFICE HOURS: 5/25 R | ||||

§ 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 | |

§ REVIEW DAY | 6/1 R | |||

FINAL EXAM 6/8 R |

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