MATH S2010Q (Section 003):
Linear Algebra
Summer 2006 (2nd Session)

Mon, Tue, Wed, and Thu, 1pm - 2:35pm, Room 417, Mathematics
July 5 - August 11

Announcements

All important course announcements will appear here. So check back regularly.

Class meets in the Mathematics building, room 417!

The first day of class is July 5th. See you there.
To make up for the missed days we will have two makeup Fridays. July 14th and July 28th. Note that the scheduled makeup date is July 21, but I can't be in class that date so please mark these dates on your callendar.


Course Details

Instructor:  Matt DeLand (x45886, 206 Mathematics, deland@math.columbia.edu)

Office Hours: 11am-12pm Monday and Wednesday (the day that homeworks are due). I'll also be around Tuesday and Thursdays or other times by appointment.

Teaching Assistant: MingMin Shen. mshen@math.columbia.edu Office Hours: TBA

Text: "Linear Algebra with Applications" Steven J. Leon (Seventh Edition) Prentice Hall.

Course description: Matrices, vector spaces, linear transformation, orthogonality, rank-nullity theorem, eigenvalues and eigenvectors, canonical forms, applications. See also the course outline below.

Prerequisites: The more you know, of course, the better. That being said though, the course is for the most part self-contained. The official requirements are posted as Calculus III or the equivalent, but even this may not be that necessary. Some familiarity with complex numbers will also be assumed. Please talk to me or the TA if you need a refresher. Email me if you have specific questions as to whether or not you're prepared to take the course.

Policies: The course is only six weeks long, and we will be moving quickly.
Please try to keep up as there won't be much time to catch up. Here are some suggested policies:

  1. Active participation is strongly encouraged. Math is best learned by asking questions and by
    practicing (and practicing some more).
  2. Reading the book is helpful. Please try to read the material we are going to cover before AND after class.
  3. Attend class. (Not everything we cover will be from the book).
  4. Do the homework.
  5. Do problems that aren't assigned. This will make sure you understand the material and help you prepare for quizzes and exams.
  6. Ask questions if something is not clear, both in class and outside of class.

Homework: Homework will be assigned daily and it is to your benefit to do it.

Resources: Help is always available from the Help Room (Mathematics 406, 10am-5pm Mon-Thur), me, or the TA.
If there's something you don't understand -- ASK.

Exams: We will have 4 quizzes, one midterm, and one final

Grading: The tentative grading scheme is as follows:


Class Schedule and Homework Assignments

This schedule is tentative and WILL change. Please check regularly for current homework information.
Date Topics/Sections covered Remarks Homework Date Due
July 5Introduction
(1.1-2) Systems of Linear Equations
Row Echelon Form.
Welcome to the first day!Homework 1July 10
July 6(1.3) Matrix Algebra
July 10(1.4-5) Elementary Matrices
Partioned Matrices
**Quiz 1**
Homework 2 was updated since its first posting
Homework 2July 12
July 11(2.1-2) Determinants
Properties of Determinants
July 12(2.3-3.1) Cramer's Rule
Vector Spaces, Definitions and Examples
Homework 3July 17
July 13(3.2-3.3) Vector Subspaces
Linear Independence
There are two extra credit problems availableExtra Credit 1
July 14Half Review/Catch up Day
(3.4) Basis and Dimension if time
Friday meeting #1
July 17(3.4) Basis and Dimension
(3.5) Change of Basis
Quiz 2Homework 4July 19
July 18(3.6)Row and Column Spaces
(4.1) Linear Transformations
July 19(4.2) Matrix Representations of Linear Transformations
(4.3) Similar Matrices
Homework 5July 24
July 20Review and Catch-Up Day
July 24Midterm Exam
July 25(5.1) Scalar Products
(5.2) Orthogonal Subspaces
Homework 6July 27
July 26(5.2) Orthogonal Subspaces
(5.3) Least Squares
July 27(5.4) Inner Product SpacesHomework 7July 31
July 28(5.5) Orthonormal Sets
Start (5.6) Gram-Schmidt?
July 31(5.6) Gram-Schmidt
(6.1) Eigenvalues and Eigenvectors
Quiz 3Homework 8
Extra Credit 2
August 2
August 1(6.2)Differential Equations
(6.3)Diagonalization
August 2(6.4)Hermitian MatricesHomework 9August 7
August 3(6.5)Brief words on Singular Value Decomposition
(6.6)Quadratic Forms
Practice Final
August 7(6.7)Positive Matrices**Quiz 4**
This Homework Can only help your score if you turn it in.
Homework 10August 9
August 8Matt Talks about Jordan Canonical Form
Review
August 9Review DayPlease Show up with Questions
August 10FINAL

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