Math 250 - Introduction to Linear Algebra. Section 10. Fall 2009.

Contact Information
Instructor: Corey Hoelscher
Office: Hill Center, room 515.
Office Phone: 732-445-2390 ext. 5935.
Office hours: Mondays and Wednesdays 2:40-3:10pm; Tuesdays 6:30-7:30pm
e-mail:

Announcements
Stay tuned here for important announcements about the course.
General Information
Class will meet Mondays and Wednesdays 7:40 PM - 9:00 PM in Frelinghuysen Hall, room B3, on the College Avenue Campus.

Some of the topics we will cover include: Systems of linear equations, Gaussian elimination, matrices and determinants, vectors in two- and three-dimensional Euclidean space, vector spaces, introduction to eigenvalues and eigenvectors. The main Math 250 website has more general information about this course.

The text for the course is Spence, Insel, & Friedberg: "Elementary Linear Algebra: A Matrix Approach, 2nd Edition" along with the companion website with additional materials. Video lectures of a similar course are available from MIT's Linear Algebra webpage.

The Material
The subject of Linear Algebra is very different from Calculus and requires a very different way of thinking. In this course you will be required to not only solve computational problems but also to understand more difficult and abstract concepts. Reading and writing simple proofs will also be a part of the course. Many students who did well in Calculus take this course and find that they are having more difficulty than they usually have in a math course. That is why this course will require a lot of hard work and a change to the way you go about doing mathematics. Here we will be focused on understanding deep concepts and applying them to solve interesting problems, and not on plugging numbers into formulas.

Homework
Doing homework problems is the best way to make sure you understand the material and to reinforce what you have learned. It is easy to sit through a lecture or read a book and think you understand everything. But when you sit down to solve problems you realize there are lots of holes in your knowledge. This is why homework is an essential part of the course.

Every week there will be a homework assignment on the material covered in class. The assignments will be posted in the course calendar below and it is your responsibility to check this calendar for the assignments and due dates. The assignments will consist of problems from the book and problems from the online homework system WebWork. The book problems will be graded for completion and the online problems will be graded automatically by WebWork.

Each homework assignment will also have assigned reading from the book. These readings are very important for several reasons. First, we will not always have time to cover everything from the book in class and you will have to read the skipped parts of the book in order to be able to do the homework and be prepared for the quizzes and exams. Second, it is an important skill to be able to read and follow written mathematics and this is one of the goals of the course.

WebWork
WebWork is an online homework system that will be used extensively in this course. Each homework assignment will have an associated WebWork assignment. To complete a WebWork assignment, follow these simple steps:

Log in to WebWork: Go to WebWork and log in using your NetID as your username and your 9 digit RUID as your initial password. You should change this password once you have logged in.

Open the current assignment: Once you have logged in, you will see a list of the assigned problem sets, along with their due dates. For example the first assignment is called WbWk01. Click on the desired problem set and you will see the list of problems on that assignment. You will also have the option to "download a hardcopy of this homework set." This option is useful if you want to print the problems out, solve them with pencil and paper, then enter the answers at another time.

Select a problem: Click on one of the problems from the list and WebWork will display the problem and the field you will use to enter your answer(s). If you are worried about the typesetting or format of the answer, you can click "Preview Answers" to see how your answer will be displayed.

Submit your answer for that problem: When you have entered your answer, click "Submit Answers" to submit your answer(s) for this problem only. WebWork will immediately tell you if your answer is correct! On most questions you will have multiple attempts allowed, so if you make a mistake try try again, without being penalized.

Move on to the next problem: Once you have submitted your answer for a problem, and you are satisfied with your score, you can move on by clicking the "Next" or "Previous" buttons at the top of the page. You can also click the "Prob. List" button to return to the problem list. This list will now show the progress you have made in completing the assignment. Keep in mind that you can log out of WebWork at any time and return later to finish the assignment.

You may notice that the problems on your WebWork assignment are different from those of your classmates. This is because WebWork randomizes each student's problems. The type of problem will be the same for everyone, but the numbers appearing in the problem will be different.

If you are having trouble with WebWork try these help sites: Logging into WeBWorK, Changing your email address or password, Completing homework online.

Quizzes
Quizzes are a good way for you to make sure you can solve important types of problems and they give you a bit more practice with the material. There will be a quiz each week in class that will cover the material from the previous homework. The quiz will usually consist of a few problems directly from the homework. The best way to study for the quizzes is to do the homework. If you know how to do all the problems on the homework then you will have no problem with the quiz. The two lowest quiz grades will be dropped at the end of the semester but no make-up quizzes will be given for any reason.

Exams
There are two in-class midterm exams and one cumulative final exam. The midterms are tentatively scheduled for 10/7/09 and 11/11/09. Let me know now if you have any problems making these dates as make-up exams will only be given under extreme circumstances. The final exam is scheduled by the university to be on Monday, December 21, 8:00-11:00pm. No notecards or calculators will be allowed on any exam or quiz.

Grading
The grading will be roughly computed according to the following table.
Component Weight
Quizzes 10%
Homework and WebWork 10%
Midterm 1 23%
Midterm 2 23%
Final exam 34%
Total 100%


Tentative syllabus
Lecture Sections Topics Notes
Wed
9/2
1.1, 1.2 Matrices, Vectors, and Linear Combinations
Tue
9/8
1.2, 1.3 Systems of Linear Equations HW 1 due
Wed
9/9
1.4 Gaussian Elimination Quiz 1
Mon
9/14
1.6 Span of a Set of Vectors HW 2 due
Wed
9/16
1.7 Linear Dependence and Linear Independence Quiz 2
Mon
9/21
1.7, 2.1 Homogeneous Systems, Matrix Multiplication HW 3 due
Wed
9/23
2.1 Matrix Algebra Quiz 3
Mon
9/28
2.3
App. E
Invertibility and Elementary Matrices, Uniqueness of Reduced Row Echelon Form HW 4 due
Wed
9/30
2.4, 2.5 Inverse of a Matrix, Partitioned Matrices and Block Multiplication Quiz 4
Mon
10/5
2.7, 2.8 Matrices as Linear Transformations, One-to-One and Onto Transformations HW 5 due
Wed
10/7

Midterm exam 1 Midterm 1 Review due
Mon
10/12
3.1 Determinants; Cofactor Expansions
Wed
10/14
3.2 Properties of Determinants Quiz 5
Mon
10/19
4.1 Subspaces HW 6 due
Wed
10/21
4.2 Basis and Dimension Quiz 6
Mon
10/26
4.3 Column Space and Null Space of a Matrix HW 7 due
Wed
10/28
5.1 Eigenvalues and Eigenvectors Quiz 7
Mon
11/2
5.2 Characteristic Polynomial HW 8 due
Wed
11/4
5.3 Diagonalization of a Matrix Quiz 8
Mon
11/9
5.5 Examples of Diagonalization HW 9 due
Wed
11/11

Midterm exam #2 Midterm 2 Review due
Mon
11/16
6.1 Geometry of Vectors; Projection onto a Line
Wed
11/18
6.2 Orthogonal Sets of Vectors; Gram-Schmidt Process; QR factorization Quiz 9
Mon
11/23
6.3 Orthogonal Projection; Orthogonal Complements HW 10 due
Wed
11/25

No class -- Happy Thanksgiving!
Mon
11/30
6.4 Least Squares; Normal Equations Quiz 10
Wed
12/2
6.5, 6.6 Orthogonal Matrices; Diagonalization of Symmetric Matrices HW 11 due
Mon
12/7
6.6 Diagonalization of Quadratic Forms, Spectral Decomposition for Symmetric Matrices Quiz 11
Wed
12/9

Review for final HW 12 due






Site created: September 1, 2009