Math 250 - Introduction to Linear Algebra. Section 10. Fall 2009.
Contact Information
Instructor: Corey HoelscherOffice: 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.
- The final exam will take place Monday December 21, 8:00-11:00pm, in the usual classroom. It will cover roughly 2/3 new material and 1/3 review. The new material consists of everything we have done since the last exam, specifically sections 6.1, 6.2, 6.3, 6.4, 6.5, and 6.6. The old material is everything that was covered on the previous exams.
- The Final Exam Equation Sheet is available here. You will be given a fresh copy of this exact sheet on the final exam. Notice that the sheet only lists expressions and does not equate them to anything or explain them. It is your responsibility to know what these expressions mean and how they are used.
- I will be giving a review session on Saturday 12/19, 5:00-7:00pm in Scott Hall room 102, on College Ave, where I will go over problems people have from the exam review, quizzes, howework, webwork or anywhere else.
- The final exam review problems are due at the final exam. Doing this exam review is the best way to study for the part of the exam which will cover new material. For the review part of the exam you should look over the midterms, quizzes, and midterm reviews. I posted blank copies of the midterms on Sakai, so you can print them out, redo them to test yourself, then check your answers with the solutions posted on Sakai.
- I will NOT hold my usual office hours during finals. Instead I will have office hours Sunday 12/20, 4:00-6:00pm and Monday 12/21, 12:00-2:00pm.
- Please take a few minutes to fill out the online course survey on Sakai. Your comments about what you like and what could be improved are especially helpful, and of course, these surveys are completely anonymous.
- Click here to log into WebWork. If you are new to the course and you do not have a WebWork account, email me with your NetID and your 9 digit RUID, and I will get you an account.
- Quiz, homework and exam grades will be posted on Sakai.
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