Applied Matrix Theory
Course Location: 10:30-11:50 am Tuesday & Thursdays in 420-041 (note the location change!)
Instructor: Angela Hicks
Office: 382-E (second floor of the math building 380, which is in the north/northwest corner of the main quad)
Office Hours: 12:30- 2:30 pm on Tuesdays, 12-1 pm on Thursdays and by appointment
Office hours: 4-6pm on Monday, 5-7pm on Tuesday, and 5:30-7:30pm Wednesdays
Office hours: 5-7pm Monday, Wednesday, and Thursday
Course Description: Linear algebra for applications in science and engineering: orthogonality, projections, the four fundamental subspaces of a matrix, spectral theory for symmetric matrices, the singular value decomposition, the QR decomposition, least-squares, the condition number of a matrix, algorithms for solving linear systems. (Math 113 offers a more theoretical treatment.)
Prerequisites: MATH 51 and MATH 52 or 53 or the equivalent. Note that we will not fully cover linear algebra concepts that have previously been covered in these courses, so if you have trouble following (especially the first few assignments) you may need to look back through your old notes or textbook.
Text: Numerical Linear Algebra by Lloyd N. Trefethen and David Bau, III. There are two copies available on hold in the math library. You will be expected to read the sections preceding every homework assignment. We will be supplementing the text liberally with notes available here which do a better job at covering some early material.
Attendance: While I will not take attendance, we will frequently pause at some point in class to work in small groups on a sample calculation. You will be asked to turn in your work on these problems with your homework and they will not be posted elsewhere, so if you are not able to attend class, it is your responsibility to get the question from a classmate and work through the computation on your own.
Course Goals: Below are the three official learning goals, as set by the department. Not coincidentally, these make a great list of things to know before the final:
|Learning Goal 1||Illustrate basic concepts (vectors, linear maps, matrices, norms, inner products) and their geometric meaning with explicit examples.|
|Learning Goal 2||State important factorization results (eigenvalue decomposition, QR factorization, LU factorization, singular value decomposition).|
|Learning Goal 3||
Apply the basic concepts and factorization results to practical problems (solving linear systems, solving least square problems, principal component analysis, low-rank approximations)
The more informal goals of this course are to give mathematical tools for thinking about problems that broadly stated can be solved using matrices and vectors--of which there are many! As is usual for an (applied) mathematics class, we will be primarily learning to use tools, not directly discussing how they apply in your particular field of interest.
Students with Documented Disabilities: Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty. For students who have disabilities that don't typically change appreciably over time, the letter from the OAE will be for the entire academic year; other letters will be for the current quarter only. Students should contact the OAE as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066, URL: http://oae.stanford.edu).
Homework is worth 30% of your grade. You can expect to have a new homework assignment (almost) every week, due on Tuesday during class or office hours.
You will notice that most assignments test three skills:
- Computation: You will be expected to demonstrate your knowledge of various concepts by direct computation. You must show your work and give precise answers, recalling that .
- Theoretical Understanding: The text contains a number of more theoretical questions, which will require short proofs as answers. This means that you must give well reasoned, complete arguments about why your answer is correct and will be graded on the clarity and completeness of your explanation as well as your solution. A good rule of thumb is that your solutions must be completely understandable and convincing to the other students in the course without additional explanation.
- Computer Experimentation: You will be expected to familiarize yourself with one of two programming languages (Matlab or Python) commonly used for real world matrix calculations. This includes the ability to use help files (and/ or google searches) to select appropriate commands to complete your assignment. If you have trouble, feel free to see the CAs for help (Allesandro for Matlab and Jesse for Python) or post a discussion question for your fellow students here. If you are explicitly asked to use a computer to compute an answer, rounded (floating point) answers are expected. You are also encouraged to check your hand computations using the same software. Further details on these two choices of software will be included in the first homework assignment.
The lowest homework grade will be dropped. Homework solutions will be posted soon after the homework is turned in, so except in rare cases of serious and unexpected illness or similar, late homework assignments will not be accepted. Note that even in the case of school approved absences, you will still be expected to make arrangements to get your solutions submitted on schedule. (The one exception to this policy is for those students who join the class after the first assignment is due. Please contact me to make special arrangements in this case as soon as you join the class.)
While you may work with other students to solve any homework assignment, you may not write up your solutions together. Similarly, you may discuss appropriate commands, but you must each write your own code for any computer experimentation.
Finally, some early computer experimentation may seem to be particularly easy using Wolfram Alpha (or even a scientific calculator), you will be required to choose between Matlab (or Octave) and Python (or Sage), as these are industry standards that contain fuller features you would very likely need if you were to do these computations "in the real world".
Midterm (30%) and Final (40%)
You will have an in class midterm on Thursday, February 11th. Your final will take place on Thursday, March 17th from 12:15-3:15 pm and will be cumulative. You may expect them both to have computational questions as well as theoretical questions requiring short proofs. You may not use a computer or calculator for either exam, but you may bring in one 3x5 card with handwritten notes.
If (for a school approved event) you will be forced to miss either exam, you must contact me in advance to arrange for a make up exam. Failure to do so (or absence for other reasons) will result in a zero on either exam. Similarly, academic accommodations for students with documented disabilities must be arranged far in advance of each exam in cooperation with OAE.
The syllabus page shows a table-oriented view of the course schedule, and the basics of course grading. You can add any other comments, notes, or thoughts you have about the course structure, course policies or anything else.
To add some comments, click the "Edit" link at the top.