M 340L Syllabus PDF

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M340L Spring 2012 Syllabus

Unique numbers: 55775 Lecture: MWF 3pm to 4pm in CPE 2.214 Textbook (required): David C. Lay, Linear Algebra and its Applications, Fourth Edition. Website: Accessible from BlackBoard, http://courses.utexas.edu/. Instructor: Dr. Zachary Miner E-mail: [email protected] Office: RLM 11.106 Office hours: MWF 10am to 11am (subject to change) TA: David Cochran E-mail: [email protected] Office: RLM 10.142 Office hours: TuTh 11am to 12:30pm

Prerequisites and degree relevance One semester of calculus, with grade of at least C, or consent of instructor.

Course description Linear algebra provides numerous computational tools employed in all branches of science, mathematics and engineering. Some notable “real-world” examples are internet search engines, satellite communications, and the global positioning system. We will start with a review of linear systems of equations and their matrix notation. We then move on to matrix algebra, namely, the addition and multiplication of matrices and their properties. Next the concepts of linear spaces and linear maps between them will be introduced. We will discuss the null space, range, rank, eigenvalues, eigenvectors and diagonalization of linear maps. Matrices, which we studied beforehand, will serve as prototypical examples (or representatives) of linear spaces as well as linear maps. 1

On the other hand, matrices will also be our primary computational tools for studying abstract linear spaces and linear maps. We will then introduce the additional structure of an inner product on our linear spaces, and study the subsequent concepts of orthogonality and approximation in such spaces. We will close the course with a discussion of “diagonalization” of inner products and the relation between inner products and quadratic forms.

Policies and requirements • Attendance is required at all class meetings, particularly for exams (dates can be found below). • University policy requires that a student must notify each instructor at least fourteen days in advance if they are going to miss required course work due to a religious observation, unless the holiday falls within the first two weeks of the term. Should it be necessary to miss an exam due to illness or other circumstances, please notify me by email as soon as possible. If an exam is missed for good cause, either a make-up exam will be offered or the student will be excused from the exam, and the weights assigned to other exams will be adjusted.

Grading There will be 2 in-class exams throughout the semester and homework every class (not graded). The grades will be calculated as follows: • 30% Problem Sets • 30% Tests • 40% Final Exam

Weekly Problem Sets Starting Friday, January 20, weekly problem sets will be posted on the course web site every Friday afternoon except when there is a test in the following week or otherwise noted. Each problem set will comprise of PROBLEMS and RECOMMENDED EXERCISES. An unannounced selection of the problems will be graded, and they will make up 50% of the grade for that problem set. Your submitted problem sets must be neat, legible, and stapled. 10% of the problem set grade will be based on clarity, accuracy, and 2

the general quality of presentation. The remaining 40% will be given if all the assigned problems are reasonably attempted. Do not submit the recommended exercises. The due date of each problem set will be clearly indicated; usually it is due in class (submission outside class will be rejected; do not slip in assignments under my office door) the Friday after it is posted. The lowest two problem set grades will be dropped (unsubmitted problem sets yield zero points). There will be computer exercises requiring the use of the symbolic computer algebra system Maple.

Tests There will be two equally weighted in-class 50-minute tests. Test 1 will be on Friday, February 10. Test 2 will also be on a Friday, roughly in late March or early April. The scopes of both tests as well as the finalized date of Test 2 will be announced in class and posted on the course web site (at least) one week prior to the tests. It is your responsibility to keep yourself informed about the tests. There will be no make-up tests except under truly extraordinary circumstances.

Final Exam Schedule Wednesday, May 9, 7pm to 10pm. For the (tentative) campus-wide final examination schedule for Spring 2012, please visit: http://registrar.utexas.edu/schedules/122/finals There will be no alternative final examination arrangements except under truly extraordinary circumstances.

Lecture schedule The following schedule is tentative and may be subject to change as needed during the semester. • Chapter I on Linear Equations in Linear Algebra (2-3 weeks) • Chapters II & III on Matrix Algebra and Determinants (2 weeks) • Chapter IV on Vector Spaces (2-3 weeks) • Chapter V on Eigenvalues and Eigenvectors (1-2 weeks) 3

• Chapter VI on Orthogonality and Least Squares (2-3 weeks) • Chapter VII on Symmetric Matrices and Quadratic Forms (1 week)

Computing resources The department of Mathematics’ undergraduate computer lab is located in RLM 7.122 and is open to all students enrolled in a Math course. You can sign up for an individual account in the computer lab using your UT EID. You will find on the lab computers most of the mainstream commercial math software: for instance, Mathematica, Maple, Matlab, Magma, and an assortment of open source programs.

Tutoring The Sanger Learning Center offers tutoring services to calculus students. They have resources available online at http://www.lifelearning.utexas.edu/. Sanger also offers “drop-in Tutoring,” a free, walk-in study environment supported by mathematics tutors located in Jester Center JES A315 on Monday-Thursday from 11a10p, Friday 11a-3p, and Sunday 5p-10p. Additionally, they offer appointment tutoring: one hour, individualizing tutoring sessions for a fee. (Tutoring credits may be subsidized by UT, depending on the student’s financial aid need level.)

Students with Disabilities The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-6441 TTY.

One more thing. . . I am committed to doing everything I can to help you make the most of this course. If you have questions, comments, or suggestions regarding our class, please do not hesitate to contact me. 4...