Tuesday, Thursday 8:30-9:50, Noyce 3821

Professor: Jeff Blanchard, Macy House 110, ext. 3304, email prefix: blanchaj

Text: There is no assigned text for this course. Lecture notes will be posted on P-web as our primary text. The library has a large collection of relevant text books.

Office Hours: By appointment; please email me to set up a time. Selecting a specific time for office hours might encourage some to come, but might discourage others with a conflict at that time. Everyone is encouraged to come to my office to talk about the mathematics in this course. I also encourage you to use the discussion board in P-web. I also have lots of meetings, so you can check my Outlook calendar to see what times are unscheduled.

Learning Goals: This course will study the fundamental ideas and mathematical background for numerical linear algebra and compressed sensing. The course will be exploratory in nature with students leading the overwhelming majority of the in-class discussions. Primary learning goals for this course are:

    • understand relevant aspects of numerical linear algebra;

    • understand the compressed sensing problem and some of its applications;

    • understand the types of algorithms used to solve the compressed sensing problem and how to analyze, compare, and select algorithms;

    • improve proficiency in implementing numerical algorithms while understanding the underlying computational costs;

    • gain experience in the craft of creating mathematics, identifying correct mathematics, seeking flaws and corrections to flaws, and asking relevant, driving questions;

    • improve mathematical and technical writing skills;

    • improve skills required to master new mathematics.

Workload: This class will meet approximately three hours per week. To accomplish the course learning goals students should expect to spend at least nine additional hours per week working on mathematics related to this course.

This type of learning will not be easy. You should feel challenged and occasionally completely stuck. This is the normal process. Everyone will struggle with material in this course. This is precisely the time to talk about mathematics with each other and with me. It is absolutely essentially that you come to class prepared to share what you have been working on, what you understand, and what questions you have identified as paths forward.

Participation: This class will be exploratory in nature and primarily discussion based. Both inside and outside of class, students will work through exercises on both the theory and computation. Participation in the class discussion is essential. Each student must voluntarily present solutions to various exercises throughout the semester. For each class session, students will score participation points as follows:

    • +1: present in class;

    • +1: presenting a solution;

    • +1: the presented solution is correct;

    • +1: posing driving questions to advance the mathematics;

    • +1: presenting an alternate proof.

Portfolio: Each student will be required to keep a portfolio of the exercises from class and homework. The portfolio corresponding to each chapter of the course notes will be submitted throughout the semester for a Homework Portfolio grade. A list of exercises will be provided in a LaTeX file and students are strongly encouraged to write their portfolio solutions in LaTeX. (This way incorrect solutions can be easily revised for the Final Portfolio.) Portfolio exercises will be graded as follows:

    • 0: Incoherent or not attempted;

    • 1: Major defect in analysis, logic, or writing;

    • 2: Minor defect in analysis, logic, or writing;

    • 3: Well written, correct solution;

    • +1: Typed submission (preferably LaTex).

At the end of the semester, a Final Portfolio will be submitted. Any exercises that were incorrect may be revised and graded as part of the Final Portfolio. The Final Portfolio must include a list of revised problems.

Final Project: The last few weeks of the semester will be spent working on a project. This project will involve reading a research article, writing a summary of the article including important proofs, implementing an algorithm, conducting and analyzing empirical testing, and presenting the project to the class.

Course Grade:

    • Participation: 25%

    • Homework Portfolio: 40%

    • Final Portfolio: 10%

    • Final Project: 25%

Academic Honesty:

    • All students must be aware of and comply with the Grinnell College Academic Honesty policy as described in the catalog.

    • In this course students may collaborate on the exercises in the portfolio provided they submit their own work and identify their collaborators. Any resource (other textbooks or online) must be cited. It is expressly forbidden to look for solutions online, in textbooks, or from other students. It is also an academic honesty violation to solicit assistance from any online forum other than the class P-web discussion board. When you are stuck, talk to your classmates and to me.

Attendance: Absences permitted by the college (athletics, performance, religious observation, etc.) must be coordinated prior to the class period in order to make arrangements for the missed homework or exams. This coordination must be done in person prior to the absence.

Accommodations: Grinnell College makes reasonable accommodations for students with documented disabilities. Students need to provide documentation to the Coordinator for Disability Resources, located on the ground level floor of Steiner Hall (641-269-3124) and discuss your needs with them. Students should then notify me within the first few days of classes so that we can discuss ways to ensure your full participation in the course and coordinate your accommodations.

Go to my homepage.