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2017 Fall Course Syllabus - Mathematics 8200.001

Course: Mathematics 8200.001.

Course Title: Topics in Applied Mathematics.

Time: TR 2:00 - 3:20.

Place: Wachman Hall 527.

Instructor: Sean Gillian Queisser.

Instructor Office: Wachman Hall 514.

Instructor Email:

Instructor Phone: 267-294-1428.

Office Hours: TR 1:00 - 2:00 and TR 3:20 - 3:50.

Prerequisites: Enrolled as mathematics graduate student or permission of instructor.

Textbook: Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, and other sources.

Course Goals: The course is intended to bring together fundamentals of biochemical and electrical signaling in brain cells, development of mathematical models, and numerical methods for solving biophysical models. Computational frameworks for simulating processes in brain cells will be introduced and used in practice.

Topics Covered: Topics will include modeling of brain cell signals as purely time-dependent processes (integrate-and-fire models), one-dimensional compartment models (Hodgkin-Huxley models), all the way to a full three-dimensional structure-function models. These modeling approaches motivate mathematical and computational topics, including numerical methods for ordinary differential equations (ODEs) and partial differential equations (PDEs). The course will give a practical approach to time-stepping, Finite Difference and Finite Element methods for solving ODEs as well as elliptic and parabolic PDEs. Introduction of computational methods for reconstructing realistic cellular morphologies and computational grid generation (domain discretization) will allow the treatment of research-relevant problems. Finally, methods for solving large linear equation systems will complete the cycle from modeling to simulation.

Course Grading: 60% homework, 40% exam.

Exam Dates: TBD.

Attendance Policy: Students are expected to attend every class. If a student cannot attend a class for some justifiable reason, he or she is expected to contact the instructor before class.

Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.

Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here.

Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar for exact dates.

During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (Opens in new tab/window) for exact dates. See the full policy by clicking here. (Opens in new tab/window)

The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here. (Opens in new tab/window)