Topic: Math Concepts in the Neuroscie
| Time | Days | Location | Instructor | GER | Credit | OPUS Class Number | Syllabus (Tentative) |
|---|---|---|---|---|---|---|---|
9:35am-10:25am | MWF | 1462 Clifton Road 100A | Olifer, Andrei. | 4 | 3569 | TBA. |
NBB 370 (000): Special Topics in Biology: Mathematical Concepts in the Neurosciences
A.Olifer, MWF, 9:35-10:25, MAX: 10, 1462 Clifton Road, Room 100A
Content: This course is intended for NBB (Neuroscience and Behavioral Biology) majors and Biology majors interested in quantitative reasoning and mathematical modeling. Several mathematical concepts which are fundamentally important in multiple areas of biology will be considered. The concepts include differential and difference equations, information measures, stochastic processes, and others. The concepts will be introduced in the context of specific problems in the neurosciences to demonstrate why and how these concepts really work. The exemplary problems will be from neuronal coding, neuronal network dynamics, and learning in neuronal networks. The course will give a foundation for quantitative reasoning and mathematical modeling in the neurosciences and biology in general. The development of the course was funded by a Howard Hughes Medical Institute (HHMI) Fellowship.
Neuroscience Topics and Mathematical Concepts covered by the course include:
· Neuronal Coding:
--Spike codes (mathematical concepts: functions, graphs of functions, elementary statistics).
--Entropy and information in spikes (mathematical concepts: probability distributions, entropy, mutual information, stochastic processes, Poisson process).
--Population coding (mathematical concepts: Vector spaces).
· Neuronal and Network Dynamics:
--Neuronal models (mathematical concepts: ODEs and their solutions, phase space).
--Steady state neuronal dynamics (mathematical concepts: stable and unstable steady states of dynamical systems).
--Periodic neuronal dynamics (mathematical concepts: stable and unstable periodic regimes of dynamical systems, bifurcations).
--Neuronal network dynamics (mathematical concepts: energy (Lyapunov) function).
· Learning in Neuronal Networks:
--Synaptic plasticity (mathematical concepts: time averaging, matrices).
Text: Dayan, P. and L.F. Abbott. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. (2001) (MIT Press)
Assessment: Grading will be based on three tests (15% each), the final exam (25%), and the homework grade (30%). There will be a discussion section every week to ensure understanding of the course material. This course will fulfill elective credit for the Biology and NBB majors.
Prerequisites: Math 115 (Life Science Calculus I) or Math 111 (Calculus 1).
The schedule of courses on O.P.U.S. is the official listing of courses, including days and times they meet and the General Education Requirements they satisfy. Students should use course descriptions as general guidelines. Course requirements, grading details, book lists, and syllabi are subject to change.