NJIT_CompNeuro

Analytical and Computational Neuroscience

Math 430 (Undergrad) & Math 635 (Grad)

Fall 2008

NJIT HONOR CODE:

All Students should be aware that the Department of Mathematical Sciences takes the NJIT Academic Honor Code very seriously and enforces it strictly. This means there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams. Under the Honor Code, students are obligated to report any such activities to the Instructor.

Please re-read Article III of the Academic Honor Code, which describes conducts that are considered unacceptable (cheating, violating the US Copyright law, etc).

Instructor: Horacio G. Rotstein

E-mail: horacio at njit edu (preferred)

Tel: (973) 596-5306

Teaching Assistant: Jessica Wright

E-mail: jessica at vision rutgers edu

Tel: TBA

Course Description:

A mathematical and computational introduction to the biophysical mechanisms that underlie physiological functions of single neurons and synapses. Topics include voltage-dependent channel gating mechanisms, the Hodgkin-Huxley model for membrane excitability, repetitive and burst firing, nerve impulse propagation in axons and dendrites, single- and multi-compartmental modeling, synaptic transmission, calcium handling dynamics and calcium dependent currents and processes.

Textbook:

None required (copies of PDF files will be made available)

Recommended Books:

"Foundations of Cellular Neurophysiology", by Daniel Johnston and Samuel M.-S. Wu. The MIT Press, 1995. ISBN 0-262-10053-3.

"Biophysics of Computation - Information processing in single neurons", by Christof Koch. Oxford University Press, 1999. ISBN 0-19-510491-9.

"Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems", by Peter Dayan and Larry F. Abbott. The MIT Press,2001. ISBN 0-262-04199-5

"Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting", by Eugene M. Izhikevich. The MIT Press, 2007. ISBN 0-262-09043-8

Class meets:

Tue & Thu: 11:30AM - 12:55PM, TIER 104 (NJIT)

Office hours

H.G.R.: Tue & Thu, 14:00 - 15:00

J.W.: Tue & Thu, 13:00 - 14:00 (except for Tue Sep 16, Tue Oct 21 and Tue Nov 18).

Grading Policy:

Weekly Quizzes: ...... 20%
Homework: ............ 20%
Midterm: ............... 30%
Project: ................. 30%
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Please note that the University Drop Date November 3, 2008 deadline will be strictly enforced

Homework Policy

A number of assignments will be given out during the semester

Assignments will be collected one week after they are given out

Only hard copies of the assignments will be accepted (NO electronic submissions)

The source code used in your calculations MUST accompany the submitted homework

Class Policies:

Attendance and Participation:

Students must attend all classes. Absences from class will inhibit your ability to fully participate in class discussions and problem solving sessions and, therefore, affect your grade. Tardiness to class is very disruptive to the instructor and students and will not be tolerated.

Makeup Exam Policy:

There will be no makeup exams, except in rare and extenuating situations where the student has a legitimate reason for missing an exam. The student must notify the NJIT Math office and the Instructor that he/she will miss an exam. In all cases, the student must present written verifiable proof of the reason for missing the exam, e.g., a doctor's note, police report, court notice, etc., clearly stating the date AND times of the mitigating problem.

Cellular Phones:

All cellular phones and beepers must be switched off during class and exam times.

Course Outline:

*Class*	*Date*	*Topic of the Class*	*Material & Homework*	*Lecture Notes*
1	Sep 2	General outline - Introduction to the Neurosciences	RR	LN-01
2	Sep 4	Passive membrane properties	RR	LN-02
3	Sep 9	How to solve ODE's	.	LN-03
4	Sep 11	Introduction to XPP	RR	LN-04
5	Sep 16	Dynamics of the passive membrane I	HW-1	LN-05
6	Sep 18	Dynamics of the passive membrane II	.	''
7	Sep 23	Integrate-and-fire neuron model	RR	LN-06
8	Sep 25	The Hodgkin-Huxley model I	RR	LN-07
9	Sep 30	The Hodgkin-Huxley model II	.	''
10	Oct 2	The cable equation I	RR	LN-08
11	Oct 7	The cable equation II	.	''
12	Oct 9	Modeling and simulations issues	HW-2	.
13	Oct 14	Introduction to Dynamical Systems - Reduced neural models	.	LN-09
14	Oct 16	Reduced one- and two-dimensional neural models	.	LN-10
15	Oct 21	One-dimensional neural models: Phase-space analysis I	RR	''
16	Oct 23	One-dimensional neural models: Phase-space analysis II	RR	''
17	Oct 28	Two-dimensional neural models: Phase-space analysis I	RR	LN-11
18	Oct 30	Two-dimensional neural models: Phase-space analysis II	HW-3	''
18	Nov 4	Two-dimensional neural models: Phase-space analysis III	RR	''
18	Nov 6	Two-dimensional neural models: Phase-space analysis IV	RR	''
21	Nov 11	Review	.	.
22	Nov 13	Exam	.	.
23	Nov 18	Subthreshold oscillations: Two- and three-dimensional models	.	LN-12
24	Nov 20	Subthreshold oscillations: The canard phenomenon	.	LN-13
25	Nov 25	Student Presentations: Dongwook, Hui, Sagar	Papers	.
--	Nov 27	Thanksgiving Recess	.	.
26	Dec 2	Student Presentations: Rorey, Iva, Shengbin	Papers	.
27	Dec 4	Student Presentations: Xinxian, Kohitij, Ben	Papers	.
28	Dec 9	Student Presentations: Mike, Nanna, Yi, Chenjing	Papers	.
--		Final Exam Period	.	.

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Department of Mathematical Sciences(DMS).
New Jersey Institute of Technology (NJIT).

Horacio
Last modified: Wed Oct 7 16:16:50 EDT 2009