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MATH 430 Course Syllabus
NJIT HONOR CODE: All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor Code very seriously and enforces it strictly. This means that 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.
Math 430-001: Analytical and Computational Neuroscience
FALL 2009
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.
Textbooks:
▪
"Foundations of Cellular Neurophysiology", by Daniel Johnston and
Samuel M.-S. Wu.
The MIT Press, 1995. ISBN 0-262-10053-3.
▪
"Dynamical Systems in Neuroscience: The Geometry of Excitability and
Bursting", by Eugene M. Izhikevich.
The MIT Press, 2007. ISBN 0-262-09043-8.
Course Website: http://web.njit.edu/~horacio/Math430and635/SyllabusMath430and635_F09.html
Recommended Books:
▪
"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.
Prerequisites: Math 211 or Math 213, and Phys 121, and CS 101, CS 113, or CS 115 all with a grade of C or better.
Grading Policy: The final grade in this course will be determined as follows:
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▪ Quizzes: |
10% |
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▪ Homework: |
30% |
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▪ Midterm: |
30% |
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▪ Final Project: |
30% |
Drop Date: Please note that the University Drop Date November 2, 2009 deadline will be strictly enforced.
NJIT Honor Code Policy: 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).
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.
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 make-up EXAMS during the semester. In the event the Final Exam is not taken, under rare circumstances where the student has a legitimate reason for missing the final exam, a makeup exam will be administered by the math department. In any case the student must notify the Math Department Office and the Instructor that the exam will be missed and present written verifiable proof of the reason for missing the exam, e.g., a doctors note, police report, court notice, etc., clearly stating the date AND time of the mitigating problem.
Further Assistance: For further questions, students should contact their Instructor. All Instructors have regular office hours during the week. These office hours are listed at the link above by clicking on the Instructor’s name. Teaching Assistants are also available in the math learning center.
Cellular Phones: All cellular phones and beepers must be switched off during all class times.
MATH DEPARTMENT CLASS POLICIES LINK
All DMS students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly. For DMS Course Policies, please click here.
| M |
Labor Day Holiday ~ University Closed |
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| M |
Last Day to Withdraw from this course |
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| T |
Classes follow a Thursday Schedule |
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November 25, 2009 |
W |
Classes follow a Friday Schedule |
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November 26-29, 2009 |
R-Su |
Thanksgiving Recess ~ University Closed |
Course Outline and Homework Assignments:
|
Class |
Dates |
Topic of the Class |
|
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|
1 |
8/31 |
General outline - Introduction to the Neurosciences |
|
2 |
9/3 |
Passive Membrane Properties |
|
└► |
9/7 |
Labor Day ~ University Closed |
|
3 |
9/10 |
How to Solve ODE's |
|
4 |
9/14 |
Introduction to XPP |
|
5 |
9/17 |
Dynamics of the Passive Membrane I |
|
6 |
9/21 |
Dynamics of the Passive Membrane II |
|
7 |
9/24 |
Integrate-and-Fire Neuron Model |
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8 |
9/28 |
The Hodgkin-Huxley Model I |
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9 |
10/1 |
The Hodgkin-Huxley Model II |
|
10 |
10/5 |
The Cable Equation I |
|
11 |
10/8 |
The Cable Equation II |
|
12 |
10/12 |
Modeling and Simulations Issues |
|
13 |
10/15 |
Introduction to Dynamical Systems - Reduced Neural Models |
|
14 |
10/19 |
Reduced One- and Two-Dimensional Neural Models |
|
15 |
10/22 |
One-Dimensional Neural Models: Phase-Space Analysis I |
|
16 |
10/26 |
One-Dimensional Neural Models: Phase-Space Analysis II |
|
17 |
10/29 |
REVIEW FOR Midterm EXAM |
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└► |
Last Day to Withdraw from this course |
|
|
18 |
11/2 |
MIDTERM EXAM: November 2, 2009 |
|
19 |
11/5 |
Two-Dimensional Neural Models: Phase-Space Analysis I |
|
20 |
11/9 |
Two-Dimensional Neural Models: Phase-Space Analysis II |
|
21 |
11/12 |
Two-Dimensional Neural Models: Phase-Space Analysis III |
|
22 |
11/16 |
Two-Dimensional Neural Models: Phase-Space Analysis IV |
|
23 |
11/19 |
Subthreshold Oscillations: Two- and Three-Dimensional Models |
|
24 |
11/23 |
Subthreshold Oscillations: The Canard Phenomenon |
|
└► |
(Tues.) Classes follow a Thursday schedule |
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25 |
11/24 |
Student Presentations |
|
26 |
11/30 |
Student Presentations |
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27 |
12/3 |
Student Presentations |
|
28 |
12/7 |
Student Presentations |
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Finals |
FINAL EXAM Week: December 11-17, 2009 |
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Prepared By: Prof. Horacio G. Rotstein
Last revised: July 15, 2009