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MATH 635 Course Syllabus
- fall 2012
NJIT Academic Integrity CODE: All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT 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 University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.
Math 635: Analytical and Computational Neuroscience
Number of Credits: 3
Course Description: This course will provide an intermediate-level mathematical and computational modeling background for small neuronal systems. Models of biophysical mechanisms of single and small networks of neurons are discussed. Topics include voltage-dependent channel gating mechanisms, the Hodgkin-Huxley model for membrane excitability, repetitive and burst firing, single- and multi-compartmental modeling, synaptic transmission, mathematical treatment of 2-cell inhibitory or excitatory networks. In this course, the students will be required to build computer models of neurons and networks and analyze these models using geometric singular-perturbation analysis and dynamical systems techniques.
Prerequisites: Math 211 or Math 213, Math 337, and CS 113 or Math 240, or departmental approval.
Textbook: Mathematical Foundations of Neuroscience” by G. B. Ermentrout & D. H. Terman – Springer (2010), 1st edition - ISBN: 978-0-387-87707-5.
Course Website: http://web.njit.edu/~horacio/Math635/Math430-635_F12.html
Recommended Books:
▪ "Foundations of Cellular Neurophysiology” by D. Johnston & S. Wu – The MIT Press (1995) - ISBN: 0-262-100053-3.
▪
"Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting” by E. M. Izhikevich
–
The MIT Press (2007), 1st edition – ISBN: 0-262-09043-8.
▪
"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.
▪
"Biophysics of Computation - Information processing in single
neurons", by Christof Koch.
Oxford University Press, 1999. ISBN 0-19-510491-9.
Instructor: (for specific course-related information, follow the link below)
|
Math 635-101 |
Grading Policy: The final grade in this course will be determined as follows:
|
▪ Homework, Quizzes & Class Participation: |
40% |
|
▪ Midterm Exam: |
30% |
|
▪ Project/Presentations: |
30% |
Your final letter grade will be based on the
following tentative curve. This curve may be adjusted slightly at the end of the semester.
|
A |
90-100 |
C |
70-74 |
|
B+ |
85-89 |
D |
60-69 |
|
B |
80-84 |
F |
0-59 |
|
C+ |
75-79 |
|
|
Drop Date: Please note that the University Drop Date November 6, 2012 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 ~ No classes |
|
| T |
Last Day to Withdraw from this course |
|
| T |
Classes follow a Thursday Schedule |
|
| W |
Classes follow a Friday Schedule |
|
| R-Su |
Thanksgiving Recess |
|
| R |
Reading Day |
|
| F- R |
Final Exams |
Course Outline & assignments:
|
Course Outline |
||||
|
Week |
Lecture |
Sections |
Topic |
Assignment |
|
1 |
1 |
|
Introduction to Computational Neuroscience
Passive membrane properties – The passive membrane
equatio |
See course website |
|
2 |
2 |
|
How to solve ordinary differential equations (ODEs)
– Review of
Analytical Methods
Introduction to XPP and Matlab for ODEs |
“ |
|
3 |
3 |
|
Dynamics of the passive membrane |
“ |
|
4 |
4 |
|
Integrate-and-fire models
The Hodgkin-Huxley model I |
“ |
|
5 |
5 |
|
The Hodgkin-Huxley model II
The cable equation I |
“ |
|
6 |
6 |
|
The cable equation II
Introduction to dynamical system methods for neural
models
Reduced one- and two-dimensional neural models |
“ |
|
7 |
7 |
|
One-dimensional neural models: Phase-space analysis |
“ |
|
8 |
8 |
|
Two-dimensional neural models: Phase-space analysis
I |
“ |
|
9 |
9 |
|
Two-dimensional neural models: Phase-space analysis
II |
“ |
|
10 |
10 |
|
Sub-threshold oscillations: Two and Three
dimensional models
Bursting |
“ |
|
11 |
11 |
|
Student Presentations |
“ |
|
12 |
12 |
|
Student Presentations |
“ |
|
13 |
13 |
|
Student Presentations |
“ |
Prepared By: Prof. Horacio G. Rotstein
Last revised: August 31, 2012