Honors Methods of Applied Mathematics II

                Math 451H - Spring 2014


    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).

    TA: R. J. Leiser

      E-mail: rjl22 at njit.edu

    Course Description:

    Theoretical, computational, and experimental research: Neuronal dynamics .

    This project will focus on the dynamic of single neurons and small networks of neurons. Electric activity in neuronal systems results from the cooperative activity of the participating electric currents, both intrinsic and synaptic. An important task of the modeling effort is to reproduce experimental results as a mean to understanding the link between the dynamic information contained in experimental data and the underlying biophysics. Mathematical models play a key role in this process. This goal of this project is to learn and use the necessary tools to address these issues.

    Theoretical component:

    (1) Biophysical (conductance-based) models of neurons and neuronal networks: Hodgkin-Huxley formalism for single neurons and synaptic connections

    (2) Dynamical systems tools for the understanding of the mechanisms underlying spike generation

    (3) Data analysis tools for the understanding of experimental data

    (4) Firing rate models

    Computational component:

    (1) Development of numerical algorithms to simulate biophysical (conductance-based) models of Hodgkin-Huxley type for single neurons and networks of interconnected neurons

    (2) Development of numerical algorithms to simulate firing rate type models

    (3) Development of numerical algorithms for the analysis of data including spike trains and firing rates, spike train statistics, spectral analysis, smoothing, spike-triggered average.

    (4) Development of numerical algorithms to fit model parameters to data.

    Experimental component:

    Carrying out electrophysiological experiments involving spiking and bursting neurons and small neuronal networks

    Textbook and recommended books:

      F. Gabbiani, S. J. Cox, Mathematics for Neuroscientists, 2010, Elsevier (ISBN: 978-0-12-374882-9)

      P. Dayan, L. F. Abbott, Theoretical Neuroscience, 2001, MIT Press (ISBN: 0-262-54185-8)

      G. B. Ermentrout, D. H. Terman, Mathematical Foundations of Neuroscience, 2010, Springer (ISBN 978-0-387-87707-5)

      B. P. Ingalls, Mathematical Modeling in Systems Biology, 2013, MIT Press (ISBN: 978-0-262-01888-3)

      Selected research articles (to be provided by the instructor).

    Class meets:

      Mon & Thu: 8:30 - 9:55, Cull-514

    Office hours: Mon 2:30-4:00

    Grading Policy:

      Projects and presentations through the semester: .................. 70%

      Final report and presentation (Math Bio seminar): ............... 30%


      Please note that the University Drop Date March 31, 2013 deadline will be strictly enforced

    Reports Policy

      A number of reports will be submitted during the semester

      Reports will not be accepted after the due date

      Only hard copies of the Reports will be accepted (NO electronic submissions) unless othewise specified

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

      Upon request, students must be able to explain their results and codes

    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

      If a student is absent for more than three classes without valid justification, he/she will be given an F for the course. If the student opts to withdraw from the class before the withdrawal deadline, the grade will be W.

      In case of serious illness or unavoidable causes, students must present appropriate documentation to the office of the Dean of Students within two lectures of returning.

      Any student who feels there are extenuating circumstances should consult the Associate Chair.

      Cellular Phones: All cellular phones, beepers and other electronic devices must be switched off during class and exam times (except when specifically allowed by the instructor).

      Chatting in class using electronic devices will not be tolerated.



Department of Mathematical Sciences(DMS).

New Jersey Institute of Technology (NJIT).