Meeting Times
Lectures: 2 sessions / week, 90 minutes / session
Recitations: 1 session / week, 1 hour / session
Prerequisites
Physics II (8.02, 8.021, or 8.022), 6.0002 Introduction to Computational Thinking and Data Science, and 9.01 Introduction to Neuroscience or permission of the instructor.
Note: several modules of 8.02 can be found in the Open Learning Library.
Course Description
This course introduces quantitative approaches to understanding brain and cognitive functions. Topics include mathematical description of neurons, the response of neurons to sensory stimuli, simple neuronal networks, statistical inference and decision making. It covers foundational quantitative tools of data analysis in neuroscience: correlation, convolution, spectral analysis, principal components analysis. Mathematical concepts include simple differential equations and linear algebra.
Homework Assignments
There will be a total of seven (7) homework assignments. Release and due dates are indicated on the class schedule. Assignments are due by 11:59 pm on the due date.
Excused extensions on assigned work will be given only for significant illness or family crisis. If an excused extension or postponement is requested, you must notify me prior to the class period for which the work is due.
You will be allowed four (4) free days of unexcused extensions on homework assignments to flexibly manage scheduling difficulties across the semester. Once these free days have been used, late work will be penalized at 20% per day.
Additionally, the lowest problem set grade will be dropped in calculating your final grade.
Software Requirements
Assignments require the use of MATLAB® version 2017b. Therefore, it is essential that you install this software on your laptop.
Note: MIT OpenCourseWare does not provide student access or discounts for MATLAB software. It can be purchased from The MathWorks®. For more information about MATLAB Pricing and Licensing, contact The MathWorks directly.
Policy on Problem Set Collaboration
Collaboration is encouraged on problem sets, but you must write up your own solutions and develop your own MATLAB code. List the names of all your collaborators on the top of each problem set submission.
Midterm Exam
There will be two midterm exams, which will be held in class. Bring a calculator for the exams. For the second midterm, a take-home programming exercise will be assigned. Instructions for submission will be provided with assignment.
Final Exam
The final exam will be focused on the material presented after the second midterm. However, we will include a question pertaining to the material covered in the first midterm and a question for the material covered in the second midterm.
Grading
Grades are not matched to a specific curve in this subject. If everyone in the class does well, everyone can get an A. Grades will be assigned based on your overall, weighted class average using the weighting scheme presented below:
| Activities | Percentages |
|---|---|
| Homework Assignments | 50% |
| 2 Midterm Exams | 30% (15% each) |
| Final Exam | 20% |
Class Schedule
L = Lecture
R = Recitation
| SES # | TOPICS | KEY DATES |
|---|---|---|
| L1 | Course Overview and Ionic Currents | PSet 1 assigned |
| R1 | Intro to MATLAB and Ionic Currents | |
| L2 | RC Circuit and Nernst Potential | |
| L3 | Nernst Potential and Integrate and Fire Models | |
| R2 | RC Model, Nernst Potential | |
| L4 | Hodgkin Huxley Model Part 1 | |
| No Class |
PSet 1 due PSet 2 assigned |
|
| R3 | Integrate and Fire Model, Hodgkin Huxley Model | |
| L5 | Hodgkin Huxley Model Part 2 | |
| L6 | Dendrites | |
| L7 | Synapses |
PSet 2 due PSet 3 assigned |
| Midterm Review | ||
| R5 | Review Session | |
| Midterm Exam | ||
| L8 | Spike Trains | PSet 4 assigned |
| R6 | Spike Train Analysis | |
| L9 | Receptive Fields | PSet 3 due |
| L10 | Time Series | |
| R7 | Spike Triggered Average, Poisson Process | |
| L11 | Spectral Analysis Part 1 | PSet 4 due |
| L12 | Spectral Analysis Part 2 | PSet 5 assigned |
| R8 | Spectral Analysis | |
| L13 | Spectral Analysis Part 3 | |
| Midterm 2 Review | ||
| R9 | Midterm 2 Review | |
| Midterm Exam 2 | ||
| R10 | Help With PSet 5 | |
| L14 | Rate Models and Perceptrons |
PSet 5 due Midterm Programming assigned |
| L15 | Matrix Operations | |
| R11 | Perceptons and Matrices | Midterm Programming due |
| L16 | Basis Sets | PSet 6 assigned |
| L17 | Principal Components Analysis | |
| R12 | Principal Components Analysis | |
| L18 | Recurrent Networks |
PSet 6 due PSet 7 assigned |
| L19 | Neural Integrators | |
| R13 | Networks | |
| L20 | Hopfield Networks | PSet 7 due |
| L21 | Sequence Generation in Songbirds | |
| R14 | Final Review |
