Syllabus

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