Materials for Mathematical Tools for Neuroscience course at Harvard (Neurobio 212)

Mathematical Tools for Neuroscience (Neurobio 212 at Harvard)

Developed and taught by Ella Batty, Lucy Lai, Alex Chen, and John Assad

Course contact: Eleanor_Batty@hms.harvard.edu

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Description of course

Numerical data analysis has become a nearly indispensable tool in modern neuroscience. This course aims to equip graduate students with the fundamental mathematical skills in quantitative modeling and data analysis necessary for neuroscience research (and for further computational neuroscience courses). This course is essentially organized into three sections: one on linear algebra, one on probabiliy & statistics, and one on the basics of machine learning. We will also cover some additional topics such as differential equations and dynamical systems).

One goal in formulating this course was to alleviate the need for taking multiple undergraduate-level courses in each of the stated topics (which may be cumbersome due to back-and-forth commute, inconvenient scheduling, or just an excess of materical with no clear applicability to neuroscience research). Our goal is to make this as fun, approachable, and applicable as possible. We would like to build mathematical intuition for these essential topics.

Course Prerequisites

You will not need any math experience beyond high school calculus. Python will be used in this class so some knowledge of it is necessary, although this course will also serve as an opportunity to practice those skills.

Description of materials

There are three components to the course: video lectures, comprehension questions, and tutorials.

Video lectures: The course consists of short video lectures each structured around a specific topic (10-20 minutes per video). We have created most of these videos using a Khan academy inspired style. We don’t want to reinvent the wheel so when great videos already exist on a specific topic, we link to those instead, but this will mostly occur in the linear algebra section.

Comprehension questions: These are short questions designed to be looked at right after watching the videos to consolidate your knowledge and try out quick computations. Both questions and answers are provided below.

Tutorials: Each week has 1 - 2 tutorials, or problem sets. These are Google colab notebooks with exercises where you might be asked to do computations by hand, engage with interactive demos, or code. They are designed to review the video material and in some cases introduce new concepts. They are not designed for repetitive problem solving (i.e. you will not be asked to solve a matrix equation by hand 100 times…).

Video links below will take you to Youtube, tutorial links will open Google colab notebooks.

We welcome constructive criticism given via opening a git issue. Note that the Week 1 videos created by me are a little rough right now due a steep learning curve (and a delay in acquiring appropriate audio equipment) but I promise they get better so bear with it.

The materials