Linear Algebra - Pre-reqs Refresher

Introduction

Lecturer: Ella Batty

Lecturer and Curriculum Developer for Computational Neuroscience at Harvard
Coordinating Academic Officer for the Comp Neuro course at Neuromatch
Interests: Comp neuro education, using Machine Learning to model neurons, methods for understanding complex networks
Hobbies: Reading, dogs, binging murder mysteries

Foundational Math: Central to many areas of math and various applications
- Used in physics, computer science, economics, etc.
- Especially used in neuroscience, particularly computational and theoretical neuroscience
Neuroscience Fit: Linear algebra is the "language of data"
- Organizes, transforms, analyzes data
- Essential for over half of the comp neuro course

Recording data from three neurons when showing images to an animal
- Image 1 (e.g., dog): Neuron 1: 10 Hz, Neuron 2: 50 Hz, Neuron 3: 2 Hz
- Image 2 (e.g., cow): Neuron 1: 12 Hz, Neuron 2: 8 Hz, Neuron 3: 30 Hz
Challenge: Messy data with lots of pairings
Solution: Organize data using "Vectors"
- Vector: Ordered list of numbers (e.g., order here is according to neurons)
- Example: [10, 50, 2] for the dog image
Operations on Vectors: Can perform operations like vector subtraction
- Example: Difference between responses to dog and cow images
  - (10 - 12), (50 - 8), (2 - 30) results in [-2, 42, -28]

Vectors Tutorial:
- Definition of a vector
- Vector properties and operations
- Defining space through vectors
Matrices Tutorial:
- How matrices transform space
- Matrix properties and operations
- Eigenvalues and eigenvectors
Bonus (if time allows): Discrete Dynamical Systems
- Modeling a simple neural circuit
- Understanding dynamics using eigenvalues

Note: No need to worry if terms seem complex; understanding will develop through the course.