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Mathematical Tools for Neuroscientists
Introduction
Linear Algebra & Dynamical Systems
Week 1: Vectors
Key concepts
Video 1.1: What is a vector?
Video 1.2: Vector properties & operations
Video 1.3: Vector spaces
Tutorial 1
Tutorial 2
Week 2: Matrices
Key concepts
Video 2.1: Linear transformations and matrices (3Blue1Brown)
Video 2.2: Matrix multiplication as composition(3Blue1Brown)
Video 2.3: The determinant (3Blue1Brown)
Video 2.4: Inverse matrices, column space, and null space (3Blue1Brown)
Video 2.5: Nonsquare matrices as transformations between dimensions (3Blue1Brown)
Tutorial 1
Tutorial 2
Week 3: Discrete Dynamics & Eigenstuff
Key concepts
Video 3.1: Intro to Dynamical Systems
Video 3.2: Discrete Dynamical Neural Circuit
Video 3.3: Eigenvalues and eigenvectors
Tutorial 1
Tutorial 2
Week 4: Continuous Dynamical Systems & Differential Equations
Key Concepts
Video 4.1: Eigenvalues & Discrete Dynamical Systems
Video 4.2: Review of Differentiation & Integration
Video 4.3: Solving differential equations
Video 4.4: Systems of differential equations
Tutorial 1
Tutorial 2
Week 5: Matrix Decomposition & Dimensionality Reduction
Video 5.1: Special Matrices
Video 5.2: Matrix Decomposition & SVD
Video 5.3: PCA
Tutorial 1
Tutorial 2
Review
Homework 1
Probability & Statistics
Week 6: Intro to Probability
Key Concepts
Reading 6.1: Intro to Probability
Tutorial 1
Week 7: Intro to Statistics
Video 7.1: Descriptive Statistics
Video 7.2: Overview of Statistical Inference
Video 7.3: Point Estimators Examples & Goodness
Video 7.4: Maximum Likelihood Estimation
Video 7.5: Bayesian Inference
Tutorial 1
Tutorial 2
Week 8: Statistical Encoding & Decoding
Video 8.1: What are encoding & decoding?
Video 8.2: Statistical encoding models
Tutorial 1
(Optional) Tutorial 2
Machine Learning
Week 9: Linear Regression
Video 9.1: What is machine learning?
Video 9.2: Types of machine learning
Video 9.3: Linear regression
Tutorial 1
Week 10: Model Selection
Key concepts
Video 10.1: Model evaluation
Video 10.2: Bootstrapping (NMA)
Video 10.3: Model selection
Tutorial 1
Tutorial 2
Week 11: Clustering & Classification
Video 11.1: Clustering Applications
Video 11.2: Types of Clustering Algorithms
Video 11.3: K-Means Clustering
Tutorial 1
Tutorial 2
Week 12: Deep Learning
Video 12.1: Feedforward networks
Video 12.2: Training Neural Networks
Video 12.3: Practical steps for training
Reaching 12.4: Intro to Pytorch
Tutorial 1
Colab
Live Code
.ipynb
.pdf
Contents
Video
Notes
Video 4.4: Systems of differential equations
Contents
Video
Notes
Video 4.4: Systems of differential equations
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