Section 1 : Data Structures for Linear Algebra
Lecture 1 INTRODUCTION TO BRAINMEASURES PROCTOR SYSTEM
Lecture 2 What Linear Algebra Is 00:23:01 Duration
Lecture 3 Plotting a System of Linear Equations 00:09:18 Duration
Lecture 4 Linear Algebra Exercise 00:05:06 Duration
Lecture 5 Tensors 00:02:33 Duration
Lecture 6 Scalars 00:13:04 Duration
Lecture 7 Vectors and Vector Transposition 00:12:19 Duration
Lecture 8 Norms and Unit Vectors 00:14:37 Duration
Lecture 9 Basis, Orthogonal, and Orthonormal Vectors 00:04:30 Duration
Lecture 10 Matrix Tensors 00:08:24 Duration
Lecture 11 Generic Tensor Notation 00:06:43 Duration
Lecture 12 Exercises on Algebra Data Structures 00:02:08 Duration

Section 2 : Tensor Operations
Lecture 1 Segment Intro 00:01:19 Duration
Lecture 2 Tensor Transposition 00:03:52 Duration
Lecture 3 Basic Tensor Arithmetic, incl 00:06:12 Duration
Lecture 4 Tensor Reduction 00:03:31 Duration
Lecture 5 The Dot Product
Lecture 6 Exercises on Tensor Operations 00:02:38 Duration
Lecture 7 Solving Linear Systems with Substitution 00:09:47 Duration
Lecture 8 Solving Linear Systems with Elimination 00:11:47 Duration
Lecture 9 Visualizing Linear Systems 00:10:59 Duration

Section 3 : Matrix Properties
Lecture 1 Segment Intro 00:02:05 Duration
Lecture 2 The Frobenius Norm 00:05:01 Duration
Lecture 3 Matrix Multiplication 00:24:29 Duration
Lecture 4 Symmetric and Identity Matrices 00:04:41 Duration
Lecture 5 Matrix Multiplication Exercises 00:07:21 Duration
Lecture 6 Matrix Inversion 00:17:06 Duration
Lecture 7 Diagonal Matrices 00:03:25 Duration
Lecture 8 Orthogonal Matrices 00:05:16 Duration
Lecture 9 Orthogonal Matrix Exercises 00:15:00 Duration

Section 4 : Eigenvectors and Eigenvalues
Lecture 1 Segment Intro 00:17:53 Duration
Lecture 2 Applying Matrices 00:07:32 Duration
Lecture 3 Affine Transformations 00:18:20 Duration
Lecture 4 Eigenvectors and Eigenvalues 00:26:13 Duration
Lecture 5 Matrix Determinants 00:08:04 Duration
Lecture 6 Determinants of Larger Matrices 00:08:42 Duration
Lecture 7 Determinant Exercises 00:04:41 Duration
Lecture 8 Determinants and Eigenvalues 00:15:43 Duration
Lecture 9 Eigendecomposition
Lecture 10 Eigenvector and Eigenvalue Applications 00:12:29 Duration

Section 5 : Matrix Operations for Machine Learning
Lecture 1 Segment Intro 00:03:22 Duration
Lecture 2 Singular Value Decomposition 00:10:50 Duration
Lecture 3 Data Compression with SVD 00:11:00 Duration
Lecture 4 The Moore-Penrose Pseudoinverse 00:12:23 Duration
Lecture 5 Regression with the Pseudoinverse 00:18:24 Duration
Lecture 6 The Trace Operator 00:04:36 Duration
Lecture 7 Principal Component Analysis (PCA)
Lecture 8 About Certification

Section 6 : Limits
Lecture 1 Segment Intro 00:03:03 Duration
Lecture 2 Intro to Differential Calculus 00:13:25 Duration
Lecture 3 Intro to Integral Calculus 00:02:24 Duration
Lecture 4 The Method of Exhaustion 00:06:45 Duration
Lecture 5 Calculus of the Infinitesimals 00:09:34 Duration
Lecture 6 Calculus Applications 00:08:35 Duration
Lecture 7 Calculating Limits 00:17:49 Duration
Lecture 8 Exercises on Limits 00:06:07 Duration

Section 7 : Derivatives and Differentiation
Lecture 1 Segment Intro 00:01:16 Duration
Lecture 2 The Delta Method 00:15:47 Duration
Lecture 3 How Derivatives Arise from Limits 00:13:53 Duration
Lecture 4 Derivative Notation 00:04:20 Duration
Lecture 5 The Derivative of a Constant 00:01:28 Duration
Lecture 6 The Power Rule 00:01:16 Duration
Lecture 7 The Constant Multiple Rule 00:03:10 Duration
Lecture 8 The Sum Rule 00:02:26 Duration
Lecture 9 Exercises on Derivative Rules 00:11:08 Duration
Lecture 10 The Product Rule
Lecture 11 The Quotient Rule 00:04:04 Duration
Lecture 12 The Chain Rule 00:06:46 Duration
Lecture 13 Advanced Exercises on Derivative Rules 00:11:48 Duration
Lecture 14 The Power Rule on a Function Chain 00:04:37 Duration

Section 8 : Automatic Differentiation
Lecture 1 Segment Intro 00:01:49 Duration
Lecture 2 What Automatic Differentiation Is 00:04:43 Duration
Lecture 3 Autodiff with PyTorch 00:06:17 Duration
Lecture 4 Autodiff with TensorFlow 00:03:52 Duration
Lecture 5 The Line Equation as a Tensor Graph 00:19:41 Duration
Lecture 6 Machine Learning with Autodiff 00:40:11 Duration

Section 9 : Partial Derivative Calculus
Lecture 1 Segment Intro 00:22:38 Duration
Lecture 2 What Partial Derivatives Are 00:29:22 Duration
Lecture 3 Partial Derivative Exercises 00:06:15 Duration
Lecture 4 Calculating Partial Derivatives with Autodiff 00:05:18 Duration
Lecture 5 Advanced Partial Derivatives 00:14:39 Duration
Lecture 6 Advanced Partial-Derivative Exercises 00:06:11 Duration
Lecture 7 Partial Derivative Notation 00:02:27 Duration
Lecture 8 The Chain Rule for Partial Derivatives 00:09:17 Duration
Lecture 9 Exercises on the Multivariate Chain Rule 00:05:18 Duration
Lecture 10 Point-by-Point Regression 00:15:24 Duration
Lecture 11 The Gradient of Quadratic Cost 00:15:16 Duration
Lecture 12 Descending the Gradient of Cost 00:12:53 Duration
Lecture 13 The Gradient of Mean Squared Error 00:23:52 Duration
Lecture 14 Backpropagation 00:05:59 Duration
Lecture 15 Higher-Order Partial Derivatives 00:11:53 Duration
Lecture 16 Exercise on Higher-Order Partial Derivatives 00:02:55 Duration

Section 10 : Integral Calculus
Lecture 1 Segment Intro 00:02:44 Duration
Lecture 2 Binary Classification 00:09:13 Duration
Lecture 3 The Confusion Matrix 00:02:29 Duration
Lecture 4 The Receiver-Operating Characteristic (ROC) Curve 00:09:42 Duration
Lecture 5 What Integral Calculus Is 00:06:14 Duration
Lecture 6 The Integral Calculus Rules 00:05:37 Duration
Lecture 7 Indefinite Integral Exercises 00:02:58 Duration
Lecture 8 Definite Integrals
Lecture 9 Numeric Integration with Python 00:04:51 Duration
Lecture 10 Definite Integral Exercise 00:04:24 Duration
Lecture 11 Finding the Area Under the ROC Curve 00:03:35 Duration
Lecture 12 Resources for the Further Study of Calculus 00:04:01 Duration