#### Section 1 : Data Structures for Linear Algebra

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

#### Section 2 : Tensor Operations

 Lecture 13 Segment Intro 1:19 Lecture 14 Tensor Transposition 3:52 Lecture 15 Basic Tensor Arithmetic, incl 6:12 Lecture 16 Tensor Reduction 3:31 Lecture 17 The Dot Product Lecture 18 Exercises on Tensor Operations 2:38 Lecture 19 Solving Linear Systems with Substitution 9:47 Lecture 20 Solving Linear Systems with Elimination 11:47 Lecture 21 Visualizing Linear Systems 10:59

#### Section 3 : Matrix Properties

 Lecture 22 Segment Intro 2:5 Lecture 23 The Frobenius Norm 5:1 Lecture 24 Matrix Multiplication 24:29 Lecture 25 Symmetric and Identity Matrices 4:41 Lecture 26 Matrix Multiplication Exercises 7:21 Lecture 27 Matrix Inversion 17:6 Lecture 28 Diagonal Matrices 3:25 Lecture 29 Orthogonal Matrices 5:16 Lecture 30 Orthogonal Matrix Exercises 15:0

#### Section 4 : Eigenvectors and Eigenvalues

 Lecture 31 Segment Intro 17:53 Lecture 32 Applying Matrices 7:32 Lecture 33 Affine Transformations 18:20 Lecture 34 Eigenvectors and Eigenvalues 26:13 Lecture 35 Matrix Determinants 8:4 Lecture 36 Determinants of Larger Matrices 8:42 Lecture 37 Determinant Exercises 4:41 Lecture 38 Determinants and Eigenvalues 15:43 Lecture 39 Eigendecomposition Lecture 40 Eigenvector and Eigenvalue Applications 12:29

#### Section 5 : Matrix Operations for Machine Learning

 Lecture 41 Segment Intro 3:22 Lecture 42 Singular Value Decomposition 10:50 Lecture 43 Data Compression with SVD 11:0 Lecture 44 The Moore-Penrose Pseudoinverse 12:23 Lecture 45 Regression with the Pseudoinverse 18:24 Lecture 46 The Trace Operator 4:36 Lecture 47 Principal Component Analysis (PCA) Lecture 48 About Certification Pdf

#### Section 6 : Limits

 Lecture 49 Segment Intro 3:3 Lecture 50 Intro to Differential Calculus 13:25 Lecture 51 Intro to Integral Calculus 2:24 Lecture 52 The Method of Exhaustion 6:45 Lecture 53 Calculus of the Infinitesimals 9:34 Lecture 54 Calculus Applications 8:35 Lecture 55 Calculating Limits 17:49 Lecture 56 Exercises on Limits 6:7

#### Section 7 : Derivatives and Differentiation

 Lecture 57 Segment Intro 1:16 Lecture 58 The Delta Method 15:47 Lecture 59 How Derivatives Arise from Limits 13:53 Lecture 60 Derivative Notation 4:20 Lecture 61 The Derivative of a Constant 1:28 Lecture 62 The Power Rule 1:16 Lecture 63 The Constant Multiple Rule 3:10 Lecture 64 The Sum Rule 2:26 Lecture 65 Exercises on Derivative Rules 11:8 Lecture 66 The Product Rule Lecture 67 The Quotient Rule 4:4 Lecture 68 The Chain Rule 6:46 Lecture 69 Advanced Exercises on Derivative Rules 11:48 Lecture 70 The Power Rule on a Function Chain 4:37

#### Section 8 : Automatic Differentiation

 Lecture 71 Segment Intro 1:49 Lecture 72 What Automatic Differentiation Is 4:43 Lecture 73 Autodiff with PyTorch 6:17 Lecture 74 Autodiff with TensorFlow 3:52 Lecture 75 The Line Equation as a Tensor Graph 19:41 Lecture 76 Machine Learning with Autodiff 40:11

#### Section 9 : Partial Derivative Calculus

 Lecture 77 Segment Intro 22:38 Lecture 78 What Partial Derivatives Are 29:22 Lecture 79 Partial Derivative Exercises 6:15 Lecture 80 Calculating Partial Derivatives with Autodiff 5:18 Lecture 81 Advanced Partial Derivatives 14:39 Lecture 82 Advanced Partial-Derivative Exercises 6:11 Lecture 83 Partial Derivative Notation 2:27 Lecture 84 The Chain Rule for Partial Derivatives 9:17 Lecture 85 Exercises on the Multivariate Chain Rule 5:18 Lecture 86 Point-by-Point Regression 15:24 Lecture 87 The Gradient of Quadratic Cost 15:16 Lecture 88 Descending the Gradient of Cost 12:53 Lecture 89 The Gradient of Mean Squared Error 23:52 Lecture 90 Backpropagation 5:59 Lecture 91 Higher-Order Partial Derivatives 11:53 Lecture 92 Exercise on Higher-Order Partial Derivatives 2:55

#### Section 10 : Integral Calculus

 Lecture 93 Segment Intro 2:44 Lecture 94 Binary Classification 9:13 Lecture 95 The Confusion Matrix 2:29 Lecture 96 The Receiver-Operating Characteristic (ROC) Curve 9:42 Lecture 97 What Integral Calculus Is 6:14 Lecture 98 The Integral Calculus Rules 5:37 Lecture 99 Indefinite Integral Exercises 2:58 Lecture 100 Definite Integrals Lecture 101 Numeric Integration with Python 4:51 Lecture 102 Definite Integral Exercise 4:24 Lecture 103 Finding the Area Under the ROC Curve 3:35 Lecture 104 Resources for the Further Study of Calculus 4:1