Course Description
This course -- The Math of AI (Course 1 of 2): Foundation Classics -- covers the mathematical foundation classics of Artificial Intelligence. It includes a quick review of calculus, linear algebra, and probability. Then delves into linear regression and logistic regression. Then constrained optimization including Lagrange multipliers, the Karush-Kuhn-Tucker conditions, Lagrangian duality, and Support Vector Machines. Next it covers Fourier analysis including Fourier series, Fourier Transforms, Discrete Fourier Transform, and the Fast Fourier Transform. Then Eigenvalue Decomposition, Singular Value Decomposition, and Principal Component Analysis.
Course Curriculum
AI Calculus Review
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- AI Calculus Part 1: Derivatives, Extrema, Chain Rule, and Gradient Operator. (13:54)
- AI Calculus Part 2: Jacobian and Hessian (18:41)
- AI Calculus Part 3: Test of Extrema via Hessian Determinant. (14:49)
- AI Calculus Part 4: Extrema Test Example, Hessian Eigenvalue Decomposition. (23:31)
- AI Calculus Part 5: Quadratic Approximation via the Hessian (22:18)
- AI Calculus Part 6: Properties of Quadratic Approximation (26:10)
Linear Algebra & Probability: Quick Review
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days
days
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Linear Regression & Logistic Regression
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days
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Constrained Optimization
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days
days
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- Lagrange Multipliers (24:34)
- Karush Kuhn Tucker (KKT) Conditions (31:43)
- Lagrangian Duality (Part 1): The Lagrangian Dual Function. (22:02)
- Lagrangian Duality (Part 2): The Dual Problem, Weak Duality, Strong Duality, and the Duality Gap. (26:30)
- Support Vector Machines (Part 1): Geometry of the Problem and Constraints. (20:45)
- Support Vector Machines (Part 2): Deriving the Constraint Optimization Problem. (16:02)
- Support Vector Machines (Part 3): Lagrangian Dual Function (28:46)
- Support Vector Machines (Part 4): Quadratic Program, Support Vectors, and Kernel Trick. (29:53)
Fourier Analysis
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days
days
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- Fourier Series (Part 1): Fourier Basis, Euler's Formula, Complex Fourier Series (29:24)
- Fourier Series (Part 2): Complex Fourier Series, Fourier Transform, Inverse Fourier Transform. (26:33)
- Discrete Fourier Transform (DFT) (25:57)
- Fast Fourier Transform (Part 1): Radix-2 and the Symmetries of the Complex Plane. (26:45)
- Fast Fourier Transform (Part 2): Order of NlogN; Matrix Representation of FFT; Sampling Theorem. (20:27)
Eigenvalue Decomposition, SVD, and PCA
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days
days
after you enroll
- Eigenvalue Decomposition (Part 1): Normal Matrices, Spectral Theorem. (27:05)
- Eigenvalue Decomposition (Part 2): Spectral Theorem, An Example. (16:15)
- Eigenvalue Decomposition (Part 3): The Hessian Matrix Revisited, Extremum Test. (17:51)
- Singular Value Decomposition (Part 1): Geometric & Algebraic View. (27:05)
- Singular Value Decomposition (Part 2): Relationship between EVD and SVD (26:26)
- Principal Component Analysis (Part 1): The Data Matrix, the PCA Objective, and the Covariant Matrix (25:09)
- Principal Component Analysis (Part 2): Eigenvalue Decomposition of Covariant Matrix. (23:06)
- Principal Component Analysis (Part 3): Proof that Principal Component is Covariant Matrix' Principal Eigenvector. (24:49)
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