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Week - 1 |
The role of mathematics in AI, fundamental mathematical concepts, and their connections to AI applications. |
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Week - 2 |
Features, feature vectors, feature spaces, classification, regression, and data representations. |
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Week - 3 |
Vectors, matrices, matrix operations, systems of linear equations, and AI applications. |
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Week - 4 |
Vector spaces, linear independence, basis, dimension, rank, and relationships among data features. |
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Week - 5 |
Linear and affine transformations, their geometric interpretations, and applications in neural networks. |
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Week - 6 |
Norms, inner products, distances, orthogonality, projections, and the least-squares method. |
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Week - 7 |
Eigenvalues, eigenvectors, singular value decomposition, low-rank approximation, and principal component analysis. |
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Week - 8 |
MidTerm |
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Week - 9 |
Partial derivatives, gradients, directional derivatives, Jacobian matrices, and matrix derivatives. |
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Week - 10 |
Chain rule, computational graphs, backpropagation, and automatic differentiation. |
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Week - 11 |
Random variables, probability distributions, expectation, variance, covariance, and Gaussian distributions. |
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Week - 12 |
Conditional probability, Bayes' theorem, likelihood, maximum likelihood estimation, and cross-entropy. |
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Week - 13 |
Optimization fundamentals, convexity, gradient descent, stochastic gradient descent, and adaptive optimization methods. |
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Week - 14 |
Integration of mathematical concepts underlying AI models, application examples, and project evaluation. |