Mathematics for AI & ML Developers : The Complete Course

Explore probability theory from coin toss simulations to card deck scenarios, using Python, introducing combinatorics, permutations, and combinations, distinguish independent, dependent, and mutually exclusive events, and conclude with expected values.

Explore probability theory, its link to statistics for AI, and how coin toss simulations in Python illustrate sample space, distributions, and using data to estimate real-world probabilities.

Explore combinatorics, including permutations and combinations, to count arrangements and subsets in finite structures, where order matters for permutations and not for combinations, with card deck examples.

Explore independent and dependent events, their impact on probabilities, and mutually exclusive and disjoint events, with examples and the concept of the expected value.

Explore probability theory foundations through coin toss simulations with Python, deck of cards, and combinatorics, covering permutations, combinations, independent and dependent events, mutually exclusive events, and the expected value.

Explore calculus fundamentals: derivatives and integrals, with limits defining continuity. Learn power rule, product rule, and chain rule, multivariate calculus, and python-driven computation.

Explore the basics of calculus, including differentiation and integration, and see how they model rates of change and the area under curves.

Discover how limits describe a function's behavior as x approaches a point, enabling us to handle infinite divisions by zero and missing values through algebraic simplification.

Explore how derivatives model change through a four-step process—interval, raw change, rate of change, and limit—demonstrated with Python and intuitive analogies to motion.

Explore how to differentiate functions using the power rule for polynomials, the product rule for products, and the chain rule for composite functions, with hands-on examples and Python demos.

Explore Euler's number e as the base of continuous growth, compare discrete versus continuous compounding, and reveal its role in exponential and logarithmic functions with applications like interest and decay.

Explore implicit differentiation by differentiating both sides with respect to x, using the chain rule and product rule to relate y as a function of x in multivariate calculus.

Explore the essence of calculus, covering derivatives, integrals, and limits, plus rules like power, product, and chain, and Euler's number, implicit and multivariate differentiation.

Explore the intuition behind integrals, including indefinite and definite integrals, and learn to compute areas, with Python demonstrations and applications to gradient descent in machine learning.

Explore integral calculus, including definite and indefinite integrals, and see how the Fundamental Theorem of Calculus links differentiation to integration. Learn how speed as a function of time yields distance.

Explore the difference between indefinite and definite integrals, including antiderivatives, the constant of integration, and when limits apply. Learn power-rule integration and how derivatives identify integrals through examples.

Define the definite integral through a limit of sums, show its interpretation as net area and net change, and illustrate evaluation via the fundamental theorem of calculus.

Learn Python-driven numerical integration with the Sci fi library, using quad and simple methods, derive expected values for continuous variables, and create your approximation algorithm to estimate areas under curves.

Explore how calculus powers machine learning by optimizing loss with gradient descent and back propagation, using partial derivatives to update weights toward global or near-minimum error.

Explore the core of integral calculus, including indefinite and definite integrals, area under a function, and limits. Apply Python for integration and relate calculus to gradient descent in neural networks.

Explore linear algebra foundations for machine learning, including vectors, linear transformations, matrices, dot products, basis vectors, linear span, and Python implementations.

Explore linear algebra foundations for machine learning by studying vectors, matrices, and operations like scalar multiplication and addition to build intuition for deep learning.

Explore linear operations, notation, and Python implementations with numpy, focusing on 2d and 3d vectors and the linear properties of scaling and addition.

Explore higher dimensional vectors and matrices, visualizing linear combinations of basis vectors, the span and full rank of spaces, and how transformations arise from linear operations.

Explore how matrices transform space, including scaling basis vectors, and enable operations like matrix multiplication, addition, and scalar multiplication in Python.

Explore the dot product, a scalar product of vectors, its geometric interpretation via magnitudes and cosine of the angle, and its role in matrix and vector multiplications.

Explore patterns in matrices, including zero, identity, inverse, and transpose, then examine rotations and shears and how these transformations affect space, rank, and determinant.

Explore vectors, linear transformations, and matrices as space transformations, and connect linear algebra to machine learning. Master dot products, matrix operations, and basis concepts with Python demonstrations.

Explore determinants, the cross product, and the gradient, then learn change of basis, eigenvectors, eigenvalues, and the eigen basis to find the square of a matrix, generalizing linear algebra.

Use the determinant to quantify how a matrix scales area or volume, i.e., the output transformation size; zero means non-invertible, and for 2x2 matrices it assesses column independence.

Explore the cross product, a three-dimensional binary operation yielding a vector perpendicular to two inputs; learn its magnitude as parallelogram area, apply the right-hand rule, and compute it in Python.

The gradient generalizes the derivative to multivariate functions and points in the direction of greatest increase. It uses partial derivatives and guides optimization in machine learning.

Explore change of basis in vector spaces, learn how to translate coordinates between bases, and derive eigenvectors and eigenvalues through linear mappings and matrix inverses.

Demonstrate how eigenvectors stay on their lines under a transformation and how eigenvalues scale them, as in i_hat and j_hat with eigenvalues 0 and 1.5.

Compute and interpret eigenvalues and eigenvectors, and implement code to calculate them. Build the eigenbasis to simplify the square of a matrix and understand linear transformations.

Explore determinants' role in scaling outputs under linear transformations and when invertibility fails. Learn cross products, gradients, change of basis, and eigenvectors, eigenvalues, and the eigen basis.

Build a neural network from scratch and tune weights via back propagation. Explore fully connected and activation layers, forward propagation, loss, on xor and mnist with Carrots TensorFlow.

Build a neural network from scratch in Python for a capstone project, then verify with libraries such as TensorFlow, exploring backpropagation, forward propagation, weights and biases, and learning rate.

Build a two-layer neural network as an MVP to learn XOR, then digits dataset, using bias, forward propagation, nonlinear activation, and gradient descent on the loss function.

Train a neural network from scratch in Python, starting with the XOR problem and progressing to handwritten digit classification with TensorFlow. Learn gradient-based optimization, backpropagation, data normalization, and assessing accuracy.

Build and train a neural network from scratch, apply backpropagation to tune weights and minimize loss, forward-propagate through fully connected layers, test on xor and mnist with CARAS and TensorFlow.