/courses/machine-learning/math-foundations/Recent content in Math Foundations for ML on DATATWEETSHugoenCopyright (c) 2025 DatatweetsFri, 14 Nov 2025 09:00:00 +0200/courses/machine-learning/math-foundations/lesson-1-understanding-linear-and-nonlinear-functions/Fri, 14 Nov 2025 09:00:00 +0200/courses/machine-learning/math-foundations/lesson-1-understanding-linear-and-nonlinear-functions/Functions are the language machine learning uses to map inputs to outputs. In this lesson you will explore linear functions with their constant slope and straight lines, contrast them with nonlinear functions that curve, and use NumPy and Matplotlib to compute and visualize both./courses/machine-learning/math-foundations/lesson-2-understanding-limits/Fri, 14 Nov 2025 09:00:00 +0200/courses/machine-learning/math-foundations/lesson-2-understanding-limits/Understand the idea of a limit: the value a function approaches as its input approaches a point, even where the function itself is undefined. You will work through the classic example of (x^2-1)/(x-1) at x=1, approach the limit numerically with NumPy, meet one-sided limits and continuity, and see why limits are the foundation of derivatives./courses/machine-learning/math-foundations/lesson-3-derivatives-and-finding-extreme-points/Fri, 14 Nov 2025 09:00:00 +0200/courses/machine-learning/math-foundations/lesson-3-derivatives-and-finding-extreme-points/Build the calculus you need for machine learning: understand the derivative as the limit of the difference quotient, master the differentiation rules, find extreme points where f’(x)=0, and see how gradient descent uses derivatives to minimize a loss function./courses/machine-learning/math-foundations/lesson-4-linear-systems/Fri, 14 Nov 2025 09:00:00 +0200/courses/machine-learning/math-foundations/lesson-4-linear-systems/Discover how multiple linear equations combine into a system, why the solution is the point where the lines cross, and how Gaussian elimination finds it step by step. You will solve a real two-equation system by hand and with np.linalg.solve, and learn when a system has one solution, none, or infinitely many./courses/machine-learning/math-foundations/lesson-5-vectors/Fri, 14 Nov 2025 09:00:00 +0200/courses/machine-learning/math-foundations/lesson-5-vectors/Learn what a vector is, how to add and scale vectors, how to compute the dot product and magnitude, and why the dot product measures similarity. You will work through every operation by hand and in NumPy using the vectors a=[2,1] and b=[1,3]./courses/machine-learning/math-foundations/lesson-6-matrix-algebra/Fri, 14 Nov 2025 09:00:00 +0200/courses/machine-learning/math-foundations/lesson-6-matrix-algebra/Understand matrices as both data tables and transformations of space. You will multiply matrices by hand and with NumPy, see how a matrix reshapes the unit square, read the determinant as an area scale factor, and connect it all to how a neural network layer works./courses/machine-learning/math-foundations/lesson-7-solution-sets-and-linear-independence/Fri, 14 Nov 2025 09:00:00 +0200/courses/machine-learning/math-foundations/lesson-7-solution-sets-and-linear-independence/Discover what it means for vectors to be linearly independent or dependent, how span and solution sets connect, and why rank matters. You will compute matrix rank with NumPy, see an independent set span the plane while a dependent set collapses to a line, and connect it all to redundant features in machine learning.