MIT 18.01: Single Variable Calculus

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MIT’s 18.01 Single Variable Calculus is a foundational mathematics course covering differential and integral calculus. It focuses on the fundamental concepts of limits, derivatives, integrals, and series, with applications in science and engineering.

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Why this course?

  1. Single Variable Calculus is one of the fundamental building blocks of AI and machine learning. Many key concepts in AI, such as gradient descent, optimization, and backpropagation, heavily rely on calculus principles.

  2. Essential for Understanding Optimization Algorithms

    • Machine learning models are trained using optimization algorithms, which minimize loss functions.
    • Gradient Descent, the most widely used optimization technique, is based on derivatives to adjust model parameters.
    • Convex functions and critical points help in finding optimal solutions.

  3. Integral Calculus in Probabilistic Models

    • Many AI models use probability distributions (e.g., Gaussian, Poisson, Exponential).
    • Integrals are needed to compute expectations, probabilities, and marginal distributions, essential in Bayesian statistics and deep learning.

  4. Foundations for Neural Networks & Deep Learning • Activation functions (e.g., Sigmoid, ReLU, Softmax) require differentiation. • Backpropagation, the core algorithm in neural networks, relies on chain rule differentiation to update weights.