Explore first-order stochastic optimization techniques in this 58-minute lecture by Rachel Ward from the University of Texas at Austin, presented at the Foundations of Data Science Boot Camp. Delve into support vector machines, deep learning, and gradient descent methods. Examine theorems, proofs, and important sampling techniques. Analyze convergence rates, adaptive learning strategies, and dynamic updates in optimization algorithms. Gain insights into the mathematical foundations underpinning modern data science and machine learning approaches.