Princeton’s COS 521: Advanced Algorithm Design, taught by Sanjeev Arora in Fall 2015, is a graduate-level course designed to move students beyond standard undergraduate algorithms toward modern research-level algorithmic thinking. Its goal is to give students enough mathematical and conceptual background to read research papers. Major themes include randomization, probability and concentration inequalities, approximation algorithms, linear and semidefinite programming, high-dimensional geometry, dimension reduction, Markov chains, spectral methods, optimization, online algorithms, game theory, coding theory, cryptography, and algorithms for big data. The course emphasizes mathematical tools rather than a single textbook and combines theoretical lectures with programming-oriented homework and a final project/examination.
The syllabus is particularly valuable because it shows how several areas of pure mathematics, applied mathematics, and computer science interact. Students encounter Markov and Chernoff bounds, randomized algorithms, linear algebra and SVD, eigenvalues of random matrices, convex optimization, LP duality, the min-max theorem, random walks, and high-dimensional geometry alongside practical problems such as hashing, similarity search, portfolio management, data analysis, and distributed computation.
The course therefore provides an excellent bridge from mathematical theory to modern computational applications, with the later topics—spectral methods, optimization, randomized algorithms, approximation, and high-dimensional data—being especially relevant to contemporary AI and data science.
COURSE
The syllabus is particularly valuable because it shows how several areas of pure mathematics, applied mathematics, and computer science interact. Students encounter Markov and Chernoff bounds, randomized algorithms, linear algebra and SVD, eigenvalues of random matrices, convex optimization, LP duality, the min-max theorem, random walks, and high-dimensional geometry alongside practical problems such as hashing, similarity search, portfolio management, data analysis, and distributed computation.
The course therefore provides an excellent bridge from mathematical theory to modern computational applications, with the later topics—spectral methods, optimization, randomized algorithms, approximation, and high-dimensional data—being especially relevant to contemporary AI and data science.
COURSE
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