Covers fundamental concepts, principles, and abstractions that underlie the design and engineering of computer systems. Students will learn how a computer works, how to write safe and performant systems software, and what systems abstractions support today’s complex, high-performance systems developed in industry. Specific topics include machine organization, systems programming and performance, key concepts of operating systems, isolation, security, virtualization, concurrent programming, and the basics of distributed systems. Combined lectures, labs, and several hands-on projects involving programming exercises in C/C++.

Covers high-level computer architecture, systems programming, assembly-language programming, C-language programming, and operating systems functions.

Covers designing and analyzing data structures and algorithms. Studies the theory of NP-completeness.

The course introduces basic models of computation including languages, finite-state automata and Turing machines. Proves fundamental limits on computation (incomputability, the halting problem). Provides the tools to compare the hardness of computational problems (reductions). Introduces computational complexity classes (P, NP, PSPACE and others).

Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communications networks and secure protocols. This course introduces the most fundamental probabilistic techniques used in computer science applications, in particular in randomized algorithms, probabilistic analysis of algorithms and machine learning.

A single algorithmic improvement can have a greater impact on our ability to solve a problem than ten years of incremental improvements in CPU speed. We study techniques for designing and analyzing algorithms. Typical problem areas addressed include hashing, searching, dynamic programming, graph algorithms, network flow, and optimization algorithms including linear programming.

Algorithms and representations used in artificial intelligence. Introduction and implementation of algorithms for search, planning, perception, knowledge representation, logic, probabilistic representation and reasoning, robotics and machine learning.

How can artificial systems learn from examples and discover information buried in data? We explore the theory and practice of statistical machine learning, focusing on computational methods for supervised and unsupervised learning. Specific topics include empirical risk minimization, probably approximately correct learning, kernel methods, neural networks, maximum likelihood estimation, the expectation maximization algorithm, and principal component analysis. This course also aims to expose students to relevant ethical and societal considerations related to machine learning that may arise in practice.

How can computers understand the visual world of humans? This course treats vision as a process of inference from noisy and uncertain data and emphasizes probabilistic and statistical approaches. Topics may include perception of 3D scene structure from stereo, motion, and shading; image filtering, smoothing, edge detection; segmentation and grouping; texture analysis; learning, recognition and search; tracking and motion estimation. Strongly recommended: basic linear algebra, basic calculus and exposure to probability.

The application of computational methods to problems in natural-language processing. In particular we examine techniques due to recent advances in deep learning: word embeddings, recurrent neural networks (e.g., LSTMs), sequence-to-sequence models, and generative adversarial networks (GANs. Programming projects include parsing, machine translation, question answering, and chat-bots.

What is deep learning? How is it related to machine learning? How is it applied to perform tasks like classifying images or translating languages? Deep Learning belongs to a broader family of machine learning methods. Deep learning-based methods (e.g., convolutional neural networks, recurrent neural networks, autoencoders) have led to rapid improvements in applications like computer vision, natural language processing, robotics, and even genomics and health. In this course, you will get an overview of the prominent techniques of deep learning and their applications. This course is designed to help you understand the underlying concepts as well as the promise and pitfalls of deep learning. It also aims at providing hands-on practice of implementing and applying deep learning methods in Python.

Data is (soon) at the core of essentially all domains from material science to health care. Mastering big data requires a set of skills spanning a variety of disciplines from distributed systems over statistics to machine learning as well as a deep understanding of a complex ecosystem of tools and platforms. Data Science refers to the intersection of these skills and is concerned with the whole processing pipeline to transform data into actionable knowledge. This course provides an overview of the various techniques and tools involved in Data Science and how they work together rather than focussing on a specific aspect. Among other things, we will cover SQL and NoSQL solutions for massive data management, basic algorithms for data mining and machine learning, information retrieval techniques, and visualization methods.

A continuation of the material of MATH 90 including further development of techniques of integration. Other topics covered are infinite series, power series, Taylor's formula, polar coordinates, parametric equations, introduction to differential equations, and numerical methods. MATH 90 and 100 or the equivalent are recommended for all students intending to concentrate in mathematics or the sciences. MATH 100 may not be taken in addition to MATH 170 or MATH 190.

This course, which covers roughly the same material and has the same prerequisites as MATH 100, covers integration techniques, sequences and series, parametric and polar curves, and differential equations of first and second order. Topics will generally include more depth and detail than in MATH 100. MATH 170 may not be taken in addition to MATH 100 or MATH 190.

This course, which covers roughly the same material and has the same prerequisites as MATH 100, is intended for students with a special interest in physics or engineering. The main topics are: calculus of vectors and paths in two and three dimensions; differential equations of the first and second order; and infinite series, including power series.

The objective of the course is to place on solid foundations the most common structures of Computer Science, to illustrate proof techniques, to provide the background for an introductory course in computational theory and to introduce basic concepts of probability theory. It introduces Boolean algebras, logic, set theory, elements of algebraic structures, graph theory, combinatorics and probability.

Probability and statistics have become indispensable tools in computer science. Probabilistic methods and statistical reasoning play major roles in machine learning, cryptography, network security, communication protocols, web search engines, robotics, program verification, and more. This course introduces the basic concepts of probability and statistics, focusing on topics that are most useful in computer science applications. Topics include: modeling and solution in sample space, random variables, simple random processes and their probability distributions, Markov processes, limit theorems, and basic elements of Bayesian and frequentist statistical inference.

A proof-based course that introduces the principles and concepts of modern abstract algebra. Topics will include groups, rings, and fields, with applications to number theory, the theory of equations, and geometry. Previous proof-writing experience is not required. MATH 1530 is required of all students concentrating in mathematics.

APMA 1650 is an integrated first course in mathematical statistics. The first half of APMA 1650 covers probability and the last half is statistics, integrated with its probabilistic foundation. Specific topics include probability spaces, discrete and continuous random variables, methods for parameter estimation, confidence intervals, and hypothesis testing.