Basic concepts, data structures, and algorithms for geometric objects. Examples of topics: Cartesian geometry, transformations and their representation, queries and sampling, triangulations. Emphasis on rigorous reasoning and analysis, advancing algorithmic maturity and expertise in its application.

Basic concepts and algorithms for manipulation of algebraic objects, such as residues, matrices, polynomials; and applications to various CS areas, such as cryptography and fault-tolerance. Emphasis on rigorous reasoning and analysis.

Introduction to basic probabilistic concepts and methods used in computer science. Develops an understanding of the crucial role played by randomness in computing, both as a powerful tool and as a challenge to confront and analyze. Emphasis on rigorous reasoning, analysis, and algorithmic thinking.

Concepts involved in the design of programming languages. Bindings, argument transmission, and control structures. Environments: compile-time, load-time, and run-time. Interpreters.

The basic concepts of the theory of computation are studied. Topics include models of computation, polynomial time, Church's thesis; universal algorithms, undecidability and intractability; time and space complexity, nondeterminism, probabilistic computation and reductions of computational problems.

Programming-centric introduction to computer systems. The course discusses system design principles, performance analysis, communication and synchronization primitives, concurrency control, database transactions, data consistency, task and data parallelism, replication, fault tolerance, and distributed consensus. Part of the discussion includes case studies of real systems from industry. All programming assignments will be in Go.