Iterative methods for solving nonlinear equations; direct and iterative methods for solving linear systems; approximations of functions, derivatives, and integrals; error analysis.

Fundamental principles and techniques of computer graphics. The course covers the basics of going from a scene representation to a raster image using OpenGL. Specific topics include coordinate manipulations, perspective, basics of illumination and shading, color models, texture maps, clipping and basic raster algorithms, fundamentals of scene constructions. CS 31400 is recommended.

Important concepts, models, algorithms, abstractions, and implementation aspects of concurrent and parallel programs. Topics include: techniques used to describe concurrent programs (e.g., threads, events, co-routines, continuations), abstractions for shared-memory and message-passing programs, relaxed memory models, livelock and deadlock detection, lock-free algorithms, data races and atomicity, scheduling techniques, process calculi, and software transactions.

An introduction to cryptography basics: Classic historical ciphers including Caesar, Vigenere, and Vernam ciphers; modern ciphers including DES, AES, Pohlig-Hellman, and RSA; signatures and digests; key exchange; simple protocols; block and stream ciphers; network-centric protocols.

An in-depth examination of relational database systems including theory and concepts as well as practical issues in relational databases. Modern database technologies such as object-relational and Web-based access to relational databases. Conceptual design and entity relationship modeling, relational algebra and calculus, data definition and manipulation languages using SQL, schema and view management, query processing and optimization, transaction management, security, privacy, integrity management.

Concepts for structuring data, computation, and whole programs. Object-oriented languages, functional languages, logic- and rule-based languages. Data types, type checking, exception handling, concurrent processes, synchronization, modularity, encapsulation, interfaces, separate compilation, inheritance, polymorphism, dynamic binding, subtyping, overloading, beta-reduction, unification.

Any intelligent robot system interacting with our environment needs to have perception, planning, and control methods in its cognition process. The perception module outlines the robot’s procedures to gather and interpret sensory observations into world models. The underlying planning and control modules use those world models to plan robot behaviors and their interaction with our natural environments. Therefore, this course will cover the fundamental topics in robot perception, planning, and control to design general-purpose robot cognition algorithms. Overall, this course is divided into four modules: Robot perception: This covers fundamental techniques needed for robot localization and mapping from raw 3D sensory data. Robot planning: This module will discuss robot behavior planning techniques such as A*, RRT*, and trajectory optimization. Robot Control: This introduces basic control techniques such as PID controller to execute the robot’s planned behaviors in the real world. Robot Learning: This part will briefly introduce machine learning techniques for robot decision-making and control.

Turing machines and the Church-Turing thesis; decidability; halting problem; reducibility; undecidable problems; decidability of logical theories; Kolmogorov complexity; time classes; P, NP, NP-complete; space classes; Savitch’s theorem, PSPACE-completeness, NL-completeness; hierarchy theorems; approximation theorems; probabilistic algorithms; applications of complexity to parallel computation and cryptography. Typically offered Fall Spring.

Supervised reading and reports in various fields.

An introductory course in rigorous analysis, covering real numbers, sequences, series, continuous functions, differentiation, and Riemann integration. MA 30100 is helpful but not required.

Theoretical background for methods and results that appear in MA 35100. Inner products, orthogonality, and applications including least squares.

Multivariate calculus; partial differentiation; implicit function theorems and transformations; line and surface integrals; vector fields; theorems of Gauss, Green, and Stokes. Credit granted for only one of MA 36200 and MA 51000.

An introduction to ordinary differential equations with emphasis on problem solving and applications. The one-hour computer lab will give students an opportunity for hands-on experience with both the theory and applications of the subject.

Propositional calculus and predicate calculus with applications to mathematical proofs, valid arguments, switching theory, and formal languages.

Solution of linear programming problems by the simplex method, duality theory, transportation problems, assignment problems, network analysis, dynamic programming.

Fundamental properties of integers, polynomials, groups, rings, and fields, with emphasis on problem solving and applications. Not open to students with credit in MA 45000.