2024–2025 Course Catalog 1st Edition - Course Descriptions DigiPen Institute of Technology 91
MAT 562 Fuzzy Sets and Logic (3 cr.)
Prerequisite(s): MAT 250, MAT 258
This course introduces the basic theory of fuzzy sets and fuzzy
logic and explores some of their applications. Topics covered
include classical sets and their operations, fuzzy sets and their
operations, membership functions, fuzzy relations, fuzzification/
defuzzification, classical logic, multi-valued logic, fuzzy logic,
fuzzy reasoning, fuzzy arithmetic, classical groups, and fuzz
groups. Students will also explore a number of applications,
including approximate reasoning, fuzzy control, fuzzy behavior,
and interaction in computer games.
MAT 563 Partial Dierential Equations and Fluid Dynamics
(3 cr.)
Prerequisite(s): None
This course explores partial dierential equations (PDEs) and
fluid dynamics. Topics covered in this class include Fourier
series, Fourier transforms, classification of PDEs, Poisson’s
equation, heat equation, wave equation, and introductory topics
of fluid dynamics. Solution methods of initial and boundary
value problems of various types will be investigated. Numerical
methods, such as finite dierence, finite volume, and finite
element will be studied.
MAT 564 Combinatorial Game Theory (3 cr.)
Prerequisite(s): MAT 258
Combinatorial Game Theory studies finite two-player games in
which there are no ties. Techniques from logic, combinatorics,
and set theory are used to prove various properties of such
games. Typical games include Domineering , Hackenbush, and
Nim. The analysis of such games can also be used to study other
more complex games like Dots and Boxes, impartial and partisan
games, winning strategies outcome classes, algebra of games.
MAT 565 Introduction to Topology (3 cr.)
Prerequisite(s): MAT 250, MAT 258
This course is an introduction to topology and its applications.
Topics include: topological spaces, quotient and product spaces,
metric and normed spaces, connectedness, compactness, and
separation axioms. Further topics may include: basic algebraic
topology, fixed point theorems, theory of knots, and applications
to kinematics, game theory, and computer graphics.
MAT 567 Fuzzy Systems and Neural Networks (3 cr.)
Prerequisite(s): None
Credit may be received for one of MAT 562 and MAT 567, but
not both
This course introduces the basic theory of fuzzy sets and fuzzy
logic, fuzzy systems, neural networks and neuro-fuzzy systems.
Topics in Fuzzy Systems include: fuzzy sets and their operations,
membership functions, fuzzy systems of various types, fuzzy
control, and fuzzy clustering. Topics in Artificial Neural Networks
include: artificial neural networks, the backpropagation
algorithm, deep learning, adaptive neuro-fuzzy inference
systems. Additional topics may include parameter selection and
regularization for neural networks, and convolutional neural
networks.
MAT 570 Real Analysis (3 cr.)
Prerequisite(s): None
This course explores topics in mathematical analysis of real
numbers and functions of real variables. Topics covered in
this course include: real numbers, metric spaces, topology of
metric spaces, the contraction principle, continuity of functions
on metric spaces, dierentiability of real-valued functions,
sequences and series of functions, continuity and dierentiability
of functions of several variables, and Riemann integration.
Additional topics may include Euclidean spaces, normed spaces,
functions of bounded variation, and Riemann-Stieltjes integrals.
MAT 571 Functional Analysis (3 cr.)
Prerequisite(s): MAT 570
This course explores topics in measure theory and functional
analysis. The topics covered in this course include: Lebesgue
measure, Lebesgue integration, normed spaces, Banach spaces,
Fourier series and wavelets, and Hilbert spaces, together with
their applications. Additional topics may include Hahn-Banach
theorem, bounded linear operators on Hilbert spaces, Riesz
representation theorem, Sobolev spaces, and self-adjoint
operators.
MAT 572 Complex Analysis (3 cr.)
Prerequisite(s): None
This course explores topics in complex analysis. Topics include:
the complex number field and its geometry, complex functions,
limits, complex dierentiation, analytic functions, conformal
mappings, contour integration, and Laurent series. Additional
topics may include: Rouche’s theorem, the maximum modulus
theorem, Liouville’s theorem, and applications.
MAT 580 Stochastic Processes (3 cr.)
Prerequisite(s): None
This course is a formal introduction to stochastic processes with
applications. The main topics are discrete and continuous time
Markov chains, Poisson processes, random walks, branching
processes, first passage times, recurrence and transience, and
stationary distributions. The course also covers Brownian motion
and martingales. Other topics may include renewal processes,
queues, optimal stopping theory, Monte Carlo methods, and
stochastic integration.
MAT 581 Statistical Inference and Data Analysis (3 cr.)
Prerequisite(s): None
This course presents modern statistical concepts and methods
developed in a mathematical framework. Topics include
statistical inference, point and interval estimation, confidence
intervals and hypothesis testing, suciency, Neyman-Pearson