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Course Criteria
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3.00 Credits
Prerequisite(s): MAT 250 & MAT 258 This course is an introduction to elementary number theory and cryptography. Among the essential tools of number theory that will be covered are divisibility and congruence, Euler's function, Fermat'slittle theorem, Euler's formula, the Chinese remainder theorem, powers modulo m, kth roots modulo m, primitive roots and indices, and quadratic reciprocity. These tools will then be used in cryptography, where we will discuss e.g. encryption schemes, the role of prime numbers, security and factorization, the DES algorithm, public key encryption, and various other topics, as time allows.
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3.00 Credits
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.
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3.00 Credits
Prerequisite(s): Permission of instructor The content of this course will change each time it is offered. It is for the purpose of offering a new or specialized course of interest to the faculty and students that is not covered by the courses in the current catalog.
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3.00 Credits
Prerequisite(s): MAT 250 This course will introduce the foundations of real analysis by means of a rigorous reexamination of the topics covered in elementary calculus. The course starts with the topology of the real line and proceeds to a formal examination of limits, continuity, and differentiability. The course will also cover the convergence of sequences and series of real numbers and the uniform convergence of sequences of real valued functions.
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3.00 Credits
Prerequisite(s): MAT 400 A continuation of MAT 400, this course emphasizes the formal treatment of the theory of integration of functions of a real variable. It reexamines the Riemann integral and the Fundamental theorem of calculus as well as the theory of the Stieltjes and Lebesgue integral and their applications in probability and Fourier analysis. The course concludes with a discussion of the topology of R^n, and the differentiability and integrability of functions of several variables, including the theorems of Green and Stokes and the divergence theorem.
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3.00 Credits
Prerequisite(s): MAT 250 & MAT 258 This course provides an introduction to the foundations of abstract algebra. The fundamental objects of study are groups, rings, and fields. The student will build on previous courses in algebra, particularly linear algebra, with an even greater emphasis here on proofs. The study of groups is an ideal starting point, with few axioms but a rich landscape of examples and theorems, including matrix groups, homomorphism theorems, group actions, symmetry, and quotient groups. This course will extend these ideas to the study of rings and fields. Topics in ring theory include polynomial rings and ideals in rings. The course will also cover fields, their construction from rings, finite fields, basic theory of equations, and Galois theory.
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3.00 Credits
Prerequisite(s): MAT 400 This course builds on the foundations established in MAT 450. It will extend the fundamental objects of groups, rings, and fields to include modules over rings and algebras. The course will give the basic ideas of linear algebra a more rigorous treatment and extend scalars to elements in a commutative ring. In this context, students will study the general theory of vector spaces and similarity of transformations. The curriculum will also discuss non-commutative algebras and rings, emphasizing examples such as quaternion algebras. Further topics may include non-associative rings and algebras, Galois theory, exact sequences, and homology.
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1.00 Credits
Prerequisite(s): None Maintaining continuous registration is a requirement for the M.S.C.S. degree. Students who have completed most course requirements but are finishing their thesis or are satisfying incomplete grades must register to maintain continuous matriculation. This course may be taken up to two semesters, at which time it is expected that all program requirements will have been met. This credit may not be applied toward degree-completion requirements.
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2.00 Credits
Prerequisite(s): None This course provides an in-depth examination of theories and techniques in product management. Lectures will cover various aspects of product management including team leadership, interaction with management, marketing, budgeting, long-range project planning, and contract negotiations. The course will include exercises that will give students insight into dealing with team effectiveness and performance issues.
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3.00 Credits
Prerequisite(s): ENG 110 This course will introduce some of the basic philosophical issues and questions related to everyday life. Topics include human nature (self, mind, consciousness, and freedom), values (ethics, morality, and aesthetics), knowledge (reasoning, rationality, and truth), philosophy of science (universe and origins of life), philosophical positions (naturalism, idealism, realism, pragmatism, and existentialism), and philosophy of religion (god(s) and religion). Students will apply these concepts to the philosophical issues related to games and video games, specifically definitional issues, philosophical themes in games, and art in games, among others.
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