Date: Tuesday, 14-Jan-97 22:31:42 GMT Server: NCSA/1.3 MIME-version: 1.0 Content-type: text/html Last-modified: Sunday, 10-Sep-95 21:12:22 GMT Content-length: 11571 Math and Computer Science Courses

Math and Computer Science Courses

200-Level Courses

MTH 210: Vectors and Matrices
Two and three dimensional vectors, inner products, vector products, matrix algebra, linear transformations, determinants, quadratic and bilinear forms.
Prerequisite or corequisite: MTH 112 or 132. Credits: 3.

MTH 211: Calculus III
Matrix algebra, vectors in space, partial differentiation, multiple integrations.
Prerequisite: MTH 112. Not open to students with credit in MTH 312. Credits: 3.

MTH 220: Programming II
Programming methodology using Pascal. Linked lists, stacks, queues, binary trees, files, recursion, elementary searching and sorting.
Prerequisite: MTH 120. Credits: 3.

MTH 224: Introduction to Probability and Statistics
Probability distributions, random variables, expection and variance, point estimation, interval estimation, testing of hypothesis, analysis of variance.
Prerequisite: One semester of calculus. Credits: 3.

MTH 228: Assembly Language Programming

MTH 230: Introduction to Abstract Mathematics
Fundamentals of set theory, logic and methods of mathematical proof.
Prerequisite or corequisite: MTH 112 or 132. Credits: 3.

300-Level Courses

MTH 309: Discrete Mathematics I
Mathematical methods of Computer Science and Computer Engineering. Mathematcial reasoning, sets, relations, functions, boolean algebra, combinatorics, graphs.
Prerequisite: MTH 111. Credits: 3.

MTH 310: Multivariable Calculus
Equations of curves, surfaces, solids; vector differential calculus; integration of scalar valued functions. Applications
Prerequisite: MTH 210 and (112 or 132). Note open to students with credit in MTH 533. Credits: 3.

MTH 311: Ordinary Differential Equations
Linear differential equations, simultaneous equations, solutions in series, numerical solutions.
Prerequisite: MTH 112 or 132. Credits: 3.

MTH 312: Vector Analysis
Vector algebra, partial differentiation, multiple integration, scalar and vector fields, line and surface integrals.
Prerequisite: MTH 112. Not open to students with credit in MTH 211. Credits: 3.

MTH 317: Introduction to Data Structures
Same course as MTH 220.

MTH 320: Introduction to Numerical Analysis
Interpolation, quadrature, numerical solution of algebraic and transcendental equations, matrix inversion.
Prerequisite: MTH 210 or 211; knowledge of a structured programming language. Credits: 3.

MTH 322: C Programming and UNIX
Fundamentals of C programming in the UNIX environment: character and string manipulations, pointer arithmetic, functions, structures, systems calls and shell programming.
Prerequisite: MTH 111, 120 Credits: 3.

400-Level Courses

MTH 471, 472: Directed Readings

500-Level Courses

MTH 504: Foundations of Geometry
Axiom systems and models of Euclidean and Non-Euclidean geometry.
Prerequisite: MTH 230 or 309. Credits: 3.

MTH 506: Logic
Propositional and first-order logic: completeness. Computational logic: Robinson's resolution. Formalized theories: arithmetic, Godel's incompleteness theorem, Tarski's theorem on undefinability of truth.
Prerequisite: MTH 230 or 309 or permission of the instructor.

MTH 508: Survey of Modern Algebra
Algebraic systems, equivalence classes, groups, rings, fields, unique factorization domains.
Prerequisite: MTH 210 and 230. Not open to students with credit in MTH 509 or 561. Credits: 3.

MTH 509: Discrete Mathematics II
Groups and combinatorics; applications of group theory to computer design and error correcting codes; Semigroups and their applications to finite state machines; rings and fields; applications of Boolean algebra to computer design.
Prerequisite: MTH 210, 309. Credits: 3.

MTH 512: Elementary Complex Analysis
Complex variables; conformal mapping, contour integraion.
Prerequisite: MTH 211 or 310. Credits: 3.

MTH 513: Partial Differential Equations I
Derivation, well posedness, and qualitative properties of initial value and boundary value problems for the heat, wave and Laplace equations. Energy methods, causality, maximum principles, heat kernels, Fourier series, and potential theory.
Prerequisite: MTH 210, 311 and either MTH 310 or 312. Credits: 3.

MTH 514: Partial Differential Equations II
Continuation of MTH 513. Approximations of solutions, distributions and integral transform methods, spectral theory and scattering. Applications to physical problems. Nonlinear equations and phenomena.
Prerequisite: MTH 513 or permission of the instructor. Credits: 3.

MTH 515: Ordinary Differential Equations
Linear systems, equilibria and periodic solutions, stability analysis, bifurcation, phase plane analysis, boundary value problems, applications to engineering and physics.
Prerequisites: MTH 311 and either MTH 211 or 310. Credits: 3.

MTH 516: Dynamics and Bifurcations
Bifurcation of equilibria and periodic solutions, global theory of planar systems, planar maps, nonlinear vibrations, forced oscillations, chaotic solutions, Hamiltonian systems, applications to engineering and physics.
Prerequisites: MTH 515 or permission of the instructor. Credits: 3.

MTH 517: Data Structures and Algorithm Analysis
Data abstraction, formal specification, trees, B-trees, balanced binary trees, graphs, searching and sorting. Algorithm analysis. Memory management.
Prerequisite: MTH 220 and 309. Credits: 3.

MTH 518: Interpreters and Compiler Theory
Translation of higher-level languages into machine language. Topics in computer translation theory include grammars, parsing, scanners precedence relations, run-time storage and symbol table organization, semantic routines, chaining and hashing, code generation and optimization, and macro implementation.
Prerequisite: MTH 519. Credits: 3.

MTH 519: Programming Languages
Formal definition of programming languages including specification of syntax and semantics; simple statements; global properties of algorithmic languages including scope of declarations, storage allocations, grouping of statements, subroutines, coroutines, and tasks; run time representation of program and data structures.
Prerequisite: MTH 517. Credits: 3.

MTH 520: Numerical Analysis I
Numerical linear algebra including the algebraic eigenvalue problem.
Prerequisite: MTH 320 or permission of department chairman. Credits: 3.

MTH 521: Numerical Analysis II
Numerical solution of ordinary and partial differential equations.
Prerequisite: MTH 320 or 520 or permission of department chairman. Credits: 3.

MTH 523: Principles of Filing and Database Systems
Theory and design of database systems with empahsis given to relational techniques. Topics include relational algebra and calculus, filing structures, relational modeling, query languages, and optimization.
Prerequisite: MTH 517. Credits: 3.

MTH 524: Introduction to Probability Theory
Probability spaces, random variables, expectation, limit theorems.
Prerequisite: MTH 310 or permission of department chariman.

MTH 525: Introduction to Mathematical Statistics
Probability distributions, theory of sampling and hypothesis testing.
Prerequisite: MTH 524. Credits: 3.

MTH 527: Theory of Automata
Finite-state automata, context-free grammars, pushdown automata, Turing machines and computability.
Prerequisite: MTH 309 or 508. Credits: 3.

MTH 528: Combinatorics
Permutations and combinations, generating functions, enumerative analysis.
Prerequisite: One of the following: MTH 508, 509 or 561. Credits: 3.

MTH 529: Introduction to Computer Graphics
Transformations, sequences, and geometry by graphical methods: representaion, manipulation and display of geometric information, 2--D and 3--D representaions, transformations and display techniques, display and input devices, software packages.
Prerequisite: MTH 517. Credits: 3.

MTH 531, 532: Topology
Set algebra, cardinal and ordinal numbers, axiom of choice, topological spaces, compactness, connectedness, separation properties, quotient spaces, Tychonoff Theorem, compactification.
Prerequisite: Permission of department chairman. Credits: 3 each.

MTH 533: Introduction to Real Analysis I
Numerical sequences and series; continuity; differentiation; integration; sequences and series of functions; Fourier series; functions of several variables; implicit and inverse function theorems.
Prerequisite: MTH 211 (or 310) and 230. Credits: 3.

MTH 534: Introduction to Real Analysis II
Continuation of MTH 533.
Prerequisite: MTH 533. Credits: 3.

MTH 540: Algorithm Design and Analysis
Design techniques include divide-and-conquer, greedy method, dynamic programming, backtracking. Time and space complexity. Sorting, searching, combinatorial and graph algorithms.
Prerequisite: MTH 517. Credits: 3.

MTH 545: Introduction to Artificial Intelligence
Artificial Intelligence principles and methods; game theory, optimal strategies, logical reasoning, heuristic and adaptive programming; Lisp and/or Prolog.
Prerequisite: MTH 220 or 317 Credits: 3.

MTH 561: Abstract Algebra
Groups, rings; linear algebra; modules.
Prerequisite: MTH 210 and permission of department chairman. Credits: 3.

MTH 562: Abstract Algebra
Continuation of MTH 561.
Prerequisite: MTH 561. Credits: 3.

MTH 596: Operating Systems and Networking
Virtual Machine, memory hierarchy and organizations, resource allocation, process models and interprocess synchronization and communication, communication protocols. Local and Wide Area Networks: OSI models, current technologies and topics of interest. Case study of Unix and the Internet.
Prerequisite: MTH220 or 317. Credits: 3.

See catalog for graduate studies.


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