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Date: Tuesday, 14-Jan-97 22:31:42 GMTServer: NCSA/1.3MIME-version: 1.0Content-type: text/htmlLast-modified: Sunday, 10-Sep-95 21:12:22 GMTContent-length: 11571<HTML><HEAD><TITLE>Math and Computer Science Courses</TITLE></HEAD><BODY><CENTER><!WA0><IMG SRC="http://www.cs.miami.edu/images/OfficialHome.gif" ALIGN=LEFT><HR SIZE=2 NOSHADE WIDTH=90%><STRONG><FONT SIZE=+2>M</FONT>ath and <FONT SIZE=+2>C</FONT>omputer<FONT SIZE=+2>S</FONT>cience <FONT SIZE=+2>C</FONT>ourses<BR></STRONG></CENTER><HR SIZE=2 NOSHADE WIDTH=90%><ul><li><!WA1><A HREF="#Level200">200 Level Courses</A><li><!WA2><A HREF="#Level300">300 Level Courses</A><li><!WA3><A HREF="#Level400">400 Level Courses</A><li><!WA4><A HREF="#Level500">500 Level Courses</A><li><!WA5><A HREF="#Level600">Graduate Courses</A></ul><p><A NAME="Level200"><b>200-Level Courses</b><p><b> MTH 210: Vectors and Matrices</b><br>Two and three dimensional vectors, inner products, vectorproducts, matrix algebra, linear transformations,determinants, quadratic and bilinear forms.<br><em> Prerequisite or corequisite: MTH 112 or 132. Credits: 3.</em><p><b> MTH 211: Calculus III</b><br>Matrix algebra, vectors in space, partial differentiation,multiple integrations.<br><em> Prerequisite: MTH 112. Not open to students with credit in MTH 312. Credits: 3.</em><p><b> MTH 220: Programming II</b><br>Programming methodology using Pascal. Linked lists, stacks,queues, binary trees, files, recursion, elementary searchingand sorting.<br><em> Prerequisite: MTH 120. Credits: 3.</em><p><b> MTH 224: Introduction to Probability and Statistics</b><br>Probability distributions, random variables, expection and variance,point estimation, interval estimation, testing of hypothesis, analysisof variance.<br><em> Prerequisite: One semester of calculus. Credits: 3.</em><p><b> MTH 228: Assembly Language Programming</b><p><b> MTH 230: Introduction to Abstract Mathematics</b><br>Fundamentals of set theory, logic and methods ofmathematical proof.<br><em> Prerequisite or corequisite: MTH 112 or 132. Credits: 3.</em><p><A NAME="Level300"><b>300-Level Courses</b><p><b> MTH 309: Discrete Mathematics I</b><br>Mathematical methods of Computer Science and Computer Engineering.Mathematcial reasoning, sets, relations, functions, booleanalgebra, combinatorics, graphs.<br><em> Prerequisite: MTH 111. Credits: 3.</em><p><b> MTH 310: Multivariable Calculus</b><br>Equations of curves, surfaces, solids; vector differentialcalculus; integration of scalar valued functions.Applications<br><em> Prerequisite: MTH 210 and (112 or 132).Note open to students with credit in MTH 533. Credits: 3.</em><p><b> MTH 311: Ordinary Differential Equations</b><br>Linear differential equations, simultaneous equations, solutions inseries, numerical solutions.<br><em> Prerequisite: MTH 112 or 132. Credits: 3.</em><p><b> MTH 312: Vector Analysis</b><br>Vector algebra, partial differentiation, multiple integration,scalar and vector fields, line and surface integrals.<br><em> Prerequisite: MTH 112. Not open to students with creditin MTH 211. Credits: 3.</em><p><b> MTH 317: Introduction to Data Structures</b><br>Same course as MTH 220.<p><b> MTH 320: Introduction to Numerical Analysis</b><br>Interpolation, quadrature, numerical solution of algebraicand transcendental equations, matrix inversion.<br><em> Prerequisite: MTH 210 or 211; knowledge of a structuredprogramming language. Credits: 3.</em><p><b> MTH 322: C Programming and UNIX</b><br>Fundamentals of C programming in the UNIX environment: characterand string manipulations, pointer arithmetic, functions, structures,systems calls and shell programming.<br><em> Prerequisite: MTH 111, 120 Credits: 3.</em><p><A NAME="Level400"><b>400-Level Courses</b><p><b> MTH 471, 472: Directed Readings</b><p><A NAME="Level500"><b>500-Level Courses</b><p><b> MTH 504: Foundations of Geometry</b><br>Axiom systems and models of Euclidean and Non-Euclidean geometry.<br><em> Prerequisite: MTH 230 or 309. Credits: 3.</em><p><b> MTH 506: Logic</b><br>Propositional and first-order logic: completeness. Computationallogic: Robinson's resolution. Formalized theories: arithmetic, Godel'sincompleteness theorem, Tarski's theorem on undefinability of truth.<br><em> Prerequisite: MTH 230 or 309 or permission of theinstructor.</em><p><b> MTH 508: Survey of Modern Algebra</b><br>Algebraic systems, equivalence classes, groups, rings, fields,unique factorization domains.<br><em> Prerequisite: MTH 210 and 230. Not open to students withcredit in MTH 509 or 561. Credits: 3.</em><p><b> MTH 509: Discrete Mathematics II</b><br>Groups and combinatorics; applications of group theory tocomputer design and error correcting codes; Semigroups andtheir applications to finite state machines; rings and fields;applications of Boolean algebra to computer design.<br><em> Prerequisite: MTH 210, 309. Credits: 3.</em><p><b> MTH 512: Elementary Complex Analysis</b><br>Complex variables; conformal mapping, contour integraion.<br><em> Prerequisite: MTH 211 or 310. Credits: 3.</em><p><b> MTH 513: Partial Differential Equations I</b><br>Derivation, well posedness, and qualitative properties of initial valueand boundary value problems for the heat, wave and Laplace equations.Energy methods, causality, maximum principles, heat kernels, Fourierseries, and potential theory.<br><em> Prerequisite: MTH 210, 311 and either MTH 310 or 312. Credits:3.</em><p><b> MTH 514: Partial Differential Equations II</b><br>Continuation of MTH 513. Approximations of solutions, distributions andintegral transform methods, spectral theory and scattering. Applicationsto physical problems. Nonlinear equations and phenomena.<br><em> Prerequisite: MTH 513 or permission of the instructor. Credits: 3.</em><p><b> MTH 515: Ordinary Differential Equations</b><br>Linear systems, equilibria and periodic solutions, stability analysis,bifurcation, phase plane analysis, boundary value problems, applicationsto engineering and physics.<br><em> Prerequisites: MTH 311 and either MTH 211 or 310. Credits: 3.</em><p><b> MTH 516: Dynamics and Bifurcations</b><br>Bifurcation of equilibria and periodic solutions, global theory ofplanar systems, planar maps, nonlinear vibrations, forced oscillations,chaotic solutions, Hamiltonian systems, applications to engineering andphysics.<br><em> Prerequisites: MTH 515 or permission of the instructor.Credits: 3.</em><p><b> MTH 517: Data Structures and Algorithm Analysis</b><br>Data abstraction, formal specification, trees, B-trees, balancedbinary trees, graphs, searching and sorting.Algorithm analysis. Memory management.<br><em> Prerequisite: MTH 220 and 309. Credits: 3.</em><p><b> MTH 518: Interpreters and Compiler Theory</b><br>Translation of higher-level languages into machine language. Topicsin computer translation theory include grammars, parsing, scannersprecedence relations, run-time storage and symbol table organization,semantic routines, chaining and hashing, code generation and optimization,and macro implementation.<br><em> Prerequisite: MTH 519. Credits: 3.</em><p><b> MTH 519: Programming Languages</b><br>Formal definition of programming languages including specification ofsyntax and semantics; simple statements; global properties ofalgorithmic languages including scope of declarations, storageallocations, grouping of statements, subroutines, coroutines, and tasks;run time representation of program and data structures.<br><em> Prerequisite: MTH 517. Credits: 3.</em><p><b> MTH 520: Numerical Analysis I</b><br>Numerical linear algebra including the algebraic eigenvalue problem.<br><em> Prerequisite: MTH 320 or permission of department chairman.Credits: 3.</em><p><b> MTH 521: Numerical Analysis II</b><br>Numerical solution of ordinary and partial differential equations.<br><em> Prerequisite: MTH 320 or 520 or permission of department chairman.Credits: 3.</em><p><b> MTH 523: Principles of Filing and Database Systems</b><br>Theory and design of database systems with empahsis given torelational techniques. Topics include relational algebra andcalculus, filing structures, relational modeling, query languages,and optimization.<br><em> Prerequisite: MTH 517. Credits: 3.</em><p><b> MTH 524: Introduction to Probability Theory</b><br>Probability spaces, random variables, expectation, limit theorems.<br><em> Prerequisite: MTH 310 or permission of department chariman.</em><p><b> MTH 525: Introduction to Mathematical Statistics</b><br>Probability distributions, theory of sampling and hypothesistesting.<br><em> Prerequisite: MTH 524. Credits: 3. </em><p><b> MTH 527: Theory of Automata</b><br>Finite-state automata, context-free grammars, pushdown automata,Turing machines and computability.<br><em> Prerequisite: MTH 309 or 508. Credits: 3.</em><p><b> MTH 528: Combinatorics</b><br>Permutations and combinations, generating functions, enumerative analysis.<br><em> Prerequisite: One of the following: MTH 508, 509 or 561.Credits: 3.</em><p><b> MTH 529: Introduction to Computer Graphics</b><br>Transformations, sequences, and geometry by graphical methods:representaion, manipulation and display of geometric information,2--D and 3--D representaions, transformations and displaytechniques, display and input devices, software packages.<br><em> Prerequisite: MTH 517. Credits: 3.</em><p><b> MTH 531, 532: Topology</b><br>Set algebra, cardinal and ordinal numbers, axiom of choice, topologicalspaces, compactness, connectedness, separation properties, quotientspaces, Tychonoff Theorem, compactification.<br><em> Prerequisite: Permission of department chairman. Credits: 3each.</em><p><b> MTH 533: Introduction to Real Analysis I</b><br>Numerical sequences and series; continuity; differentiation;integration; sequences and series of functions; Fourier series;functions of several variables; implicit and inverse function theorems.<br><em> Prerequisite: MTH 211 (or 310) and 230. Credits: 3.</em><p><b> MTH 534: Introduction to Real Analysis II</b><br>Continuation of MTH 533.<br><em> Prerequisite: MTH 533. Credits: 3.</em><p><b> MTH 540: Algorithm Design and Analysis</b><br>Design techniques include divide-and-conquer,greedy method, dynamic programming, backtracking. Time and space complexity. Sorting, searching, combinatorialand graph algorithms.<br><em> Prerequisite: MTH 517. Credits: 3.</em><p><b> MTH 545: Introduction to Artificial Intelligence</b><br>Artificial Intelligence principles and methods; game theory,optimal strategies, logical reasoning, heuristic and adaptiveprogramming; Lisp and/or Prolog.<br><em> Prerequisite: MTH 220 or 317 Credits: 3.</em><p><b> MTH 561: Abstract Algebra</b><br>Groups, rings; linear algebra; modules.<br><em> Prerequisite: MTH 210 and permission of department chairman.Credits: 3.</em><p><b> MTH 562: Abstract Algebra</b><br>Continuation of MTH 561.<br><em> Prerequisite: MTH 561. Credits: 3.</em><p><b><a name="MTH596"> MTH 596: Operating Systems and Networking</a></b><br>Virtual Machine, memory hierarchy and organizations,resource allocation, process models and interprocess synchronizationand communication, communication protocols. Local and Wide Area Networks:OSI models, current technologies and topics of interest.Case study of Unix and the Internet.<br><em> Prerequisite: MTH220 or 317. Credits: 3.</em><p><A NAME="Level600">See catalog for graduate studies.<BR><HR SIZE=2 NOSHADE><!WA6><A HREF="http://www.cs.miami.edu/OfficialHome.html"><!WA7><IMG SRC="http://www.cs.miami.edu/images/OfficialHome.gif">Official Home Page<HR><!WA8><A HREF="mailto:www@cs.cs.miami.edu"><EM>www@cs.cs.miami.edu</EM></A></BODY></HTML>⌨️ 快捷键说明
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