independence, integrity, privacy, security, application development, and therole of the database administrator.  Students use several database managementsystems.  Students may not receive credit for both CS&nbsp;364 and&nbsp;<!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><!WA15><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs564">564</A>.Prereq:&nbsp;<!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><!WA16><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs302">CS&nbsp;302</A> or consent of instructor.<A NAME="cs367">&#160;</A><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><!WA17><A NAME="tex2html38" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION00099000000000000000">367 Introduction to Data Structures 3 cr.</A></H2><P>Study of data structures - specification, application and implementation.Stacks, queues, trees and other important structures.  Application to garbagecollection, dynamic storage allocation, sorting and searching, symbol tables,and arithmetic expressions.  Emphasis on development and analysis of efficientalgorithms, including use of structured programming methodology.Prereq:&nbsp;<!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><!WA18><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs302">CS&nbsp;302</A>; Pascal or equivalent.<A NAME="cs371">&#160;</A><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><!WA19><A NAME="tex2html39" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000910000000000000000">371 Technology of Computer-Based Business Systems 3 cr. (also BUS)</A></H2><P>Overview of computers, their attendant technology, and the implications ofthis technology for large-scale, computer-based information systems.  Topicsinclude hardware, system software, program development, files, and datacommunications.  Prereq:&nbsp;Bus&nbsp;370 and <!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><!WA20><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs367">CS&nbsp;367</A>, or equivalentexperience with consent of instructor.<A NAME="cs412">&#160;</A><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><!WA21><A NAME="tex2html40" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000911000000000000000">412 Introduction to Numerical Methods 3 cr.</A></H2><P>Interpolation, solution of linear and nonlinear systems of equations,approximate integration and differentiation, numerical solution of ordinarydifferential equations.  Prereq:&nbsp;Math&nbsp;223,<!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><!WA22><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs302">CS&nbsp;302</A>, or equivalent and knowledge of matrix algebra. <A NAME="cs425">&#160;</A><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><!WA23><A NAME="tex2html41" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000912000000000000000">425 Introduction to Combinatorial Optimization 3 cr. (also Math &amp; IE)</A></H2><P>Exact and heuristic methods for key combinatorial optimization problems suchas: shortest path, maximum flow problems, and the traveling salesman problem.Techniques include problem-specific methods and general approaches such asbranch-and-bound, genetic algorithms, simulated annealing, and neuralnetworks. Prereq:&nbsp;Math&nbsp;221 or <!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><!WA24><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs302">CS&nbsp;302</A> or consent of instructor.<A NAME="cs458">&#160;</A><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><!WA25><A NAME="tex2html42" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000913000000000000000">458 Computer Graphics 3 cr. <!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><!WA26><A NAME="tex2html43" HREF="http://www.engr.wisc.edu/me/courses/me458.html">(also ME</A> &amp; <!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><!WA27><A NAME="tex2html44" HREF="http://www.engr.wisc.edu/ece/courses/ece458.html">ECE)</A></A></H2><P>Principles of computational geometry and computer graphics and theirapplication; homogeneous coordinates, projective geometry, 3-D curve andsurface representations; data structures and geometric databases, wire-frameand solid geometric representations; graphic I/O device characteristics andcost considerations.  Programming exercises and projects based onapplications.  Prereq:&nbsp;<!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><!WA28><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs302">CS&nbsp;302</A> and Math&nbsp;320 or&nbsp;340, or consent of instructor.<A NAME="cs460">&#160;</A><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><!WA29><A NAME="tex2html45" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000914000000000000000">460 Artificial Intelligence Programming Languages and Tools 3 cr.</A></H2><P>Symbolic computation; Lisp programming; Prolog programming; knowledgerepresentation languages based on logic, objects, frames, rules; symbolicpattern matching; automatic inferencing and reasoning techniques;special-purpose languages and computer architectures for artificialintelligence applications.  Prereq:&nbsp;<!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><!WA30><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs367">CS&nbsp;367</A>.(Infrequently offered.)<A NAME="cs475">&#160;</A><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><!WA31><A NAME="tex2html46" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000915000000000000000">475 Introduction to Combinatorics 3 cr. (also Math&nbsp;&amp; Stat)</A></H2><P>Problems of enumeration, distribution and arrangement.  Inclusion-exclusionprinciple.  Generating functions and linear recurrence relations.Combinatorial identities.  Graph coloring problems.  Finite designs.  Systemsof distinct representatives and matching problems in graphs.  Potentialapplications in the social, biological, and physical sciences.  Puzzles.Emphasis on problem solving.  Prereq:&nbsp;Math&nbsp;320 or 340 and consent ofinstructor.<A NAME="cs509">&#160;</A><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><!WA32><A NAME="tex2html47" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000916000000000000000">509 Mathematics for Computer Science 3 cr.</A></H2><P>Program correctness and termination, invariants, pre- and post-conditions,axiomatic semantics.  Representing time and space requirements of programs bysummations, recurrences, and generating functions.  Exact and asymptoticsolutions.  Analysis of algorithms for sorting, searching, and data structuretraversal.  Prereq:&nbsp;<!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><!WA33><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs367">CS&nbsp;367</A> and Math&nbsp;222, or consent of instructor.(Infrequently offered.)<A NAME="cs513">&#160;</A><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><!WA34><A NAME="tex2html48" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000917000000000000000">513 Numerical Linear Algebra 3 cr. (also Math)</A></H2><P>Direct and iterative solution of linear and nonlinear systems and ofeigenproblems.  LU and symmetric LU factorization.  Complexity, stability, andconditioning.  Nonlinear systems. Iterative methods for linearsystems. QR-factorization and least squares. Eigenproblems: local and globalmethods.  Prereq:&nbsp;Math&nbsp;340 or equivalent; <!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><!WA35><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs302">CS&nbsp;302</A> or equivalent.<A NAME="cs514">&#160;</A><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><!WA36><A NAME="tex2html49" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000918000000000000000">514 Numerical Analysis 3 cr. (also Math)</A></H2><P>Polynomial forms, divided differences.  Polynomial interpolation.  Polynomialapproximation: uniform approximation and Chebyshev polynomials, least-squaresapproximation and orthogonal polynomials.  Splines, B-splines and splineapproximation.  Numerical differentiation and integration.  Numerical methodsfor solving initial and boundary value problems for ordinary differentialequations.  Prereq:&nbsp;Math&nbsp;340 or equivalent; <!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><!WA37><A HREF="#cs320">CS&nbsp;302</A> or equivalent.<A NAME="cs520">&#160;</A><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><!WA38><A NAME="tex2html50" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000919000000000000000">520 Introduction to Theoretical Computer Science 3 cr.</A></H2><P>Survey of the basic concepts of theory, including context-free andcontext-sensitive languages, regular sets, finite and pushdown automata,Turing machines, undecidable problems, complexity with respect to time andspace, NP-completeness, and reducibilities.  Prereq:&nbsp;<!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><!WA39><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs367">CS&nbsp;367</A> and Math&nbsp;222, orconsent of instructor.