Use of methods from combinatorics, complex analysis, and asymptotics inobtaining precise analyses of quicksort, chained hashing, and otheralgorithms.  Prereq:&nbsp;<!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><!WA99><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs577">CS&nbsp;577</A>, knowledge of complex variables at the level ofMath&nbsp;321.(Infrequently offered.)<A NAME="cs712">&#160;</A><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><!WA100><A NAME="tex2html80" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000946000000000000000">712 Finite Difference Methods 3 cr.</A></H2><P>Development of finite difference methods for initial and boundary valueproblems for hyperbolic, parabolic, and elliptic partial differentialequations.  Analysis of accuracy and stability of difference schemes.  Directand iterative methods for solving elliptic difference schemes.  Applicationsfrom science and engineering.  Prereq:&nbsp;<!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><!WA101><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs302">CS&nbsp;302</A>,<!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><!WA102><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs412">412</A>, Math&nbsp;419 or equivalent, or consent of instructor.<A NAME="cs713">&#160;</A><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><!WA103><A NAME="tex2html81" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000947000000000000000">713 Numerical Analysis of Differential Equations 3 cr.</A></H2><P>Analysis of numerical methods for ordinary differential equations.  Singlestep and multistep methods.  Stiff equations.  Introduction to Galerkinmethods; collocation, least squares, etc.  Analysis of methods for thesolution of large sparse systems of boundary value problems. Prereq:&nbsp;Graduatestanding and consent of instructor.<A NAME="cs717">&#160;</A><A NAME="cs718">&#160;</A><H2><A NAME="SECTION000948000000000000000">717(-718) <!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><!WA104><A NAME="tex2html82" HREF="http://www.cs.wisc.edu/~deboor/cs717.html">Numerical Functional Analysis</A> 3 cr. per sem. (also Math)</A></H2><P>Fundamentals of normed spaces and linear operators; analysis of nonlinearoperators; existence of, and iterative methods for, solutions of linear andnonlinear operator equations, error estimation; variational theory andminimization problems; monotonicity theory.  Development of abstract tools andapplication of them to the general analysis of numerical methods for suchproblems as differential and integral equations.Prereq:&nbsp;<!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><!WA105><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs513">CS&nbsp;513</A>, <!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><!WA106><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs514">514</A> and Math&nbsp;223 or consentof instructor.  (CS&nbsp;718 is infrequently offered.)<A NAME="cs719">&#160;</A><H2><A NAME="SECTION000949000000000000000">719 <!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><!WA107><A NAME="tex2html83" HREF="http://www.cs.wisc.edu/~ferris/cs719.html">Network Flows</A> 3 cr. (also IE)</A></H2><P>Optimization problems and techniques for networks, including single andmulti-commodity network flow, critical path, and facilities location problems.The theory of totally unimodular matrices and its relationship to networkoptimization.  Prereq:&nbsp;<!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><!WA108><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs525">CS&nbsp;525</A> or consent of instructor.<A NAME="cs720">&#160;</A><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><!WA109><A NAME="tex2html84" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000950000000000000000">720 Integer Programming 3 cr. (also IE)</A></H2><P>Formulation of integer programming problems and the characterization ofoptimization problems representable as integer and mixed-integer programs.The degree of difficulty of classes of integer programs and its relation tothe structure of their feasible sets.  Optimality conditions.Branch-and-bound, cutting plane, and decomposition methods for obtainingsolutions or approximating solutions. Prereq:&nbsp;<!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><!WA110><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs525">CS&nbsp;525</A> or consent of instructor.<A NAME="cs723">&#160;</A><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><!WA111><A NAME="tex2html85" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000951000000000000000">723 Dynamic Programming and Associated Topics 3 cr. (also IE)</A></H2><P>A generalized optimization model; discrete and continuous state spaces;deterministic and stochastic transition functions.  Multistage decisionprocesses.  Functional equations and successive approximation in function andpolicy spaces.  Relationship to linear programming and acyclic networks.Markovian decision processes.  Solution methods and computational problems.Associated topics and applications such as calculus of variations; feedbackcontrol processes; and optimal trajectories, inventory and maintenancepolicies, and stopping rules.  Prereq:&nbsp;<!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><!WA112><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs525">CS&nbsp;525</A> or IE&nbsp;623;Math&nbsp;521 or <!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><!WA113><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs726">CS&nbsp;726</A>; Math&nbsp;431 and computer programming, orconsent of instructor.  (Infrequently offered.)<A NAME="cs726">&#160;</A><H2><A NAME="SECTION000952000000000000000">726 <!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><!WA114><A NAME="tex2html86" HREF="http://www.cs.wisc.edu/~ferris/cs726-all.html">Nonlinear Programming Theory and Applications</A> 3 cr. (also IE &amp; Stat)</A></H2><P>Separation theorems and other properties of convex sets in finite-dimensionalspaces.  Formulation of nonlinear programming problems.  Saddle-point(Lagrangian) optimality criteria for convex nonlinear programs.  Dualitytheorems for convex programs.  First, and second-order Kuhn-Tuckerstationary-point theory for differentiable non-convex programs.  Perturbationand sensitivity analysis.  Applications and extensions.  Prereq:&nbsp;Familiaritywith basic mathematical analysis (e.g., Math&nbsp;521) and either Math.&nbsp;443 or&nbsp;320,or consent of instructor.<A NAME="cs727">&#160;</A><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><!WA115><A NAME="tex2html87" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000953000000000000000">727 Advanced Nonlinear Programming 3 cr. (also IE)</A></H2><P>Conjugate convex functions and Fenchel-Rockafellar duality. Monotone operatorsand subdifferentials. Advanced methods for nonconvex problems, such asvariational principles, generalized gradients, degree and index arguments, andmultivalued ordinary differential equations. Applications to economics andoperations research.  Prereq:&nbsp;<!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><!WA116><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs726">CS&nbsp;726</A> or consent of instructor.<A NAME="cs730">&#160;</A><H2><A NAME="SECTION000954000000000000000">730 <!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><!WA117><A NAME="tex2html88" HREF="http://www.cs.wisc.edu/~olvi/cs730.html">Nonlinear Programming Algorithms</A> 3 cr. (also IE)</A></H2><P>Rigorous description, and convergence proofs of various nonlinear programmingalgorithms.  Emphasis on algorithms that are important, can be proved toconverge and are practical.  Unification of classes of algorithms andconvergence rates.  Each student will code and test one of the algorithmsdescribed in the course.  Prereq:&nbsp;Consent of instructor.<A NAME="cs731">&#160;</A><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><!WA118><A NAME="tex2html89" HREF=""http://www.cs.wisc.edu/~pubs/grad-guidebook/></A><H2><A NAME="SECTION000955000000000000000">731 Advanced Artificial Intelligence 3 cr.</A></H2><P>Learning and hypothesis formation; knowledge acquisition; deductive andinductive inference systems; reasoning techniques involving time, nonmonotonicreasoning, spatial reasoning, truth maintenance systems; planning strategies.Prereq:&nbsp;<!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><!WA119><A HREF="http://www.cs.wisc.edu/~pubs/grad-guidebook/node9.html#cs540">CS&nbsp;540</A>.(Infrequently offered.)<A NAME="cs732">&#160;</A><!WA120><!WA120><!WA120><!WA120><!WA120><!WA120><!WA120><!WA120><!W