D01L03 C Niculescu - Mathematical Research and Mathematical Education

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Transcript of D01L03 C Niculescu - Mathematical Research and Mathematical Education

  • 1. Math Research & Math Education in Romanian Universities

2. Dan Voiculescu Simion Stoilow Alexandra Below Preda Mihailescu Ciprian Foias Viorel Barbu Traian Lalesu Dimitrie Pompeiu 3. Mathematics is one of the pillar of Science The laws of Nature are written in thelanguage of mathematics Philosophy is written in this grand book,the universe, which stands continuallyopen to our gaze.But the book cannot be understoodunless one first lea r ns to comprehendthe language and read the charactersin which it is written. It is written in thelanguage of mathematics, and itscharacters are triangles, circles, andother geometric figures without whichit is humanly impossible to understanda single word of it; without these one iswandering in a dark labyrinth. Galileo Galilei ( Il saggiatore ,1623) 4. 5. Art does not reproduce what we see;rather, it makes us see. Paul Klee (18791940) V incent van Gogh : Starry night ( June18 89 ) 6. Science is facts. Just as houses are made of stones,so is science made of facts. But a pile of stones is nota house and a collection of facts is not necessarilyscience. JulesHenriPoincar (18541912) 6 8 1 5 2 4 3 9 1 3 8 7 4 5 2 4 1 7. Institute of Mathematics Simion Stoilow of the Romanian Academy Working Groups Operator Theory and Functional Analysis Operator Algebras Evolution Eq and Control Theory,PDEand Mathematical Physics Algebra Algebraic Geometry Complex Analysis Geometry and Topology Continuum Mechanics Potential Theory 8.

  • Participation on European Research Projects
  • Advanced Mathematical Methods for Finance- ESF Program
  • Laboratoire Europeen Associe CNRS : Mathematique et Modelisation - Math-Mode
  • Network in Noncommutative Geometry- FP6 (EC Grant Ref: MRTN-CT-2006-031962)
  • Euro-GDR"Mathematics and Quantum Physics"
  • German-Romanian cooperation project in the frame of the agreement between
  • Deutsche Forschungsgemeinschaft and the Romanian Academy (Project
  • GZ: 436 RUM 113/23/0-1
  • Potential Theoretical Methods for the Analysis of Infinite Dimensional Proceses
  • Organization of the 10-edition of the Mathematical Results in Quantum
  • Theory International Conference Series(part of theSPECT Programof ESF)
  • National Research Projects : 4 PN2 Programs

9. Scoala Normala Superioara Bucharest (SNSB) Scoala Normala Superioara Bucharest (SNSB) was set up in 2001 on the model of the french Ecole Normale Superieure, by the initiative of a group of young researchers. Its mission is to guide towards research the best romanian students, and offer them a top-quality working environment. It contributes to society through the pursuit of education and research at highest standards.Each year the SNSB admits in each discipline(mathematics, informatics and biochemistry) , via a thorough selection process, up to ten student swho have just completed two undergraduate years of study. The ybecome SNSB students for three years. In the first year (the preliminay cycle) they graduate from their home university, and follow complementary courses at the SNSB. The last two SNSB years (the master cycle) is devoted to a Master's Program, offered by SNSB, finalized through a Master's thesis. SNSB charges no tuition fees. On the contrary, it grants scholarship in proportion to the academic achievements (as measured by final exams).At present: 4+11+5 students in mathematics 10. SNSB:L ist ofM aster lecture courses in Mathematics 2009 2010 Lucian BEZNEA:Quasi-regular Dirichlet Forms Liviu IGNAT:Evolution equations Paltin IONESCU:Introduction to birational geometry: classification of algebraicsurfaces Eugen MIHAILESCU:Analysis on fractals Sergiu MOROIANU:Riemann surfaces Liviu ORNEA:Topics in Riemannian geometry Nicolae POPA:Wavelets Ionel POPESCU:Brownian Motion, Itos Calculus and Stochastic Differential Equations 11. Bucharest University Founded 1864 Algebra Geometry PDE and Mechanics Constantin Nastasescu Sorin Dascalescu Dorin Mihai Popescu Stefan Dragos Liviu Ornea Paltin Ionescu Aurelian Cernea Sanda Tigoiu 12.

  • I. Cuza University of Iasi

Viorel Barbu Constantin Zalinescu, Ioan Vrabie Sebastian Anita, Aurel Rascanu Dorin Iesan, Stan Chirita Catalin Lefter, Marius Durea Ovidiu Carje Stochastic Differential Equations Control and Optimization Convex Analysis "Alexandru Myller" Mathematical Seminar Centennial Conference June 21 to June 26, 2010 ;http://www.math.uaic.ro/~Myller2010/ 13. Babes-Bolyai University at Cluj-Napoca Founded: 1872 and 1919 AgebraPDE Geometric Function Theory Convex Analysis and Optimization Mechanics and Astronomy Andrei-Dorin MarcusAlexandru Kristaly Gabor Kassay Gabriela Kohr Mirela Kohr Alexandru Marcu Radu Precup Gyrgy Csaba Varga 14. Mathematics at Craiova Faculty of Mathematics and Informatics Department of Mathematics Center for Nonlinear Analysis and its Applications 15. Bachelor Studies in Mathematics-Computer ScienceSyllabus 1st Year 1st Sem . Linear Algebra2+2 Real Analysis (of one real variable)3+3 Logic and Set Theory2+2 Algorithms and Data Structures2+2 Laboratory ofComputer Science 2 2nd Sem. Algebra (fundamental structures)2+2 Differential Calculus on R n 3+3 Analytic Geometry2+2 Two optional courses in Computer Science 2 x (2 + 2) 16. 2nd Year 1st Sem .Algebra (Arithmetic in rings, Galois Theory)2+2 Integral Calculus (of several variables)2+2 Geometry of Curves and Surfaces2+2 Complex Analysis2+2 Differential Equations2+2 Data Bas e s2+2 2nd Sem. Measure Theory and Probabilities2+2 Mechanics2+2 NumericalMethods2+2 An optional course inMathematics2+2 Object Oriented Programming2+2 An optional course in Computer Science2+2 17. 3rd Year 1st Sem. Probabilities andMathematical Statistics 2+2 Partial Differential Equations 2+2 An optional course inMathematics 2+2 Advanced Programming Techniques 2+2 An optional course in Computer Science 2+2 2nd Sem. Operational Research 2+2 Functional Analysis and Approximation Theory 2+2 Algorithms and Numerical Simulation in C++ 2+2 An optional course in Mathematics 2+2 An optional course in Computer Science 2+2 18. Master al Program Dynamical Systems and Evolution Equations First Semester CM511: Modeling by Differential Equations CM512: Elliptic Equations and Variational Problems CM513: Special Topics in Functional AnalysisCM514: Dynamical Systems CM515: Measure Theory and Fine Properties of Functions Second Semester CM521: Numerical Methods for PDEsCM522: Semilinear Evolution EquationsCM523: Categorical Methods in Mathematical Analysis CM524: Stochastic Calculus I 19. Third Semester CM611: Ergodic Theory of Dynamical SystemsCM612: Stochastic Calculus II CM613: Mathematics of Contact Media CM614: Oscillations CM615: Nonlinear PDEs Fourth Semester CM621: Financial Mathematics CM622: Control Theory CM623: Bifurcation Theory with Applications to Biology CM624: Lab of Experimental Mathematics 20. First Semester CM711:Convex Analysis and Optimization CM712:Monotone Methods in PDEs CM713: Elements of Category TheorySecond Semester CM721:Topological Methods in Nonlinear Analysis CM722:Critical Point Theory CM723: Algebra ic Logic +Four semesters research activities Doctoral Program at Craiova Dumitru Busneag,Algebra and Logic(1)Sorin Micu,Control Theory(0)Constantin P. Niculescu,Analysis (17)Vicentiu Radulescu,PDE(4) 21. Center for Nonlinear Analysis and its Applications http:// www.cnaa.ucv.ro / CNAA(founded in 2001)is aimed to promote research inNonlinear Analysisat the University of Craiova.CNAAwasofficially recognized as aCentre of excellenceby theNational University Research Council in 2005. Scientific Committeeof CNAA :Constantin P. Niculescu(Director),Sorin Daniel Micu and Viceniu Rdulescu Members :Andaluzia Matei,Mihai Mihailescu,Octavian Genghiz Mustafa, Carmen Rocoreanu,Ionel Roventa,Mihaela Sterpu and Cristian Vladimirescu. Publications of CNAA 22. Degenerate and Singular Nonlinear Processes (Grant ID_36/2007) 1.Mihai Mihailescu, Patrizia Pucci, Vicentiu Radulescu, Nonhomogeneous boundaryvalue problems in anisotropic Sobolev spaces, C. R.Acad. Sci. Paris ,345 (2007), 561-566.2.Mihai Mihailescu, Patrizia Pucci, Vicentiu Radulescu, Eigenvalue problems for ani - sotropic quasilinear elliptic equations with variable exponent,Journal of Math . Analysis and Appl . ,340 (2008), 687-698.4.Mihai Mihailescu, Vicentiu Radulescu, Eigenvalue problems associated to non - homogeneous differential operators in Orlicz-Sobolev spaces,Analysis andAppl.6 (2008), 83-98.5.Mihai Mihailescu, Vicentiu Radulescu, Continuous spectrum for a class of nonho - mo geneous differential operators,Manuscripta Mathematica ,125 (2008), 157-167.6.M. Mihailescu ,V. Radulescu, Nonhomogeneous Neumann problems in Orlicz- Sobolev spaces,C. R. Acad. Sci. Paris ,Ser. I 346(2008), 401-406.7.M. Mihailescu, V. Radulescu, Neumann problems associated to nonhomogeneousdifferential operators in Orlicz-Sobolev spaces,Ann. Inst. Fourier ,58 (2008),2087-2111. 23. 8.M. Ghergu, V. Radulescu, A singular Gierer-Meinhardt system with differentsourceterms,Proceedings of the Royal Society of Edinburgh : Section A (Math . ) 138A (2008 ),1215-123 4. 9.Roberta Filippucci, Patrizia Pucci, Vicentiu Radulescu, Existence and Non- Existence Results for Quasilinear Elliptic Exterior Problems with Nonlinear BoundaryConditions,Communications in Partial Differential Equations ,33,2008, 706-717.10. M. Ghergu, Steady-state solutions for Gierer-Meinhardt type systems with Dirichletboundary condition, Transactions of the Amer .Math .Soc . ,361(2009), 3953-3976 . 11. M. Ghergu, On the global solutions to a class of strongly degenerate parabolicequations,Nonlinear Analysis: Theory, Methods & Applications ,70 (3),2009,1430-1442.12. M. Ghergu, Large time behavior of solutions to degenerate parabolic equations withweights, Journal of Mathematical Analysis and Applications ,352 (2009), 132-138.13. V. Radulescu, D. Repovs, Perturbation effects in nonlinear eigenvalue problems,Nonlinear Analysis: Theory, Methods and Applications ,70(2009), 3030-3038 . 14.M. Mihailescu, V. Radulescu, A continuous spectrum for nonhomogeneousdifferential operators in Orlicz-Sobolev spaces,Mathematica Scandinavica ,104 (2009), 132-146 . 15.A. Kristaly, M. Mihailescu, V. Radulescu, Two nontrivial solutions for a non- homogeneous Neumann problem: an Orlicz-Sobolev setting,Proceedings of theRoyal Society of Edinburgh: Section A (Mathematics),139A(2009), 367-379 . 24. Problems of convex analysis, numerical analysis and control in the study of complex physical systems (Grant ID_420/2008) 1. C. P. Niculescu ,The Hermite-Hadamard inequality for convex functions on aglobal NPC space,J. Math. Anal. Appl.356(2009), no. 1, 295301. doi:10.1016/j.jmaa.2009.03.007(ISI1.046 ) 2.C. P. NiculescuandIonel Rovena ,Fan's inequality in geodesic spaces , Appl. Math. Letters22(2009), 1529-1533. doi:10.1016/j.aml.2009.03.020(ISI0.948 ) 3.C. P. NiculescuandIonel Rovena ,Schauder Fixed Point Theorem in Spaceswith Global Nonpositive Curvature , Fixed Point Theory and Applications,vol.2009, Article ID 906727, 8 pages, 2009. doi:10.1155/2009/906727.(ISI 0.728) 4. M. Boureanu andA. Matei ,Weak solutions for antiplane models involving elastic materials with degeneracies , accepted, Zeitschrift fr Angewandte Mathematik und Physik (ZAMP), 2009, doi 10.1007/s00033-009-0008-0.(ISI1.139 ) 5.Micu Sorinand Luz de Teresa,A Spectral Study of the Boundary Controllability of the Linear 2-D Wave Equation in a Rectangle,Asymptotic Analysis, 2009, doi 10.3233/ASY-2009-0963.(ISI0.662 ) 25. Understanding, Learning, and Teaching Problem Solving A great discovery solves a great problem, but there is a grainof discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery. George Polya(1887-1985) H ow problem-solving should be taught and learned? The four principles of Polyas heuristics (fromHow to solve it ): Understanding the problem ; Devising a plan ; Carrying out the plan ; Looking back . http://en.wikipedia.org/wiki/George_P%C3%B3lya 26.