D01L03 C Niculescu - Mathematical Research and Mathematical Education


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D01L03 C Niculescu - Mathematical Research and Mathematical Education

  1. 1. Math Research & Math Education in Romanian Universities
  2. 2. Dan Voiculescu Simion Stoilow Alexandra Below Preda Mihailescu Ciprian Foias Viorel Barbu Traian Lalesu Dimitrie Pompeiu
  3. 3. Mathematics is one of the pillar of Science The laws of Nature are written in the language of mathematics Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first lea r ns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth. Galileo Galilei ( Il saggiatore ,1623)
  4. 4.  
  5. 5. Art does not reproduce what we see; rather, it makes us see. Paul Klee (1879–1940) V incent van Gogh : Starry night ( June 18 89 )
  6. 6. Science is facts. Just as houses are made of stones, so is science made of facts. But a pile of stones is not a house and a collection of facts is not necessarily science. Jules Henri Poincar é (1854–1912) 6 8 1 5 2 4 3 9 1 3 8 7 4 5 2 4 1
  7. 7. Institute of Mathematics Simion Stoilow of the Romanian Academy Working Groups Operator Theory and Functional Analysis Operator Algebras Evolution Eq and Control Theory, PDE and Mathematical Physics Algebra Algebraic Geometry Complex Analysis Geometry and Topology Continuum Mechanics Potential Theory
  8. 8. <ul><li>Participation on European Research Projects </li></ul><ul><li>Advanced Mathematical Methods for Finance - ESF Program </li></ul><ul><li>Laboratoire Europeen Associe CNRS : Mathematique et Modelisation - Math-Mode </li></ul><ul><li>Network in Noncommutative Geometry - FP6 (EC Grant Ref: MRTN-CT-2006-031962) </li></ul><ul><li>Euro-GDR &quot;Mathematics and Quantum Physics&quot; </li></ul><ul><li>German-Romanian cooperation project in the frame of the agreement between </li></ul><ul><li>Deutsche Forschungsgemeinschaft and the Romanian Academy (Project </li></ul><ul><li>GZ: 436 RUM 113/23/0-1 </li></ul><ul><li>Potential Theoretical Methods for the Analysis of Infinite Dimensional Proceses </li></ul><ul><li>Organization of the 10-edition of the Mathematical Results in Quantum </li></ul><ul><li>Theory International Conference Series (part of the SPECT Program of ESF) </li></ul><ul><li>National Research Projects : 4 PN2 Programs </li></ul>
  9. 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 s who have just completed two undergraduate years of study. The y become 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. 10. SNSB: L ist of M 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 algebraic surfaces Eugen MIHAILESCU: Analysis on fractals Sergiu MOROIANU: Riemann surfaces Liviu ORNEA: Topics in Riemannian geometry Nicolae POPA: Wavelets Ionel POPESCU: Brownian Motion, Ito’s Calculus and Stochastic Differential Equations
  11. 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. 12. <ul><li>I. Cuza University of Iasi </li></ul>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 &quot;Alexandru Myller&quot; Mathematical Seminar Centennial Conference June 21 to June 26, 2010 ; http://www.math.uaic.ro/~Myller2010/
  13. 13. Babes-Bolyai University at Cluj-Napoca Founded: 1872 and 1919 Agebra PDE Geometric Function Theory Convex Analysis and Optimization Mechanics and Astronomy Andrei-Dorin Marcus Alexandru Kristaly Gabor Kassay Gabriela Kohr Mirela Kohr Alexandru Marcu Radu Precup Győrgy Csaba Varga
  14. 14. Mathematics at Craiova Faculty of Mathematics and Informatics Department of Mathematics Center for Nonlinear Analysis and its Applications
  15. 15. Bachelor Studies in Mathematics-Computer Science Syllabus 1st Year 1st Sem . Linear Algebra 2+2 Real Analysis (of one real variable) 3+3 Logic and Set Theory 2+2 Algorithms and Data Structures 2+2 Laboratory of Computer Science 2 2nd Sem. Algebra (fundamental structures) 2+2 Differential Calculus on R n 3+3 Analytic Geometry 2+2 Two optional courses in Computer Science 2 x (2 + 2)
  16. 16. 2nd Year 1st Sem . Algebra (Arithmetic in rings, Galois Theory) 2+2 Integral Calculus (of several variables) 2+2 Geometry of Curves and Surfaces 2+2 Complex Analysis 2+2 Differential Equations 2+2 Data Bas e s 2+2 2nd Sem. Measure Theory and Probabilities 2+2 Mechanics 2+2 NumericalMethods 2+2 An optional course inMathematics 2+2 Object Oriented Programming 2+2 An optional course in Computer Science 2+2
  17. 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. 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 Analysis CM514: Dynamical Systems CM515: Measure Theory and Fine Properties of Functions   Second Semester   CM521: Numerical Methods for PDEs CM522: Semilinear Evolution Equations CM523: Categorical Methods in Mathematical Analysis CM524: Stochastic Calculus I 
  19. 19. Third Semester   CM611: Ergodic Theory of Dynamical Systems CM612: 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. 20. First Semester   CM711: Convex Analysis and Optimization CM712: Monotone Methods in PDEs CM713: Elements of Category Theory Second 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. 21. Center for Nonlinear Analysis and its Applications http:// www.cnaa.ucv.ro / CNAA (founded in 2001) is aimed to promote research in Nonlinear Analysis at the University of Craiova. CNAA was officially recognized as a Centre of excellence by the National University Research Council in 2005. Scientific Committee of CNAA : Constantin P. Niculescu (Director), Sorin Daniel Micu and Vicenţiu Rădulescu Members : Andaluzia Matei, Mihai Mihailescu, Octavian Genghiz Mustafa, Carmen Rocşoreanu, Ionel Roventa, Mihaela Sterpu and Cristian Vladimirescu. Publications of CNAA
  22. 22. Degenerate and Singular Nonlinear Processes (Grant ID_36/2007) 1. Mihai Mihailescu, Patrizia Pucci, Vicentiu Radulescu, Nonhomogeneous boundary value 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 and Appl. 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 nonhomogeneous differential operators in Orlicz-Sobolev spaces, Ann. Inst. Fourier , 58 (2008), 2087-2111.
  23. 23. 8. M. Ghergu, V. Radulescu, A singular Gierer-Meinhardt system with different sourceterms, 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 Boundary Conditions, Communications in Partial Differential Equations , 33, 2008, 706-717. 10. M. Ghergu, Steady-state solutions for Gierer-Meinhardt type systems with Dirichlet boundary condition, Transactions of the Amer . Math . Soc . , 361 (2009), 3953-3976 . 11. M. Ghergu, On the global solutions to a class of strongly degenerate parabolic equations, Nonlinear Analysis: Theory, Methods & Applications , 70 (3), 2009, 1430-1442. 12. M. Ghergu, Large time behavior of solutions to degenerate parabolic equations with weights, 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 nonhomogeneous differential 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 the Royal Society of Edinburgh: Section A (Mathematics) , 139A (2009), 367-379 .
  24. 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 a global NPC space, J. Math. Anal. Appl. 356 (2009), no. 1, 295–301. doi:10.1016/j.jmaa.2009.03.007 (ISI 1.046 ) 2. C. P. Niculescu and Ionel Rovenţa , Fan's inequality in geodesic spaces , Appl. Math. Letters 22 (2009), 1529-1533. doi:10.1016/j.aml.2009.03.020 (ISI 0.948 ) 3. C. P. Niculescu and Ionel Rovenţa , Schauder Fixed Point Theorem in Spaces with 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 and A. Matei , Weak solutions for antiplane models involving elastic materials with degeneracies , accepted, Zeitschrift fűr Angewandte Mathematik und Physik (ZAMP), 2009, doi 10.1007/s00033-009-0008-0. (ISI 1.139 ) 5. Micu Sorin and 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. (ISI 0.662 )
  25. 25. Understanding, Learning, and Teaching Problem Solving A great discovery solves a great problem, but there is a grain of 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 Polya’s heuristics (from How to solve it ): Understanding the problem ; Devising a plan ; Carrying out the plan ; Looking back . http://en.wikipedia.org/wiki/George_P%C3%B3lya