D01L03 C Niculescu - Mathematical Research and Mathematical Education

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Math Research & Math Education in Romanian Universities

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Transcript of D01L03 C Niculescu - Mathematical Research and Mathematical Education

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Math Research & Math Educationin

Romanian Universities

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Dan VoiculescuSimion Stoilow

Alexandra Below

Preda Mihailescu Ciprian Foias Viorel BarbuTraian Lalesu

Dimitrie Pompeiu

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Mathematics is one of the pillar of ScienceThe 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 learns 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)

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Art does not reproduce what we see; rather, it makes us see.

Paul Klee (1879–1940)

Vincent van Gogh: Starry night (June 1889)

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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 Poincaré (1854–1912)

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Institute of Mathematics Simion Stoilow

of the Romanian Academy

Working Groups

Operator Theory and Functional AnalysisOperator Algebras

Evolution Eq and Control Theory, PDE and Mathematical Physics Algebra

Algebraic Geometry Complex Analysis

Geometry and Topology Continuum Mechanics

Potential Theory

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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 the SPECT Program of ESF)

National Research Projects: 4 PN2 Programs

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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 students who have just completed two undergraduate years of study. They 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

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SNSB: List of Master lecture courses in Mathematics2009 – 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

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Bucharest UniversityFounded 1864

AlgebraGeometryPDE and Mechanics

Constantin NastasescuSorin DascalescuDorin Mihai PopescuStefan DragosLiviu OrneaPaltin IonescuAurelian CerneaSanda Tigoiu

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A. I. Cuza University of Iasi

Viorel Barbu

Constantin Zalinescu, Ioan VrabieSebastian Anita, Aurel RascanuDorin Iesan, Stan ChiritaCatalin Lefter, Marius DureaOvidiu Carje

Stochastic Differential EquationsControl and OptimizationConvex Analysis

"Alexandru Myller" Mathematical Seminar Centennial Conference June 21 to June 26, 2010; http://www.math.uaic.ro/~Myller2010/

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Babes-Bolyai University at Cluj-Napoca

Founded: 1872 and 1919

Agebra PDEGeometric Function TheoryConvex Analysis and OptimizationMechanics and Astronomy

Andrei-Dorin Marcus Alexandru KristalyGabor KassayGabriela KohrMirela KohrAlexandru MarcuRadu PrecupGyőrgy Csaba Varga

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Mathematics at Craiova

Faculty of Mathematics and Informatics

Department of Mathematics

Center for Nonlinear Analysis and its Applications

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Bachelor Studies in Mathematics-Computer Science Syllabus

1st Year

1st Sem.Linear Algebra 2+2Real Analysis (of one real variable) 3+3Logic and Set Theory 2+2Algorithms and Data Structures 2+2Laboratory of Computer Science 2

2nd Sem.

Algebra (fundamental structures) 2+2Differential Calculus on Rn 3+3Analytic Geometry 2+2Two optional courses in Computer Science 2x(2+2)

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2nd Year

1st Sem.

Algebra (Arithmetic in rings, Galois Theory) 2+2Integral Calculus (of several variables) 2+2Geometry of Curves and Surfaces 2+2Complex Analysis 2+2Differential Equations 2+2Data Bases 2+2

2nd Sem.

Measure Theory and Probabilities 2+2Mechanics 2+2NumericalMethods 2+2An optional course inMathematics 2+2Object Oriented Programming 2+2An optional course in Computer Science 2+2

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3rd Year

1st Sem.

Probabilities andMathematical Statistics 2+2Partial Differential Equations 2+2An optional course inMathematics 2+2Advanced Programming Techniques 2+2An optional course in Computer Science 2+2

2nd Sem.

Operational Research 2+2Functional Analysis and Approximation Theory 2+2Algorithms and Numerical Simulation in C++ 2+2An optional course in Mathematics 2+2An optional course in Computer Science 2+2

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Masteral Program

Dynamical Systems and Evolution Equations

First Semester CM511: Modeling by Differential Equations CM512: Elliptic Equations and Variational ProblemsCM513: Special Topics in Functional Analysis CM514: Dynamical SystemsCM515: Measure Theory and Fine Properties of Functions 

Second Semester CM521: Numerical Methods for PDEs CM522: Semilinear Evolution Equations CM523: Categorical Methods in Mathematical AnalysisCM524: Stochastic Calculus I 

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Third Semester CM611: Ergodic Theory of Dynamical Systems CM612: Stochastic Calculus IICM613: Mathematics of Contact MediaCM614: OscillationsCM615: Nonlinear PDEs 

Fourth SemesterCM621: Financial MathematicsCM622: Control TheoryCM623: Bifurcation Theory with Applications to BiologyCM624: Lab of Experimental Mathematics

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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: Algebraic Logic

+ Four semesters research activities

Doctoral Programat Craiova

Dumitru Busneag, Algebra and Logic (1) Sorin Micu, Control Theory (0)

Constantin P. Niculescu, Analysis (17) Vicentiu Radulescu, PDE (4)

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Center for Nonlinear Analysis and its Applicationshttp://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

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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- mogeneous 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.

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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), 1215-1234.9. 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.

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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)

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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)

How 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

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