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Μελάς Ευάγγελος – Μαθηματικά ιδιαίτερα μαθήματα

Μελάς Ευάγγελος – Μαθηματικά

Περιοχή κατοικίας: Δάφνη

Online μαθήματα: Ναι

Εξυπηρετεί τις περιοχές: Άγιος Δημήτριος, Αθήνα-Αμπελόκηποι, Αθήνα-Βοτανικός, Αθήνα-Γκύζη, Αθήνα-κέντρο, Αθήνα-Κυψέλη, Αθήνα-Νέος Κόσμος, Αθήνα-Παγκράτι, Αθήνα-Πατήσια, Αθήνα-Πετράλωνα, Αθήνα-Σεπόλια, Βύρωνας, Δάφνη, Ηλιούπολη, Καισαριανή, Καλλιθέα, Νέα Σμύρνη, Παλαιό Φάληρο, Υμηττός,


Αναλαμβάνει:

Παιδιά Φοιτητές Ενήλικες

Μαθητές με μαθησιακές δυσκολίες

Διαθεσιμότητα

 

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Βασικός Τίτλος Σπουδών

ΕΚΠΑ

Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών

Τμήμα Φυσικής



Μεταπτυχιακός Τίτλος Σπουδών

Quantum Fields and Fundamental Forces, University of London

Διδακτορικός Τίτλος Σπουδών

Mathematical Physics, University of London

Διδακτική Πείρα στα Ιδιαίτερα Μαθήματα Μαθηματικών

For seventeen years I have had extensive teaching  and research experience in the  Department of Mathematics, University of Thessaly, in the Department of Economics, University of Athens, Division of Mathematics and Informatics, as well as in the in the Department of Applied Mathematics, University of Crete, and in a number of Ex-Polytechnics which have now acquired  University status. Most of my teaching experience has been focused on Analytic Geometry, Calculus, Introduction to Applied Mathematics, Linear Algebra, Probability and Statistics,  Differential Equations and Physics.

 

I hold a BSc in Physics and a PHD in Mathematical Physics. I teach Mathematics (Calculus I and Calculus II, Differential Equations, Linear Algebra, Applied Mathematics, Statistics, Operational Research, SPSS) for students in Universities and Polytechniques (Open University included). I also teach Mathematics to high School students.

You can see  me teaching Calculus I here

https://opencourses.uoa.gr/modules/video/?course=ECON101

You can see me teaching Calculus II here

https://opencourses.uoa.gr/courses/ECON8/

I also teach Physics (Classical Physics, Analytical Mechanics, Quantum Mechanics, Electromagnetism) to University students and high school students.

 

I have advised three undergraduate students on their Theses, in the Department of Logistics, Agricultural University of Athens. The theses were on `Useful algorithms in Operational Research’, `Use of Data Mining in Marketing’, and ‘Use of mathematical software packages in High School Education’.

 

Academic Positions

10/2010-Up to now: Lecturer in Mathematics Department of Economics, Unit of Mathematics and Informatics, University of Athens, Greece

10/2019-6/2020: Lecturer in Mathematics Department of Industrial and Product Design Engineering, University of West Attica, Greece

10/2019-1/2020: Lecturer in Mathematics Department of Mathematics, University of Thessaly, Greece

10/2018-9/2019: Assistant Professor in Mathematics Department of Logistics, Agricultural University of Athens, Greece

10/2017-7/2018: Assistant Professor in Mathematics Department of Business Administration, Unit of Health and Welfare Management, Athens University of Applied Sciences, Greece

10/2014-9/2017, 10/2006-9/2008: Assistant Professor in Mathematics Department of Informatics and Computer Technology, Central Greece University of Applied Sciences, Greece

10/2013-9/2014: Assistant Professor in Mathematics Department of Business Administration, Technological Educational Institute of Western Greece, Greece

10/2010-9/2012: Assistant Professor in Mathematics Department of Logistics, Central Greece University of Applied Sciences, Greece

10/2008-9/2010: Assistant Professor in Mathematics Department of Commerce and Advertisement, Central Greece University of Applied Sciences, Greece

10/2006-9/2008, 10/2004-9/2005: Assistant Professor in Mathematics Department of Electrical Engineering, Central Greece University of Applied Sciences, Greece

10/2006-9/2007: Assistant Professor in Mathematics Department of Electrical Engineering, Technological Educational Institute of Crete, Greece

10/2005-9/2006: Lecturer in Mathematics Department of Applied Mathematics, University of Crete, Greece

03/2004-07/2007: Assistant Professor in Mathematics Department of Informatics Applications in Management & Economy, Technological Educational Institute of Ionian Islands, Greece

03/2002-05/2002: Assistant Professor in Mathematics Department of Mathematics, City University, London, England

 

Αwards

State Scholarships Foundation, 16/10/1992-15/01/1998

British Chevening Scholarship, 1995-1996

 

Research Experience

In all my academic posts I have had research duties. Over the years I have been doing research on Quantum Gravity, Quantum Cosmology, Representation Theory of Infinite Dimensional Lie Groups, Lie symmetries and how to use them in order to solve them, Differential Galois Theory of Linear ODEs and how to use it in order to find Liouvillian solutions of these ODEs.

 

2018-2021 Postdoc Position, University of Athens, Department of Economics, Unit of Mathematics and Informatics. The Postdoc Position is on `Use of Lie symmetries in order to solve equations in Finance’. The two publications E.Melas ‘Classes of elementary function solutions to the CEV model. I.’ Journal of Computational and Applied mathematics 360 62-77 (2019), and E. Melas ‘Classes of elementary function solutions to the CEV model. II.’ submitted to Journal of Computational and Applied Mathematics fall within the duties of this Postdoc Position.

 

Reviewer

2011 - Up to now  Classical and Quantum Gravity

2018 - Up to now Mathematical Reviews

2019 - Up to now Computational and Applied Mathematics

 

Professional   Experience

Advisor on cryptographic algorithms: Since 09/01/2008 I have been working in the Cyber Security Company `OBRELA SECURITY INDUSTRIES LTD as advisor on cryptographic algorithms.

Languages

Greek: Native. English: Fluent. French: Reading knowledge. German: Reading knowledge.

References

THEODOSIOS CRISTODOULAKIS, PROFESSOR OF THEORETICAL PHYSICS, UNIVERSITY OF ATHENS, DEPARTMENT OF PHYSICS

- GLENN BARNICH, PROFESSOR OF THEORETICAL PHYSICS, UNIVERSITE LIBRE DE BRUSSELS & INTERNATIONAL SOLVAY INSTITUTES

- THEOCHARIS APOSTOLATOS, ASSOCIATE PROFESSOR OF THEORETICAL PHYSICS, UNIVERSITY OF ATHENS, DEPARTMENT OF PHYSICS

- IOANNIS DEMETRIOU, PROFESSOR OF MATHEMATICS, UNIVERSITY OF ATHENS, DEPARTMENT OF ECONOMICS, UNIT OF MATHEMATICS AND INFORMATICS

- IOANNIS   LEVENTIDIS, ASSOCIATE PROFESSOR OF MATHEMATICS, UNIVERSITY OF ATHENS, DEPARTMENT OF ECONOMICS

- STELIOS   KOTSIOS, PROFESSOR OF MATHEMATICS, UNIVERSITY OF ATHENS, DEPARTMENT OF ECONOMICS, UNIT OF MATHEMATICS AND INFORMATICS

 

PhD in Mathematical Physics School of Mathematical Sciences, QMW, University of London, England, Supervisors: Patrick J. McCarthy and Peter J. Cameron, Title of Dissertation: Aspects of Asymptotically Flat Space-Times (11/1993-1/2002).

M.Sc. in Theoretical Physics:  Department of Theoretical Physics, Imperial College, University of London, England, Supervisor: Chris Isham, Dissertation: Symmetric Spaces, Causal Structure of Space-Time (10/1992-9/1993).



Δημοσιεύσεις:

Publications in Journals

1. P. J. McCarthy &  E. Melas On   irreducible  representations  of  the  ultahyperbolic BMS group.  Nucl. Phys. B.  653/3, 369-399 (2003).

2. E. Melas  The BMS group and generalised gravitational  instantons.       Journal of Mathematical Physics     45/3, 996-1003 (2004).  

3. E.Melas Construction of the Irreducibles of B(2,2).J.  Phys. A : Math.  Gen., 39, 3341-3366 (2006).

4.T. Christodoulakis, G. Doulis, P.Terzis, E.Melas, Th. Grammnenos,     G.Papadopoulos, A. Spanou    Towards canonical quantum gravity for G1  geometries  in 2+1 dimensions with a Λ-term Classical and Quantum Gravity  25  235014 (20 pages) (2008).

5.T. Christodoulakis,   G. Doulis,   P.Terzis,   E.Melas,    Th.Grammnenos,   G.Papadopoulos, A. Spanou    Towards Canonical Quantum Gravity forGeometries Admitting Maximally Symmetric Two-dimensional Surfaces  Classical and Quantum Gravity  27 145018 (21 pages) (2010).

6. E. Melas  Generalization of Hajicek and Kuchars canonical quantization scheme to  the 3+1 geometries admitting maximally symmetric two-dimensional  surfaces  Ann. Phys. (Berlin) 39, No. 3-5, 294-298 (2010)

7. T. Christodoulakis, N. Dimakis, Petros A. Terzis, G. Doulis, Th. Grammenos, E. Melas, A. Spanou Conditional symmetries and the canonical quantization of constrained minisuperspace  actions: The Schwarzschild case Journal of Geometry and Physics 71 (2013) 127–138

8. T. Christodoulakis, N. Dimakis, Petros A. Terzis, Babak Vakili, E. Melas, Th. Grammenos Minisuperspace Canonical Quantization of the Reissner-Nordstrom Black Hole via Conditional Symmetries Physical Review D 89, 044031 (2014) (15 pages)

9. E.Melas Representations of the ultrahyperbolic BMS group HB. II. Determination of the representations induced from infinite little groups arxiv:1312.0532v1(41 pages)

10. E.Melas Representations of the ultrahyperbolic BMS group HB. III. Determination of the representations induced from finite little groups arXiv:1402.1428 (44 pages)

11.S. Kotsios and E.Melas NONLINEAR INVARIANTS OF PLANAR POINT CLOUDS TRANSFORMED BY MATRICES FACTA UNIVERSITATIS Ser. Math. Inform 33 5 751-771 (2018)

12.E.Melas On the representation theory of the Bondi-Metzner-Sachs group and its variants in three space-time dimensions JMP 58 (2017) 071705 (28 pages)

13.E.Melas On the Liouvillian solutions to the perturbation equations of the Schwarzschild black hole  JMP 59, 082502  (2018)

14.E. Melas Classes of elementary function  solutions to the CEV model. I. Journal of Computational and Applied mathematics 360 62-77  (2019)

15 I. Leventidis, .E.Melas DIFFUSION BANK NETWORKS AND CAPITAL FLOWS submitted to Mathematics and  Financial Economics (2020)

16.E. Melas Classes of elementary function  solutions to the CEV model. II. Submitted to Journal of Computational and Applied Mathematics

17. E. Melas On irreducible representations of the Bondi-Metzner-Sachs group in three space-time dimensions in the Hilbert topology. Submitted to Nuclear Physics B.

 

Publications in Conference Proceedings

1) E. Melas Approaching quantum gravity via the representation theory of the BMS group and its variants. Some conceptual issues and a conjecture. Nucl. Phys. B. (Proc.Suppl.)  104, 212-216 (2002).       

2) E. Melas Generalizations of the BMS group and results IOP Journal of  Physics : Conference series 33, 260-265  (2006).     

3) E. Melas The Ultrahyperbolic BMS group and its representation theory AIP Conference Proceedings  861,  420-427 (2006).

4)T. Christodoulakis, G. Doulis, P.Terzis, E.Melas, Th. Grammnenos,      G.Papadopoulos, A. SpanouCanonical quantization of some midi-superspace models in 2+1 and 3+1 dimensions (IOP Publishing) Journal of Physics: Conference Series 189, 012008 (26 pages) (2009).    

5) T. Christodoulakis, G. Doulis, P.Terzis, E.Melas, Th. Grammnenos,   G.Papadopoulos, A. Spanou    Canonical Quantization of  Some Midi-Superspace Models in 3+1 Dimensions IOP Conference Series 222, 012045 (18 pages) (2010) .

6) Ε.Μelas Generalization of Hajicek and  Kuchar's canonicalquantization scheme to the 2+1 geometries admitting one Killingvector field    AIP Conference Proceedings 1241, 652-662 (2010).

7) Ε.Μelas Probing Further Ultrahyperbolic GR by Using Group Theory Proceedings of the Twelfth Marcel Grossmann Meeting on General Relativity, edited by Thibault Damour, Robert T Jantzen and Remo Ruffini, World Scientific, Singapore, 2011, p. 2237-2240.  

8) Ε.Μelas Generalization of Hajicek and  Kuchar's  canonical quantization  scheme to the 3+1 geometries admitting maximally symmetric two-dimensional surfaces Grassmannian Conference in  Fundamental Cosmology (Grasscosmofun'09) . Ann. Phys. (Berlin) 19, No. 3 – 5, 294 – 298.   

9) E. Melas Open problems and results in the group theoretic approach to quantum gravity via the BMS group and its generalizations Journal of Physics: Conference Series 283, 012023 (16 pages) (2011).

10) E.Melas Generalization of Hajicek and Kucharsquantization scheme in a midi-superspace modelin 3+1 canonical quantum gravity. Proceedings of the 11th International Symposium on Frontiers of Fundamental Physics, edited by Joseph Kouneiher, Cecile Barbachoux & al, American Institute of Physics, NY. Open Access Journal of Physics: Conference Series. (JPCS), Institute of Physics Publishing, 306, 012062 (12 pages) (2011).

11) E. Melas A field theoretic generalization of Hajicek and Kuchar's quantization scheme in 3+1 canonical quantum gravity IOP Journal of Physics: Conference Series 306, 012062 (10 pages) (2011). 

12) E. Melas CANONICAL QUANTIZATION OF CONSTRAINED LAGRANGIANS AND CONDITIONAL SYMMETRIES: THE SCHWARZSHILD CASE World Scientific, The Thirteenth Marcel Grossmann Meeting, 2015, pp. 1367-1369.

13)  T. Christodoulakis, N. Dimakis, G. Doulis, Th. Grammnenos, P.Terzis, E.Melas, P.Terzis, Canonical quantization of static spherically symmetric geometries IOPJournal of Physics: Conference Series 453,  012002 (9 pages) (2013).

14) E. Melas Quantization of the Schwarzschild geometry was published by  Journal of Physics: Conference Series. (JPCS), Institute of Physics Publishing 442, 012037 (8 pages) (2013).  

15) E. Melas Canonical Quantization of the Reissner-NordstromBlack Hole via Conditional Symmetries Journal of Physics: Conference Series. (JPCS), Institute of Physics Publishing 574, 012063 (4 pages) 2015.  

16) E. Melas On the Representation Theory of the Ultrahyperbolic BMS group UHB(2,2). I. General Results Journal of Physics: Conference Series. (JPCS), Institute of Physics Publishing 574, 012126 (4 pages) 2015.  

17) E. Melas Representations of the ultrahyperbolic BMS group UHB(2,2). I. General Results Journal of Physics: Conference Series. (JPCS), Institute of Physics Publishing 626, 012066 (7 pages) (2015).

18) E. Melas First results on the representation theory of theUltrahyperbolic BMS group UHB(2,2)  Conference Series (JPCS), IOP CONFERENCE SERIES 670, 012035 ((2016).

19) E. Melas Representations of the ultrahyperbolic BMS group UHB(2; 2). I. General Results  after a peer review of the referees was accepted for publication by Proceedings of the Fourteenth Marcel Grossman Meeting on General Relativity edited by Massimo Bianchi, Robert T Jantzen, Remo Ruffini World Scientific, Singapore, 2016 , p. 2689.

20) E. Melas 2016 BMS groups in three space-time dimensions. B(2; 1) and its irreducible representations. NEB-17 RECENT DEVELOPMENTS IN GRAVITY, SEPTEMBER 19-22, MYKONOS, GREECE (Accepted for publication in the Proceedings of the Conference)

21) E. Melas Representations of the Bondi-Metzner-Sachs group in three space-time dimensions ISQS24 Integral systems and quantum symmetries, June 14-18, Prague, http://www.intsystems.cz/2016-2/ Institute of Physics Publishing Journal of Physics: Conference Series  (στο Ηνωμένο Βασίλειο),  804 (2017) 012030.  

22) E. Melas ASYMPTOTIC SYMMETRIES IN 3-DIM GENERAL RELATIVITY: THE B(2,1) CASE 6th International Conference on Mathematical Modeling in Physical Sciences Αugust 28-31, 2017, Paphos, Cyprus,   http://www.icmsquare.net/. Open Access, Institute of Physics Publishing Journal of Physics: Conference Series  (στο Ηνωμένο Βασίλειο),  936 (2017) 012072.  

23) E. Melas Solutions in quadratures to the CEV model 8th National Conference of the Financial Engineering and Banking Society, December 18-19, 2017 Αthens, International Journal of Financial Engineering  and Risk Management 3 No. 2 172-179 (2019) InderScience Publishers, in a special issue, devoted to the Conference,  entitled Advances in Banking and Finance in the Post-crisis Era.

24) E. Melas First Congress of Greek Mathematicians FGCM-2018 June 25-30,  2018 Αthens, Greece. I submitted three papers to the Conference: Invariants of a planar point cloud undergoing a linear transformation, BMS groups in 3 space-time dimensions. B(2,1) and its irreducible representations, New solutions in terms of quadratures to the CEV model . They were all accepted and published in the Conference Proceedings First Congress of Greek Mathematicians, Department of Mathematics, Athens, Greece, June 20-26, 2018. They are in pages 94-105, 105-116, and 116-127 correspondingly.



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