Assoc.Prof.Dr.Ahmet TEKCAN

Address: Uludag University , Faculty of Arts & Science , Department of Mathematics , Görükle , 16059, Bursa – TÜRKİYE

e-mails : tekcan@uludag.edu.tr , tekcan77@gmail.com

http: http://matematik.uludag.edu.tr/AhmetTekcan.htm

Office: + 90 (224) 294 17 51

Fax: + 90 (224) 294 18 98

Room: B-216

1) PERSONAL INFORMATION:

Birth date: 17 November 1977

Birthplace: Kayseri - TÜRKİYE

Citizenship: Turkish

Language: Turkish (native), English (advanced)

Married: 28 April 2001

Children: Melisa Yaren ( 28 June 2002 ), Ahmet Kağan ( 25 April 2008 )

2) EDUCATIONS:

3) ACADEMIC PROMOTIONS:

4) THESIS COMPLETED:

1

MSc

Covering spaces and the transformation groups of the covering spaces.

Uludag University, Inst. of Sci., Dept. of Maths .

Prof. Dr. Mustafa BAYRAKTAR

2

PhD

Discrete groups and quadratic forms.

Uludag University, Inst. of Sci., Dept. of Maths .

Prof. Dr. Mustafa BAYRAKTAR

5) MATHEMATICS SUBJECT CLASSIFICATION 2000:

11Bxx

Sequences and sets

11B37, 11B39, 11B50

11-xx

Number theory

11A55, 11D25, 11D70, 11E11, 11E15, 11E16, 11E18, 11E25, 11F03, 11F22, 11G05, 11G07, 11G16, 11G20, 11J70

11Dxx

Diophantine equations

11D04, 11D09, 11D25, 11D41, 11D68, 11D72, 11D85

11Exx

Forms and linear algebraic groups

11E04, 11E08, 11E12, 11E16, 11E25, 11E39, 11E76.

11Fxx

Discontinuous groups and automorphic forms

11F03, 11F11, 11F23, 11F27, 11F30.

11Gxx

Arithmetic algebraic geometry

11G05, 11G07, 11G16, 11G30, 11G40, 11G50.

57Mxx

Low-dimensional topology

57M05, 57M07, 57M10, 57M12.

6) RESEARCH AREAS:

1

COVERING SPACES

Covering spaces, universal, regular and Galois covering spaces, automorphism groups of covering spaces, fundamental group, Riemann surfaces, covering of Riemann surfaces.

2

DISCRETE GROUPS

Discrete groups, modular and extended modular group, special congruence subgroups, signature of the special and principal congruence subgroups.

3

BINARY QUADRATIC FORMS

Quadratic forms, cycle of forms, equivalence of forms, representation of positive integers by quadratic forms, theta series and Eisenstein series associated positive quadratic forms, ternary forms, Hermitian forms, representation of integers by Hermitian forms, cusp form, modular form.

4

IDEALS

Quadratic ideals, primitive ideals, cycles of ideals, ambiguous ideals, equivalence of ideals, relationship between ideals and quadratic forms, quadratic irrationals.

5

ELLIPTIC CURVES

Elliptic curves over finite fields, rational points on elliptic curves, rank of elliptic curves, torsion groups of elliptic curves, group structure of elliptic curves.

6

ELLIPTIC DIVISIBILITY SEQUENCES

Elliptic divisibility sequences, the connection between elliptic curves and elliptic divisibility sequences, elliptic divisibility sequences and Fibonacci and Lucas sequences.

7

EQUATIONS

Pell and Diophantine equations and their integer solutions, recurrence relations on integer solutions of Pell and Diophantine equations, finite continued fractions and fundamental solutions, Pell and Diophantine equation over finite fields.

8

NUMBERS

Kaprekar numbers, Fibonacci, Lucas, Pell and Carmichael numbers.

9

CONGRUENCES

Quadratic and cubic congruence and their connections with binary quadratic forms, integer solutions of cubic and quadratic congruences over finite fields.

10

CONICS

Conics over finite fields and the number of rational points on conics related to binary quadratic forms over finite fields.

 

7) PUBLICATIONS:  (Indexed by MathSci Net) (Indexed by Zentralblatt MATH)    

  1. A.Tekcan, M.Bayraktar, O.Bizim. On the Covering Space and the Automorphism Group of the Covering Space. Balkan J. of Geo. and Its Appl. 8(1) (2003), 101-108.  (SCI-Exp)

  2. A.Tekcan, O.Bizim. The Connection between Quadratic Forms and the Extended Modular Group. Mathematica Bohemica 128(3) (2003), 225-236.

  3. A.Tekcan, O.Bizim. On the Number of Representations of Positive Integers by Quadratic Forms as the Basis of the Space $S_{4}(\Gamma_{0}(47),1) $.  Int. Jour. of Maths.  and Math. Sci.2004(12) (2004), 637-646.

  4. A.Tekcan, O.Bizim. On the Representation of Positive Integers by Quadratic Forms with Seven Variables. South East Asian Bull. of Mathematics 28 (5) (2004), 875-886.

  5. A.Tekcan. Representations of Positive Integers by a Direct Sum of Quadratic Forms. Results in Maths. 46(2004), 146-163.(SCI-Exp)

  6. A.Tekcan. Pell Equation $x^{2}-Dy^{2}=2$, II. Irish Mathematical Society Bulletin 54(2004), 73-89.

  7. A.Tekcan. Formulas for the Fourier Coefficients of Cusp Form for Some Quadratic Forms. Turkish Journal of Mathematics 29(2005), 141-156. (SCI-Exp)

  8. A.Tekcan. Representation of Integers by Hermitian Forms. Acta Mathematica Universitatis Comenianae LXXIV(2) (2005), 205-209.

  9. A.Tekcan. Cycles of Indefinite Quadratic Forms and Cycles of Ideals. Hacettepe Journal of Maths.and Statistics 35(1) (2006), 63-70.

  10. A.Tekcan, O.Bizim, M.Bayraktar. Solving the Pell Equation using the Fundamental Element of the Field $\mathbb{Q}(\sqrt{\Delta })$. South East Asian Bull. of Mathematics  30(2)(2006), 355-366.

  11. A.Tekcan. Signatures of the Special Congruence Subgroup of the Extended Modular Group. South East Asian Bulletin of Mathematics 30(6) (2006), 1147-1156.

  12. A.Tekcan, H.Özden. On the Quadratic Irrationals, Quadratic Ideals and Indefinite Quadratic Forms. Irish Mathematical Society Bulletin 58(2006), 69-79.

  13. A.Tekcan, O.Bizim, I.N.Cangül. The Number of Representations of Positive Integers by Positive Quadratic Forms. Proc. of the Jangjeon Math. Soc. 9(2) (2006), 125-136.

  14. A.Tekcan. A Second Approach to the Proper Cycles of Indefinite Quadratic Forms and their Right Neighbors. Int. Journal of Contemporary Math. Sci. 2(6) (2007), 249-260.

  15. A.Tekcan. The Pell Equation $x^{2}-Dy^{2}=\pm 4$. Applied Mathematical Sciences 1(8)(2007), 363-369.

  16. A.Tekcan. Representations of Positive Integers by Positive Quadratic Forms and the Fourier Coefficients of Cusp Forms. South East Asian Bull. of Mathematics  31(2)(2007), 349-362.

  17. A.Tekcan. The Number of Rational Points on Conics $C_{p,k}:x^{2}-ky^{2}=1$ over Finite Fields $\mathbb{F}_{p}$. Int. Jour. of Math.Sci. 1(2) (2007), 150-153.

  18. A.Tekcan. The Elliptic Curves $y^{2}=x^{3}-t^{2}x$ over $\mathbb{F}_{p}$. International Journal of Computational and Mathematical Sciences 1(3)(2007), 165-171.

  19. B.Gezer, H.Özden, A.Tekcan, O.Bizim. The Number of Rational Points on Elliptic Curves $y^{2}=x^{3}+b^{2}$ over Finite Fields. Int. Jour. of Comp. and Math. Sci.  1(3) (2007), 178-184

  20. A.Tekcan. On Indefinite Binary Quadratic Forms, Cubic Congruence and Elliptic Curves. Int. Jour. of Comp. and Math. Sci.2(21)(2007), 1031–1037.

  21. A.Tekcan, B.Gezer, O.Bizim. On the Integer Solutions of the Pell Equation $x^{2}-dy^{2}=2^{t}$. Int. Jour. of Comp. and Math. Sci.  1(3)(2007), 204-208.

  22. A.Tekcan. Some Algebraic Properties of Universal and Regular Covering Spaces. Int. Jour. of Computational and Mathematical Sciences  1(4)(2007), 251-254.

  23. A.Tekcan. Some Remarks on Indefinite Binary Quadratic Forms and Quadratic Ideals. Hacettepe Journal of Math.and Statistics 36(1)(2007), 27-36. (SCI-Exp)

  24. A.Tekcan. On the Pell Equation $x^{2}-(k^{2}-2)y^{2}=2^{t}$. Crux Mathematicorum with Math. Mayhem 33(6)(2007), 361-365.

  25. A.Tekcan. Proper Cycle of Indefinite Quadratic Forms and their Right Neighbors. Applications of Mathematics 52(5) (2007), 407-415.   

  26. A.Tekcan. The Cubic Congruence $x^{3}+ax^{2}+bx+c \equiv 0 (\mod p)$ and Binary Quadratic Forms F(x,y)=ax^{2}+bxy+cy^{2}$. Ars Combinatoria 85(2007), 257-269. (SCI-Exp)

  27. A.Tekcan, B. Gezer, O. Bizim. Some Relations on Lucas Numbers and their Sums. Advanced Studies in Contemporary Mathematics 15(2)(2007), 195-211.

  28. A.Tekcan. The Base Points of Indefinite Quadratic Forms in the Cycle and Proper Cycle of an Indefinite Quadratic Form. Hacettepe Journal of Mathematics and Statistics  36(2)(2007), 101-114. (SCI-Exp)

  29. A.Tekcan. The Pell Equation $x^{2}-(k^{2}-k)y^{2}=2^{t}$. Int. Journal of Comp.and Math.Sci. 2(1)(2008), 5-9.

  30. B.Gezer, A.Tekcan, O.Bizim. The Number of Rational Points on Elliptic Curves and Circles over Finite Fields. Int. Journal of Comp.and Math.Sci. 2(2)(2008), 58-63.

  31. A.Tekcan. On Indefinite Binary Quadratic Forms and Quadratic Ideals. Novi Sad Journal of Mathematics 38(1)(2008), 83-96.

  32. A.Tekcan, A.Özkoç, B.Gezer, O.Bizim. Some Relations Involving the Sums of Fibonacci Numbers. Proceedings of the Jangjeon Math. Soc. 11(1) (2008), 1-12.

  33. A.Tekcan, O.Bizim. The Pell Equation $x^{2}+xy-ky^{2}=\pm1$. Global Journal of Pure and Applied Mathematics 4(2)(2008), 105-112.

  34. A.Tekcan. On the Cycles of Indefinite Quadratic Forms and Cycles of Ideals III. Comptes rendus mathématiques-Mathematical Reports 30(1)(2008), 22-32.

  35. A.Tekcan, A.Özkoç, B.Gezer, O.Bizim. Elliptic Curves, Conics and Cubic Congruencies associated with Indefinite Binary Quadratic Forms. Novi Sad Journal of Mathematics 38(2)(2008), 71-81

  36. A.Tekcan. The Number of Rational Points on Singular Curves $y^{2}=x(x-a)^{2}$ over Finite Fields $mathbb{F}_{p}$. Int. Journal of Comp.and Math.Sci. 3(1)(2009), 14-17.

  37. A.Tekcan, A.Özkoç. Quadratic Irrationals, Quadratic Ideals and Indefinite Quadratic Forms II. Int. Journal of Comp.and Math.Sci. 3(2)(2009), 56-59.

  38. A.Tekcan. Representation of Integers by Quadratic Forms in Several Variables. Creative Mathematics and Informatics 18(2009), 65-75.

  39. A.Tekcan, A.Özkoç. Positive Definite Binary Quadratic Forms, Quadratic Congruences and Singular Curves. Comptes ren.math.-Math.Reports 31(2)(2009), 53-64

  40. A.Tekcan. The Elliptic Curves $y^{2}=x^{3}-1728x$ over Finite Fields. Jour.of Algebra, Number Theory: Adv. and Appl.1(1)(2009), 61-74.

  41. A.Tekcan, A.Ozkoç, H.Alkan. The Diophantine Equation $y^{2}-2yx-3=0$ and Corresponding Curves over $mathbb{F}_{p}$. Int. Jour. of Math.and Statis. Sci. 1(2)(2009), 66-69.

  42. B.Gezer, A.Tekcan, O.Bizim. Elliptic Divisibility Sequences over Finite Fields. Int. Journal of Comp.and Math.Sci. 4(1)(2010), 12-19

  43.  A.Tekcan, A.Özkoç. The Diophantine Equation $x^{2}-(t^{2}+t)y^{2}-(4t+2)x+(4t^{2}+4t)y=0$. Revista Matemática Complutense 23(1)(2010), 251-260 (SCI-Exp)

  44. A.Tekcan, A.Özkoç, C.Kocapınar, H.Alkan. The Diophantine Equation $x^{2}-Py^{2}=Q. Int. Journal of Comp.and Math.Sci. 4(2)(2010), 59-62.

  45. A.Tekcan. On the Cycles of Indefinite Quadratic Forms and Cycles of Ideals II. South East Asian Bul.of Maths. 34(2010), 185-192.

  46. A.Tekcan. Positive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences. Int. Journal of Comp.and Math.Sci. 4(2)(2010), 100-104

  47. A.Tekcan. The Cubic Congruence $x^{3}+ax^{2}+bx+c \equiv 0 (\mod p)$ and Binary Quadratic Forms F(x,y)=ax^{2}+bxy+cy^{2}$ II. Acta Universitatis Apulensis 22(2010), 53-63.

  48. A.Özkoç, A.Tekcan. Quadratic Diophantine Equation $x^{2}-(t^{2}-t)y^{2}-(4t-2)x+(4t^{2}-4t)y=0$. Bul.of the Malaysian Math. Sci. Society 33(2)(2010), 273-280.

  49. A.Tekcan, A.Özkoç. The Family of Indefinite Binary Quadratic Forms and elliptic Curves over Finite Fields. General Mathematics.

  50. A.Tekcan. Neighbors of Indefinite Binary Quadratic Forms. Int. Journal of Comp.and Math.Sci. 5(1)(2011), 16-22.

  51. A.Tekcan. The Elliptic Curves $y^{2}=x(x-1)(x-\lambda)$. Ars Combinatoria (SCI-Exp)

  52. A.Tekcan. The Number of Solutions of Pell Equations $x^{2}-ky^{2}=N$ and $x^{2}+xy-ky^{2}=N$ over $\mathbb{F}_{p}$.Ars Combinatoria. (SCI-Exp)

  53. A.Tekcan. Positive Definite Binary Quadratic Forms and Modules over a Field. South East Asian Bulletin of Mathematics

  54. A.Tekcan, O.Bizim. Elliptic Curves and Cubic Congruences Associated with Indefinite Binary Quadratic Forms. Global Journal of Pure and Applied Mathematics.

  55. A.Tekcan, A.Özkoç, B.Gezer, O.Bizim. Representations of Positive Integers by Positive Quadratic Forms. South East Asian Bulletin of Mathematics

  56. A.Tekcan. Some Algebraic Identities on Pell Numbers and Sums of Pell Numbers Ars Combinatoria (SCI-Exp)

  57. A.Tekcan. Principal Indefinite Quadratic Forms and Singular Curves over Finite Fields. South East Asian Bulletin of Mathematics.

  58. A.Tekcan, A.Özkoç . $n$-Universal Quadratic Forms and Quadratic Forms over Finite Fields. Irish Math. Soc.Bulletin.

  59. A.Tekcan, A.Özkoç, H.Alkan. On Cycles and Products of Ideals and Corresponding Indefinite Quadratic Forms. Comptes ren.math Math.Reports

  60. C.Kocapınar, A.Özkoç, A.Tekcan. The Integer Sequence $B=B_{n}(P,Q)$ with Parameters $P$ and $Q$. Ars Combinatoria (SCI-Exp)

  61. A.Tekcan. On Kaprekar Numbers. Advances in Theoretical and Applied Mathematics.

  62. A.Tekcan, H.Alkan, A.Özkoç, E.Çetin, İ.N.Cangul. Rational Points on Curves over Finite Fields. Antarctica Journal of Mathematics

    8) SYMPOSIUM ATTENDED:

A) National:

  1. A.Tekcan. Quadratic Forms and Ideals. XVII. National Mathematics Symposium, Abant İzzet Baysal University, 2004, Bolu-TURKIYE.

  2. A.Tekcan. Base Points of Positive Definite Quadratic Forms. XVIII National Mathematics Symposium, İstanbul Kültür University, 2005, İstanbul- TURKIYE.

  3. A.Tekcan, O.Bizim, H.Özden, İ.İnam. Cycles of Indefinite Quadratic Forms.  XIX. National Mathematics Symposium, Dumlupınar University, 2006, Kütahya- TURKIYE.

  4. H.Özden, İ.İnam, A.Tekcan, O.Bizim. The Number of Rational Points on Elliptic Curves $y^{2}=x^{3}+b^{2}$ over Finite Fields. XIX. National Mathematics Symposium, Dumlupınar University, 2006, Kütahya-TURKIYE.

  5. İ.İnam, O.Bizim, A.Tekcan, H.Özden. The Rational Points on Frey Elliptic Curves over Finite Fields. XIX. National Mathematics Symposium, Dumlupınar University, 2006, Kütahya-TURKIYE.

  6. A.Tekcan, A.Özkoç. Right and Left Neighbors of Indefinite Binary Quadratic Forms. XXII. National Mathematics Symposium, Nesin Mathematics Willage, 2009, Selçuk-İzmir, TURKIYE.

  7. A.Özkoç, A.Tekcan, Indefinite Binary Quadratic Forms, Elliptic Curves and Cubic Congruences. XXII. National Mathematics Symposium, Nesin Mathematics Willage, 2009, Selçuk-İzmir, TURKIYE.

  8. A.Tekcan, A.Özkoç. Equivalence of Indefinite Quadratic Forms, Base Points and Neighbours. 5 th Ankara Mathematics Days, 2010, TOBB University, Ankara, TURKIYE.

  9. A.Özkoç, A.Tekcan. The Diophantine Equation $x^{2}-(t^{2}-t)y^{2}-(4t-2)x+(4t^{2}-4t)y=0$.5 th Ankara Mathematics Days, 2010, TOBB University, Ankara, TURKIYE.

B) International:

  1. A.Tekcan, B.Gezer, O.Bizim. The Connection between Principal Indefinite Quadratic Forms and Elliptic Curves. Antalya Algebra Days IX, 22-27 May 2007, Antalya-TURKIYE.

  2. B.Gezer, O.Bizim, A.Tekcan. On the Singular Elliptic Curves over Finite Fields. Antalya Algebra Days IX, 22-27 May 2007, Antalya-TURKIYE.

  3. A.Tekcan, B.Gezer, O.Bizim. Right Neighbors and Base Points of Indefinite Binary Quadratic Forms. Workshop on Math. Methods in App. Sci., 22-23 May 2008, Bursa-TURKIYE.

  4. B.Gezer, O.Bizim, A.Tekcan. Some Properties of the Elliptic Divisibility Sequences over Finite Fields. Workshop on Math.Methods in App. Sci., 22-23 May 2008, Bursa-TURKIYE.

  5. A.Tekcan, A.Özkoç. The Number of Rational Points on Elliptic Curves Related to Binary Quadratic Forms. Antalya Algebra Days X, 28 May-01 June 2008, Antalya-TURKIYE.

  6. B.Gezer, A.Özkoç, A.Tekcan, O. Bizim. The Relationship among Elliptic Divisibility Sequences, Elliptic Curves and Binary Quadratic Forms. Antalya Algebra Days X, 28 May-01 June 2008, Antalya-TURKIYE.

  7. B.Gezer, O.Bizim, A.Tekcan. On the Elliptic Divisibility Sequences over Finite Fields. 5-th Europan Congress of Mathematics, 14-18 July 2008, Amsterdam-HOLLAND.

9) BOOKS:

1. O.Bizim, A.Tekcan, B.Gezer. General Mathematics I (ISBN:978-605-4118-18-2). Dora Publishing, Bursa, 2009.

2. O.Bizim, A.Tekcan, B.Gezer. General Mathematics II (ISBN:978-605-4118-41-0). Dora Publishing, Bursa, 2009

 10) OTHERS ACADEMIC ACTIVITIONS:

      A) Reviewer for

              1. Mathematical Reviews MR (2005-)

              2. Zentralblatt MATH (2007-)

              3. Journal of Number Theory (2008-)

    B) Member of Editorial Board:

            1. Int. Journal of Computational and Mathematical Science  (2007-)
            2. International Journal of Applied Science, Engineering and Technology (2007-)
            3. International Journal of Inequalities and Applications (2007-)
            4. Antartica Journal of Mathematics (2010-)
            5. Archimedes Journal of Mathematics (2010-)

    C) Local Organization Committee of:

           1.  Workshop on Mathematical Methods in Applied Sciences, May 22-23, 2008, Uludag University, Bursa-TURKIYE.

           2.  The 20 th International Congress of Jangjeon Mathematical Society, August 21-23, 2008, Uludag University, Bursa-TURKIYE.

           3. Int. Cong. in Honour of Professor H.M.Srivastava on his 70th Birth Anniversary, 18-21 August, 2010, Uludag University, Bursa, TURKIYE

  11) TEACHING: 

             A) Undergraduate: Analysis I, Analysis II, Analysis III, Analysis IV, Functional Analysis, Metric Spaces, Vectorial Analysis, Mathematics I,
                  Mathematics II, Basic Mathematics I, Basic Mathematics II, General Mathematics I, General Mathematics II, Engineering Mathematics,
                  Advanced Mathematics.

             B) Graduate: Analytic Number Theory, Theory of Elliptic Curves and Its Applications I, Theory of Elliptic Curves and Its Applications II,
                   Number Theory I, Number Theory II, Algebraic Number Theory I, Algebraic Number Theory II, Advanced Analytic Number Theory,
                   Geometric Number Theory.
 

   12) LINKS:

1.       Mathematics Journals List

2.       Mathematics on the web

3.       MathSciNet

4.       Zentralblatt MATH - ZMATH Online Database

5.       History Topics: Alphabetical Index

6.       The Electronic Library of Mathematics: Mathematical Journals

7.      Mathematical Reviews Electronic Review Submission Home

8.      Alphabetical List of Mathematical Societies

9.       Mathematical Reviews Database

10.   European Mathematical Society

11.   2000 Mathematics Subject Classification

12.   Science Citation Index

13.   Science Citation Index-Expanded

14.   Academic Search Premier

15.   Turkish Mathematical Society

16.   Turkish Journal of Mathematics

17.   Tubitak

18.   BCMATH programs for binary quadratic form

19.   Finding the reduced binary quadratic form

 

13) UMAT:

Counselor of Uludag University, Society of Mathematics (UMAT)

 

Last Updated: June 2010

 

 

 

 

 

Anasayfa