Ayoub Barsoum Ayoub

Professor of Mathematics

aba2@psu.edu
 
Penn State University
 Abington College
333 SUTHERLAND BUILDING
 

Tel:   215-881-7553 
 Fax:  215-881-7317
 
 

PROFESSIONAL INFORMATION

DEGREES

Ph.D. Temple University, May 1980; Mathematics, Algebraic Number Theory.

M.A. Temple University, May 1977; Mathematics.

B.Sc. Ain-Shams University, Egypt, May 1951; Mathematics.

AWARDS AND HONORS

1. Penn State-Ogontz Campus OUTSTANDING TEACHER AWARD, 1988.

2. Penn State-Ogontz Campus SCHOLAR AWARD, 1989.

3. Penn State University GEORGE ATHERTON AWARD for Excellence in Teaching, 1990.

4. Penn State, Mathematics Department TERESA COHEN AWARD for distinguished service to undergraduates, 1994.

5. Penn State Abington FACULTY SCHOLAR AWARD, 2003

6. Listed in AMERICAN MEN & WOMEN of SCIENCE, 1998

7. Listed in WHO'S WHO in Science and Engineering, 1994; WHO'S WHO in American Education, 1995; and WHO'S WHO in America, 1996.

 

MEMBERSHIP IN PROFESSIONAL ASSOCIATIONS

1. Mathematical Association of America (MAA).

2. The American Mathematical Association of Two Year Colleges (AMATYC).

3. Pennsylvania State Mathematical Association of Two Year Colleges (PYSMATIC)

4. National Council of Teachers of Mathematics (NCTM).

5. Pennsylvania Council of Teachers of Mathematics (PCTM).

6. Association of Mathematics Teachers Of New York State (AMTNYS).

PUBLICATIONS

1. Integral Solutions to the Equation : A Geometrical Approach. Mathematics Magazine, 57 (4), 1984.

2. Behold! The Graphs of and are Reflections About the Line . The College Mathematics Journal, 18 (1) 1987.

3. The Harmonic Triangle and the Beta Function. Mathematics Magazine, 60(4), 1987.

4. Which One is the Bisector of the Acute Angle? Mathematics and Computer Education, 23 (1), 1989.

5. Proof Without Words: The Reflection Property of the Parabola. Mathematics Magazine, 64 (3), 1991.

6. Inductive and Deductive Reasoning in Pascal's Triangle. NYS Mathematics Teacher, 41 (3), 1991.

7. A Geometrical Proof of the Directional Derivative Form. Mathematics and Computer Education, 25 (3), 1991.

8. A Note on the Sum of Squares of Natural Numbers. Mathematics and Computer Education, 26 (3), 1992.

9. A Note on the Mean Value Theorem and the Natural Logarithm Function. Mathematics and Computer Education, 27 (1), 1993.

10. The Central Conic Sections Revisited. Mathematics Magazine, 66 (4), 1993.

11. A Non-Complex Approach to the Complex Case of . Mathematics and Computer Education, 28 (1), 1994.

12. A Note on the Sum of Geometric Series. Mathematics and Computer Education, 29 (2), 1995.

13. A Weighted AM-GM-HM Inequality. Pi Mu Epsilon Journal, 10 (3), 1995.

14. A Classroom Note on the Regular Polygon and Associated Star. Mathematics and Computer Education, 30 (1), 1996.

15. The Square Roots, Means and Nested Intervals. Mathematics and Computer Education, 30 (2), 1996.

16. Integral Triangles From Euler's Quadrinomial Identity. NYS Mathematics Teacher, 46 (2), 1996.

17. A Note on Simpson’s Rule. Mathematics and Computer Education. 30 (3), 1996

18. Proof Without Words: Arithmetic Mean-Geometric Mean Inequality. Mathematics and Computer Education, 31 (2), 1997.

19. Why the Oscillations on a Cycloid are Isochronous. Mathematics and Computer Education, 31 (2), 1997.

20. Summation of Arithmetic Sequences of Higher Degree. The AMATYC Review, 18 (2), 1997.

21. Concavity and Inequalities. Mathematics and Computer Education, 31(3), 1997.

22. The Harmonic Triangle and Its Relation to Pascal’s Triangle. NYS Mathematics Teacher, 47 (3), 1997.

23. A Closed Expression for the Sum of Powers of Positive Integers. Mathematics and Computer Education, 32 (2), 1998.

24. Triangles With the Same Centroid. Mathematics Magazine, 71 (3), 1998.

25. Napoleon’s Theorem Revisited. Mathematics and Computer Education, 32 (3), 1998.

26. Proof Without Words: A Weighted Arithmetic Mean-Geometric Mean Inequality. Mathematics and Computer Education, Vol. 33 (1), 1999.

27. Making Connections with the AM-GM Inequality. NYS Mathematics Teacher, Vol. 49 (1), 1999.

28. Proof without Words : Mathematics and Computer Education, Vol. 33 (1), 1999.

29. The Pythagorean Triples . Mathematics and Computer Education, Vol. 33 (3), 1999.

30. More Solutions to the Equation : Mathematics and Computer Education, Vol. 34 (3), 2000.

31. General Forms of Some Trigonometric Identities. The AMATYC Review, Vol. 22 (1), 2000.

32. Factorization of the Primes. Pi Mu Epsilon Journal, Vol. 11 (3), 2000.

33. Tests for Divisibility by Primes. NYS Mathematics Teacher, Vol. 51 (1), 2001.

34. A Note on the Sums of and . Mathematics and Computer Education, Vol. 35 (2), 2001.

35. A Connection Between a Function, its Inverse, and the Arithmetic Mean. Mathematics and Computer Education, Vol. 35 (3), 2001.

36. Circles. An essay in the book Encyclopedia of Mathematics Education; edited by L. Grinstein and S. Lipsy. Routledge Falmer Publishing, NY, 2001.

37. Conic Sections. An essay in the book Encyclopedia of Mathematics Education; edited by L. Grinstein and S. Lipsy. Routledge Falmer Publishing, NY, 2001.

38. Parametric Equations. An essay in the book Encyclopedia of Mathematics Education; edited by L. Grinstein and S. Lipsy. Routledge Falmer Publishing, NY, 2001.

39. Polygons. An essay in the book Encyclopedia of Mathematics Education; edited by L. Grinstein and S. Lipsy. Routledge Falmer Publishing, NY, 2001.

40. Symmetry. An essay in the book Encyclopedia of Mathematics Education; edited by L. Grinstein and S. Lipsy. Routledge Falmer Publishing, NY, 2001.

41. Transformational Geometry. An essay in the book Encyclopedia of Mathematics Education; edited by L. Grinstein and S. Lipsy. Routledge Falmer Publishing, NY, 2001.

42. Transformations. An essay in the book Encyclopedia of Mathematics Education; edited by L. Grinstein and S. Lipsy. Routledge Falmer Publishing, NY, 2001.

43. A Cyclotomic Determinant. Pi Mu Epsilon Journal, Vol. 11 (6), 2002.

44. The Pell Sequence. Mathematics and Computer Education, Vol. 36 (1), 2002.

45. Power Means and Related Inequalities. Mathematics and Computer Education, Vol. 36 (1), 2002.

46. Eulers' Quadrilateral Theorem and Its Connection to Apollonius' Theorem. Mathematics and Computer Education, Vol. 36 (3), 2002.

47. Generalizations of a Similarity Theorem. Mathematics and Computer Education, Vol. 36 (3), 2002.

48. The Excentricity of a Conic Section. The College Mathematics Journal, Vol 34 (2), 2003.

49. Why the Laws of Cosines on the Sphere and in the Plane are Equivalent. Mathematics and Computer Vol. 37 (2), 2003.

50. The Curvature in a Family of Nested Conics, Pi Mu Epsilon Journal, Vol. 11 (9), 2003.

51. What Did Garfield Miss?  NYS Mathematics Teacher, Vol. 53(3), 2003.

52. The Centers of Similarity of two Non-Congruent Squares, The AMATYC Review, Vol 25(2), 2004.

53. The Law of Cosines and Apollonius Theorem, NYS Mathematics Teacher, Vol 54 (2), 2004.

54. Partitioning a Circular Region, Mathematics and Computer Education, Vol 38 (3), 2004.

55. Proof Without Words: Power Means Inequalities, Mathematics and Computer Education, Vol 39 (1), 2005.

56. Counting Primitive Pythagorean Triples, Mathematics and Computer Education , Vol. 39 (1), 2005.

57. Proof Without Words: Arctan(a/a+b) + Arctan(b/2a+b) = Pi/4, Mathematics and Computer Education , Vol. 39 (2), 2005.

58. Cramer Rule Revisited. The AMATYC Review,Vol.27(1),2005.

59. Where does the Extra One Come From ?. NYS Mathematics Teacher, Vol.55(2),2005.

60. Area,Diagnals,and Circumcircle of a Cyclic Quadrilateral. Mathematics and Computer Ed.,Vol.40(1),2006.

61. A special Trinomial Expansion. Mathematics and Computer Ed., Vol.40(2),2006.

62. Integral Solutions to the Law of Cosines Equation. PI MU EPSILON Journal,Vol.12(4),2006.

63. Fibonacci and Lucas Numbers as Sums of Binomial Coefficients. Mathematics and Computer Ed.,Vol.40(3),2006.

64. Fibonacci- Like Seqences and Pell Equations, The College Mathematics Journal, Vol.38(1),2007.

65. Generalizations of Ptolemy and Brahmagupta Theorems, Mathematics and Computer Ed, Vol.41(1),2007.

66. The Director Circle of the Central Conic Section, Mathematics andComputer Ed, Vol.41(2),2007.

67. What is the Converse of the Median Theorem of Right Triangles, NYS Mathematics Teacher’s Journal,Vol.57(2),2007.


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