Badih Najib Ghusayni

Full professor
Mathematics department - Section I - Hadath
Speciality: Mathematics
Specific Speciality: Complex Analysis, Analytic Number Theory

Teaching 9 Taught Courses
(2016-2017) Math 415 - Number theory

M1 Mathematics

(2016-2017) Math 415 - Number theory

M1 Mathematics

(2016-2017) M2270 - Math appliquées

BS Physics

(2016-2017) M2207 - Analyse numérique et calcul formel

BS Mathematics

(2016-2017) M2207 - Analyse numérique et calcul formel

BS Mathematics

(2015-2016) Math 283 - Linear Algebra

BS Chemistry

(2015-2016) Math 283 - Linear Algebra

BS Chemistry

(2015-2016) Math 208 - Applied Mathematics II (Statistics & informatics)

BS Mathematics

(2015-2016) Math 278 - Analysis II (differential equations)

BS Chemistry


Auburn University, USA

Publications 23 publications
Badih Ghusayni Half a Dozen Famous Unsolved Problems in Mathematics with a Dozen Suggestions on How to Try to Solve Them http://ijmcs.future-in-tech.net/11.2/R-GhusayniHalf.pdf Int. J. Math. Comput. Sci., Vol. 11, no. 2, (2016), 257-273. 2016

Littlewood stated "Try a hard problem. You may not solve it, but you will solve something else". In this paper, we concentrate on six of the most famous and important unsolved problems in Mathematics. For each such problem we offer two suggestions to try to solve it. Even though some of these suggestions have been tried by the author with interesting results, he hopes that others will have more success thus attaining the objective of advancing knowledge. Our first problem begins with (clear) prime numbers while our last problem concludes with (hidden) prime numbers.

Badih Ghusayni A generalization of Wallis Formula http://ijmcs.future-in-tech.net/10.1/R-GhusayniGeneralizationWallis.pdf Int. J. Math. Comput. Sci., Vol. 10, No. 1, 2015, 51-54. 2015

We generalize the famous Wallis Formula using the Riemann Zeta Function.

Badih Ghusayni Solved Exercises in Classical Real Analysis Ghusayni 2012

This book contains exercises in Classical Real Analysis with their solutions. It is supposed to serve as a companion to an undergraduate course in Real Analysis. I hope that, with such exposure to solved problems, the students will excel in their study of such a course which is basic for their first university mathematics degree.

Badih Ghusayni Results Connected to the Riemann Hypothesis http://m-hikari.com/ijma/ijma-2012/ijma-25-28-2012/ghusayniIJMA25-28-2012.pdf 2012

The famous Riemann Hypothesis asserts that all the non-trivial zeros of the zeta function have real part 1/2. Based on some recent computer calculations showing that the first discovered 10 trillion non-trivial zeros, ordered by increasing positive imaginary part, have real part 1/2, it may be worthwhile to look at some important consequences if the Riemann Hypothesis is true. We then phrase the Riemann hypothesis in terms of the completed zeta function rather than the zeta function. We finally find results in that direction.

Badih Ghusayni Generalized Integration Formulas Int. J. Math. Comput. Sci., 5(2010), no. 1, 7-14. 2010

The purpose of this paper is three-fold. First, we generalize formula of Brychkov. Next, we consider an open problem. Finally, we supply a proof of formula 3 in section 3.415 of Gradshteyn.

Badih Ghusayni Classical Real Analysis Ghusayni 2009

This textbook covers Real Analysis from a classical point of view. This is not a Calculus textbook but a rather more advanced one. Therefore, the student is advised to take the material very seriously for not only it provides him/her with a solid background for other courses but also supplies essential tools to increase his/her mathematical maturity and logic to even help in real-life situations like avoiding stereotyping. The author would like to draw the attention of students to the fact that this book, like other mathematics books, contains "polished" proofs that will be best understood if the student makes the effort of reading "between the lines"; that is, to pause and ask oneself related questions in an effort to understand the mathematical argument. This may require at times a blank piece of paper and a pen to jot a few lines.

Badih Ghusayni The Value of the Zeta Function at an Odd Argument Int. J. Math. Comput. Sci., 4(2009), no. 1, 21-30. 2009

For over 300 years the values of the zeta function at odd integers greater than or equal to 3 have remained a mystery. The PSLQ algorithm which is implemented in the Computer Algebra System Maple is considered one of the top ten algorithms of the 20-th Century. We employ PSLQ to discover an Euler-type identity for such an odd argument.

Badih Ghusayni Solved Problems in Analysis: A Companion to Math Majors Ghusayni 2008

This book covers the wide area of Analysis and includes 525 problems and their complete solutions covering undergraduate Classical Analysis, Graduate Real and Complex Analysis, Functional Analysis and Nonharmonic Fourier Series. As a result this book is targeted for math majors at all levels.

Badih Ghusayni Towards a proof of the twin prime conjecture http://ijpam.eu/contents/2008-47-1/5/5.pdf International Journal of Pure and Applied Mathematics, 47(2008), no. 1, 31-40. 2008

Prime numbers differing by 2 are called twin primes. The twin prime conjecture states that the number of twin primes is infi nite. Many at- tempts to prove or disprove this 2300-year old conjecture ha ve failed. The objective of this paper is two-fold. We first tie the twin prim e conjecture to complex variable theory. We then look at some of the most recent progress on it.

Badih Ghusayni Online Book on Complex Analysis (as part of Avicenna Virtual Campus, supported by UNESCO) http://ijmcs.futureintech.net/OnlineCourseOnComplexAnalysis/ Ghusayni 2005

This online course is about Complex Variables, one of the very important subjects of mathematics. This course serves as a basis and provides a solid background rich in both theory and applications. At the end of this course the student should be able to understand the theory of complex functions in one variable and its applications. It should provide a solid teaching background if the student goes to secondary teaching. It should prepare the student for graduate studies as well as in later interdisciplinary courses like Analytic Number Theory, where Complex Variables plays a major role in handling problems in Number Theory .

Badih Ghusayni Maple explorations, Perfect numbers, and Mersenne primes http://www.tandfonline.com/doi/full/10.1080/00207390500064080#.VMy6uXKSySo International Journal of Mathematics Education in Science and Technology, 36 (2005), no. 6, 643-654. 2005

Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.

Badih Ghusayni A collection of number and function characterizations WSEAS Transactions on Mathematics, 5 (2005), no. 1, 12-17. 2005

The objective of this paper is to give characterizations of some numbers and many functions which are the exponential, identity, constant, Gamma, trigonometric and hyperbolic functions.

Badih Ghusayni Exploring new identities with Maple as a tool WSEAS Transactions on Information Science and Applications, 1 (2004), no. 5, 1151-1157. 2004

Algorithms, like LLL, and Computer Algebra Systems, like Maple, are modern tools that can be used to discover identities. Hopefully, these discoveries can then be coupled with mathematical proofs to become valid. As a result, this provides a unique and excellent venue to advance our knowledge.

Badih Ghusayni Number Theory from an analytic point of view Ghusayni 2003

This book has emerged from the author's interest in Number theory which began in 1980 when the author wrote his masters thesis on Tauberian Theorems and the Prime Number Theorem. This interest turned out to be an increasing function of time. Some results were discovered by using the Computer Algebra System Maple and then proved mathematically thus providing new venues of mathematical research. To each chapter, I have supplied exercises which range from simple to unsolved (needless to say, I would of course let the reader know which problem remains unsolved but hopefully, by doing so, the reader's interest in trying to solve it won't diminish). This is among the reasons why the author thinks that this book is targeted towards amateurs and professionals alike. At the end of some chapters, we shed some light on lives of relevant mathematicians which the author feels attracts the interest of readers and may put things in perspective. Each chapter has its own references.

Badih Ghusayni Theorie de Nombre d'un Point de Vue Analytique Ghusayni 2003

Ce livre est paru motive par l'interet que son auteur a manifeste pour la theorie des nombres. L'auteur a decouvert ce domaine des mathematiques pendant la preparation de son memoire de master sur les Theoremes Tauberiens et le Theoreme des Nombres Premiers. Cet interet s'est avere une fonction croissante du temps. Quelques resultats ont ete decouverten utilisant le systeme informatique d'algebre de Maple puis prouves mathematiquement. Ce procede, l'utilisation des logiciels mathematiques pour deviner des comportements des nombres, s'inscrit parmi les nouveles techniques de la recherche mathematique. Pour chaque chapitre, j'ai fourni des exercices de difficulte variee, qui s'etendent de simple a non resolu (bien sur, les questions ouvertes sont signalees et les lecteurs interesses sont invites a y reflechir avec bon espoir de les resoudre). C'est pourquoi, l'auteur pense que ce livre peut interesser les amateurs tout comme les professionnels. A la fin de quelques chapitres, nous avons donne un apercu rapide sur la vie de mathematiciens celebres directement concernes par ce domaine de mathematique. Ceci est dans le but de divertir et d'informer le lecteur sur le deroulement historique des decouvertes dans l'espoir de mettre chaque resultat dans sa perspective historique.

Badih Ghusayni Characterizations of arithmetic progression functions with counterexamples in interpolation http://cs.ucmo.edu/~mjms/2003-2pdf.html Missouri Journal of Mathematical Sciences, 15 (2003), 110-128. 2003

Characterizations of a couple of important functions are given. We also give counterexamples to show that some generalized problems on interpolation do not hold.

Badih Ghusayni Euler-type formula using Maple Palma Research Journal, 1 (2001), 175-180. 2001

Badih Ghusayni Perfect numbers and some of their properties Proceedings of the International Conference on Scientific Computations held at Lebanese American University (1999), 117-126. 1999

Perfect numbers have fascinated people for a very long time and continue to do so. In this paper we look at some of their interesting properties and mention some questions that still await answers. A good venue, nowadays, is numerical computation.

Badih Ghusayni Some representations of Zeta(3) http://cs.ucmo.edu/~mjms/1998-3p.html Missouri Journal of Mathematical Sciences, 10 (1998), 169-175. 1998

Badih Ghusayni Entire functions of order one and infinite type http://cs.ucmo.edu/~mjms/1998-1p.html Missouri Journal of Mathematical Sciences, 10 (1998), 20-27. 1998

In this paper we rst prove an auxiliary result that an entire function of order one and innite type must have innitely many nonzero zeros We then give an explicit canonical representation for those functions We apply the representation to prove a result and its converse about entire functions of order one and innite type Next we mention a few interesting examples of entire functions of order one and innite type Finally we formulate and disprove a conjecture which serves as an analogue to the PaleyWiener Theorem for entire functions of order one and innite type

Badih Ghusayni Products and sums with applications http://cs.ucmo.edu/~mjms/1997-2d.html Missouri Journal of Mathematical Sciences, 9 (1997), 90-94. 1997

The Twin Prime Conjecture states that the number of twin primes is innite Many attempts to prove or disprove the conjecture have failed The objective of this note is to tie the Twin Prime Conjecture to complex variable theory and prove some results that make it possible to consider the conjecture from a complex variable viewpoint rather than from a purely number theoretic one

Badih Ghusayni On approximation by a nonfundamental sequence of translates http://ac.els-cdn.com/S0022247X96901547/1-s2.0-S0022247X96901547-main.pdf?_tid=c92b3ccc-be93-11e5-8487-00000aab0f6b&acdnat=1453197945_d32507ce0965287900a2f75e276ccc22 Journal of Math Analysis and Applications, 199 (1996), 469-477. 1996

If f(t) and its Fourier transform F(t) satisfy some growth conditions and if {cn}∞ 0 is a sequence of distinct real numbers satisfying a certain separation condition, we represent those functions g(t) which are in the closure of the linear span of a nonfundamental sequence {f(cn − t)} in L2(R). A result about the degree of approximation is also proved.

Badih Ghusayni Integral representations of 2-Pi periodic and trigonometrically convex functions http://www.tandfonline.com/doi/pdf/10.1080/17476939008814411/ Complex Variables, 14 (1990), 129-138. 1990

The integral representation given by Levin of 2-Pi periodic and p-trigonometrically convex functions which are indicators of holomorphic functions of non-zero order p is incorrect. Counterexamples are given here as well as a corrected version of the representation.


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