Professor Badih Ghusayni's Books:

  Classical Real Analysis

  ISBN 978-9953-0-1496-8

 

  Badih Ghusayni

 
  Paperback:  127 pages

    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.

 

An e-book is available for $19.99. Click on the button below.

Contents

1.  The Real Number System. 
2.  Numerical Sequences. 
3.  Limits and Continuity.
4.   Differentiation.
5.  Usual Functions.
6.  Finite Expansions.
7.  Adjacent Sequences, Recursive Sequences, Cluster Points, Limit Inferior and Limit Superior of a Sequence.
8.  Numerical Series.
9.  Series of Functions and the Special Case of a Power Series.





  Solved Exercises in Classical Real Analysis

  ISBN 978-9953-0-2484-4

 

  Badih Ghusayni

An e-book is available for $19.99. Click on the button below.

 
  Paperback:  141 pages

    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.

 




  Solved Problems in Analysis:

  A Companion to Math Majors

  ISBN 978-9953-0-1306-0

 

  Badih Ghusayni

An e-book is available for $37.99. Click on the button below.

 
  Paperback:  360 pages

    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.

 


The expanded 426-page Second Edition is out and is available as a PDF file which can be ordered by clicking on the same button below and e-mailing badih@future-in-tech.org and requesting the Second Edition

Contents

1.  Number Systems. 
2.  Numerical Sequences and Series. 
3.  Limits and Continuity.
4.   Differentiation.
5.  Abstract Integration.
6.  Borel Measures.
7.  LP-Spaces.
8.  Hilbert Spaces.
9.  Banach Spaces.
10.  Complex measures..
11.  Product Measures..
12.  Analytic Functions.
13.  Entire Functions of Exponential Type..
14.  Completness of sets of complex exponentials.





  Number Theory

  from an analytic point of view

  ISBN 978-9953-0-0282-7

 

The Solutions'  Manual is available to instructors ONLY upon request

  Badih Ghusayni

An e-book is available for $27.99. Click on the button below.

 
  Paperback  198 pages

    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.

 



Contents

1.  Overview of Complex Numbers and Functions. 
2.  Hadamard Factorization Theorem and Entire Functions of Order One
and Infinite Type. 
3.  The Goldbach and Twin Prime Conjectures.
4.  Zeta of 3.
5.  Maple Explorations.
6.  Function Characterizations.
7.  Exploring New Identities with Maple as a Tool.
8.  Mersenne Primes, Perfect Numbers, and  Friendly Numbers.
9.  The Prime Number Theorem from an Analytic Point of View.
10.  Cryptography.



 


Theorie de Nombre 

d'un Point de Vue Analytique                                                  

ISBN 978-9953-0-0283-5

Badih Ghusayni

An e-book is available for $37.99. Click on the button below.

 


   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.  

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Table des matieres                                                  

1.  Vue d'ensemble des Nombres et des Fonctions Complexes .
2.  Theoreme de Factorization du Hadamard et les Fonctions Entieres d'Ordre Un et Type Infini.
3.  Conjectures de Goldbach et nombres premiers Jumeaux.
4.  Zeta de 3.
5.  Exploration du Maple,
6.  Caracterisations des Fonctions,
7.  Exploration de Identites Nouvelles avec Maple comme un Outil,
8.  Mersenne Premiers, Nombres Parfaits, et Nombres Amicaux.
9.  Le Theoreme de Nombre Premier d'un Point de Vue Analytique
10.  Cryptographie.




  Online Complex Analysis Course

  Badih Ghusayni

    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 .




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