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.

 

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.

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A US resident may order this book by a personal check in the amount of $29.99 (including shipping and handling) payable to: Gus Ghusayni, 10548 Lurline Ave., Chatsworth, CA 91311.




  Solved Problems in Analysis:

  A Companion to Math Majors

  ISBN 978-9953-0-1306-0

 

  Badih Ghusayni

 
  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.

 

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.

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A US resident may order this book by a personal check in the amount of $47.99 (including shipping and handling) payable to: Gus Ghusayni, 10548 Lurline Ave., Chatsworth, CA 91311.




  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

 
  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.

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A US resident may order this book by a personal check in the amount of $37.99 (including shipping and handling) payable to: Gus Ghusayni, 10548 Lurline Ave., Chatsworth, CA 91311.



 

Théorie de Nombre 

d'un Point de Vue Analytique                                                  

ISBN 978-9953-0-0283-5

Badih Ghusayni

 


   Ce livre est paru motivé par l'intérêt que son auteur a manifesté pour la  théorie des nombres.  L'auteur a découvert ce domaine des mathématiques  pendant la préparation de son mémoire de master sur les Théorèmes Tauberiens et le Théorème des Nombres Premiers. Cet intérêt s'est avéré une  fonction croissante du temps. 
  Quelques résultats on tété découverten utilisant le système informatique d'algèbre de Maple puis prouvés mathématiquement. Ce procédé, l'utilisation des logiciels mathématiques pour deviner des comportements des nombres, s'inscrit parmi les nouveles techniques de  la recherche mathématique. Pour chaque chapitre, j'ai fourni des exercices de  difficulté variée, qui s'étendent de simple à non résolu (bien sur, les questions ouvertes sont signalées et les lecteurs intéressés sont invités a y réfléchir avec bon espoir de les résoudre). C'est pourquoi, l'auteur pense que ce livre peut  intéresser les amateurs tout comme les professionnels.  A la fin de quelques chapitres, nous avons donné un aperçu rapide sur la vie de mathématiciens célèbres directement concernés par ce domaine de mathématique.  Ceci est  dans le but de divertir et d'informer le lecteur sur le déroulement historique  des découvertes dans l'espoir de mettre chaque résultat dans sa perspective historique.  

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Table des matières                                                  

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


http://www.future-in-tech.net/books/e-mailbirdlogo.gif For speedy delivery e-mail me after ordering: badih@future-in-tech.net