المرجع الالكتروني للمعلوماتية
المرجع الألكتروني للمعلوماتية

الرياضيات
عدد المواضيع في هذا القسم 9761 موضوعاً
تاريخ الرياضيات
الرياضيات المتقطعة
الجبر
الهندسة
المعادلات التفاضلية و التكاملية
التحليل
علماء الرياضيات

Untitled Document
أبحث عن شيء أخر
{ان أولى الناس بإبراهيم للذين اتبعوه}
2024-10-31
{ما كان إبراهيم يهوديا ولا نصرانيا}
2024-10-31
أكان إبراهيم يهوديا او نصرانيا
2024-10-31
{ قل يا اهل الكتاب تعالوا الى كلمة سواء بيننا وبينكم الا نعبد الا الله}
2024-10-31
المباهلة
2024-10-31
التضاريس في الوطن العربي
2024-10-31

مـتطلبات ادارة التـغييـر
7-8-2019
ماهية مبدأ القناعة القضائية
10-5-2017
الفرق بين الضياء والنور
20-10-2014
التعارض المستقر
1-9-2016
تعيين أماكن تلقيح وتزاوج الحشرات
14-11-2021
المولى الحاج حسين النيشابوري
19-7-2017

Jacques Tits  
  
124   01:30 مساءً   date: 18-3-2018
Author : H Abels
Book or Source : Cantor-Medaille für Jacques Tits, Jahresber. Deutsch. Math.-Verein. 103
Page and Part : ...


Read More
Date: 19-3-2018 123
Date: 19-3-2018 116
Date: 19-3-2018 131

Born: 12 August 1930 in Uccle, Belgium


Jacques Tits was born in Uccle, on the southern outskirts of Brussels. His parents were Léon Tits, who was a professor, and Lousia André. Jacques attended the Athénée of Uccle and then studied at the Free University of Brussels. His thesis advisor in Brussels was Paul Libois, and Tits graduated with his doctorate in 1950 having submitted his dissertation Généralisation des groupes projectifs basés sur la notion de transitivité . From 1948 to 1956 he was funded by the Belgium Fonds National de la Recherche Scientifique.

Tits' first papers, following the work he had undertaken for his doctoral dissertation, were on generalisations of triply transitive groups. He published a two part paper Généralisations des groupes projectifs in 1949 on this topic generalising the group of one-dimensional projective transformations. Among the results proved were characterisations of projective groups among triply transitive groups. In Groupes triplement transitifs et généralisations (1950), Tits went on to look at generalisations of n-tuply transitive groups, defining an almost n-tuply transitive group. This generalises the group of collineations of the plane which is almost quadruply transitive. In Sur les groupes triplement transitifs continus; généralisation d'un théorème de Kerékjártó (1951) Tits looked at triply transitive groups of transformations of a topological space using his earlier results which characterised the projective groups among triply transitive groups.

Tits married Marie-Jeanne Dieuaide, a historian, on 8 September 1956. From 1956 to 1962 he was an assistant at the University of Brussels. He was promoted to professor in 1962 and remained in this role at Brussels for two years before accepting a professorship at the University of Bonn in 1964. Among Tits' doctoral students in Brussels we mention Francis Buekenhout who was awarded his doctorate in 1965. In 1973 Tits accepted the Chair of Group Theory at the Collège de France. Shortly after taking up this post, he became a naturalised French subject in 1974. Tits held this chair until he retired in 2000.

The large and important mathematical developments introduced by Tits are far too numerous to cover here in any detail. Perhaps the most important part of his work was the introduction of buildings and this is put into context by Ronan in [3]. We give his summary:-

This paper is an essay on how the development of group theory led to the discovery of various families of simple groups, and how these in turn led to the theory of buildings. In outline the story is this. Galois first used the term 'group' in the technical sense, and found the first simple groups. Jordan, in his famous Traité des substitutions et des équations algébriques, published in 1870, promoted Galois' work and put the theory of groups on a firm foundation. At this time groups were treated as groups of permutations, but other aspects of group theory were soon on the way. Lie visited Paris in 1870 as a graduate student, and went on to create the theory of continuous transformation groups. Killing came to such groups independently, and in 1888 found the classification of the simple Lie groups, using semisimple complex Lie algebras (families A through G). Cartan refined this classification in 1894, correcting some errors in the proofs, and it is now known as the Killing-Cartan classification. The classical families (A through D) soon led to groups over fields other than the real or complex numbers, and a comprehensive study was published by Dickson in 1901. Later he dealt with E6 and G, but progress on the others did not occur until after the Second World War. Tits was working on the problem, as was Chevalley, who was a more established mathematician at that time. Chevalley succeeded in 1955, and his paper was soon followed by variations due to Steinberg, Tits, Suzuki, and Ree. During this time Tits was gradually developing the theory of buildings, and his book "Buildings of spherical type and finite BN-pairs" in 1974 produced a fully-fledged theory that has since found many uses. ... we mention some of Tits' early work on buildings, and we discuss the contents of his above-mentioned book concerning buildings of spherical type. Finally ... a later approach to buildings, also due to Tits, is mentioned, and we return at the end to the construction of the exceptional groups of Lie type using building theory.

Though a lage number of other important roles, Tits had played a major part in mathematical life. For example he was editor-in-chief for mathematical publications at I.H.E.S. from 1980 to 1999. He served on the committee awarding the Fields medals in 1978 and again in 1994. He also served on the committee awarding the Balzan Prize in 1985.

Tits has received, and continues to receive, many honours. Among these we mention the Prix scientifique Interfacultataire L Empain (1955), the Wettrems Prize of the Royal Belgium Academy of Science (1958), the Prix décennal de mathématique from the Belgium government (1965), the Grand Prix of the French Academy of Sciences (1976), the Wolf Prize in Mathematics (1993), and the Cantor Medal from the German Mathematical Society (1996). He was elected to many academies and societies including the German Academy of Scientists Leopoldina (1977), the Royal Netherlands Academy of Sciences (1988), founder member of Academia Europaea (1988), the Royal Belgium Academy of Science (1991), the American Academy of Arts and Sciences (1992), the National Academy of Sciences of the United States (1992), and London Mathematical Society (1993). He has been awarded honorary doctorates from the universities of Utrecht (1970), Ghent (1979), Bonn (1988) and Leuwen (1992). He was made Chevalier de la Légion d'Honneur (1995) and Officier de l'Ordre National du Mérite (2001).

After retiring in 2000, Tits became the first holder of the Vallée-Poussin Chair from the University of Louvain. He gave his inaugural lecture Immeubles : une approche géométrique des groupes algébriques simples et des groupes de Kac-Moody on 18 October 2001. He followed this with three series of lectures on the following topics

(1) Généralités sur les nombres p-adiques. Groupes algébriques simples sur les corps p-adiques; 
(2) Schémas en groupes à fibre générique simple sur les anneaux d'entiers; 
(3) Réseaux invariants dans les espaces de représentations. Applications algébriques.

In 2008 the Norwegian Academy of Science and Letters awarded the Abel Prize to John Griggs Thompson and Jacques Tits:-

... for their profound achievements in algebra and in particular for shaping modern group theory.

The Press Release gives the following summary of Tits's contributions:-

Tits created a new and highly influential vision of groups as geometric objects. He introduced what is now known as a Tits building, which encodes in geometric terms the algebraic structure of linear groups. The theory of buildings is a central unifying principle with an amazing range of applications, for example to the classification of algebraic and Lie groups as well as finite simple groups, to Kac-Moody groups (used by theoretical physicists), to combinatorial geometry (used in computer science), and to the study of rigidity phenomena in negatively curved spaces. Tits's geometric approach was essential in the study and realisation of the sporadic groups, including the Monster. He also established the celebrated "Tits alternative": every finitely generated linear group is either virtually solvable or contains a copy of the free group on two generators. This result has inspired numerous variations and applications. The achievements of John Thompson and of Jacques Tits are of extraordinary depth and influence. They complement each other and together form the backbone of modern group theory.


 

Articles:

  1. H Abels, Cantor-Medaille für Jacques Tits, Jahresber. Deutsch. Math.-Verein. 103 (1) (2001), 7-18.
  2. F Buekenhout, A Belgian mathematician : Jacques Tits, Bull. Soc. Math. Belg. Sér. A 42 (3) (1990), 463-465.
  3. M Ronan, From Galois and Lie to Tits buildings, in The Coxeter legacy (Amer. Math. Soc., Providence, RI, 2006), 45-62.
  4. A Valette, Quelques coups de projecteurs sur les travaux de Jacques Tits, Gaz. Math. No. 61 (1994), 61-79.

 




الجبر أحد الفروع الرئيسية في الرياضيات، حيث إن التمكن من الرياضيات يعتمد على الفهم السليم للجبر. ويستخدم المهندسون والعلماء الجبر يومياً، وتعول المشاريع التجارية والصناعية على الجبر لحل الكثير من المعضلات التي تتعرض لها. ونظراً لأهمية الجبر في الحياة العصرية فإنه يدرّس في المدارس والجامعات في جميع أنحاء العالم. ويُعجب الكثير من الدارسين للجبر بقدرته وفائدته الكبيرتين، إذ باستخدام الجبر يمكن للمرء أن يحل كثيرًا من المسائل التي يتعذر حلها باستخدام الحساب فقط.وجاء اسمه من كتاب عالم الرياضيات والفلك والرحالة محمد بن موسى الخورازمي.


يعتبر علم المثلثات Trigonometry علماً عربياً ، فرياضيو العرب فضلوا علم المثلثات عن علم الفلك كأنهما علمين متداخلين ، ونظموه تنظيماً فيه لكثير من الدقة ، وقد كان اليونان يستعملون وتر CORDE ضعف القوسي قياس الزوايا ، فاستعاض رياضيو العرب عن الوتر بالجيب SINUS فأنت هذه الاستعاضة إلى تسهيل كثير من الاعمال الرياضية.

تعتبر المعادلات التفاضلية خير وسيلة لوصف معظم المـسائل الهندسـية والرياضـية والعلمية على حد سواء، إذ يتضح ذلك جليا في وصف عمليات انتقال الحرارة، جريان الموائـع، الحركة الموجية، الدوائر الإلكترونية فضلاً عن استخدامها في مسائل الهياكل الإنشائية والوصف الرياضي للتفاعلات الكيميائية.
ففي في الرياضيات, يطلق اسم المعادلات التفاضلية على المعادلات التي تحوي مشتقات و تفاضلات لبعض الدوال الرياضية و تظهر فيها بشكل متغيرات المعادلة . و يكون الهدف من حل هذه المعادلات هو إيجاد هذه الدوال الرياضية التي تحقق مشتقات هذه المعادلات.