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Carol Ruth Karp  
  
37   02:08 مساءً   date: 20-2-2018
Author : D W Kueker
Book or Source : Infinitary Logic : In memoriam Carol Karp
Page and Part : ...


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Date: 21-2-2018 53
Date: 24-2-2018 41
Date: 20-2-2018 27

Born: 10 August 1926 in Forest Grove, Ottawa County, Michigan, USA

Died: 20 August 1972 in Maryland, USA


Carol Karp was born Carol van der Velde. She attended Manchester College in Indiana receiving her BA from there in 1948. Her Master's Degree was obtained two years later from Michigan State University and following this she spent the summer as an instructor at Michigan State University, and then for a time travelled around the United States as a violinist in an all-woman orchestra. She then continued her studies at the University of Southern California, working for a doctorate.

Her doctoral thesis was on mathematical logic. The thesis, Languages with expressions of infinite length, was supervised by L Henkin and submitted to the University of Southern California in 1959. However Karp was teaching several years before the award of her Ph.D. having accepted a position as instructor at New Mexico College of Agriculture and Mechanic Arts in 1953. In 1960 the name of the New Mexico College of Agriculture and Mechanic Arts was changed to its present name of New Mexico State University. Karp spent a year at the College in Las Cruces, New Mexico.

Her thesis advisor had moved to Berkeley in 1953 and Karp was appointed as a teaching assistant here from 1954 to 1956 while she worked on her doctoral thesis. Karp had married Arthur L Karp in 1952 and, in 1957, she moved to Japan with her husband who was in the US Navy. On her return from Japan, Karp accepted a post as instructor at the University of Maryland.

Soon after the award of her doctorate Karp was promoted, in 1960, to assistant professor at the University of Maryland. She was to remain at the University of Maryland until her early death from cancer in 1972 but there she was promoted again, to associate professor in 1963 and then to full professor in 1966.

Karp was a mathematical logician but, as noted in [1], her work was closely related to algebra:-

Karp considered herself to be principally an 'algebraic logician'. Her inclination towards algebra was never completely forgotten and she always seemed to draw results concerning Boolean algebras from her results about infinitary languages.

In 1964 she published a book on her research Languages with expressions of infinite length but she had hoped to write another work which would take her ideas considerably further. She lectured on this later work as described in [1]:-

Karp did give lectures at Maryland in the Fall of 1970 on infinitary logic and recursion theory. Basically Karp wanted to return to Gödel's original proof-theoretic definitions of recursive sets but of course using more liberal notions of proof so as to obtain generalisations of recursion theory.

It was both as a teacher and researcher that Karp made her reputation. She cared personally for her students and worried greatly for their futures during her illness. Again quoting from [1]:-

To her, teaching had always been more than a duty, and even during her illness she taught all her classes in addition to carrying out all her administrative tasks. Her research, too, was pushed forward with her usual determination....

Judy Green, who was one of Karp's doctoral students, wrote the article in [2]. In it she writes:-

Karp's intellectual standards were extremely high, and she was unfailingly honest in applying them. Although she showed almost familial concern for her students and younger colleagues, she was consistently candid in appraising their mathematical contributions and promise. In particular, she advised working towards a doctorate only if one expected to make research the most important part of one's professional career, and she refused to allow her students to graduate until their results met her own high standard for publishability.


 

Books:

  1. D W Kueker (ed.), Infinitary Logic : In memoriam Carol Karp (Berlin - Heidelberg - New York, 1975).

Articles:

  1. J Green, Carol Karp (1926-1972), in L S Grinstein and P J Campbell (eds.), Women of Mathematics (Westport, Conn., 1987), 86-91.

 




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.