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Mina Spiegel Rees  
  
14   02:23 مساءً   date: 26-9-2017
Author : R Dan and P J Hilton
Book or Source : Mina Rees, in D J. Albers and G J Alexanderson
Page and Part : ...


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Date: 21-9-2017 64
Date: 26-9-2017 15
Date: 12-9-2017 65

Born: 2 August 1902 in Cleveland, Ohio, USA

Died: 25 October 1997 in New York City, USA


Mina Rees grew up in New York City and attended public school there. She attended Hunter College High School with which she was to have a long association. She graduated with distinction in 1923 and was appointed as an assistant teacher at the school while she continued her studies at Columbia University. In an interview, see [1], she spoke of the attitude that she encountered there:-

When I had taken four of their six-credit graduate courses in mathematics and was beginning to think about a thesis, the word was conveyed to me - no official ever told me this but I learned - that the Columbia mathematics department was really not interested in having women candidates for Ph.D's. This was a very unpleasant shock. ... I decided to switch to Teacher's College and take the remaining courses necessary for an M.A. there.

After receiving her M.A. in 1925 she returned to Hunter College where she was appointed to the post of instructor. Determined not to allow the attitude of Columbia University to prevent her from completing her doctorate, she enrolled at the University of Chicago in 1929 after obtaining leave of absence from Hunter College. At Chicago her doctorate was supervised by Dickson who agreed to a topic in associative algebra despite his own interests having moved to number theory by this time. In 1931 Rees graduated with her doctorate for a thesis entitled Division algebras associated with an equation whose group has four generators. Saunders Mac Lane writes in [4]:-

Now for a missed opportunity for mathematics in connection with Mina. Mina's thesis was finished in the spring of 1931. Professor Dickson might then have recommended her for an NRC postdoctoral fellowship. If she had won one, and if she had heard of Noether, she could have gone to Göttingen, where she would surely have attended Noether's lectures on hypercomplex systems and factor sets. From Mina's subsequent accomplishments we know that she would have understood these notions and made use of them to simplify her earlier proof. We know that Emmy Noether took care of her associates and students, both men and women. We also know about Mina and so can imagine many splendid research results.

The opportunity was missed, however, and Rees retuned to Hunter College where she was promoted to assistant professor in 1932 and then to associate professor in 1940. However, in 1943 she took leave so that she could contribute to the war effort. She worked as a technical aide and executive assistant with the Applied Mathematics Panel in the Office of Scientific Research and Development. In this job she had to take problems submitted to Panel, find the underlying mathematics behind the problems, and then find the right university mathematician to solve it.

For this work, Rees was received the President's Certificate of Merit at the end of the war. She also received the King's Medal for Service in the Cause of Freedom from the British government.

In 1946 the US Navy invited Rees to become Head of the mathematics branch of the Office of Naval Research to support scientific and mathematical research. In 1949 she became Director of the Mathematical Sciences Division and then, in 1952, Deputy Science Director. At the December 1953 meeting of the American Mathematical Society, Rees's achievements in these important roles was recognised with the following resolution (see Bull. Amer. Math. Soc. 60 (1954), 134):-

Under her guidance, basic research in general, and especially in mathematics, received the most intelligent and wholehearted support. No greater wisdom and foresight could have been displayed and the whole post-war development of mathematical research in the United States owes an immeasurable debt to the pioneer work of the Office of Naval Research and to the alert, vigorous and farsighted policy conducted by Miss Rees.

In 1953 Rees returned to Hunter College that she had left on extended leave 10 years previously to undertake war work. She was appointed professor of mathematics and dean of the faculty, positions she held until 1961. However, during these eight years back at Hunter College she served on numerous committees bodies which included the National Research Council, the National Bureau of Standards and the National Science Foundation. Rees also acted as a consultant on the machine handling of data for the 1960 census.

Rees left Hunter College in 1961, taking up the post of dean of graduate studies in the newly established City University of New York. Graduate studies at CUNY were very much directed by Rees during her 11 years there as she was appointed provost of the graduate division for 1968-1969 and then president of the Graduate School and University Center from 1969 until she retired in 1972. While dean of graduate studies at CUNY she wrote in 1965 (see [4]):-

It may be because the Graduate Dean is a woman, or it may be for completely objective reasons, that ours is proving an ideal university to draw into advanced graduate work the most obvious source of unused talent in a society that desperately needs additional numbers of persons with training through the doctorate, namely women.

Rees received many awards for her outstanding contributions. In 1962 Rees received the first Award for Distinguished Service to Mathematics from the Mathematical Association of America:-

... for outstanding service to mathematics, other than mathematical research ... [and for] contributions [that] influence significantly the field of mathematics or mathematical education on a national scale.

In 1970 she became president elect of the American Association for the Advancement of Science and in 1971 she became the first woman president of the Association. In 1983 Rees was awarded the National Academy of Sciences Public Welfare Medal:-

... in recognition of distinguished contributions in the application of science to the public welfare.

In addition Rees was awarded honorary degrees from around twenty universities and colleges.

In [4] Uta Merzbach describes Rees in these terms:-

Mina Rees was eminently rational. Her devotion to reason helped her formulate goals clearly and allocate resourses judiciously in accordance with these goals. ...

Mina Rees was eminently intelligent. She comprehended quickly, communicated effectively, and thought creatively. Her ability to attach raelisable pieces of basic research to mission-oriented applications of mathematics did much to develop a broadened base of support for mathematicians' work.

Mina Rees was eminently civilised. Her diplomatic skills were considerable; her conversational technique bespoke her broad knowledge base as well as her wide interest in mathematical and non-mathematical topics. Experience and reflection led her to a balanced outlook on teaching and research, the arts and sciences, long-range and short-range planning and obligations of the professional and the private life.


 

Articles:

  1. R Dan and P J Hilton, Mina Rees, in D J. Albers and G J Alexanderson (eds.), Mathematical People (Boston, 1985), 256-267.
  2. P Fox, Mina Rees (1902--), in Women of mathematics (Westport, CT, 1987), 175-181.
  3. J Green and J LaDuke, Mina S Rees : 1902-1997, Newsletter of the Association for Women in Mathematics 28 (1) (1998), 10-12.
  4. J Green, J LaDuke, S Mac Lane and U C Merzbach, Mina Spiegel Rees (1902-1997), Notices Amer. Math. Soc. 45 (7) (1998), 866-873. 
    http://www.ams.org/notices/199807/memorial-rees.pdf
  5. Rees Awarded Medal, Newsletter of the Association for Women in Mathematics 13 (3) (1983), 9-10.
  6. F J Weyl, Mina Rees, President-Elect 1970, Science 167 (1970), 1149-1151.

 




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.