Florence Jessie Collinson MacWilliams (4 January 1917 – 27 May 1990) was an English mathematician who contributed to the field of coding theory, and was one of the first women to publish in the field. MacWilliams' thesis "Combinatorial Problems of Elementary Group Theory" (or "Combinatorial Problems of Elementary Abelian Groups")[2] contains one of the most important combinatorial results in coding theory, which is now known as the MacWilliams Identity.
In 1955 she became a programmer and learned coding theory at Bell Labs where she spent most of her career. Although she did major research at Bell Labs, she was denied a promotion to a mathematics research position until she received a Ph.D. She would proceed to fulfill some of the PhD's requirements while working at Bell Labs and taking care of her family, but she completed her PhD after returning to Harvard for one more year (1961–1962), under the supervision of Andrew Gleason.[4][5] MacWilliams worked with Gleason to produce her thesis entitled "Combinatorial Problems of Elementary Group Theory".[2] Both MacWilliams and her daughter Anne, who later obtained a PhD in Mathematics, were studying mathematics at Harvard that year.
Contributionsedit
Her formula is known as the MacWilliams identity, and is how MacWilliams is known. MacWilliams' result was later critical in proving an important bound on code rate, called the 'linear programming bound'.
From 1962 to 1976, Macwilliams produced important results on algebraic constructions and combinatorial properties of codes. She worked on cyclic codes, generalizing them to Abelian group codes.[6] With H.B. Mann, MacWilliams gave a solution to a difficult problem involving certain design matrices, which they published in their paper titled "On the p-rank of the design matrix of a difference set".[7]
One of MacWilliams' significant achievements was her encyclopedic book, The Theory of Error-Correcting Codes, which she wrote in collaboration with Neil Sloane[1][8] and was published in 1977. The book is stated as being "Perhaps the most comprehensive text on the algebraic and combinatorial properties of error-correcting codes, and of abiding interest to both mathematicians and engineers. It was one of the major works responsible for laying the foundation for a revolution in communication technology that is being played out even today".[9]
^ abMacWilliams, F. J (1962). Combinatorial problems of elementary Abelian groups (Thesis). OCLC 23168354.
^"F. Jessie MacWilliams", Biographies of Women Mathematicians, Agnes Scott College, retrieved 2013-04-05.
^Pollak, H. O. (February 1996), "Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Andrew Gleason", American Mathematical Monthly, 103 (2): 105–106, doi:10.1080/00029890.1996.12004708, JSTOR 2975102.
^ ab. Association for Women in Mathematics. 2005. Archived from the original on 6 January 2014. Retrieved 5 November 2013.
^MacWilliams, F.J.; Mann, H.B. (1 May 1968). "On the p-rank of the design matrix of a difference set". Information and Control. 12 (5): 474–488. doi:10.1016/S0019-9958(68)90534-2. ISSN 0019-9958.
^"MacWilliams Error Correcting Codes". www.agnesscott.edu. Retrieved 20 March 2021.
^Shankar, Priti (1 January 2005). "Florence Jessie Mac Williams (1917-1990)". Resonance. 10 (1): 2–3. doi:10.1007/BF02835886. ISSN 0973-712X. S2CID 121982124.
Further readingedit
Gallian, Joseph A. (2006). Contemporary Abstract Algebra (Sixth ed.). Houghton Mifflin. ISBN0-618-51471-6.
May 07, 2024
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Florence Jessie Collinson MacWilliams 4 January 1917 27 May 1990 was an English mathematician who contributed to the field of coding theory and was one of the first women to publish in the field MacWilliams thesis Combinatorial Problems of Elementary Group Theory or Combinatorial Problems of Elementary Abelian Groups 2 contains one of the most important combinatorial results in coding theory which is now known as the MacWilliams Identity Florence Jessie MacWilliamsBorn 1917 01 04 January 4 1917Stoke on Trent EnglandDiedMay 27 1990 1990 05 27 aged 73 Alma materUniversity of Cambridge BA 1938 MA 1939 Johns Hopkins University Harvard University PhD under Andrew GleasonOccupation s Mathematician programmerEmployerBell LabsKnown forThe MacWilliams identities in coding theoryNotable workThe Theory of Error Correcting Codes with Neil Sloane 1 ChildrenDaughter Anne two sons Contents 1 Education and career 2 Contributions 3 Recognition 4 References 5 Further readingEducation and career editMacWilliams was born in Stoke on Trent England and studied at the University of Cambridge receiving her BA in 1938 and her MA in the following year 3 She moved to the United States in 1939 and studied at Johns Hopkins University One year later she left Johns Hopkins for Harvard University In 1955 she became a programmer and learned coding theory at Bell Labs where she spent most of her career Although she did major research at Bell Labs she was denied a promotion to a mathematics research position until she received a Ph D She would proceed to fulfill some of the PhD s requirements while working at Bell Labs and taking care of her family but she completed her PhD after returning to Harvard for one more year 1961 1962 under the supervision of Andrew Gleason 4 5 MacWilliams worked with Gleason to produce her thesis entitled Combinatorial Problems of Elementary Group Theory 2 Both MacWilliams and her daughter Anne who later obtained a PhD in Mathematics were studying mathematics at Harvard that year Contributions editHer formula is known as the MacWilliams identity and is how MacWilliams is known MacWilliams result was later critical in proving an important bound on code rate called the linear programming bound From 1962 to 1976 Macwilliams produced important results on algebraic constructions and combinatorial properties of codes She worked on cyclic codes generalizing them to Abelian group codes 6 With H B Mann MacWilliams gave a solution to a difficult problem involving certain design matrices which they published in their paper titled On the p rank of the design matrix of a difference set 7 One of MacWilliams significant achievements was her encyclopedic book The Theory of Error Correcting Codes which she wrote in collaboration with Neil Sloane 1 8 and was published in 1977 The book is stated as being Perhaps the most comprehensive text on the algebraic and combinatorial properties of error correcting codes and of abiding interest to both mathematicians and engineers It was one of the major works responsible for laying the foundation for a revolution in communication technology that is being played out even today 9 Recognition editIn 1980 she was the first Noether Lecturer 6 References edit a b MacWilliams Florence Jessiem Sloane Neil James Alexander 2007 1977 Written at AT amp T Shannon Labs Florham Park New Jersey USA The Theory of Error Correcting Codes North Holland Mathematical Library Vol 16 digital print of 12th impression 1st ed Amsterdam London New York Tokyo North Holland Elsevier BV ISBN 978 0 444 85193 2 LCCN 76 41296 xxii 762 6 pages a b MacWilliams F J 1962 Combinatorial problems of elementary Abelian groups Thesis OCLC 23168354 F Jessie MacWilliams Biographies of Women Mathematicians Agnes Scott College retrieved 2013 04 05 Pollak H O February 1996 Yueh Gin Gung and Dr Charles Y Hu Award for Distinguished Service to Andrew Gleason American Mathematical Monthly 103 2 105 106 doi 10 1080 00029890 1996 12004708 JSTOR 2975102 Florence Jessie MacWilliams at the Mathematics Genealogy Project a b Profiles of Women in Mathematics F Jessie MacWilliams Association for Women in Mathematics 2005 Archived from the original on 6 January 2014 Retrieved 5 November 2013 MacWilliams F J Mann H B 1 May 1968 On the p rank of the design matrix of a difference set Information and Control 12 5 474 488 doi 10 1016 S0019 9958 68 90534 2 ISSN 0019 9958 MacWilliams Error Correcting Codes www agnesscott edu Retrieved 20 March 2021 Shankar Priti 1 January 2005 Florence Jessie Mac Williams 1917 1990 Resonance 10 1 2 3 doi 10 1007 BF02835886 ISSN 0973 712X S2CID 121982124 Further reading editGallian Joseph A 2006 Contemporary Abstract Algebra Sixth ed Houghton Mifflin ISBN 0 618 51471 6 Retrieved from https en wikipedia org w index php title Jessie MacWilliams amp oldid 1214018811, wikipedia, wiki, book, books, library,
