G. Baley Price (14 March 1905, Brookhaven, Mississippi – 7 November 2006, Lawrence, Kansas) was an American mathematician and historian of American mathematics. He was a president of the Mathematical Association of America.^[1]

Career

After graduating with an A.B. from Mississippi College in 1925, G. B. Price went to Harvard University, where he received his M.A. in 1928 and his Ph.D. in 1932 under G. D. Birkhoff with thesis Double Pendulum and Similar Dynamical Systems.^[2] Apart from a period of service with the U.S. Army Air Force in England in World War II, Price was a mathematics professor at the University of Kansas from 1937 to 1975 and chair of the mathematics department from 1951 to 1970. He was the co-author of two textbooks (published in 1966 and 1968) and the author of a history of the department of mathematics of the University of Kansas and several articles related to the role of mathematics and mathematicians in World War II. He was president of the Mathematical Association of America (MAA) for the two years 1957–1958 and received the MAA's distinguished service award in 1970.^[1]

Price based his book about multicomplex spaces and functions on Corrado Segre's work where ${\displaystyle \mathbb {C} _{n}}$ has n imaginary units ${\displaystyle i_{1},\ i_{2},\dots ,i_{n}}$ all of which commute. But the book primarily treats bicomplex numbers ${\displaystyle \mathbb {C} _{2}\ .}$

Since ${\displaystyle (i_{1}i_{2})^{2}=+1}$ the numbers ${\displaystyle e_{1}={\tfrac {1}{2}}(1+i_{1}i_{2})}$ and ${\displaystyle e_{2}={\tfrac {1}{2}}(1-i_{1}i_{2})}$ are idempotent. The idempotents provide an alternate basis for the bicomplexes:

${\displaystyle z_{1}+z_{2}i_{2}=(z_{1}-i_{1}z_{2})e_{1}+(z_{1}+i_{1}z_{2})e_{2}.}$ (page 19)

Differentiable bicomplex functions f are shown to correspond to a pair of differentiable complex functions f₁ and f₂:

${\displaystyle f(z_{1}-i_{1}z_{2})=f_{1}(z_{1}-i_{1}z_{2})e_{1}+f_{2}(z_{1}+i_{1}z_{2})e_{2}.}$ (page 131)

Works

• 1935: "On reversible dynamical systems", Transactions of the American Mathematical Society 37(1): 51–59, doi:10.1090/s0002-9947-1935-1501778-0, MR1501778
• 1947: "Some identities in the theory of determinants", American Mathematical Monthly 54:75–90, MR00190078
• 1951: "Bounds for determinants with dominant principal diagonal", Proceedings of the American Mathematical Society 2: 497–502, doi:10.1090/s0002-9939-1951-0041093-2, MR0041093
• 1976: History of the department of mathematics at the University of Kansas, 1866–1970. Lawrence, Kansas: K. U. Endowment Association, U. of Kansas. 1976; xii+788 p.{{cite book}}: CS1 maint: postscript (link), link from Google Books
• 1984: Multivariable analysis. NY: Springer-Verlag. 11 June 1984. ISBN 0387909346; xiv+655 p.{{cite book}}: CS1 maint: postscript (link)
• 1991: An introduction to multicomplex spaces and functions. NY: Marcel Dekker. 23 October 1990. ISBN 082478345X; xiii+402 p.{{cite book}}: CS1 maint: postscript (link)

References