Philip Franklin (October 5, 1898 – January 27, 1965) was an American mathematician and professor whose work was primarily focused in analysis.
Dr. Franklin received a
B.S. in 1918 from
City College of New York (who later awarded him its Townsend Harris Medal for the alumnus who achieved notable postgraduate distinction). He received his
M.A. in 1920 and
Ph.D. in 1921 both from
Princeton University. His dissertation, The Four Color Problem, was supervised by
Oswald Veblen. After teaching for one year at Princeton and two years at
Harvard University (as the
Benjamin Peirce Instructor), Franklin joined the
Massachusetts Institute of Technology Department of Mathematics, where he stayed until his 1964 retirement.
In 1922, Franklin gave the first proof that all planar graphs with at most 25 vertices can be four-colored.[1]
In 1934, Franklin disproved the
Heawood conjecture for the
Klein bottle by showing that any map drawn on the Klein bottle can be coloured with at most six colours. An example which shows that six colours may be needed is the 12-vertex
cubic graph now known as the
Franklin graph.[3][4][5]
Franklin, Philip (1933). Differential equations for electrical engineers. New York: John Wiley & Sons.[7]
Differential equations for engineers. Dover Publications. 1960.
ASINB000859ANA.
Franklin, Philip (1940). A treatise on advanced calculus. John Wiley & Sons.[8]5th printing edition. 1955.
ASINB00JCV5MYW. Franklin, Philip (2016). Dover reprint. Courier Dover Publications.
ISBN978-0486807072.[9]
Franklin, Philip (1941). The four color problem.
OCLC03049925.
Franklin, Philip (1944). Methods of advanced calculus.
ISBN978-0070219007.
Franklin, Philip (1949). Fourier methods. McGraw-Hill.
ASINB001U3912Y.
An Introduction to Fourier Methods and the Laplace Transform. Dover Publications.
ASINB004QPEH18.
Franklin, Philip (1953). Differential and integral calculus. McGraw-Hill.
ASINB0000CIJ2B.
Franklin, Philip (1958). Functions of complex variables. Englewood Cliffs, New Jersey: Prentice Hall.[10]2021 edition. Hassell Street Press. 9 September 2021.
ISBN978-1014075574.
Franklin, Philip (1963). Compact calculus. McGraw-Hill.
ASINB0000CLVV1. 2021 edition. Hassell Street Press. 9 September 2021.
ISBN978-1014263575.
References
^Franklin, P. "The Four Color Problem." Amer. J. Math. 44 (1922), 225-236.
doi:
10.2307/2370527
^Franklin, P. "A set of continuous orthogonal functions", Math. Ann. 100 (1928), 522-529.
doi:
10.1007/BF01448860