100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection

This book is an outgrowth of a collection of 100 problems chosen to celebrate the 100th anniversary of the undergraduate math honor society Pi Mu Epsilon. Each chapter describes a problem or event, the progress made, and connections to entries from other years or other parts of mathematics. In places, some knowledge of analysis or algebra, number theory or probability will be helpful. Put together, these problems will be appealing and accessible to energetic and enthusiastic math majors and aficionados of all stripes.

Table of Contents:
1913. Paul Erdos 1914. Martin Gardner 1915. General relativity and the absolute differential calculus 1916. Ostrowski's theorem 1917. Morse theory, but really Cantor 1918. Georg Cantor 1919. Brun's theorem 1920. Waring's problem 1921. Mordell's theorem 1922. Lindeberg condition 1923. The circle method 1924. The Banach-Tarski paradox 1925. The Schrodinger equation 1926. Ackermann's function 1927. William Lowell Putnam Mathematical Competition 1928. Random matrix theory 1929. Godel's incompleteness theorems 1930. Ramsey theory 1931. The ergodic theorem 1932. The $3x 1$ problem 1933. Skewes's number 1934. Khinchin's constant 1935. Hilbert's seventh problem 1936. Alan Turing 1937. Vinogradov's theorem 1938. Benford's law 1939. The power of positive thinking 1940. A mathematician's apology 1941. The Foundation triology 1942. Zeros of $\zeta(s)$ 1943. Breaking Enigma 1944. Theory of games and economic behavior 1945. The Riemann hypothesis in function fields 1946. Monte Carlo method 1947. The simplex method 1948. Elementary proof of the prime number theorem 1949. Beurling's theorem 1950. Arrow's impossibility theorem 1951. Tennenbaum's proof of the irrationality of $\sqrt{2}$ 1952. NSA founded 1953. The Metropolis algorithm 1954. Kolmogorov-Arnold-Moser theorem 1955. Roth's theorem 1956. The GAGA principle 1957. The Ross program 1958. Smale's paradox 1959. $QR$ decomposition 1960. The unreasonable effectiveness of mathematics 1961. Lorenz's nonperiodic flow 1962. The Gale-Shapely algorithm and the stable marriage problem 1963. Continuum hypothesis 1964. Principles of mathematical analayis 1965. Fast Fourier transform 1966. Class number one problem 1967. The Langlands program 1968. Atiyah-Singer index theorem 1969. Erdos numbers 1970. Hilbert's tenth problem 1971. Society for American Baseball Research 1972. Zaremba's conjecture 1973. Transcendence of $e$ centennial 1974. Rubik's Cube 1975. Szemeredi's theorem 1976. Four color theorem 1977. RSA encryption 1978. Mandlebrot set 1979. TeX 1980. Hilbert's third problem 1981. The Mason-Stothers theorem 1982. Two envelopes problem 1983. Julia Robinson 1984. 1984 1985. The Jones polynomial 1986. Sudokus and Look and Say 1987. Primes, the zeta function, randomness, and physics 1988. Mathematica 1989. PROMYS 1990. The Monty Hall problem 1991. arXiv 1992. Monstrous moonshine 1993. The 15-theorem 1994. AIM 1995. Fermat's last theorem 1996. Great Internet Mersenne Prime Search (GIMPS) 1997. The Nobel Prize of Merton and Scholes 1998. The Kepler conjecture 1999. Baire category theorem 2000. R 2001. Colin Hughes founds Project Euler 2002. PRIMES in P 2003. Poincare conjecture 2004. Primes in arithmetic progression 2005. William Stein developed Sage 2006. The strong perfect graph theorem 2007. Flatland 2008. 100th anniversary of the $t$-test 2009. 100th anniversary of Brouwer's fixed-point theorem 2010. Carmichael numbers 2011. 100th anniversary of Egorov's theorem 2012. National Museum of Mathematics Index of people Index

About the Author :
Stephan Ramon Garcia is WM Keck Distinguished Service Professor and professor of mathematics at Pomona College. He is the author of four books and over eighty research articles in operator theory, complex analysis, matrix analysis, number theory, discrete geometry, and other fields. He has coauthored dozens of articles with students, including one that appeared in The Best Writing on Mathematics: 2015. He is on the editorial boards of Notices of the AMS, Proceedings of the AMS, American Mathematical Monthly, Involve, and Annals of Functional Analysis. He received four NSF research grants as principal investigator and five teaching awards from three different institutions. He is a fellow of the American Mathematical Society and was the inaugural recipient of the Society's Dolciani Prize for Excellence in Research. Steven J. Miller is professor of mathematics at Williams College and a visiting assistant professor at Carnegie Mellon University. He has published five books and over one hundred research papers, most with students, in accounting, computer science, economics, geophysics, marketing, mathematics, operations research, physics, sabermetrics, and statistics. He has served on numerous editorial boards, including the Journal of Number Theory, Notices of the AMS, and the Pi Mu Epsilon Journal. He is active in enrichment and supplemental curricular initiatives for elementary and secondary mathematics, from the Teachers as Scholars Program and VCTAL (Value of Computational Thinking Across Grade Levels), to numerous math camps (the Eureka Program, HCSSiM, the Mathematics League International Summer Program, PROMYS, and the Ross Program). He is a fellow of the American Mathematical Society, an at-large senator for Phi Beta Kappa, and a member of the Mount Greylock Regional School Committee, where he sees firsthand the challenges of applying mathematics.