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

Stephan Ramon Garcia Pomona College, Claremont, CA
Steven J. Miller Williams College, Williamstown, MA
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Softcover ISBN: 978-1-4704-3652-0
Product Code: MBK/121
List Price: $60.00 MAA Member Price:$54.00
AMS Member Price: $48.00 Electronic ISBN: 978-1-4704-5330-5 Product Code: MBK/121.E List Price:$60.00
MAA Member Price: $54.00 AMS Member Price:$48.00
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List Price: $90.00 MAA Member Price:$81.00
AMS Member Price: $72.00 Click above image for expanded view 100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection Stephan Ramon Garcia Pomona College, Claremont, CA Steven J. Miller Williams College, Williamstown, MA Available Formats:  Softcover ISBN: 978-1-4704-3652-0 Product Code: MBK/121  List Price:$60.00 MAA Member Price: $54.00 AMS Member Price:$48.00
 Electronic ISBN: 978-1-4704-5330-5 Product Code: MBK/121.E
 List Price: $60.00 MAA Member Price:$54.00 AMS Member Price: $48.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$90.00 MAA Member Price: $81.00 AMS Member Price:$72.00
• Book Details

2019; 581 pp
MSC: Primary 00; 05; 11; 30; 54; 60;

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.

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.

For undergraduate and graduate students and faculty interested in the math honor society, Pi Mu Epsilon.

• Chapters
• 1913. Paul Erdős
• 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
• 1925. The Schrödinger equation
• 1926. Ackermann’s function
• 1927. William Lowell Putnam Mathematical Competition
• 1928. Random matrix theory
• 1929. Gödel’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
• 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
• 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. Erdős 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. Szemerédi’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. Poincaré 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

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
2019; 581 pp
MSC: Primary 00; 05; 11; 30; 54; 60;

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.

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.

For undergraduate and graduate students and faculty interested in the math honor society, Pi Mu Epsilon.

• Chapters
• 1913. Paul Erdős
• 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
• 1925. The Schrödinger equation
• 1926. Ackermann’s function
• 1927. William Lowell Putnam Mathematical Competition
• 1928. Random matrix theory
• 1929. Gödel’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
• 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
• 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. Erdős 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. Szemerédi’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. Poincaré 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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