Softcover ISBN:  9781470436520 
Product Code:  MBK/121 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 
Electronic ISBN:  9781470453305 
Product Code:  MBK/121.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 

Book Details2019; 581 ppMSC: 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 atlarge senator for Phi Beta Kappa, and a member of the Mount Greylock Regional School Committee, where he sees firsthand the challenges of applying mathematics.ReadershipFor undergraduate and graduate students and faculty interested in the math honor society, Pi Mu Epsilon.

Table of Contents

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

1924. The Banach–Tarski paradox

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

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. 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 15theorem

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 fixedpoint theorem

2010. Carmichael numbers

2011. 100th anniversary of Egorov’s theorem

2012. National Museum of Mathematics


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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 atlarge 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

1924. The Banach–Tarski paradox

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

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. 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 15theorem

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 fixedpoint theorem

2010. Carmichael numbers

2011. 100th anniversary of Egorov’s theorem

2012. National Museum of Mathematics