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100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection
Share this pageStephan Ramon Garcia; Steven J. Miller
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.
Readership
For undergraduate and graduate students and faculty interested in the math honor society, Pi Mu Epsilon.
Table of Contents
Table of Contents
100 Years of Math Milestones: The Pi Mu Epsilon Centennial Collection
Table of Contents pages: 1 2 3
- Cover Cover11
- Title Page iii4
- Preface xi12
- Notation xiii14
- 1913. Paul Erdős 116
- 1914. Martin Gardner 722
- 1915. General Relativity and the Absolute Differential Calculus 1126
- 1916. Ostrowski’s Theorem 1732
- 1917. Morse Theory, but Really Cantor 2136
- 1918. Georg Cantor 2742
- 1919. Brun’s Theorem 3348
- 1920. Waring’s Problem 3954
- 1921. Mordell’s Theorem 4560
- 1922. Lindeberg Condition 5166
- 1923. The Circle Method 5772
- 1924. The Banach–Tarski Paradox 6176
- 1925. The Schrödinger Equation 6782
- 1926. Ackermann’s Function 7186
- 1927. William Lowell Putnam Mathematical Competition 7590
- 1928. Random Matrix Theory 7994
- 1929. Gödel’s Incompleteness Theorems 85100
- 1930. Ramsey Theory 89104
- 1931. The Ergodic Theorem 95110
- 1932. The 3𝑥+1 Problem 101116
- 1933. Skewes’s Number 107122
- 1934. Khinchin’s Constant 113128
- 1935. Hilbert’s Seventh Problem 117132
- 1936. Alan Turing 121136
- 1937. Vinogradov’s Theorem 127142
- 1938. Benford’s Law 131146
- 1939. The Power of Positive Thinking 137152
- 1940. A Mathematician’s Apology 141156
- 1941. The Foundation Trilogy 145160
- 1942. Zeros of 𝜁(𝑠) 151166
- 1943. Breaking Enigma 157172
- 1944. Theory of Games and Economic Behavior 163178
- 1945. The Riemann Hypothesis in Function Fields 169184
- 1946. Monte Carlo Method 175190
- 1947. The Simplex Method 181196
- 1948. Elementary Proof of the Prime Number Theorem 187202
- 1949. Beurling’s Theorem 193208
- 1950. Arrow’s Impossibility Theorem 199214
- 1951. Tennenbaum’s Proof of the Irrationality of √2 205220
- 1952. NSA Founded 209224