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Reading Classics is a VIGRE Working
Group. Its aim is to read various classic mathematical texts and
understand something of the history of mathematics. We also have some
ongoing Translation Projects.
2002-3:
Winter,
Spring
2003-4:
Fall,
Winter,
Spring
2004-5:
Fall,
Winter,
Spring
2005-6:
Fall,
Winter,
Spring
2006-7:
Fall,
Winter,
Spring
2007-8:
Fall,
Winter,
Spring
2008-9:
Fall,
Winter,
Spring
2009-10:
Fall,
Winter,
Spring
2010-11:
Fall,
Winter,
Spring
2011-12:
Fall,
Winter,
Spring
Winter, 2003: We
looked at Diophantus and the background of modern number theory and arithmetic
algebraic geometry.
Some references:
- I. G.Bashmakova: Diophantus and Diophantine Equations, MAA
1997
- T.L. Heath: Diophantus of Alexandria, Dover 1964
Talks:
- Ronnie Pavlov: Polygonal numbers
- Roux Heyns: Greek algebraic notation
- Michael Chmutov: Diophantus and Fermat
- Wade Claggett: Projective geometry
- Brian Morton: The group law on elliptic curves: elliptic functions
- Alex Ustian: The group law on elliptic curves: algebraic approach
- Rafal Pikula: A proof of Fermat's two square theorem via the Gauss-Jacobi
triple product identity (after John Ewell)
Spring, 2003: We looked at the
works of Archimedes.
Some references:
- S. Stein: Archimedes: What did he do besides cry Eureka? MAA
1999
- T.L.Heath: The Works of Archimedes, Dover 1953
Talks:
- Michael Chmutov: Optical properties of conic
sections
- Roux Heyns: Archimedean approximations to π and √3
- Jamie Wingate: The Sand Reckoner
- Ronnie Pavlov: Volume and surface area of the sphere and the cone
- Brian Morton: Spirals
- Chaoyi Zhao: The area of a circle: Archimedes and Liu Hui
- Alex Ustian: The quadrature of the parabola
- Benjamin Buco: The quadrature of the parabola
Fall, 2003: We looked at the
works of Euler.
Some references:
- W. Dunham: Euler: the Master of Us All, MAA 1999
Talks:
- Scott Arms: Perfect numbers
- Cory Christofferson: The Euler line
- Bill Mance: Zeta(2) and other formulas
- Joseph Brinkmeier: Sums of two and four squares
- Cory Christopherson: Euler circuits and the Euler characteristic
- Daniel File: the Fundamental Theorem of Algebra
- Rafael Pikula: Infinite series
- Ari Solomon: Euler and mechanics
Notes on the talks (prepared by Steve Miller).
Winter, 2004: We continued with the
works of Euler.
Some references:
- W. Dunham: Euler: the Master of Us All, MAA 1999
Talks:
- Seth Hulett: Euler and the Fountains at Sanssouci
- Steven J. Miller: Introduction to continued fractions
- Daniel File: Series expansions of continued fraction
- Warren Sinnott: Euler's work on the zeta function
- Vitaly Bergelson: Euler and Continued Fractions II
- Scott Arms: Prime-generating polynomials
- Michael Chmutov: Eulerian integrals: the Gamma and Beta functions
- Eric Conrad: Continued fractions related to elliptic functions
Notes on the talks (prepared by Steve Miller).
Spring, 2004: More Euler!
Some references:
- W. Dunham: Euler: the Master of Us All, MAA 1999
Talks:
- Daniel File: Euler and Combinatorics
- Scott Arms: The Euler brick
- Bruce Adcock: The Gamma function and fractional derivatives
- Matthew Beiglboeck: Lambert's proof of the irrationality of pi
- Seth Hulett: Euler and the fountains at Sanssouci
- Parthena Avramidou: Euler and the Development of Complex Analysis
- Bill Mance: The zeta function, the partition function, the totient
-
Fall, 2004: We looked at the
works of Gauss.
Talks:
- Christian Schnell: The Gauss-Bonnet theorem
- Bruce Adcock: Continued fractions
- Terri Lynn Easter: The leminiscate
- Martin Nikolov: The Fundamental Theorem of Algebra
- Isabel Averill: The arithmetic-geometric mean
- Adam Chawansky: Quadratic Reciprocity
Winter, 2005: We are looking at the
works of Fermat and his contemporaries.
Talks:
- John Griesmer: Squares in arithmetic progressions
- Adam Chawansky: Sums of two, three, and four squares
- Martin Nikolov: Fermat's Last Theorem
- Timothy All: Fermat's Little Theorem
- Sue Kim and Dina Huang: Probablity, Pascal, and Fermat
- Badal Joshi: Quadrature of the Folium of Descartes
- Donny Seelig: Finding Tangents and Fermat's Method for Maxima/Minima
- Joon-Ku Im: Snell's Law and Fermat's Principle of Least Time
Spring, 2005: We are continuing with the
work of contemporaries of Fermat.
Talks:
- Michael Cap Khoury: Pascal
- Justin Young: Desargues
- Pasha Puliyambalath: Wallis
- Gabor Revesz: Viete
- Marko Samara: Kepler
- Timothy All: Lord Brouncker
- Nicholas Werner: Galileo
- Donny Seelig: Huygens
Fall, 2005: Abel and Galois
Talks:
- Michael Cap Khoury: Abel and the division of the lemniscate
- John McSweeney: Abel and infinite series
- Eric Conrad: Elliptic functions after Jacobi and Abel
- Timothy All: Galois on purely periodic continued fractions
- Jim Brown: Abel and the insolvability of the quintic
- Kyung-Mi Kim: Galois imaginaries
- Jeff Freeman: Abel and fractional integration
- Holly Swisher: Abel and the division of the lemniscate (revisited)
- Michael Cap Khoury: Abel on functional equations
Winter, 2006: More contemporaries of Newton (but not Newton himself!)
Talks:
- Martin Nikolov: Leibniz
- Sung Woo Ahn: Cavalieri, Torricelli, and Viviani
- Andy McSherry: Wren and Hooke
- Adam Chawansky: van Schooten and Huygens
- Min Ro: James and John Bernoulli
- Ryan Stuffelbeam: Gregory
- John McSweeney: James and John Bernoulli
- Timothy All: Vieta
Spring, 2006: Mostly Leibniz
Talks:
- Michael Khoury: de Sluze, Hudde, Collins, .... and Leibniz
- Brad Waller: Leibniz and combinatorics
- Deepak Bal: Leibniz and Bernoulli on log(-1)
- Alex Mominee: Leibniz and logic
- Juan Rodriguez: Leibniz's work on a calculus for geometry
- Adam Rusnak: Euler's paper "The sum of the series formed from the reciprocals of the odd prime numbers,
where prime numbers of the form 4n-1 are taken with a positive sign, and those of the form 4n+1 with a
negative sign
- John McSweeney: Newton versus Leibniz
- Badal Joshi: Leibniz and partial differentiation
Fall, 2006: Euler redux
Talks:
- Nick Sparks: The sum of the reciprocal squares
- Justin Wiser: The Euler-MacClaurin formula
- Trent Ohl: Odds and ends: the divisor function, amicable pairs, Euler products, the exponential and the logarithm
- Jillian McLeod: Partition identities
- Wen Chean Teh: The St. Petersburg paradox
- John McSweeney: Probability
- Adam Rusnak: Euler's paper "Analytic Exercises"
Winter, 2006:
Talks:
- Warren Sinnott: Euler and the zeta function
- Adam Rusnak: Euler's paper "Analytic Exercises"
- Hong Zhang: Euler's formula, the Riemann hypothesis, and the distribution of prime numbers
- Alyson Sewell: Euler and geometry
- Eric Conrad: Introduction to hypergeometric functions
Spring, 2007:
Talks:
- Kyle Joecken: Continued Fractions
- John McSweeney: On "Solution d'une question tres difficile dans le calcul des probabilites" (E412) and a paper on the Genovese lottery (E812)
- Brad Waller: Euler's first proof that the sum of reciprocal squares is pi^2/6
- Sam Fotis: Continued fractions and the Riccati equation
- Hong Zhang: Euler's approach to the Fundamental Theorem of Algebra
- Younghwan Son: On the series 1-1!+2!-3!...
- Moy Easwaran:
- Adam Rusnak: The Sum of a Series Formed from the Prime Numbers
Fall, 2007: Newton's Principia
We worked through parts of Newton's Principia.
Talks: Fabrizio Polo, Justin Wiser, Kitzeln Siebert, Eric Swartz, Zhizhang Xie, Inger Knutson
Winter, 2008: Newton's Principia
Spring, 2008: more Newton
Talks: John McSweeney, Marc Carnovale, Sam Fotis, Craig Jackson, Kyle Joecken, Kitzeln Siebert, Jared Hirsch, Ilya Volynin
Fall, 2008: Lagrange
Talks:
- Cory Staten: Fundamental Theorem of Algebra
- Hari Ravindran: the Lagrange spectrum
- Marc Carnovale: Calculus of variations
- Andy Nicol: The Four Square Theorem
- John McSweeney: Lagrange's Lectures on Elementary Mathematics
- Dan Poole:
- Nikki Thomas: Solving polynomial equations by radicals
- Ulrich Gerlach: Lagrangian mechanics
Winter, 2009: Lagrange and his contemporaries
Talks:
- Ulrich Gerlach: Lagrange points
- Nikki Thomas: Lagrange's Theorem in group theory
- Sam Fotis: Lobachevsky
- Dan Poole:
- Jim Talamo: Legendre
- Rob Woodruff:
- John McSweeney: Cauchy
- Craig Jackson: Dedekind
Spring, 2009: The early 1800s
Talks:
- Rob Denomme: Gauss and Legendre
- Rob Bradford: Cauchy's Theorem in group theory
- Clark Butler: Polygonal numbers
- Jack Jeffries: Jacobi's spherical curve theorem
- Cory Staten: Apollonius circles
- Marc Carnovale: The Riemann mapping theorem
- Trent Ohl: Polyhedral rigidity
- Hari Ravindran: Theta functions and solving quintic polynomials
Fall, 2009: Euler !?
Talks: Cory Staten, Trent Ohl, Robert Bradford, Marc Carnovale, Charles Baker
Winter, 2010: Euler!
Talks:
- Zara Axelrod: the Königsberg bridges problem
- Paul Apisa: Perfect and amicable numbers
- Charles Baker: The arclength of the ellipse
- Trent Ohl: Factorials and the Gamma function
Spring, 2010: Unrestricted!
Talks:
- Dan Poole: The probability proof of the Weierstrass Approximation Theorem
- Charles Baker: Tschebyshef polynomials
- Robert Bradford: Greco-Latin squares
- Trent Ohl: Gödel's Theorem
- Nguyen Minh: "General Researches on the Mortality and the Multiplication of the Human Race" by Leonhard Euler
- Paul Apisa: Hilbert's 10th Problem
- Ted Dokos: The Prime Number Theorem
Fall, 2010: the Bernoullis
Talks:
- Robert Badford: The Law of Large Numbers, after Jacob Bernoulli
- Robert Keith Stevens: The history of the divergence of the harmonic series
- Hang Guo: Paradoxes in logic and set theory
- Pak Ki Henry Tsang: (Daniel) Bernoulli's Principle in fluid dynamics
- Drew Meyer: Ars Conjectandi
- Ross Askanazi: Cassini Ovals, Bernoulli's Lemniscate, and Lissajous Figures.
Winter, 2011: the Bernoullis
Talks:
- Robert Keith Stephens: L'Hôpital's rule
- Charles Baker: Bernoulli numbers
- Ross Askanazi: Probability
- Scott McKinney: Spirals
- Paul Apisa: Bernoulli numbers and the zeta function
- Pak Ki Henry Tsang: The catenary amd the calculus of variations
- Jeff Lindquist: The brachistochrone
Spring, 2011: the Bernoullis
Talks:
- Charles Baker: Isochrone problems
- Ted Dokos: the arithmetic-geometric mean
- Robert Keith Stephens
- Jeff Lindquist
- Zara Axelrod: The catenary
- Clark Butler: the Von Staudt-Clausen theorem on Bernoulli numbers
Fall, 2011: Early mathematics: 500 B.C.E.--1000 C.E.
Talks:
- Ross Askanazi: Circles (Book III of Euclid's Elements)
- Charles Baker: The Classical Age of Indian Mathematics: Pell's Equation
- Robin Baidya: The "neusis" construction of the regular heptagon (attributed to Archimedes)
- Jonathan Michel: Spirals (after Archimedes)
- Qing Chu: The quadrature of the parabola (after Archimedes)
- Patrick Schnell: Ancient Chinese derivations -- the area of the circle and Cavalieri's Principle
Winter, 2012: Early mathematics: 500 B.C.E.--1000 C.E.
Talks:
- Robin Baidya: Appollonian circles
- Clark Butler: The area of the parabola (after Archimedes)
- Charles Baker: Infinite series in India, 1300-1530 CE
- Jonathan Michel: Astronomy: Ptolemy and his predecessors
- Robert Keith Stephens: The parallel postulate
- Jacob Miller: Egyptian fractions
- Chris Altomare: Graph theoretic models of the development of mathematics
Spring, 2012: *****
Talks:
Translation projects: Another goal of this working group
is to produce readable modern English versions of various mathematical works:
either papers that have not been translated into English, or older English
works that would benefit from a modern treatment.
We have various such projects in progress:
Roux Heyns: Weyl, Cantor, Koksma
Michael Chmutov: Morduchay-Boltovskoy
Alex Ustian: Kolmogorov, Gelfond
and some completed:
- Michael Chmutov:
- Daniel File:
- Seth Hulett:
- Brian Morton: