Reading Classics Home
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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.
Winter, 2003
Spring, 2003
Fall, 2003
Winter, 2004
Spring, 2004
Fall, 2004
Winter, 2005
Spring, 2005
Fall, 2005
Winter, 2006
Spring, 2006
Fall, 2006
Winter, 2007
Spring, 2007
Fall, 2007
Winter, 2008
Spring, 2008
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:
- 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:
- Moy Easwaran:
- Adam Rusnak:
Fall, 2007:
![Newton]()
Winter, 2008:
![Newton]()
Spring, 2008:
![Newton]()
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:
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