Research
My research interests span a broad spectrum of mathematics generally classified
as geometry, including
- General topology
- Differential topology
- Differential geometry
- Algebraic geometry
- Manifold theory in the categories of smooth, analytic, and complex manifolds
Feel free to download an overview of my research
interests.
Reprints and preprints
- Harmonic Volume Can Be Computed As An Iterated Integral, by William
M. Faucette, Canadian Mathematical Bulletin, vol. 35, no. 3, 1992
- Harmonic Volume, Symmetric Products, and the Abel-Jacobi Map, by
William M. Faucette, Transactions of the American Mathematical Society, vol.
335, no. 1, January 1993
- Geometric
Interpretation of the Reduction of the General Quartic by Galois Theory,
by William M. Faucette, American Mathematical Monthly, vol. 103, no. 1, January
1996
- The Generalized Torelli Problem:
Reconstructing a Curve and its Linear Series From its Canonical Map and Theta
Geometry, by William M. Faucette, submitted
- Circling
up the Wagons: Unifying Mathematics for the Calculus Student, by
William M. Faucette, submitted
- Divisibility
Rules for 7 and 13, by William M. Faucette, submitted
- How
Not To Prove Fermat's Last Theorem,
by William M. Faucette, submitted
- The
Miracle Substitution: How and Why It Works, by William M. Faucette,
submitted
- Trisecting
an Angle . . . By Cheating, by William M. Faucette and Wendy C. Davidson,
submitted
- Generalized Geometric Series,
The Ratio Comparison Test and Raabe's Test, by William M. Faucette,
accepted by The Pentagon
- Pascal's Theorem in Degenerate Cases,
by William M. Faucette,
submitted
- Around the Cubic Curve in Fifty Minutes,
by William M. Faucette,
completed
- A Poor Man's Derivation
of the Double Angle Formula for Sine, by William M. Faucette,
submitted
- Ceva's Therem and Its Applications, by William M. Faucette,
completed
- The Nine Point Circle, by William M. Faucette,
completed
- The Euler Line of a Triangle, by William M. Faucette,
completed
Recent Presentations
- Math Makes the World(s) Go 'Round: A Mathematical Derivation of Kepler's
Laws of Planetary Motion
- How Many Ways Can 945 be Written as the Difference
of Squares: An Introduction to the Mathematical Way of Thinking
Lectures on Public Key Cryptography
- Cryptography:
Public Key vs. Private Key Cryptosystems
- Public Key Cryptography: The RSA Cryptosystem
- Public Key Cryptography: Elliptic Curve Cryptography
Lectures on Hodge Theory
- Lecture 1: Calculus on Smooth Manifolds
- Lecture 2: The Hodge Theory of a Smooth, Oriented,
Compact Riemannian Manifold
- Lecture 3: Complex Manifolds
- Lecture 4: Hermitian Linear Algebra
- Lecture 5: The Hodge Theory of Hermitian Manifolds
- Lecture 6: Kähler Manifolds
- Lecture 7: The Hard Lefschetz Theorem and the Hodge-Riemann Bilinear Relations
- Lecture 8: Mixed Hodge Structures
Lectures on Multivariable Calculus
- Multivariable Differentiation
- The Inverse Function Theorem
- The Implicit Function Theorem