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David Charles Terr - Number Theorist

Born in 1962, David Terr received a BA degree in physics from University of Michigan in 1984, a MS degree in physics from the University of Chicago, and a Ph.D. in number theory from UC Berkeley in 1997. I also enjoy other areas of math, as well as physics and computer programming. I live in Goleta, CA, near Santa Barbara and work at Raytheon. Was a kernel developer at Wolfram Research Institute (makers of Mathematica) in Champaign, Illinois.

Has two publications in The Fibonacci Quarterly from 1996 and one in Mathematics of Computation from 1999. My mathematical intererst is mainly in computational and algebraic number theory, but I'm also interested in abstract algebra, complex analysis, and statistics.

Terr's Top 10 Matlab M Files - Over 20,000 downloads from Mathworks.com

1. Binomial - Given nonnegative integers m and n with m <= n, this program computes the binomial coefficient C(n,m). It's about time someone wrote code to do this! I couldn't find it anywhere.
    
2. Fibonacci Numbers - Given an integer n, return the nth Fibonacci number.
    
3. Hermite Poly - Given a nonnegative integer n, HermitePoly(n) returns the coefficients of the Hermite polynomial H_n, given n. polyval(HermitePoly(n),x) evaluates H_n(x).
    
4. Chebyshev Poly - Given a nonnegative integer n, ChebyshevPoly(n) returns the coefficients of the Chebyshev polynomial T_n, given n.
   polyval(ChebyshevPoly(n),x) evaluates
   T_n(x).
    
5. Legendre Poly - This program returns the coefficients of the Legendre polynomial P_n, given n. The result is a row vector with powers of x decreasing from left to right (standard MATLAB notation). Like for other polynomials, LegendrePoly(n) can be evaluated at x by typing
   polyval(LegendrePoly(n),x).
    
6. Laguerre Poly - Given a nonnegative integer n, LaguerrePoly(n) returns the coefficients of the Laguerre polynomial L_n, given n.
   
   polyval(LaguerrePoly(n),x) evaluates
   L_n(x).
    
7. Wigner 3J - Wigner3j(j1,j2,j,m1,m2,m) returns the Wigner 3j-symbol, where j1, j2, j, m1, m2, and m are half-integers. Physically, the Wigner 3j-symbol is closely related to the Clebsch-Gordon coefficient <j1,j2,m1,m2|j1,j2,j,m>, the square of which is the probability that a system of two particles with angular momentum j1 and j2 respectively and z-component of angular momentum m1 and m2 respectively has total angular momentum j and z-component of total angular momentum m.
    
8. Generalized Lucas - For fixed integers a and b such that D = a^2 + 4*b is nonnegative, the sequence V_n = GeneralizedLucas(n,a,b) satisfies the recurrence
   V_n = V_{n-1} + V_{n-2} and the initial conditions V_0 = 2 and V_1 = a. When a=b=1, this is the Lucas sequence.
    
9. Minkowski Question Mark Function - Given x from 0 to 1, this program computes ?(x), where ? is the Minkowski question mark function, defined by
   
   ?(0)=0, ?(1)=1, and ?((a+b)/(c+d))=
   (?(a/c) + ?(b/d))/2, where a/b and c/d are consecutive terms in the Farey sequence. ?(x) is continuous but nowhere differentiable. ?(x) is rational whenever x is rational or a quadratic irrational. If x is rational, the denominator of ?(x) is a power of 2, otherwise it is not.
    
10. Continued Fraction Expansion - fromcfrac.m returns the number whose continued fraction coefficieints are given as a row or column vector. This vector may be taken as the first column vector of the output of cfrac,
    roundcfrac, QCF, or RoundQCF.