Andy Novocin's Brief Mathematical Page
Last updated: November 2011
Currently Employed at University of Waterloo as
the Symbolic Computation Group.
Ph.D. from Florida State University's Department of Mathematics in April of 2008.
- Preprint of journal version of complexity analysis of the polynomial factoring algorithm given in ISSAC 2011.
- Preprint on A Reduction Algorithm for Algebraic Function Fields. Needs to be re-emphasized,
it was my first attempt at a paper, and would likely take more time to write than other, more pressing, results.
- Preprint on Reparametrizations of Algebraic Curves. Idea and an old MAPLE implementation are
from 2003 as a means of learning some computer algebra. Ideas were presented at the ACA in 2003, wrote up a brief
pre-print and toyed with the idea of including it in my PhD.
- Bill Hart and I programmed most of what is new to FLINT 1.6. In particular we introduced fairly well optimized LLL, polynomial factoring, some linear algebra, multi-word modulus polynomial arithmetic and other things I'm liekly forgetting. Some early timings for factoring can be found here. We're currently making a push (late 2011) to improve that code and move it into FLINT 2
- Have developed an algorithm for gradually finding simultaneous Diophantine approximations
of many real numbers. The algorithm is written in SAGE and might be submitted when I find the time. This
algorithm works in stages and returns a sequence of increasingly accurate approximations faster than
current algorithms return a single high-precision approximation. This project was based on work with
- Bill Hart and I developed the Polynomial Composition algorithm (fmpz_poly_compose) in the development version of
FLINT. It is asymptotically faster than MAGMA's procedure (on one example FLINT took 10s and MAGMA
- Created a simple patch for the NTL library inside of SAGE which dramatically improves the speed of its basic polynomial factorization procedure.
This will be included in future releases of SAGE, and already allows SAGE to beat MAGMA's timings on some classes of
examples. Although I recently discovered that it is not yet a part of SAGE, it's hidden in SAGE's TRAC patches waiting
for review or something like that.
- Developed a method for expanding (a+b)^n (n>7) with asymptotically less additions than Horner's method for this problem (not Horner's method for
- Wrote MAPLE code (based on the 'polred' algorithm from Henri Cohen's Computational Algebraic Number Theory text) for quickly improving the quality
of output on many types of problems including: polynomial system solving, finding a primtive
element of an extension, and any other problem that returns an answer in terms of an algebraic extension.
- Developed, in MAPLE, a procedure which tries to quickly improve the quality for a given parametrization of an algebraic curve.
- Awarded the Dwight Goodner Teaching Fellowship for 2006
- Nominee for the PIE Excellence in Teaching Award in 2007
- Instuctor of record for the follwing courses at Florida State University:
- Calculus 2: Spring 2008 (a large lecture hall class)
- Modern Algebra for Math Education Majors: Spring 2007 (a class of 8 students)
- Linear Algebra: Fall 2006
- Calculus I: Summer 2006
- Calculus I: Spring 2006
- Trigonometry: Two Simultaneous Sections in Fall 2005
- Pre-Calculus: Spring 2005
- Teaching Assistant in the Summer of 2005 for several sections of Pre-Calculus
Talks (not updated recently):
- Knowledge Issues in Mathematics, IB Theory of Knowledge Class, Ridgeview High School, Orange Park Florida, February 16
- A Recent History of Factoring Polynomials, FSU Mathematics Colloquium, Tallahassee Florida, February 12 2010
- Gradual Sub-Lattice Reduction*, 4th Meeting of EVA-Flo, September 23 2009, ENS Lyon
- Gradual sub-lattice reduction at CACAO group, June 23 2009 Nancy,
- Gradual sub-lattice reduction at INRIA Paris-Rocquencourt, June 22
2009 Paris, France
- Some ideas for Parallel fpLLL at SCSCP SCIEnce workshop, Jan. 2009,
- The following talks were given on my Ph.D. result in Polynomial Factorization:
- Ecole Polytechnique, LIX, March 2009, Paris, France
- Warwick Mathematics Institute, Dec., 2008, Warwick, England
- Arithemtic Team at LIRMM, Oct. 9th, 2008, Montpellier, France
- LAREDA group, Oct. 2nd, 2008, Paris, France (included some mention of my work in Diophantine approximations)
- Computational Mathematics Work Group, August 16th, 2008, Kassel, Germany
- Mathematics Department, August 6th, 2008, Dusseldorf, Germany
- A Series of talks in the Algebra Seminar at Florida State University Fall 2007 and Spring 2008
- An independent series of talks introducing some Class Field Theory in Fall 2005
- A series of talks about Finding all Subfields of a given Field Extension for the Algebra Seminar at FSU in Spring 2005
- I led (and gave many talks in) the Graduate Student Seminar at FSU from Fall 2004 until Spring 2006
- Presented my work on Algebraic Simplifications for the Algebra Seminar in Fall 2004
- Presented my work on reparametrizing curves for the Algebra Seminar in Fall 2003
- Presented the reparametrization results at the Applications of Computer Algebra conference in June 2003, at North Carolina State University
Other interesting things:
- Serving as the chairman of the poster committee for ISSAC
Seoul, South Korea.
- Co-founded the small business CardBoardGames.net, a boardgame
retailer with an emphasis on family time and home education.
- Led a coding-sprint group at SAGE days 10 in Nancy, France
dedicated to polynomial factorization in Z[x].
- Ran the Pat Thomas planetarium outreach program in Talahassee from
- Honor Bar recipient in the International Thespian Society Troup 3929.
- Presided over operations for the USFIRST robotics team 86 (Team
Resistance) in 2000-2001.
- President of the Florida State Beta Chapter of Pi Mu Epsilon
Mathematics Honor Fraternity, 2005-2006.
- Co-President of the Mu Alpha Theta mathematics club at Stanton
College Prep. in 2000-2001.
- Performed in the Florida State Flying High Circus Home Show in April
2003 (bicycle built for five).
- Co-Rookie of the Year of the SectionB Animals in 2003.
- Participated in the National Scrabble Association
National SCRABBLE Championships in New Orleans, 2004.
Interests, some vague:
- Computational Complexities of Algorithms
- Fine-tuning Algorithms in Practice
- Developing/analyzing/speeding-up algorithms in:
- Computational Algebraic Number Theory
- Linear Algebra
- Lattice Reductions
- Polynomial Arithmetic
- Integer Arithmetic
- p-adic Arithmetic
- Small Characteristic Field Arithmetic
- Discrete Geometry
- Word Combinatorics
- Galois Theory
- Financial Analysis (determining the value of a given financial instrument)
- Investing for Retirement
CV in pdf format
Some wild musings
An out of date personal page is here
- By Mail:
19 Courtland Ave. E.
Kitchener, Ontario, Canada N2G 2T4
- By Phone:
- By email:
andy (at symbol) novocin (dot) com