Math 418 Paper Plan, Spring 2014
PAPER #1: Technical paper
Requirements:
• 3–5 pages
• Written in LaTeX
• Must have at least one proof
• At least 3 references (at least one book or paper)
• Topic must be pre-approved, on some major theorem, famous conjecture, or subfield of math,
preferably connected to analysis.
• You need not prove the major result; it might be that you only prove a minor point at the
beginning or end.
• The point is to be able to speak intelligently and in some detail about some mathematical
topic.
• This paper need not connect to the second one.
PAPER #2: Practical paper
Requirements:
• 7–10 pages
• Written in LaTeX
• Must have at least one figure
• At least 3 references (at least one book or paper)
• Topic must be pre-approved, but the point is to describe the math behind some well-known
product/phenomenon/something.
• Title should be something like “Why clouds form” or “How airplanes fly.”
• The point is to answer your parents’ of interviewer’s question “So what good is math?”
• You need to discuss the math in some depth.
• Your 20-ish minute talk will be on this paper.
Deadlines
F 2/21 Topic #1 due to Dan
F 3/14 Draft of #1 due to Dan
M 3/24 Dan returns marked-up draft of #1
M 3/31 Final version due for paper #1 due
F 3/28 Topic #2 due to Dan
F 4/18 Draft of #2 due to Dan
W 4/23 Dan returns marked-up draft of #2
F 5/9 Final version due for paper #2 due
1
I am hoping that each of you will have your own pair of topics (i.e., hopefully no overlaps!),
so I would suggest starting to think about both papers very soon. Please check with me about
your topic before you get too deeply invested in the research. Also, feel free to contact me with
questions; I would be happy to meet from time to time, as necessary.
Those items with stars are already taken, though they might become free if people change their
minds. You should feel free to change your mind, too, if some topic turns out to be a dud. I’ll keep
a running list on the course website.
Topic Ideas
Practical paper
– Acoustics
(Cesàro, Euler, Lambert, etc.)
– Why do airplanes fly?
– Convolutions of functions
– How are flights scheduled?
– Distributions (for differentiating
– Why do clouds form?
non-differentiable functions)
– How does vehicle stability control work?
– Discontinuous Darboux functions
– How does facial recognition work?
– Lagrange inversion theorem
– How google’s search methods work
– Chebyshev’s inequality
-*- Will Twitter survive?
– Orthogonal polynomials
– How to store a song on an iPod
– Fourier analysis (some part(s) of it)
– How to process satellite images
-*- What makes for a good parameterization?
– Modeling disease spread
– Hermite and/or Lagrange interpolation
– How tsunamis work
– Splines and/or Bézier curves
– How cell phones find each other
– Chebyshev functions and/or points
– Fighting fires optimally
– Aitken’s delta-squared process
– Social networks
– Hundred dollar, hundred digit challenge
– Meteorology
– Interval arithmetic
– Climate forecasting
– Kahan summation algorithm
– Inventory control
– Strassen’s algorithm
– Paper bag problem
– Horner’s method
– Trajectory optimization
– Stone–Weierstrass theorem
– How to predict earthquakes
– Wilkinson’s polynomial
– Medical imaging
– LLL algorithm
– Vehicle routing
– Line searches (Fibonnaci, Golden Section, etc.) – Cryptography
– Tabu searches
– Controlling spacecraft
– Algebraic Riccati equation
– Neuroscience
– Genetic algorithms
– Why are bubbles round?
– KKT conditions
– Forecasting crime
– Finite element methods
– Why lenses help you to see
– Monte Carlo methods
– Protein folding
– Residue calculus
– Traveling salesman problem
– Harmonic functions
– Invisibility
-*- Projective space
– GPS
– Any of the 7 Millenial Prize problems
– Math and the genome
(http://www.claymath.org/millennium-problems)
– Speech recognition
– Choose your own adventure!!
– Math in video games
– Choose your own adventure!!
Technical paper
– Alternative forms of summation
2