\documentstyle{article}
\begin{document}
\title{List of activities}
\author{Kevin Iga}
\date{As of Dec. 26, 1991}
\maketitle

{\Large Original Math Problems in which I have had reasonable success:}

\begin{itemize}
\item Half-composites: given a continuous real function $g(x)$, can we find
all functions $f(x)$ such that $f(f(x))=g(x)$?  I have solved this problem
for $g(x)$ monotonic, and for a small class of non-monotonic $g(x)$.
I have also found conditions on $f$ for $C^n$ functions, n finite.  Using
an entirely different method, I have solved the problem when $g(x)$ is
analytic and has fixed points, and when analytic solutions are sought.
I am close to finishing writing these findings up, and I plan to submit them
for publication soon thereafter.

Generalizations include widening the class of $g(x)$, changing the space
from the real line to the complex plane, the circle, or higher-dimensional
analogs, changing the class of functions from continuous or $C^n$ to
$C^\infty$, or analytic, changing the number of times $f$ is composed with
itself, possibly obtaining a one-parameter group of functions, with the
group operation being composition.

\item Using Feynmann path integrals to investigate translated harmonic
oscillators in various bases.  This involves developing a generalized
form of Poisson process where each event has a different mean rate, and
counting the number of paths that have a certain (unordered) set of
transitions, among other problems.  I have not yet completed solving the
complete path integral.

\end{itemize}

{\Large Special Awards:}

Selected by the MIT Mathematics department to receive an honorary membership
to the MAA.

\newpage
{\bf Teaching Experience:}

\begin{tabular}{|rllll|} \hline
& Subject & Age group & Class size & Organization\\ \hline
Jan. 92 & Klingon Language & 18-20 & 4 & Independent\\
Jan. 92 & PostScript (comp. lang.) & 18-30 & 8 & SIPB\\
Fall 91 & Physics, Calculus & 19 & 1 & Tutoring\\
Sum. 91 & Algebra I & 14-21 & 30 & Subst. teacher--Public high school\\
Sum. 90 & Physics (mechanics) & 14-18 & 10 & Educational Studies Program\\
Sum. 89 & Pre-Calculus & 14-17 & 12 & Educational Studies Program\\
89-91 & CPR & 17-40 & 6-20 & American Red Cross\\
Spr. 89 & Geometric Symmetry & 13-15 & 2 & Educational Studies Program\\
Spr. 88 & Group Theory & 14-18 & 5 & High school math team\\
Sum. 86-88 & Nature, Pioneering, etc. & 11-16 & 4-40 & Boy Scouts\\ \hline
\end{tabular}

%Summer 1988, 1987, 1986 & Boy Scout Camp counselor, taught nature,\\
%& environmental science, mammals, first aid, pioneering.\\
%
%item[Tutoring:] Tutoring a student in Calculus and AP Physics, Fall 1991.
%
%item[Klingon:] Taught a class the Klingon Language as developed by Marc
%Okrand for Star Trek III, during January 1992.

{\bf Other work experience:} EECS ECF---software design and programming,
hardware repair, documentation writing, user consulting and support

{\bf Education:} Student at the Massachusetts Institute of Technology, double
majoring in Mathematics and Physics.  Expected date of graduation: June 1992

{\bf Computer Languages:} Assembly(6502), BASIC, C, Fortran, Pascal,
Perl, PostScript, SCHEME, Unix shells (sh, csh, bash)
 
{\Large Extracurricular Activities:}

The following is a list of student activities of which I am a member.

\begin{description}
\item[Alpha Phi Omega] National service fraternity: A group of volunteers
(not a living group), working in the Boston inner city, scout camps
in the vicinity, on campus, and in neighboring communities, doing
painting, fundraising, construction, ushering, proctoring, encouraging,
and so on.  Member since Fall 1988, recipient of the Distinguished
Service Key, served as Historian, Service Vice President, Press Shop
Manager, CPR Chair, and Treasurer.  Taught at least 20 Community CPR
classes through the American Red Cross between January 1989 and now.

\item[Educational Studies Program:] Runs programs to allow MIT students
to teach high school students.  Member since Spring 1989, taught
Geometric Symmetry and Group Theory in HSSP (Spring 1989), taught
higher-dimensional polytopes and particle physics in Splash (Fall
1989, Fall 1990), taught precalculus in Junction (Summer 1989), taught
mechanics in Junction (Summer 1990).  Splash director, Fall 1989.

\item[Assassin's Guild:] Runs real-time, real-space role-playing games
investigating social dynamics of power, trust, management, and
problem-solving.  Also an acting experience.  Member since Spring 1989,
played in eight games, and helped write and run one.

\item[Residence/Orientation Committee:] Organizes the welcoming and
orientation of incoming freshmen and transfer students, and prepares
them for the residence choice decision.  Served in 1990 as one of
three R/O Center coordinators, and in 1991 as one of three Clearinghouse
coordinators.

\item[TCA] (Technology Community Association): Runs blood drives six
times a year, produces {\em How To Get Around MIT} for incoming students,
sells cards for UNICEF.  Member since Fall 1990, served as Office Manager,
and logistics chair for blood drives.

\item[HANDS] (Deaf Awareness/Sign Language group): Practices signing
weekly, runs projects to increase deaf awareness on campus, and
works to increase MIT accessibility to deaf students.  Charter member
(since January 1991), Community Service chair, Publicity codirector.

\item[SIPB] (Student Information Processing Board): Provides several
computer services not offered by MIT, including user consulting and
documentation.  Prospective member since Spring 1991, member since Winter
1992, helping user consulting.

\item[Institute Committee on Curricula:] Meets monthly to discuss
changes in curricula and reviews petitions relevant to curricula.
Three student representatives chosen each year.  Representative for
the 1991-1992 school year.

\item[United Christian Fellowship:] Member since Fall 1991.

\item[Gilbert \& Sullivan Players:] Performs shows every term.
Helped with crew in {\em The Mikado}, sang in chorus for {\em Yeomen
of the Guard}.

\item[Concert Choir:] Singing tenor (though I am really a bass) since
Fall 1991.

\item[Track \& Field:] Running in the 1500m event, beginning this past term.
\end{description}

{\Large Other major projects}

\begin{description}
\item[Three-dimensional Postscript:] Helped design and wrote postscript
code to allow easy drawing of three-dimensional objects, with user-defined
perspective and angle.  Version 1.0 released to public, July 1991.

\item[Dormitory Housing Software:] Helped design, and wrote software to assign
freshmen and transfer students to houses, depending on their first choices.
Written Summer, 1991.

\item[Tutoring:] Tutoring a student in Calculus and AP Physics, Fall 1991.

\item[Klingon:] Taught a class during Januray 1992 on the Klingon Language
as developed by Marc Okrand for Star Trek III.

\end{description}

\newpage
\noindent
{\bf References:}
\begin{description}
\item[Joseph Kuchta, Sr.,] Advisor, Alpha Phi Omega.\\
100 Memorial Drive\\
Cambridge, MA 02139

\item[Elias Tiliakos,] Former student, Physics.\\
9 Eaton St.\\
Winchester, MA 01890\\
(H) 729-8934

\item[Joseph Shaine,] Teacher, Educational Studies Program, Founder of
the Massachussetts Academy.\\
62 California St.\\
Watertown, MA 02172\\
(H) 926-5564\\
(W) 731-3990

\item[Alan Wu,] Current employer\\
MIT EECS ECF\\
77 Mass. Ave.\\
38-390\\
Cambridge, MA 02139\\
(W) 253-2737

\end{description}

\end{document}