Undergraduate Mathematics Institute

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The Undergraduate Mathematics Institute (UMI) is the outreach leg of the CNA. Directed by W.O. Williams, and supported by grants from the NSF, NSA, and CNA, its program focus on African-Americans, Hispanics, women, and other under-represented groups, and on students from smaller universities and colleges. CNA members actively participate in the lecturing and supervising of research projects at the UMI.

The research experience sometimes leads to publication. Of course, publishable form only occurs after further development of the project, sometimes at the home institution, with local advisors, as in the case of Amy Smith (1999) [1], sometimes through continued research-at-a-distance with the CMU director, as with Keshav Dani (1997) [2]and Jabari Harris and Carter Gay (2001) [3].

In the nine years of the current program there have been a total of 121 students (a full listing of the students is given below). Their distribution is given in the following tables (all figures are rounded percentages).

	European-	Asian-	African-	Hispanics &
	Americans	Americans	Americans	Native Americans
1994-1996	51 %	3 %	26 %	21 %
1997-2002	52 %	7%	33%	7 %
Total	52 %	6 %	31 %	12 %

	Female	Male
1994-1996	56 %	44 %
1997-2002	59 %	41 %
Total	58 %	42 %

	Small College	University
1994-1996	49 %	51 %
1997-2002	75 %	25 %
Total	66%	34 %
(Excludes CMU Students)

A systematic effort was begun in 1997 to track previous and current students in the Institute. This has been only partially successful, due to changes in ``permanent''addresses and to non-response. Our data is summarized as follows.

	Undergrad	Term. MS	PhD	Working	No Resp.	Total
				After BS
1994		1	5	3	5	14
1995			5	1	6	12
1996			10	1	2	13
1997		3	6		3	12
1998		1	8	2	2	13
1999		3	7	2	3	15
2000	1	2	5	1	5	14
2001	3	2	1	2	6	14
Total	4	12	47	12	32	107
Tot. %	4	11	44	11	30	100

``PhD'' and ``MS'' include both degrees attained and currently being sought. ``Working'' comprises those who began technical work without completing an advanced degree.

In the period of the last three years the project areas and project directors were:

Topic	Project Director
Computational Finance	Prof. Steve Shreve
Partial Differential Equations	Prof. Jack Schaeffer
Statistics of Finance	Prof. Pantelis Vlachos (Statistics)
Discrete Models for Computation	Prof. Shlomo Ta'asan
Variational Calculus	Prof. Deborah Brandon
Bayesian Methods	Prof. Pantelis Vlachos (Statistics)
Electoral Models	Prof. John Tolle
Logic and Discrete Mathematics	Prof. Richard Statman
Differential Equations & Variational Calculus	Prof. Deborah Brandon
Computational Finance	Prof. Bill Hrusa
Discrete Mathematics	Prof. Richard Statman

In the same period the seminar series consisted of the following speakers. (Not including repeat speakers.)

Speaker	Title
Paul Komarek, Grad. Student	What I do as a Grad Student:
	Research and Real-life
Prof. Dave Handron, CMU	An Introduction to Morse Theory
Prof. Reha Tütüncü, CMU	Optimization for a Better Tomorrow
Prof. Bill Eddy, Statistics, CMU	Flight-Data Analysis and Data Flight-Analysis
Prof. Lubos Thoma, CMU	Ramsey Theory through Examples
Prof. Hyung Kim, Chemistry, CMU	Molecular Dynamics Computer
	Simulation of Liquids
Dr. Clarissa Howison, NSA	What's up with Astrodynamics
Profs. L. Wasserman &J.Cummings	Graduate School Admissions
Prof. Deborah Brandon, CMU	Young's Tacking Problem
Monica Van Dieren, Grad. Student	Introduction to Non-standard Analysis
Prof. Steve Shreve	The Black-Scholes Formula
Aris Winger, Grad. Student	The Experiences of Graduate Life
Prof. Reha Tütüncü	Rendezvous Search Problems
Prof. Shlomo Ta'asan	Stochastic Processes and PDE
Prof. Ramamoorthi Ravi	Reconstructing the tree of life
Profs. B. Hrusa & Nicole Lazar	Graduate School Admissions
Prof. David Kinderler	Math through a Microscope:
	new horizons for mathematics
Prof. Monica VanDieren	A Connection Between Model Theory
	and Number Theory
Prof. Tom Bohman	Methods in Extremal Combinatorics
Prof. John Tolle	Power in Weighted Voting Systems
Prof. Bard Ermentrout	Mathematics Applied to Neuroscience
Prof. Jack Schaeffer	Some Comments on Working in PDE
Prof. Noel Walkington	Automated Mesh Generation
Scott E. Greenholt	Career Options for A Math Major

In this period, projects were:

 Speaker 		  Title




Jessica Elder, Jeffrey Fernandez, 		  Money, Money, Money


Thomas Oliver, and Steven Tobar 		 




Miyuki Breen and Ebony Graves 		 HIV Modeling    




David Van Valen 		 Optimal Investment in 


Continuous Time  




Aarthi Gopal 		 The Capital Asset Pricing Model -


in a Bayesian Framework




Vincent Costanzo 		 String Vibrations 




Elizabeth Chester 		  Modeling Traffic Flow   


with PDE's




John Hinrichsen 		Traffic Flow -  


A Discrete Model




Bennie Garrett  and 		 Population Modelling: the      


Oluwatosin Otitoju		Importance of being Discrete 




Phillip Nguyen 		 Numerical Solutions of     


Differential Equations




Amy Bardeen, Brandon Chaubaud 		 Brachistoland

& Colin Hinde




Brooke Anderson		Lower Bounds on


Circuit Complexity




Pamela Merkh & Megan Strohm		 Does NP-Complete You?




Bridgett Barlow & Krystal Williams		 Completeness of


the Resolution Proof




Michael Hussey & Abby Mroczenski		 The Federalist Papers

(a 200+ year old dispute)




Carter Gay & Jabari Haris		A Serious Weight Problem




Leotis Lastrapes & Christina Webb		 Apportionment Methods




Mary Lee 		 Mathematical Modeling in  

& Jennifer Sorkin 		 Population Dynamics




Laura Bland 		The Max Flow/Min Cut Theorem     


and its Applications




Amanda Glenn 		 Chaos in Systems of

& Lamesha Junior 		 Ordinary Differential Equations




Mark Herman 		Minimum Transit Time for


a Zero-Dmensional Boat  




Carl Westine		 On the Pricing of Perpetual 


American Put Options




Pamela Pei 		 The Agent-Client Maximizing 


Utility (A-CMU) Problem




Tiffany Kinnibrugh 		Four Colors!

& Michael Young		   




David Korpi 		Optimal Consumption and Investment  


with Two Utility Functions




Juliet Anderson,  Vivian Bishay, 		Portfolio Optimization Using 

& Marian Hernandez-Viera 		 the Double Binomial Model