22M:151:001 Discrete Mathematical Models Project:

20% 1.) Write 1-2 paragraph descriptions (in html format) of 3 potential projects. Include references for each potential project. When you e-mail your file, please also e-mail me the following html code: <a href="SPRING09/filename"> project titles, your name </a></P>. E-mail URL to me by 11:59pm Monday, Feb 9).

Hat Guessing Games, Playing golf with 2 balls, Exact Analysis of Exact Change, Ang, Wei Zou

Networks: A Mathematical Approach to Friendships, Voting: The Mathematically Impossible Fair Contest, How Many Colors Does It Take to Color a Map?, Susan Gates

Computerized Recognition of Facial Expressions and Emotion, Carl Henning

Mathematical Properties of Knights, Ranking Players in Tournaments, Coupon Collector's Problem, Jeremy Madison

1. Literature Review: Optical Mapping As A Method of Whole Genome Analysis, 2. Literature Review: Optimizing Patient Flow in the Healthcare System, 3. Application: Automated Building Block Definitions Using Graphs and Graph Tree Searching, Austin Ramme

Snow Plow Project, Prey-Predator Model, Graph Theory, Morgan Schiller

Stehno, Krystle

1 Helicopter Cops and Robbers, 2 Stopping Time and Blackjack, 3 Slot Bandit, Tigges, Peter

Math Model Research Topic Options, Laura Williams     (in .doc format)

Applications of Combinatorial Designs in Computer Science, Covering Arrays and Software Testing, Mutually Orthogonal Latin Squares and Error-Correcting Codes, Stanley Ziewacz

10% 2a.)   By Tuesday March 10, e-mail me a 1-2 paragraph description of your project. One e-mail per group is sufficient (please cc everyone in the group).
2b.)   By 11:59pm Wednesday March 18, e-mail me a first draft with a good introduction and references.

20% 3.)  Slides or outline for talk (due Monday April 27).

25% 4.) Written report due Friday May 1 (turn in hard copy at the beginning of class).

25% 5.)  Present your work in class during the last week of class (May 4 - 8).  Presentation should be about 10 minutes/person.  Hence a group of 2-3 people should give a 20-25 minute presentation.

The following information should be included in your written report

Title:
5 key words:
Mathematics used:
Mathematical Difficulty:
Area of Application:
Application Area Difficutly:

The report should focus on
(1) the problem -- describe the problem so that a layperson can understand what you would like to do.
(2) the mathematical model -- explain in detail how discrete mathematics can be used to model the problem.
(3) the mathematics -- fully describe the mathematics needed to solve the mathematical model.
(4) How do the mathematical results relate to your problem (this can be included in (2) the mathematical model.

The report should be organized into sections logically. For example, an introduction should tell what the purpose is and how your paper is organized. Following the introduction, one or more sections should present your main points, the mathematical ideas, applications, history, reasoning, etc. Finally, a last section should summarize what you have done, emphasizing the significant points. There should be a bibliography of at least 3 sources used.  When you use quotes, figures, ideas, or other material directly or indirectly from a source, you must cite the source with the page number at that point.  Your written report can also include writing a worksheet which can be used in a future M151 class.

Create Your Own Personal Web Page at UI

HTML special characters and symbols

Getting started with HTML

In html, you can start a new paragraph, but putting <P> between your paragraphs.


You may choose one of the following projects or you may find your own.  Extra credit will be given for finding a good project.

References are given to introduce the topics below.  These references are a good place to start, but you need to find additional, preferably more current references.

The following are potential topics OR may be covered in class.  Some require more biology background than others.

1.)  Sequence Comparison

Chapter 3 in Setubal, Meidanis, Introduction to Computational Molecular Biology.


2.)  Fragment Assembly

Chapter 4 in Setubal, Meidanis, Introduction to Computational Molecular Biology.


3.)  Physical Mapping of DNA

Chapter 5 in Setubal, Meidanis, Introduction to Computational Molecular Biology.


4.)  Phylogentic trees

Chapter 6 in Setubal, Meidanis, Introduction to Computational Molecular Biology.


5.)  Genome rearrangements

Chapter 7 in Setubal, Meidanis, Introduction to Computational Molecular Biology.


6.)  RNA/Protein Folding

Chapter 8 in Setubal, Meidanis, Introduction to Computational Molecular Biology.


7.)  DNA computing

DNA Computation, Leonard Adleman

1  2  3  4  5  6  7  8  9  10  11  12  13  14  15 

Jonoska N, Karl SA, Saito M.Three dimensional DNA structures in computing, Biosystems. 1999 Oct;52(1-3):143-53.

8.)  Pairwise alignment using hidden markov models

Biological sequence analysis by Durbin, Eddy, Korgh, Mitchenson.


9.)  Genetics Inbreeding

Section 2.9 in An introduction to stochastic processes with applications to biology by Allen

I am not familiar with this book, but will look more at this section when we get to Markov chains.


10.)  Chemical chirality

When Topology Meets Chemistry : A Topological Look at Molecular Chirality by Erica Flapan  

11.)  Chen J. Rauch CA. White JH. Englund PT. Cozzarelli NR. The topology of the kinetoplast DNA network. Cell. 80(1):61-9, 1995 Jan 13.

12.)  Voting?

13.)  Eulerian closed chain algorithm and applications

Other methods of finding project material.

1.)  Search the web.

    1a.)  Use MathSciNet (05 and ...) MSC list
    1b.)  Search the Dimacs, Rutgers website.

    1c.)  Search the web for Research Experiences for Undergraduates (REU) and Discrete Mathematics.

    1d.)  Search for any area of interest.

2.)  Look at Humanities Math books such as For all Practical Purposes, COMAP.

3.)  Check other discrete math books such as Discrete Mathematical Models by Fred Roberts.