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Archive for January, 2009


founders-north-directions-2Please be advised, our meeting room for tomorrow has changed to accommodate a high expected turnout and a robotics competition being held in the ECSS.

We will meet in Founders North building (Kush auditorium, FN2.102).   Founders North is just a bit to the north and east of our regular meeting room.

We will have people at the ECSS to help direct you if you have any problems. I apologize for any inconvenience.

Please see the map showing the route from our current room to the new building.

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alexey-rootMetroplex Math Circle Announces Dr. Alexey Root’s Lecture on Chess and Mathematics

Dallas, TX, January 31, 2009. Dr. Alexey Root will present on chess applications of graph theory to secondary math education. She will highlight the concepts of domination and independence and show how they can be illustrated through chess problems. “The concept of domination is one of the central ideas in graph theory, and is especially important in the application of graph theory to the real world” according to Watkins in Across the Board: The mathematics of chessboard problems. Dr. Root’s lecture will be held on January 31st at 2:00 PM in room 2.410 of the Engineering and Computer Sciences Building (South), at the University of Texas at Dallas.

children-and-chessDr. Alexey Root has a Ph.D. in education from UCLA. Root has been a tournament chess player since she was nine years old. Her most notable chess accomplishment was winning the U.S. Women’s championship in 1989. She also holds the title of Women’s International Master. Since the fall of 1999, Root has been a senior lecturer at The University of Texas at Dallas (UTD). science-math-checkmate

From 1999-2003 Dr. Root was the Associate Director for the UTD Chess Program, the number one college chess team in the U.S. Root’s current assignment for UTD is to teach education courses that explore the uses of chess in classrooms. Her courses are available worldwide, via the UT TeleCampus online platform. Her books are Children and Chess: A Guide for Educators (2006), Science, Math, Checkmate: 32 Chess Activities for Inquiry and Problem Solving (2008), and Read, Write, Checkmate: Enrich Literary with Chess Activities (2009).

read-write-checkmateIn Dr. Alexey Root’s presentation, participants will try two domination activities from her books: Mobility (Children and chess: A guide for educators) and Covering the Board: Kings (Science, math, checkmate: 32 chess activities for inquiry and problem solving). Participants will also solve the eight-queens problem (Science, math, checkmate: 32 chess activities for inquiry and problem solving). The eight-queens problem highlights the concept of independence.

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In anticipation for our speaker this Saturday I thought I would post what Wikipedia has to say about Thebault’s Theorem.   No preparation is required for each Math Circle lecture, but then again it can never hurt:

thebault_theoremThébault’s problem I

Given any parallelogram, construct on its sides four squares external to the parallelogram. The quadrilateral formed by joining the centers of those four squares is a square.

It is a special case of van Aubel’s theorem.

Thébault’s problem II

Given a square, construct equilateral triangles on two adjacent edges, either both inside or both outside the square. Then the triangle formed by joining the vertex of the square distant from both triangles and the vertices of the triangles distant from the square is equilateral.

Thébault’s problem III

Given any triangle ABC, and any point M on BC, construct the incircle and circumcircle of the triangle. Then construct two additional circles, each tangent to AM, BC, and to the circumcircle. Then their centers and the center of the incircle are colinear.

Until 2003, acadamia thought this third problem of Thébault the most difficult to prove. It was published in the American Mathematical Monthly in 1938, and proved by Dutch mathematician H. Streefkerk in 1973. However, in 2003, Jean-Louis Ayme discovered that Y. Sawayama, an instructor at The Central Military School of Tokyo, independently proposed and solved this problem in 1905.[1]

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Dr. Ng gave a terrific talk on the field of natural language processing which combines many disciplines to address pressing problems.  He also introduced many of our students to the problems they will encounter on the North American Computational Linguistics Olympiad being held at UTD.

To help participants prepare for NACLO, Dr. Ng will host a problem session this Sunday to go over selected NACLO problems. Here are the date and location of the problem session:

Date and Time: Sunday, Jan 25, 2-5 PM
Location: Room 2.201, Engineering and Computer Science South Building, University of Texas at Dallas

You may also get updated information about the local NACLO competition, as well as additional sample NACLO problems from Dr. Ng’s website: http://www.hlt.utdallas.edu/~vince/naclo

Dr. Ng has provided his slides from the lecture.  Members of the Metroplex Math Circle e-mail group can download these files from the group site. To join the e-mail group simply click below.



Click to join MetroplexMathCircle

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Please come join us for the first Metroplex Math Circle of 2009.  On January 17 we will have Dr. Vincent Ng from UT Dallas talk to us about an exciting new field of applied mathematics as well as a new Olympiad with national and international competitions.

Statistical Natural Language Processing and the North American Computational Linguistics Olympiad

Abstract:
People have long believed that technology will eventually produce a machine that can speak to us. Natural language processing (NLP), one of most fascinating subfields of artificial intelligence, is devoted to enabling computers to use human languages both as input and as output. However, more than fifty years have passed since the inception of artificial intelligence, and we still have not been able to construct such a “talking machine.” In the first part of this talk, we will examine why NLP is so difficult, and take a look at how statistics have revolutionized the way computers understand human languages.

In the second part of the talk, we will give an overview of the North American Computational Linguistics Olympiad (NACLO), an international contest that aims to stimulate high-school students’ interest in natural language processing by having them solve linguistic puzzles. A local contest will be held at the University of Texas at Dallas on February 4, 2009.   Interested high-school students can now register through the NACLO website (www.naclo.cs.cmu.edu).

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Discrete mathematics and problem solving skills can lead to a very wide variety of careers.  With the upcoming NACLO competition and a lecture on Natural Language Processing, we will profile the emerging field of Computational Linguistics.  The following description is offered by Dr. Hans Uszkoreit:

Computational linguistics (CL) is a discipline between linguistics and computer science which is concerned with the computational aspects of the human language faculty. It belongs to the cognitive sciences and overlaps with the field of artificial intelligence (AI), a branch of computer science aiming at computational models of human cognition. Computational linguistics has applied and theoretical components.

Human language is a most exciting and demanding puzzle.

Theoretical CL takes up issues in theoretical linguistics and cognitive science. It deals with formal theories about the linguistic knowledge that a human needs for generating and understanding language. Today these theories have reached a degree of complexity that can only be managed by employing computers. Computational linguists develop formal models simulating aspects of the human language faculty and implement them as computer programmes. These programmes constitute the basis for the evaluation and further development of the theories.  In addition to linguistic theories, findings from cognitive psychology play a major role in simulating linguistic competence.  Within psychology, it is mainly the area of psycholinguistics that examines the cognitive processes constituting human language use. The relevance of computational modeling for psycholinguistic research is reflected in the emergence of a new subdiscipline: computational psycholinguistics.

We teach computers to communicate with people.

Applied CL focusses on the practical outcome of modelling human language use. The methods, techniques, tools and applications in this area are often subsumed under the term language engineering or (human) language technology. Although existing CL systems are far from achieving human ability, they have numerous possible applications. The goal is to create software products that have some knowledge of human language. Such products are going to change our lives. They are urgently needed for improving human-machine interaction since the main obstacle in the interaction beween human and computer is a communication problem. Today’s computers do not understand our language but computer languages are difficult to learn and do not correspond to the structure of human thought. Even if the language the machine understands and its domain of discourse are very restricted, the use of human language can increase the acceptance of software and the productivity of its users.

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wsj-storyThe Wall Street Journal published the results of a survey in an article called “Doing the Math to Find the Good Jobs.” It will be encouraging to Math Circle participants to know that mathematicians topped the list when considering such factors as work conditions and income.

In fact the first six careers in the list all draw heavily from the types of discrete mathematics taught at Math Circle

  1. Mathematician
  2. Actuary
  3. Statistician
  4. Biologist
  5. Software Engineer
  6. Computer Systems Analyst

This is what the article has to say about at least one person’s experience as a professional mathematician:

According to the study, mathematicians fared best in part because they typically work in favorable conditions — indoors and in places free of toxic fumes or noise — unlike those toward the bottom of the list like sewage-plant operator, painter and bricklayer. They also aren’t expected to do any heavy lifting, crawling or crouching — attributes associated with occupations such as firefighter, auto mechanic and plumber.

The study also considers pay, which was determined by measuring each job’s median income and growth potential. Mathematicians’ annual income was pegged at $94,160, but Ms. Courter, 38, says her salary exceeds that amount.

Her job entails working as part of a virtual team that designs mathematically based computer programs, some of which have been used to make films such as “The Matrix” and “Speed Racer.” She telecommutes from her home and rarely works overtime or feels stressed out. “Problem-solving involves a lot of thinking,” says Ms. Courter. “I find that calming.”

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