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Posts Tagged ‘discrete mathematics’


A good friend of the Metroplex Math Circle, Dr. Arthur Benjamin, is a popular speaker at the world famous TED conference.  Recently, he offered his own idea for fundamentally changing math education in our country.  Like Richard Rusczyk, he sees the singular focus on Calculus as insufficient and distracting from a full math education.

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discrete mathA good friend of the Metroplex Math Circle, Dr. Arthur Benjamin, has just released a new lecture course through the Teaching Company titled “Discrete Mathematics.” We have our pre-ordered copy and its seems to have the unique combination of humor and depth that we know from Dr. Benjamin’s excellent “mathemagic” presentations.

For any students just starting with Math Circles, they will benefit greatly from becoming familiar with the topics on these DVDs: number theory,  combinatorics and graph theory.

Here is the description of the course from the Teaching Company:

Welcome to Discrete Mathematics, a subject that is off the beaten track that most of us followed in school but that has vital applications in computer science, cryptography, engineering, and problem solving of all types.

Most of the mathematics taught after elementary school is aimed at preparing students for one subject—calculus, which is the mathematics of how things grow and change continuously, like waves in the water or clouds in the sky. Discrete mathematics, on the other hand, deals with quantities that can be broken into neat little pieces, like pixels on a computer screen, the letters or numbers in a password, or directions on how to drive from one place to another.

While continuous mathematics resembles an old-fashioned analog clock, whose second hand sweeps continuously across a dial, discrete mathematics is like a digital watch, whose numbers proceed one second at a time. As a result, discrete mathematics achieves fascinating mathematical results using relatively simple means, such as counting.

Explore this modern realm of digital math in Discrete Mathematics, 24 mind-expanding lectures by veteran Teaching Company Professor Arthur T. Benjamin, an award-winning educator and mathemagician who has designed a course that is mathematically rigorous and yet entertaining and accessible to anyone with a basic knowledge of high school algebra.

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Netflix just announced the winners of their $1 million prize to make at least a 10% improvement in the performance of their prediction engine.

NEW YORK, Sept. 21 /PRNewswire/ — After almost three years and submissions by more than 40,000 teams from 186 countries, Netflix, Inc., the world’s largest online movie rental service (NASDAQ: NFLX), today awarded the $1 million Netflix Prize to a team of engineers, statisticians and researchers who achieved the competition’s goal of a 10 percent improvement over the accuracy of the Netflix movie recommendation system when the competition was launched in Oct. 2006. Netflix members already are benefiting from improvements Netflix Prize contestants have contributed to the recommendations system.

Moments after bestowing the $1 million prize, Netflix announced a second $1 million challenge, asking the world’s computer science and machine learning communities to keep the improvements coming…

The winning team is comprised of software and electrical engineers, statisticians and machine learning researchers from Austria, Canada, Israel and the United States. All seven team members – Bob Bell, Martin Chabbert, Michael Jahrer, Yehuda Koren, Martin Piotte, Andreas Toscher and Chris Volinsky – attended the awards ceremony. It was the first time all seven had met one another in person. How the $1 million is split is to be determined by the team.

Its not surprising that the winners have careers that depend heavily on mastery of discrete math topics and have cultivated the same competitive spirit found in math circles.

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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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Achieve and the Dana Center at UT Austin have developed a series of benchmarks for high school students to succeed in post secondary education.  The entire list may be of interest, but the benchmark for Discrete Mathematics covers many of the topics that students experience only through Math Circle.  Here is the description of the importance of Discrete Math:

Discrete mathematics, sometimes called finite mathematics, can be thought of as the science of counting, arrangements, and algorithms. It offers a plethora of concrete, practical problems (e.g., fair apportionment, searching algorithms, error-correction methods) and a wealth of subtle problems whose statements are deceptively simple but whose solutions provide significant challenge. While events in the physical world are most often modeled by continuous mathematics (i.e., the calculus and prerequisite topics in algebra, geometry, and trigonometry), the increasingly important world of computers, information technology, and logistics employs a different type of mathematics. New approaches and applications require the use of discrete processes, many of which have not traditionally been included in core high school courses. To be well prepared for the future, all students need to understand the concepts and applications of this important area of mathematics.

Hat tip:  Math Forum Internet News

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