Explain the theory in your own words based on applications and suggested readings. Including the following in your explanation. Counting/set theory/logic/relations/graph theory/analysis of algorithms. give an example how this could be applied.
Discrete Mathematics is a rapidly growing and increasingly used area of mathematics, with many practical and relevant applications.
Because it is grounded in real-world problems, discrete mathematics lends itself easily to implementing the recommendations fo the National Council of Teachers of Mathematics (NCTM) standards. (The recently publishedStandards and Principles for School Mathematics notes that "As an active branch of contemporary mathematics that is widely used in business and industry, discrete mathematics should be an integral part of the school mathematics curriculum.")
Because many discrete math problems are simply stated and have few mathematical prerequisites, they can be introduced at all grade levels, even with children who are not yet fluent readers.
Discrete mathematics will make math concepts come alive for your students. It's an excellent tool for improving reasoning and problem-solving skills, and is appropriate for students at all levels and of all abilities. Teachers have found that discrete mathematics offers a way of motivating unmotivated students while challenging talented students at the same time.
EXAMPLE: Linear Programming
Minimize C = 3x + 2y on the given feasible set.
Students spent a lot of time graphing lines without seeing how it can be useful. Linear programming is a powerful tool for finding the optimal value of a linear function on some feasible set. The feasible set is created by solving a system of linear inequalities. Solutions can be found graphically so even students who have not studied systems of equations can solve these problems.
Aug 14th, 2014
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