Students who are mathematically inclined can use the student version of a program like MatLab or Mathematica to convert a digital image into numbers, then perform operations such as sharpening or special effects. This is a great way to learn about image processing algorithms.
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Math is used by many different types of scientists to model phenomenon and evaluate data from an experiment. By building mathematical models scientists can understand how different physical, chemical, and biological processes are affected by different variables. The most important tools are: making a graph to give a visual representation of the relationships between your variables and making an equation to give a way of computing the relationships between your variables. Find a source of data,…
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Here is a challenging problem for anyone with an interest in geometry. This project requires background research to solve it, but it is an excellent illustration of visual thinking in mathematics.
Figure 1 below shows a series of circles (iC₁, iC₂, iC₃, ..., iC₃₀), inscribed inside an arbelos. What is an arbelos? The arbelos is the white region in the figure, bounded by three semicircles. The diameters of the three semicircles are all on the same line segment, AC,…
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Math_p011

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Time Required

Average (6-10 days)

Prerequisites

Good grasp of Euclidean geometry, a firm understanding of how to construct a mathematical proof, determination

Can computer games be used to educate? Pick a game that incorporates educational material. There are a variety of educational computer games on the market in the areas of math, history, science, and language, as well as many simpler versions free on the Internet. Make up a test based on the subject area covered by the computer game. Have your volunteers take the test before and after playing the game. Does playing the computer game improve people's score on the test?
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Research the famous collapse of the Tacoma Narrows suspension bridge.
What lessons were learned about the potentially damaging effects of wind on bridges? What structures stabilize a bridge against wind forces? Build models and use a wind tunnel to test your hypothesis.
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Math can make you money! If you understand some basic math, you can make good decisions about how to keep, spend, and use your hard earned dollars. Try an experiment comparing the same balance in different types of bank accounts. How much better is a savings account than a checking account? What difference does the interest rate make? Which is better, an account that earns compound or simple interest? Can you compare the short and long term costs of borrowing money compared to saving the cash…
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Sudoku puzzles have become extremely popular over the past couple of years. You can find books of puzzles for beginners to experts, and many newspapers print Sudoku puzzles daily. This project challenges you to write a computer program to check if your Sudoku solution is correct.
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CompSci_p023

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Time Required

Average (6-10 days)

Prerequisites

An understanding of the material covered in [# ProjectIdea Name="CompSci_p002" Value="HtmlAnchor" #]

Take shots at a set distance from the basket, but systematically vary the angle to the backboard. For a basic project: How do you think your success rate will vary with angle? Draw a conclusion from your experimental results. A bar graph showing success rate at different angles can help to illustrate your conclusion. For a more advanced project: Use your knowledge of geometry and basketball to come up with a mathematical expression to predict your success rate as a function of angle…
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Block off one-third of a soccer net with a cone, 5-gallon bucket or some other suitable object. Shoot into the smaller side from a set distance, but systematically varying the angle to the goal line. Take enough shots at each angle to get a reliable sample. How does success vary with angle? For a basic project: How do you think your success rate will vary with angle? Draw a conclusion from your experimental results. A bar graph showing success rate at different angles can help to…
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Here's an interesting project idea with a variation that combines computer science, physics and music. You'll need a piano in a quiet room, a microphone and a computer with digital sound recording and analysis software. The project shows you how you can make a piano string start vibrating without hitting its key. You can record the sounds on the computer, and use sound analysis software to measure the frequencies of the induced vibrations. For more details see: . Be sure to check out the…
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