What are models and simulations? Identify real-world examples of models and simulations. Models and simulations are used to generate new knowledge, as well as to formulate, refine, and test hypotheses. simulations allow hypotheses to be tested without the constraints of the real world.

Question: If I flip a coin 10 times, is it possible to predict exactly how many times will come up heads? Why or why not? Theoretical probability is the exact probability of a situation taking every factor into account (chance of heads is 1 result out of two possible outcomes, 1/2 = 50%). Experimental probability is basically a guess of the theoretical probability of an event using knowledge of the relative frequency of the event occurring (calculating using test or simulation data, 30 heads/50 Flips = 60%). (Vocabulary from: http://www.systems-thinking.org/modsim/modsim.htm) https://www.flickr.com/photos/jeffanddayna/4081090389

Using models and simulations What is the chance it will rain tomorrow? How many hits will your favorite baseball player make in his next game? If you toss a crumpled sheet of paper into the recycle bin from across the classroom, how likely is it to make it in? (Does it catch the wind?) What information is needed to figure out the answers to these questions? How can you make your estimate as accurate as possible? Most of the time we need to use experimental probability instead of theoretical Would you rather have the computer to access data or actually perform the paper throwing experiment? Will it rain? Using a meteorological model, a meteorologist will run a program with current data for the forecast (simulation). How many hits? Use the players batting average (the mathematical model) to calculate the number of hits in an average game (the simulation). How many "baskets"? The paper and basket are the model; running the trials is the simulation.

Abstraction Reducing the details in a problem to focus on concepts necessary to understand and solve the problem. Time and money are always practical considerations. How accurate do you NEED to be? What details are necessary?

Medical simulation: The heart Watch this human heart simulation Multi-scale Multi-physics Heart Simulator UT-Heart (5:15) * Stop after 2:00 What’s an advantage to having so many data points? a disadvantage? watch up to 2:00, the rest is interesting but not necessary 2:46 graphing blood pressure. (gathering data) 3:30 shows different layers in the simulation 4:40 applications of the simulation uses: what-if scenarios for surgery options.

Space simulation How can you test a parachute to be used on Mars? https://www.youtube.com/watch?v=_jOzxEOlDJg (1:11) describes the physical test. Before they test, they create models and simulate on the computer. Why? the cost to construct a prototype and run the tests is very high so they need to be sure, before they do it, that it passes a simulated test.

Math and Science simulations Bouncing Turtle The Game of Life, cellular automata

Additional Simulation models Chile Tsunami model (NOAA) Epidemic simulation Coffee Shop Game *Yes, this is a cool math game 