1. Lec 1. Course Overview Intuition Programming
Computer-based problem solving
Theory vs Practice
0ther Perspectives
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2. The Course Goals 1. To develop a practical intuition about
computer problem-solving and its role in
science and engineering.
2. To learn how to build graphical user
interfaces (GUIs) using Matlab.
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3. The Vehicle… …is the Matlab Environment where you can easily
Develop programs.
Display results & ideas graphically.
Interact with large data sets.
Process images and sound.
Develop graphical user interfaces
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4. The Course Goal… …is to develop a practical intuition about
computer problem-solving and its role in
science and engineering.
Let’s discuss the key words
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5. What do we mean by “Intuition”?
If intuition is a sense of direction,
then computational intuition is a sense
of computational direction.
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6. A Sense of Geometry
Ray Tracing
100 million triangles
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7. A Sense of Complexity Search Trees Design Space Billions of Choices
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8. A Sense of Probability and Statistics Via Simulation
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9. A Sense of Approximation, Error, and Noise
1/3 = .3333
Pi = 22/7 g
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10. The Course Goal… …is to develop a practical intuition about
computer problem-solving and its role in
science and engineering.
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11. What Goes on In Science? Data is Gathered Models Are Built
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12. Enter the Computer
In one way, "computational science" is the ultimate triumph of terminology, coupling the respectability of science with whatever is computational. But instead of regarding the term as a marketing ploy, think of computational science as a point of view. Science can be seen as a triangle with theory,
experiment, and computation at its vertices. Each vertex represents a style of research and provides a window through which we can look at science in the large. The vibrancy of what we see inside the triangle depends upon the ideas that flow around the edges of the triangle. A good theory couched in
the language of mathematics may be realized in the form of a computer program, perhaps just to affirm its correctness. Running the program results in a simulation that may suggest a physical experiment. The experiment in turn may reveal a missed parameter in the underlying mathematical model, and
around we go again.
But interesting ideas can flow in the other direction as well. A physical experiment may be restricted in scope for reasons of budget or safety, so the scene shifts to computer simulation. The act of writing the program to perform the simulation will most likely have a clarifying influence, prompting some
new mathematical pursuit. Innovative models are discovered, leading to a modification of the initial set of experiments, and so forth.
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13. Looking For Patterns
DNA
A Protein
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14. Build one of these for Proteins...
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15. A Challenge The data is there. (“Tycho has cataloged the stars.”)
Now make sense of it!
(Where are the “genomic Keplers”!)
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16. The Course Goal… …is to develop a practical intuition about
computer problem-solving and its role in
science and engineering.
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17. What Goes On in Engineering?
Design
Experimentation
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18. Enter the Computer Engineering Engineering Engineering
In one way, "computational science" is the ultimate triumph of terminology, coupling the respectability of science with whatever is computational. But instead of regarding the term as a marketing ploy, think of computational science as a point of view. Science can be seen as a triangle with theory,
experiment, and computation at its vertices. Each vertex represents a style of research and provides a window through which we can look at science in the large. The vibrancy of what we see inside the triangle depends upon the ideas that flow around the edges of the triangle. A good theory couched in
the language of mathematics may be realized in the form of a computer program, perhaps just to affirm its correctness. Running the program results in a simulation that may suggest a physical experiment. The experiment in turn may reveal a missed parameter in the underlying mathematical model, and
around we go again.
But interesting ideas can flow in the other direction as well. A physical experiment may be restricted in scope for reasons of budget or safety, so the scene shifts to computer simulation. The act of writing the program to perform the simulation will most likely have a clarifying influence, prompting some
new mathematical pursuit. Innovative models are discovered, leading to a modification of the initial set of experiments, and so forth.
Engineering
Engineering
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19. The Course Goal… …is to develop a practical intuition about
computer problem-solving and its role in
science and engineering.
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20. What Do We Mean By “Computer Problem-Solving”?
The key idea:
Algorithm. A step-by-step procedure that takes you from a prescribed set of inputs to a prescribed set of outputs.
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21. The “Traveling Salesperson” Problem Make a roundtrip visiting each
city exactly
once. Find
the
shortest
possible
path.
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22. Algorithm:
always go
to the
nearest
unvisited
city
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23. The Course Goal… …is to develop a practical intuition about
computer problem-solving and its role in
science and engineering.
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24. What Do We Mean By “Practical”?
It means that you carry away
useful computer skills.
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25. Theory versus Practice
Prove that
the program
controlling
this missile
silo is correct.
A theoretical exercise with
great practical importance.
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26. A Note on the GUI Part The Matlab GUIDE facility makes life easy.
A vehicle for learning about object-oriented
programming.
An opportunity to refine your communication
skills.
A platform for follow-up ugrad research
in the spring.
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