Final Exam Topics
CS145: Images and Imagination, Spring 2014

The Final Exam will focus primarily on material covered since the Exam 1 and Exam 2. However, keep in mind, that most of the material is cumulative, so you need to know the earlier material in order to do the new material.

This exam will be closed book.

Suggestions:

• Practice (among other things) problems on earlier exams
• Review class notes and exercises.
• Review lab work.

Topics

• Recursion

  • What is recursion? A recursive program is a program which calls itself, usually it calls itself on a problem with smaller size.
  • Problems which lend themselves to recursive solutions are generally problems with the properties:
    • A solution for the problem of a given size (e.g. n) can be expressed simply in terms of the same problem with smaller size, e.g. n-1
    • There is size, called the "base case", which is trivial to solve. This serves as the condition for stopping the recursion.
    • Program solutions usually have the form

      myFunc(n)
      if n is the base case, return the answer
      else apply the recursion
      

  • The type of examples you should know (e.g. see Lab 6):
    • Printing the numbers from a to b, forwards or backwards
    • Computing factorial.
    • Computing the Fibonacci series
  • Using recursion in turtle graphics (see Lab 6)

• Complex Numbers

  • What is an imaginary number? What is i and how does one compute powers of i, e.g. i², i³, etc.
  • What is a complex number?
  • What is the complex plane and how does one plot numbers in the complex plane?
  • Know the standard form of a complex number: (a + b i).
  • Know the polar form z = r e^{i Θ} = r(cos Θ + i sin Θ ). What is the geometric meaning of r (the length or modulus) and Θ?
  • How does one add, subtract, and multiply complex numbers and place the result in standard form?
  • How does one multiply complex numbers in polar form?
  • Given a complex number in standard form, how does one compute r?
  • You should understand how to do problems similar to the ones found here (pdf). Solutions to these can are here (pdf)
  • You should know how to convert back and forth between the syntax we used in Processing and the typical math syntax.
  • You should have a general intuition about what a transformation (e.g. #1-8 in Lab 7) will do to an image.

• While and Do-While loops

  • What is a while loop?
  • What is the difference between a while and do-while loop?
  • What is the minumum number of times a while loop could possibly loop?
  • What is the minumum number of times a do-while loop could possibly loop?
  • How does one convert a for-loop to a while-loop?
  • Look at loop examples that were done in class and those discussed in Lab 8.

• Other items

  • How does one use the map function to do rescaling (e.g. see the Mandelbrot code)
  • What does it mean to iterate on a variable?
  • How might one use a while or do-while loop to perform iteration?
  • What is the Mandelbrot Set?

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