1. Briefly explain the differences and similarities between private cloud, public cloud, and community cloud.
2. Solve the following constraint optimization problem: minimize the expression x2 + 2y2 under the constraint 2x + y = 1. Give two examples when optimization is important for cloud computing.
3. Use Least Squares to find, step-by-step, the parameters m and b for which yi ~ m * xi + b, when x1 = −1, x2 = 0, x3 = 1, y1 = −0.9, y2 = 0.0, and y3 = 1.1.
4. Explain, step-by-step, how, given the values xi and yi, we can find the parameters of the corresponding power law y ~ A * xα. Explain why this problem is important for cloud computing.
5-7. In the RSA algorithm, let us start with the prime numbers p = 3 and q = 5, and let us take e = 5. Show, step-by-step, how the RSA algorithm will generate the secret code d, and how it will encode the message m = 3. Then decode and check that you get the original message back. Use the actual RSA algorithms on all steps, do not just guess for d and raise to the power to encode. Why is security especially important for cloud computing?
8. Show how, given seven numbers a1, a2, ..., a7, we can compute the partial sums s1 = a1, s2 = a1 + a2, s3 = a1 + a2 + a3, ..., s7 = a1 + a2 + ... + a7 in parallel. Why cloud computing strongly encourages parallelization?
9. Explain how to use MapReduce to find the largest of n values.
10. Briefly describe what you have done for your project.