Introduction to Mathematical Software

21-126, Spring 2000
Dr. David Handron

Homework Assignment 1

Exercises

1) Construct simple lists to illustrate the operation of the following commands:
	Sort[]
	Permutations[]
	AppendTo[]	(How does this differ from Append[] ?)
	PrependTo[]	(How does this differ from Prepend[] ?)
	Insert[]
	Partition[]

2) Verify that Mathematica interprits

Sin[x]^2

as "sin squared x" and not as "sin of x squared".

3) Given a list of n positve numbers, the arithmetic mean is their sum divided by n and their goemetric mean is the n-th root of their product. 

Theorem: The arithmetic mean of a list of positive numbers is greater than or equal to their geometric mean.

Illustrate this theorem on for list of 10 real numbers in the range (0,1] and also for 10  chosen  in the range [1,99]. Can you find a list of numbers for which the two means are equal?

Hint: Random[] is useful for generating arbitrary data.