Today I looked at a few course materials available on mecr.org and these are available for reading. One of the topics I looked at was evaluating complexity in terms of big O, Omega and Theta.  I want to briefly mention them here.

If we take a few methods f and g  where f is O(g(n)) we can show there are non-unique values of coefficient c and n that satisfy this i.e c > 1 n > 1 and there are different forms of polynomials that can satisfy the relationship for f and g.
Typically in calculating complexity, usually only the higher term matters. This becomes important in polynomials as it simplifies the discussion on complexity.
While O is applicable to a single algorithm. Omega is applicable to a class of algorithms. For example, we say that Omega for sorting algorithms is nlogn. This we see from different sorting algorithms having a complexity of O(nlogn).
Theta on the other hand is used for a range. For example if f(n) lies between c1.g(n) and c2.g(n) i.e
c1.g(n) < f(n) < c2.g(n) then we say f(n) is theta for g(n) for all n0, c1, c2 such that n > n0.
These two functions are generally of the same order.
big O, Omega, Theta are all related.
For example, f(n) is O(g(n)) and g(n) is Omega(f(n)). Then we can take two coefficients c and 1/c for which we can say f(n) <= c.g(n) and 1/c .f(n) <= g(n)
and consecutively we can say f(n) is Theta(g(n). In other words, f(n) is  O(g(n)) and also f(n) is Omega(g(n)).
There is also an interesting observation that
if f1 is O(g1(n))
and f2 is O(g2(n))
the f1 + f2 is O( max(g1, g2))
This is true even if we have more than two such functions. Its easier to visualize these as applicable to a  sequence of code blocks in a program where the overall program complexity is the max of any one of the blocks of code.
Also, we can show that with a choice of coefficients for the functions above, where say n3 is max of n1, n2 and c3 is max of c1, c2, then f1 + f2 = c3g1(n) + c3g2(n) = 2.c3.(max (g1,g2)) and that leads to
f1 + f2 is O(max(g1, g2))