Proof by Induction
A proof aims to establish a fact by taking a proposition - conjecture - and applying by the mathematical axioms (given truths) establish a proved theorum. Induction is a general method for establishing a proof, and is usually used to establish that a proposition is true for any natural number.
Lets Talk About Sets
A set is a collection of distinct objects considered as a whole.
[Wikipedia - http://en.wikipedia.org/wiki/Set ]
A set can be thought of as a collection of objects - or elements - and these objects can be anything, data - numerical - or indeed other sets. Elements in a set are in no particular order, and elements in a set must by definition be unique.
Propositional and Predicate Logic
A Proposition is a declarative sentence, which may be shown to be either true, or false, whether the statement is true or false is not - however - relevant. Both "1+2-=3" and "1+2=4" are example of propositions. Predicate logic allows us to explore the truthfulness of a statement, it has an expressive power which propositional logic does not.
Combinatorics
Combinatorics is a branch of mathematics concerned with the study of finite objects, and has many applications in the field of Computer Science. Combinatorics is useful in problem solving, and is most often involves ideas such as counting elements in a set, or calculating permutations or combinations of elements in a set.
Algorithms & Time Complexity
Rosen describes an algorithm as:
"An algorithm is a finite set of precise instructions for performing a computation or for solving a problem."
An algorithm can be expressed in a number of different ways however, it could be explained in plain English, written in a generic pseudocode (not a true programming language in itself, but a loose language system useful to describe algorithms in) or in a particular programming language.
De Morgan's Theorum
Augustus De Morgan was a 19th century mathematician working in the field of propositional logic, he established a series of rules concerned with conversion between different operators using inversion. The fundamental basis of his theory is that NOT ( P AND Q) = (NOT P) OR (NOT Q), and similarly NOT (P OR Q) = (NOT P) AND (NOT Q), this is often known as De Morgan Duality.