Collections in Java
The Java API contains numerous classes for managing collections (or sets) of objects. A collection allows us to easily model a large number of data values or objects. There are four main types of collections which are available through various API packages; firstly lists. A list is an ordered collection of objects, we'd use this where the order elements appear in a list is meaningful (such as modeling a queue, or ordered list of items). A set is an unordered collection of objects, in which each element may only appear once (as per the normal rules of Set Theory). A stack is a collection type where elements are only added and removed from the front of the list, for example maintaining a list of recent events where the topmost item is always the most recent. Finally, a map is a collection of data pairings, where an element from a data collection is paired with an element from a key collection - for example pairing works (keys) to their definitions (data).
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.
The Application Layer
The application layers provides applications with access to the communications environment. A network-enabled application will create a user interface as well as interfacing with application layer network protocols.
Introducing Networks
"A network is a system or group of interconnected elements. A computer network is a group of computers and peripherals connected together to communicate with each other and to share information and resources."
http://www.micro2000.co.uk/network_glossary.htm