Paul’s ComSci Wafflings

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).

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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.

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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.

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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.

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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.

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“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
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File management is a key function of the Operating System. The OS must effectively manage reading and writing data from different storage media, using different file systems and different disk access methods. The OS may also choose to cache data to improve performance of disks.

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Another key role of the Operating System is to manage memory resources, there are two separate conceptual levels of memory. Firstly, physical memory - this is what the operating system sees, and it relates directly to your actual physical hardware. Secondly, there is virtual memory, which is what a programmer will see when developing an application to run within an operating system. Virtual memory is viewed as limitless, and is not dependent on the physical memory available - so applications can be programmed to run on systems with different physical memory capabilities.

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A process is a program in execution. The distinction is that a program is a static bit of code; the process is the instance of that program being executed. For example, if the same program is running twice, the program will be loaded into memory once, but it will have two processes - one for each instance of the program.

The operating system maintains information about all the processes in the process control block (PCB). The contains information such as the process’s unique ID, the current state of the process (explained in a moment), the program counter, pointers to allocated memory space and resources, CPU time used so far, and estimated time to completion.

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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.

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