Discussion --Why learn Discrete Structures?--

Questions:
Define the following terms:
- What is Discrete? (lookup in a dictionary)
- What is Structures?
- So, what is Discrete Structures (DS)?
- Why is DS important?
- How do we apply DS?
- Read in History of DS (refer to Links)



Solutions:

1.

Collins COBUILD Advanced Learner's English Dictionary

discrete
Discrete ideas or things are separate and distinct from each other. (FORMAL)
...instruction manuals that break down jobs into scores of discrete steps.
= separate

Longman Dictionary of Contemporary English

discrete
di·screte /dɪˈskriːt/ adj
–adjective

1.	apart or detached from others; separate; distinct: six discrete parts.

2.	consisting of or characterized by distinct or individual parts; discontinuous.

3.	Mathematics. a. (of a topology or topological space) having the property that every subset is an open set. b. defined only for an isolated set of points: a discrete variable. c. using only arithmetic and algebra; not involving calculus: discrete methods.

Oxford Advanced Learner's Dictionary

discrete

ect(formal or technical) independent of other things of the same type
Synonym: SEPARATE
The organisms can be divided into discrete categories.

2. Essential English Dictionary structure -noun 1. a thing constructed; a complex entity constructed of many parts 2. the manner of construction of something and the arrangement of its parts 3. the complex composition of knowledge as elements and their combinations 4. a particular complex anatomical part 5. the people in a society considered as a system organized by a characteristic pattern of relationships -verb give a structure to WordNet Online structure -Noun · structure, construction (a thing constructed; a complex entity constructed of many parts) "the structure consisted of a series of arches"; "she wore her hair in an amazing construction of whirls and ribbons" · structure (the manner of construction of something and the arrangement of its parts) "artists must study the structure of the human body"; "the structure of the benzene molecule" · structure (the complex composition of knowledge as elements and their combinations) "his lectures have no structure" · structure, anatomical structure, complex body part, bodily structure, body structure (a particular complex anatomical part of a living thing) "he has good bone structure" · social organization, social organisation, social structure, social system, structure (the people in a society considered as a system organized by a characteristic pattern of relationships) "the social organization of England and America is very different"; "sociologists have studied the changing structure of the family" -Verb · structure (give a structure to) "I need to structure my days" Oxford Advanced Learner's Dictionary structure -noun -the way in which the parts of sth are connected together, arranged or organized; a particular arrangement of parts: the structure of the building / human body ◆ changes in the social and economic structure of society ◆ the grammatical structures of a language ◆ a career / salary / tax structure - a thing that is made of several parts, especially a building: a stone / brick / wooden structure - the state of being well organized or planned with all the parts linked together; a careful plan: Your essay needs (a) structure. 3. Discrete structures are sets of distinct or unconnected elements. Discrete mathematics is mathematics that deals with discrete objects. Discrete objects are those which are separated from (not connected to/distinct from) each other. Integers (aka whole numbers), rational numbers (ones that can be expressed as the quotient of two integers), automobiles, houses, people etc. are all discrete objects. On the other hand real numbers which include irrational as well as rational numbers are not discrete. As you know between any two different real numbers there is another real number different from either of them. So they are packed without any gaps and can not be separated from their immediate neighbors. In that sense they are not discrete. We will be concerned with objects such as integers, propositions, sets, relations and functions, which are all discrete. 4. Related to the problem of correctness of computer programs, there is the well known "Halting Problem". This problem, if put into the context of program correctness, asks whether or not a given computer program stops on a given input after a finite amount of time. This problem is known to be unsolvable by computers. Thus we need some kind of formal approaches here to avoid dealing with a extremely large number (if not infinite) of possibilities. Discrete mathematics is the foundation for the formal approaches. It discusses languages used in mathematical reasoning, basic concepts, and their properties and relationships among them. Discrete mathematics is also concerned with techniques to solve certain types of problems such as how to count or enumerate quantities. The kind of counting problems includes: a) How many routes exist from point A to point B in a computer network ? b) How much execution time is required to sort a list of integers in increasing order ? c) What is the probability of winning a lottery ? d) What is the shortest path from point A to point B in a computer network ? 5. We apply discrete structures to the computer science includes: Functions, relations, and sets, Basic logic, Proof techniques, Basics of counting, Graphs and trees, Discrete probability From computer science of view, it concerns mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking & applications and modeling. It provides much of the basic concept for data structures, automate theory, operating systems, database, formal languages and more.