Community Outreach I Disability Attorneys I Disability Attorneys of Michigan

Network Outreach I Disability Attorneys I Disability Attorneys of Michigan Inability Attorneys of Michigan Participate in a Volunteer Day Helping Southwest Solutions, Beautification Day. The Neighborhood Beautification Day is a basic piece of Southwest Solutions exertion to â€Å"engage accomplices, occupants and different volunteers with an end goal to actuate parcels, make network nurseries and workmanship, tidy up parks and battle scourge and decay.†Erika Riggs and staff individuals from Disability Attorneys of Michigan, as of late chipped in the â€Å"Southwest Solutions Beautification Day.†Southwest Solutions is an association precious to our firm the same number of our customers have gotten significant treatment there for an assortment of psychological well-being debilitations at practically no cost.Southwest Solutions is likewise known for their lodging and workforce help programs, veterans’ administrations, and youth mentorship.This year’s Beautification Day tidied up 15 distinct regions of Southwest Detroit, including:Bennett ParkCabrini ClinicCorktown ViaductGo-Getters Drop-in CenterHousing Resource CenterHubbard Farms Community GardenLafayette Park (UNI)Larkins/McGraw Early Childhood OfficesMatrix Theater Company Community GardenMichigan Avenue Business AssociationSaint Anthony’sSouthwest CornerstoneSpringdale/Woodmere Block Club Community GardenStanton ParkWilshire ApartmentsWith the assistance of several network volunteers, including staff individuals from Disability Attorneys of Michigan every one of these locales were beautified.Thank you to each and every individual who came out to help Southwest Solutions and our community!Disability Attorneys of Michigan. Humane Excellence. network occasions, Community Outreach, DA Michigan, Disability Attorneys, Disability Attorneys of Michigan, government managed savings inability lawyers, Southwest Solutions

Nixon’s “Southern Strategy” and Forces Against Brown

Do you recall your first day of school ? How was it ? Was it frightening? I wager heading off to an isolated school where you were getting a wide range of looks , its way changed the mid 1900's. from individuals making a decision about you about the garments you were to the style of your hair. This article examines Richard M . Nixon , the United States President in 1968 brought forth the advanced change development through open vouchers and other instructive change quantifies under his † Southern Strategy † that was intended to pick up the votes of people who contradict school integration . The political exercises in school integration after Brown by the two significant ideological groups , to be specific the democrats and the republicans are talked about. President Richard Nixon responded to the 1971 court choice on Swann stanzas Charlotte-Mecklenburg school locale , a school integration case that affirmed to utilization of race to dole out understudies to class by the utilization of transporting , by teaching the U.S. equity office to draft an established correction to invalidate the court's choice. (Kruger 1975 ) In my view President Richard Nixon was simply attempting to get white American votes . Transporting is as yet going today for instance ; where I stay I'm between two primary school's and you would imagine that my kids could go to the two schools yet that is not the case . I surmise the manner in which the school area settled the issue was by splitting up the area. Which I consider insane on the grounds that back when I was going to class my street specifically wasn't viewed as a bus station and our folks had the option to pick whichever school .they needed us to go to . Presently , the manner in which they isolated the area the cut off spot or street I should state is the street directly before mine . We didn't have that issue since we needed to go to the following street in any case to get the transport the equivalent precise street they use as a cut off for the primary grade school. I think its so childish how we as a people can't get along enough to join and become equivalent enough to get training . I believed that was the explanation behind the different however equivalent regulation . Restriction to class integration was extraordinary from the earliest starting point and proceeds right up 'til the present time ; and the outcomes are clear , that is , the whitest American don't bolster school integration ( Jeffries , 1994 ; Motley , 1998 ; Olgetree , 2004). This is so evident on the grounds that In 1970 , Vigor High School on Wilson Avenue , which had been Prichard's white secondary school during isolation , was 70% white . By 1980 , It was 80% dark . Albeit the vast majority of Prichard's outstanding larger part white territories were in this region , numerous families had placed their understudies into parochial or tuition based schools . Before this came about Prichard was predominately white until they move dark in the zone to work at the paper plant. I thoroughly concur with blunt browns contention preferring combination on transports and in every aspect of open settlement and travel . Individuals have battled with/on hundreds of years to increase equivalent rights . Western human advancement has been described by the authoritative control by white guys. This force structure has much of the time and verifiably barred ladies and minorities . In the United States , in spite of the fundamental doctrine that † all men are made equivalent , † it has taken a very long time of battle to increase equivalent rights . Equivalent rights , of correspondence under the steady gaze of the law , implies that all people are dependent upon similar laws of equity. Individuals must be dealt with similarly with/as/for respect to race , sexual orientation , national cause , skin shading , religion or inability. African Americans were one of the primary gatherings allowed equivalent rights in the United States , through the entry of the fourteenth Amendment , which banned servitude . Accomplishing equivalent rights as a general rule took one more century of battle . Ladies , also , albeit allowed the option to decide in favor of/by 1920 , keep on moving in the direction of equivalent rights , most as of late through compensation value . Congress ought to end all projects in light of the damage they caused minority understudies. I am so happy they passed the Title VI of the Civil Rights Act of 1964 states that No individual in the United States will , on the ground of race , shading , or national starting point , be rejected from cooperation in , be prevented the advantages from claiming , or be exposed to separation under any program or action accepting Federal budgetary help . Uniformity implies everybody has an indistinguishable amount of everything ; nobody is viewed as unrivaled or sub-par. Fairness implies that all youngsters can grow up and go to class with equivalent access to the English language here in America . Everybody ought to be treated as reasonably and as deserving of regard and fundamental rights as their companions from the second they are conceived . Individuals having the option to act naturally , strolling through existence with inborn qualities that ought to be viewed as nonpartisan, for example, ethnicity , skin shading , sexual orientation , physical incapacities , mental inability without confronting separation dependent on their essence or attributes.

Types Of Tourism And Their Importance Tourism Essay Essay Example

Kinds Of Tourism And Their Importance Tourism Essay Orchestrating to The World Tourism Organization ( WTO ) , Tourism is directly the biggest business known to man. The World Tourism Organization ( WTO ) is relied upon there is making a trip to be 1.6 billion overall tourers by 2020, contrasted with 2002, there is simply 715 million overall tourers in 2002. Along these lines, a group of states, no undertaking immature and creating, touristry head start of remote money total compensations and making occupation chances for individuals. Fitting to McIntosh et Al, touristry can be delegated the figure of the marvels and connections take topographic point from the deals of tourers, friendly gathering administration provider, concern merchant, the host authoritiess, the start of the authoritiess and nearby networks in the system of pulling and facilitating these tourers and other visitant. Fitting to Page, touristry as a buyer movement is consistently being created by the touristry business and individual worries, as selling is utilized to grow new build, stocks and benefits and finishs. This reflected in the worldwide association in creating specialty stocks: excursion yearss concentrated on explicit inclusion and exercises. We will compose a custom paper test on Types Of Tourism And Their Importance Tourism Essay explicitly for you for just $16.38 $13.9/page Request now We will compose a custom article test on Types Of Tourism And Their Importance Tourism Essay explicitly for you FOR ONLY $16.38 $13.9/page Recruit Writer We will compose a custom article test on Types Of Tourism And Their Importance Tourism Essay explicitly for you FOR ONLY $16.38 $13.9/page Recruit Writer Murphy contend that, as the touristry developed in size and range it become clear that this industry, similar to other people, strive for restricted assets and capital, that its non-wasteful properties did non needfully stay away from the erosion or modification of appealing powers. 2.2 Sustainable Tourism Economical touristry hypothetical record is identified with the ethical standard of practical turn of events, which in theory upheld that individuals battle to run into their ain requests, in all probability estimated against the model of life by and by delighted in ( World Commission on Environment and Development, 1987 ) . Manageable advancement can indicate as the measure of the tradeoff between the interest s and point of the present, and those of the great beyond ( Archer and Cooper, 1994 ) . Blending to Butler ( 1993 ) , he challenges the utilization of the term maintainable touristry, in perniciousness of its cash, thinking that it suggests the consideration of touristry itself, whatever its effects, rather than the consideration of the human or physical setting inside which the touristry happens. Fitting to Butler et al upheld the term supportability touristry advancement, influencing touristry which is improvement and in such a way, that nation ( network and condition ) , in such a graduated table, it will remain functional in an erroneous term, non chop down or adjust the wonders ( human and physical ) , of which there is such an extent, its prosperity advancement and illegal exercises and systems each piece great as different advantages. Clarke ( 1997 ) proposed that the improvement of the idea of reasonable touristry include four assaults which are perfect inverse, whereby economical touristry and mass touristry were viewed as polar antonyms ; a degree, whereby practical touristry and mass touristry were no longer observed as polar antonyms, yet rather it was recognize that there were distinctive sunglassess of manageable and total touristry, which would bring together at the inside ; movement, an assault which recommended that positive activity could do total touristry female pony maintainable ; assembly, is the idea that a wide range of touristry can attempt to be supportable. ( J. Swarbrooke, 1999 ) 2.3 Ecotourism Each examination laborers and essayists have the distinctive portrayal and definition on the term of ecotourism. Out of the grouping of definition about ecotourism, there is one of the most cited definition originated from Hector Ceballos-Lascurain ( 1987:13 ) . He characterized that, the ecotourism or other than referred to as biological touristry can sort as a kind of touristry that includes going nearly without break. Ecotourism other than can indicate as going to unadulterated common nations with the main purpose of breaking down, turn upward toing, and take pleasance in the regular scene and its wild vegetations and zoologies each piece great as any gettable social aspects ( both days of old and these days ) that can be found in these nation. ( Luck, 2003 ) Ceballos-Lascurain ( 1990 ) other than contended, nature-arranged touristry implies logical, tasteful and philosophical push toward to travel, despite the fact that environmental tourer is non a talented researcher, inventive individual or logician. The a large portion of import ground is that the individual who complete ecotourism gets the opportunity of procuring nearer with regular habitat in a mode ordinarily non bing in the city life that normally loaded with power per unit region. ( Weaver, 2009 ) In light of Stanford Research Institute ( 1990 ) , the ecotourism portrayed as the quickest turning area of the entire universal touristry industry, it has expanded pace of 30 percent for each twelvemonth. Ecotourism watched the effects, both positive and negative, of house workers and worldwide touristry. Other than that, ecotourism is other than a kind of touristry stock that advances security and bolster supportable improvement while holding an insignificant effect on the earth. Ecotourism other than includes going to removed areas to larning the vegetation, zoology and untamed life vitalize being in their local home grounds. It other than offers the chance to perceive how nearby individuals live and work. ( Abraham, 2010 ) Blending to Hundloe, to summarize, great misgiving of administrations, social affectability and commitment with the neighborhood network are the three boss issues which separate ecotourism from its cousins green touristry and supportable touristry. 2.3.1 Significance of Ecotourism Sierra et all ( 1999 ) accepted, ecotourism can be depict as one of the most potential instruments in the arsenal of the cutting edge earthy people . Ecotourism is an earth more amiable and possibly progressively maintainable interchange to extractive exercises. For delineation, logging, agribusiness, uncovering, or chasing of untamed life. Nearby individuals may hold an opportunity being off from a mood of poverty and, by sharing their data among neighborhood individuals and tourer about the nearby geography and biology, which can help to develop up a more grounded awareness of network pride and a more extensive, increasingly planetary position that is conscious of the significance of biodiversity to person in the great beyond. Ecotourism give an opportunity to since quite a while ago run insurance of nature and its assets. The hot topographic purpose of organic decent variety is generally the least immature state which is the financial arrangement of the state is unconventionally in drive individuals to destruct the common habitat. Ecotourism other than give an opportunity to ensure the earth and organic decent variety that about nonextant. Whereby, this is other than chance to deliver more pay to keep investigate endeavors. An eco-visitor appealing powers, the arrangement enlistment expense can be more distant coordinated to the logical comprehension about the natural condition ; bolster detainment, recovery or re-afforestation ; or semisynthetic effect checking, to ensure that does non chop down dish assets. Orchestrating to Sierra et Al ( operation cit ) , to additionally confirm the developing of planetary touristry, the relationship sandwiched among touristry and the earth is requires being obviously course to chop down the hurtful and gain by significant effects. The visual part of ecotourism offers emphasize to the interest for future experts to create fit achievements in touristry and biological heading. 2.3.2 Ecotourism in Malaya Malaysia is one of the states from South-East Asia and it is notable as a multicultural state. Multicultural has non simply made the state as a supplement Eden, it has other than made Malaysia topographic point to keeping hundred vivid celebrations. Malaysia was other than celebrated with the warm and benevolent nearby individuals. Fitting to Smith, In Malaysia, touristry division is directly the second-biggest industry after the manufacture was the biggest business in Malaysia. The specialists association mindful on propelling touristry industry in Malaysia is Tourism Malaysia or other than name as Malaysia Tourism Promotion Board. Due to the land foundation, Malaysia is each piece varying as its progress. The state is isolated into two sections, promontory of Malaysia with 11 regions and two regions on the northern bit of Borneo which is Sabah and Sarawak. The state is covers a whole nation of 329 758 km2 in South East Asia. The run of the mill states of the state is ever warm and sticky all through the twelvemonth. Malaysia was recorded as one of the most organically assorted states known to mankind. Malaysia is a bewildering state with army abundance of biodiversity. The nation of the state is allowed with numerous regular completion and alluring power, for example, vegetations, zoologies and untamed life, wonderful coastline, outsider Marine water life, large downpour woods and the greatest and most seasoned collapses the universe. ( Daud, 2010 ) An alone common and social in addition to variegation is the thing that Malaysia genuinely had. Along these lines, eco-the travel industry in Malaysia was extremely positive, executable, manageable and strong signifier of touristry. In the twelvemonth of 2008, Malaysia has won The Best Ecotourism grant by TravelWeekly ( Asia ) during the Industry Award 2008 which s held in Singapore. It is the second clasp that Malaysia was regarded after 2007. It wa

Equality Diversity on Disabled Persons Essay - 2750 Words

Equality Diversity on Disabled Persons (Essay Sample) Content: Equality Diversity on Disabled PersonsName:Institution:Task:Tutor:Date:Equality Diversity on Disabled PersonsIntroductionIndividuals in the society need to be given services from government institutions without any biasness. This means that all people regardless of their gender, religion, age, race or disability should be given equal treatment. It is identified that all human beings are equal irrespective of their background or their physical or mental conditions (Bagihole, 2009, p.76). There are some instances that the people who offer services assume that certain group of people in the society should get better services than others. This is usually based on the class and the social status in the society. This practice is unethical and limits the enjoyment of human rights, which dictates that all people should be treated equally. This is to prevent incidences of some section of the population feeling inferior and left out. It is the role of the government and the pub lic to ensure that these basic rights on human beings are not denied on any individual.In social and health care sector, the problem of discrimination is common especially to the people with disability when they want to access services. Disability can be in different forms with the most common being physical disability followed by mental disability. Most of the times, the individuals with these kind of disabilities are relatively less helpless than other healthy and normal individuals. This makes them require increased attention from medical practitioners in addition to being assisted in a number of things. Inequality based on disability in the health care sector is unprofessional and does not match with the roles and responsibilities of medical practitioners (Bagihole, 2009, p.87). Disability is not a choice of an individual but a condition that may be related to genetics, accidents or hereditary. Therefore, people with disability should be treated equally and thus get better servi ces as other people. This paper looks at inequality due to disability and how it affects the experience of individuals or groups. Further, the paper uses Personal Cultural Structure model to understand how inequality affects disabled people and the problems associated with the trend. Finally, the paper looks at organizations campaigning against inequality and the services they provide to achieve this objective.How disability discrimination influence experiences of individuals and groupsInequality related to disability is influenced by the extent to which the patients can be able to take care of themselves. Individuals who have disabilities which are physical may be prevented by health care management from accessing the health care. This is especially so if the hospital has no special attendants to serve the disabled individuals. The patients are seen as a nuisance to the operations of the hospital and they are regarded as a bother. This is from the fact that the physically disabled persons need to be assigned health practitioners to keep watch on them. This is in addition to ensuring that the things that they may require are provided in time. Disabled patients especially those who have problems in moving about require that the health practitioners carry out activities such as washing them. Some of the practitioners find this unwelcome and this influences their decisions to turn them down from accessing their services (Mental Health Commission, 2012, p.27). The disabled persons thus feel oppressed in that they are denied a chance for better health service based on their disability. This increases their chances of getting depressed and they suffer from lowered self-esteem.As a group of disabled persons, the individuals may be isolated from the other patients making them feel unwanted by the society. When individuals are not given a chance to interact with others in the hospital set up due to their disability; they feel left out (Mental Health Commission, 2012, p .28). It is common to find incidences that as a group they are taken to a common ward or location where they are not given the necessary attention. The disabled patients most of who may be weak and lack physical capacity to feed themselves may go hungry for hours. It is also common to find incidences when these groups of disabled individuals fail to take medicine in the required time frames. Bringing the disabled individuals together and failing to offer necessary attention may further lead to injuries. This could happen when there are individuals among the group who have mental problems and may start fights. When this kind of a thing happens and the health practitioners are not around, those with physically disability end up suffering more. This is from the fact that they are relatively helpless to defend the selves from injuries and fights.Structural, cultural and personal impacts on disabled individual and group experiencesIn understanding how the inequality related to disability is practiced and spread in social and health sector; a PCS model is relevant. The PCS model is a tool that is used to analyse how personal, cultural and structural factors influence the behaviour and beliefs of people resulting to incidences of inequality and discrimination (Singh, 2012, P.3). Personal discrimination is influenced by actions of individuals who perpetuate behaviours that lead to discrimination. In disability discrimination, personal discrimination is common from the health care practitioners where an individual thinks that disabled individuals are a liability to the hospital. This is from the fact that once a patient is brought to the hospital the individual expected to provide care, gives more attention to the more healthy patients. The individual may also not give the disabled person an ability to get services before other patients, though he or she may be weak or unable to support himself or herself. This attitude of individualà ¢Ã¢â€š ¬s results to suffering o f the disabled who feel helpless and have little they can do to assist them self. This type of discrimination may be out of ignorance or prejudice to certain members in the society, which means that the behaviour may be persistent for relatively a long time.Cultural discrimination on the other hand is based on the attitudes and the beliefs of the society towards certain people (Singh, 2012, P.3). The cultural may be based on the society or it may be a characteristic of the identified organization. Through cultural discrimination, individuals as a group think that no people are entitled to special favours including in a health care set up. This means that in instances that a person with disability is brought to hospitals, the other patients waiting to be served cannot give him a chance to be served first. There is the cultural believe that people should be served by the medical practitioners on the basis of when they arrived in the hospital. This is discriminatory in that; disabled individuals may not make to wait for long in the queues due to their physical problems. Therefore, it is expected that the patients should offer these individuals and groups to get medical attention first.Structural discrimination originates from the political, social and economic environment and the power relations as well as process in a given system (Singh, 2012, P.3). Structural discrimination plays a role in discrimination of groups and individuals with disability by looking down on their social status. Individuals with disabilities who come from poor background rarely get adequate services as they are unable to finance them. In some health care structures, it is passed that people should not be treated if they cannot afford to pay for the bills. Therefore, this makes the health care practitioners in such institutions fail to offer necessary services to groups with disability, who most of them have limited funds. The structures of health care set ups are also characterized by differing social classesà ¢Ã¢â€š ¬ wards and services. This makes the disabled persons fail to get quality treatment because they are also considered to belong to a lower social class in the society. Therefore, through structural discrimination, inequality in health services offered to disabled individuals as well as groups is common. The discrimination leads to suffering of the disabled individuals who may succumb to death in some instances.Problems related to multifaceted oppression on disabled personsDiscrimination that is related to disability is multifaceted and results to various oppressions on the affected individuals or groups (Thompson, 2012, p.91). One of the oppression on this group is through manipulation of different powers by the health practitioners and the society. The health practitioners, who have expertise power, know that the disabled persons must want to get their services to get well. This makes them use this power to manipulate them through giving the service s in prejudiced manners. They understand that the disabled persons are less empowered and they may not be in a position to take legal actions against them. The services therefore given to the disabled person at times are seen as a favour instead of their right. This is because the health practitioners assume that they can decide when to give the services and when to withdraw them. The disabled groups and individuals sometimes suffer from discrimination to an extent they have to beg to get services (Mental Health Commission, 2012, p.31). This kind of behaviour is unacceptable in a civilized society where equality should be upheld on all individuals irrespective of their health status or social status.Disabled persons further suffer from oppression related to the services offered once admitted in the hospitals (Mental Health Commission, 2012, p.32). The individuals and groups that are characterized by mental health problems are regarded as unequal...

Act Utilitarianism Versus Kant s Principle Of Ends Essay

Act Utilitarianism versus Kant’s Principle of Ends. Introduction There are many theories out there when it comes to any kind of ethics. I will be discussing Act Utilitarianism and Kant’s Principle of Ends. Both are good theories, but they do have their differences. I think that how we perceive either of these depends on how we were brought up by our families and what we believe in when it comes down to making decisions. While both are similar theories they are also different in their own way. All of my research on this paper I pulled from our book â€Å"Ethical Choices† 2011. Theories, Pros, Cons and Opinion Act Utilitarianism is the morally right act, for any situation, is that act which produce the greatest overall utility in its consequences. (â€Å"Ethical Choices† 2011). Act utilitarians believe that we need to understand what is right and what is wrong in order for us to make ethical decisions. In doing so, it tells us what we ought to do to promote the greatest amount of utility. In this view, we are focused on the scope, duration, intensity and probability of our actions. The scope tells us how many people are affected by certain actions; The duration tells us the amount of time that the effects our actions last; Intensity tells us how differently people are affected by our actions in that no two situation affect people the same; and, The probability tells us that we can’t predict our futures, but we can estimate how are actions affect others. In act utilitarianism weShow MoreRelatedKant And The Moral Law1451 Words   |  6 PagesIntroduction: Kant argues that mere conformity with the moral law is not sufficient for moral goodness. I will argue that Kant is right. 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How My Writing Has Improved - 1515 Words

After this semester of English 102, at Bristol Community College I feel that I have gained the skill to articulate what I want to convey to the reader in many ways. I don’t just look at grammatical error, but instead I look for ways to make my sentences more effective and concise. Nevertheless, I hope that this strategy will continue to help me improve my writing even further on in the future. My strong points as a reader have also definitely improved after reading the poems and stories we experienced this semester. Writing has been an important form of expression for me. I find myself to be very soft spoken and speaking verbally is usually difficult for me because I can’t always seem to find the right words to say. I feel that I am more expressive and have more control over what I want to say. While this semester progressed toward its end, I have learned new writing skills and gradually learned how to engage with audiences. This skill was very useful in meeting my course goals in English 102. I believe that I have grown at organization and careful stream my thoughts as well. Before I would just begin writing my papers without any plans or organization, along with no definite idea of where I would be going with the assignments, but throughout this course I’ve learned that you should base your paper around your thesis statement. Another skill I took from this class was to value my classmate’s responses, from their reactions made me much more aware that my main ideasShow MoreRelatedHow My Writing Has Improved Greatly Improved After Taking English 103928 Words   |  4 Pagesterm â€Å"writing†, they don’t really associate this with a single course that they have taken in high school or college. Rather, most people view â€Å"writing† as a process that evolves as we become capable of thinking in more abstract manners. 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Applications of Discrete Mathematics free essay sample

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying smoothly, the objects studied in discrete mathematics such as integers, graphs, and statements in logic do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in continuous mathematics such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been haracterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the integers, including rational numbers but not real numbers). However, there is no exact, universally agreed, definition of the term discrete mathematics. Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions. The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete athematics that deals with finite sets, particularly those areas relevant to business. Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in discrete steps and store data in discrete bits. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in applying ideas from discrete athematics to real-world problems, such as in operations research. Although the main objects of study in discrete mathematics are discrete objects, analytic methods from continuous mathematics are often employed as well. Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. The term discrete mathematics is therefore used in contrast with continuous mathematics, which is the branch of mathematics dealing with objects that can vary smoothly (and which includes, for example, calculus). Whereas discrete bjects can often be characterized by integers, continuous objects require real numbers. The study of how discrete objects combine with one another and the probabilities of various outcomes is known as combinatorics. Other fields of mathematics that are considered to be part of discrete mathematics include graph theory and the theory of computation. Topics in discrete mathematics Complexity studies the time taken by algorithms, such as this sorting routine. Theoretical computer science includes areas of discrete mathematics relevant to computing. It draws heavily on graph theory and logic. Included within theoretical computer science is the study of algorithms for computing mathematical results. Computability studies what can be computed in principle, and has close ties to logic, while complexity studies the time taken by computations. Automata theory and formal language theory are closely related to computability. Petri nets and process mathematics are used in analyzing VLSI electronic circuits. Computational geometry applies algorithms to geometrical problems, while computer image analysis applies them to representations of images. Theoretical computer science also includes the tudy of continuous computational topics such as analog computation, continuous computability such as computable analysis, continuous complexity such as information-based complexity, and continuous systems and models of computation such as analog VLSI, analog automata, differential petri nets, real time process algebra. Information theory The ASCII codes for the word Wikipedia, given here in binary, provide a way of representing the word in information theory, as well as for information-processing algorithms. Information theory involves the quantification of information. Closely elated is coding theory which is used to design efficient and reliable data transmission and storage methods. Information theory also includes continuous topics such as: analog signals, analog coding, analog encryption. Logic Logic is the study of the principles of valid reasoning and inference, as well as of consistency, soundness, and completeness. For example, in most systems of logic (but not in intuitionistic logic) Peirces law is a theorem. For classical logic, it can be easily verified with a truth table. The study of mathematical proof is particularly important in logic, and has applications to automated theorem proving nd formal verification of software. Logical formulas are discrete structures, as are proofs, which form finite trees[8] or, more generally, directed acyclic graph structures[9][10] (with each inference step combining one or more premise branches to give a single conclusion). The truth values of logical formulas usually form a finite set, generally restricted to two values: true and false, but logic can also be continuous-valued, e. . , fuzzy logic. Concepts such as infinite proof trees or infinite derivation trees have also been studied,[11] e. g. infinitary logic. Set theory Set theory is the branch of mathematics that studies sets, which are collections of objects, such as {blue, white, red} or the (infinite) set of all prime numbers. Partially ordered sets and sets with other relations have applications in several areas. In discrete mathematics, countable sets (inc luding finite sets) are the main focus. The beginning of set theory as a branch of mathematics is usually marked by Georg Cantors work distinguishing between different kinds of infinite set, motivated by the study of trigonometric series, and further development of the theory of infinite sets is outside the scope of discrete mathematics. Indeed, contemporary work in descriptive set theory makes extensive use of traditional continuous mathematics. Combinatorics Combinatorics studies the way in which discrete structures can be combined or arranged. Enumerative combinatorics concentrates on counting the number of certain combinatorial objects e. g. the twelvefold way provides a unified framework for counting permutations, combinations and partitions. Analytic combinatorics concerns the enumeration of combinatorial structures using tools from complex analysis and probability theory. In contrast with enumerative combinatorics which ses explicit combinatorial formulae and generating functions to describe the is a study of combinatorial designs, which are collections of subsets with certain intersection properties. Partition theory studies various enumeration and asymptotic problems related to integer partitions, and is closely related to q-series, special functions and orthogonal polynomials. Originally a part of number theory and analysis, partition theory is now considered a part of combinatorics or an independent field. Order theory is the study of partially ordered sets, both finite and infinite. Graph theory Graph theory has close links to group theory. This truncated tetrahedron graph is related to the alternating group A4. Graph theory, the study of graphs and networks, is often considered part of combinatorics, but has grown large enough and distinct enough, with its own kind of problems, to be regarded as a subject in its own right. [12] Algebraic graph theory has close links with group theory. Graph theory has widespread applications in all areas of mathematics and science. There are even continuous graphs. Probability Discrete probability theory deals with events that occur in countable sample spaces. For example, count observations such as the numbers of birds in flocks comprise only atural number values {O, 1, 2, . On the other hand, continuous observations such as the weights of birds comprise real number values and would typically be modeled by a continuous probability distribution such as the normal. Discrete probability distributions can be used to approximate continuous ones and vice versa. For highly constrained situations such as throwing dice or experiments with decks of cards, calculati ng the probability of events is basically enumerative combinatorics. Number theory The Ulam spiral of numbers, with black pixels showing prime numbers. This diagram ints at patterns in the distribution of prime numbers. Main article: Number theory Number theory is concerned with the properties of numbers in general, particularly integers. It has applications to cryptography, cryptanalysis, and cryptology, particularly with regard to prime numbers and primality testing. Other discrete aspects of number theory include geometry of numbers. In analytic number theory, techniques from continuous mathematics are also used. Topics that go beyond discrete objects include transcendental numbers, diophantine approximation, p-adic analysis and function fields. Algebra Algebraic structures occur as both discrete examples and continuous examples. Discrete algebras include: boolean algebra used in logic gates and programming; relational algebra used in databases; discrete and finite versions of groups, rings and fields are important in algebraic coding theory; discrete semigroups and monoids appear in the theory of formal languages. Calculus of finite differences, discrete calculus or discrete analysis A function defined on an interval of the integers is usually called a sequence. A sequence could be a finite sequence from some data source or an infinite sequence from a discrete dynamical system. Such a discrete function could be defined explicitly by a list (if its domain is finite), or by a formula for its general term, or it could be given implicitly by a recurrence relation or difference differentiation by taking the difference between adjacent terms; they can be used to approximate differential equations or (more often) studied in their own right. Many questions and methods concerning differential equations have counterparts for difference equations. For instance where there are integral transforms in harmonic analysis for studying continuous functions or analog signals, there are discrete ransforms for discrete functions or digital signals. As well as the discrete metric there are more general discrete or finite metric spaces and finite topological spaces. Geometry Computational geometry applies computer algorithms to representations of geometrical objects. Main articles: discrete geometry and computational geometry Discrete geometry and combinatorial geometry are about combinatorial properties of discrete collections of geometrical objects. A long-standing topic in discrete geometry is tiling of the plane. Computational geometry applies algorithms to geometrical problems. Topology Although topology is the field of mathematics that formalizes and generalizes the intuitive notion of continuous deformation of objects, it gives rise to many discrete topics; this can be attributed in part to the focus on topological invariants, which themselves usually take discrete values. See combinatorial topology, topological graph theory, topological combinatorics, computational topology, discrete topological space, finite topological space. Operations research Operations research provides techniques for solving practical problems in business and other fields † problems such as allocating resources to maximize profit, or cheduling project activities to minimize risk. Operations research techniques include linear programming and other areas of optimization, queuing theory, scheduling theory, network theory. Operations research also includes continuous topics such as continuous-time Markov process, continuous-time martingales, process optimization, and continuous and hybrid control theory. Game theory, decision theory, utility theory, social choice theory I Cooperate I Defect I Cooperate | 1-10,0 1 Defect 10, -10 1-5, -5 | Payoff matrix for the Prisoners dilemma, a common example in game theory. One player chooses a row, the other a column; the resulting pair gives their payoffs I Decision theory is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision. Utility theory is about measures of the relative economic satisfaction from, or desirability of, consumption of various goods and services. Social choice theory is about voting. A more puzzle-based approach to voting is ballot theory. Game theory deals with situations where success depends on the choices of others, which makes hoosing the best course of action more complex. There are even continuous games, see differential game. Topics include auction theory and fair division. Discretization into discrete counterparts, often for the purposes of making calculations easier by using approximations. Numerical analysis provides an important example. Discrete analogues of continuous mathematics There are many concepts in continuous mathematics which have discrete versions, such as discrete calculus, discrete probability distributions, discrete Fourier transforms, discrete geometry, discrete logarithms, discrete differential geometry, iscrete exterior calculus, discrete Morse theory, difference equations, and discrete dynamical systems. In applied mathematics, discrete modelling is the discrete analogue of continuous modelling. In discrete modelling, discrete formulae are fit to data. A common method in this form of modelling is to use recurrence relations. Hybrid discrete and continuous mathematics The time scale calculus is a unification of the theory of difference equations with that of differential equations, which has applications to fields requiring simultaneous modelling of discrete and continuous data.