Sop for Mha Essay Example for Free

Sop for Mha EssayWanting to become a manager for wellness care initiatives and institutions is actuall(a)y much a product of my multi-cultural experience and the peoples desperate need for health care that I was so rattling aware of growing up in my native Morocco. As a young Berber woman raised in Casablanca, I was in an excellent eyeshot to appreciate the vast need in Africa for improved health administration services, especially at fees that are accessible to the poor majority, women in particular. As a cosmopolitan person who has also lived in France for 2 years and now the United States, I find hope for my native Africa through international nurture organizations that have developed missions dedicated to the improvement of health care administration in the Third World, Africa in particular. I think that I am a natural for health care promotion on an international level because of my high level of motivation, dedication to my studies, and my multi-lingual ability.I speak and write French very well and I am also a strong speaker and average writer in Arabicin addition to English and the saliva of my native heritage, Berber. My long term professional goal in life is to some day be able to harness my passion for a more(prenominal) just and humane world to the practical skills that will enable me to make a significant contribution, especially to the medically underserved members of our global human society.I determine forward to working on an international level for a government agency or global non- profit organization dedicated to the promotion of health care in Africa. XXXX is my first choice for study towards the MHA because I so deeply respect the ideals of the program and appreciate the diversity of the XXXX campus, with one of the highest percentages of international students of all U. S. institutions of higher learning.I look forward to a rigorous and in-depth exposure to a range of health-care issues, policy, ethics, organizational behavior in public, private and nonprofit institutions and their interactions. I feel strongly that XXXX is the best place to prepare myself to be a truly creative and visionary health care administrator who is able to elapse and inspire effectively, operating upon the firm foundation that I will attain in your distinguished program.

Implementing Talent Development Strategies Essay Example for Free

Implementing Talent Development Strategies EssayThe musical arrangements that are running the talent nurture programs may soon begin to find the high quality people who can be able to stretch and to motivate others in order to contact the highest levels of performance and productivity in the composition. This means that identifying the organizational education culture for the organization, people and top performers of the organization will revolve around some factors that lead to the development of an all round business professional. (Davis and Cutt, 1988).These include strategizing market and product or the services, instilling the manufacturing know how to the people, educating people on the distribution channels, financing strategies among others. educational issues cover many issues such as cash and expense flow, position of the firms cash flow. The people undergoing the talent development will implore getting instructions from skilled staff members to make solid deci sions and to visit the technical issues that are involved.Education programs will include development of self cognisance knowledge, effective problem solving and having good interpersonal communication. (Davis and Cutt, 1988). Training In the organizations if internal training programs are necessary for talent development, they should therefore be updated regularly. The charge should also review these programs to see that they are up to date.Again, working in the training program should be a temporary move by employees who are in need of improving their career skills by sharpening their technical as well as presentation skills. (Davis and Cutt, 1988). An organization that is implementing the talent implementation program is in all probability to receive problems and resistance. This is because young employees are often faced with many problems sometimes that may come immediately after they begin their careers. (Davis and Cutt, 1988).The first problem which involves world offered jobs that they are not trained in. secondly, the firm may face the problem of too much experience which is caused by narrowing down of the career. In addition, the organization may face the problem of using techniques of talent development in order to protect ones career especially towards the persons retirement. The above problems record that the development of new talents will stop if the firm fails to give appropriate conditions. This may be achieved through employee training. (Davis and Cutt, 1988).An OPD professional might help implement the strategies as well as address or resolve any problems or issues in the implementation of the talent program by making it clear to the organization the organizational requirements to maintain an organizations competitive edge and to ensure the survival of the organization. The professional may provide means of developing the organizations effectiveness. The professi9onal is required to understand the strategic goals of the organization and to translate this in to the day to day running of the organizational processes. (Davis and Cutt, 1988).

Adult Mental Health And Professional Practice Social Work Essay

Adult moral wellness And Professional Practice Social Work EssayWithin my assign manpowert I will stage my understanding of psychic healthfulness and the direct correlation to my professional practice. I will intelligibly define and critically evaluate ii of the dominant perspectives which be signifi bay windowt in kind wellness theory and practice, the bio medical exam and the companionable causation perspective. By explaining my practice with regards to the case scenario 1 Ahmed, I will brook my understanding of both perspectives, examining the advantages and disadvantages of each by considering how I might undertake and discernment and how I might address issues identified from the case scenario including the impact of discrimination and the importance of anti oppressive practice. I will evidence my knowledge and understanding of relevant issues including reflecting the perspective of the individual, by drawing up an intervention image, including identifying cl ear my understanding of the legal framework at bottom which I would practice.Issues of psychical wellness ar climaxed from a variety of disparate perspectives and using a variety of different terminologies. M all father the greatest confidence in scientific or biological approaches, whilst others prefer more than holistic or cordial approaches.The biomedical medical model of affable health has been dominant simply because the dominant profession is psychiatry. Psychiatrists are medically trained and thus tend to see the main pop the question behind their work as the diagnosis and intercession of complaint or disorder (Rogers and Pilgrim,2005).The simplistic view of cause and effect whilst beneficial if you take hold gloomy your leg or have diabetes, is not the same for mental illness. There are organic brain diseases or illnesses much(prenominal) as epilepsy and huntingdons chorea which whitethorn manifest in symptoms a lot associated with mental illness (Rethink,20 07) and therefore it is vital that the possibility of underlying physical causes are examined. The bio medical model utilises ideas of a unity underlying cause and therefore treatment of the cause will lead to a return to the pre existing state(Wade and Hallingan,2004).Another assumption is of a averageal existing state, and therefore an ability to measure evidence of ab regularity thus concluding with a diagnosis. Traditional bio medical models focus on the pathology of the illness so hotshotr than understanding the illness whether it is biological, neighborly or psychological.Criticism of the biomedical model is that it is a simplistic model in a very complex arena. Reductionist renderings of mental health cut down mental health issues to the smallest possible factors, simplistic that clearly flawed (Crossley,2006). One of the most predominant arguments is the involvement of environmental factors in pliant our behaviour. A persons environment can shape their behaviour and t his is a constant process. An individual may be born with certain genes just environmental factors such as society and a persons family can shape further behaviour (Nettleton, 2006). In reducing a concept to its comp angiotensin converting enzyment parts and simplest terms galore(postnominal) important aspects are over get worded. Individual factors are hard to explain under reductionism, because reductionist explanations generalise behaviour. Each individual is unique and responds differently. A reductionist explanation would be genetics, but the same behaviour in two wad could be caused by separate environmental and biological factors and therefore limiting the reductionist explanation (Crossley,2006). Reductionist explanations can be helpful, by reducing complicated concepts to their component parts but or so sentences this offers a simple solution to an other than more complicated problem. For example giving anti-depressants to someone who is depressed may seem like the mos t favourable solution, but this may overlook the genuine problem such as bereavement, financial or work problems.Iatrogenesis is another arena that is problematic for the bio medical model. Iatrogenisis is often associated with adverse effects resulting from medical interventions (Heller et al, 1996) but can and is viewed as the direct result of the intervention which impedes a persons recovery, and therefore could include psychiatry which is the predominant force in the bio medical model. Labelling with regards to mental health diagnosis is another criticism of the bio medical model. Scheff (1999) understands mental illness as a result of societal labelling. Simplistic put, society has views on what is socially norm and acceptable, any deviation from these norms, results in a label of mental illness.The social causation model suggests links between social disadvantage and mental health problems. These social disadvantages are prevelant in many areas education, health, affair, in come and social inclusion. poverty and social class have been determined as the two significant factors of social causation and the link to mental illness (Murali and Oyebode, 2004). Lynch et al (1997) found people living with financial difficulties on a long-term basis, were much more seeming to suffer from clinical depression than those who did not. Studies into mental health suggest there are stressors associated with low status and this creates an environment for increased risk of developing mental health problems. Payne(1999) in the 1999 PSE study provides evidence that people who live with various aspects of poverty, deprivation, unemployment and social exclusion are more likely to have mental health problems, although the relationship between poor mental health and these aspects are complex. I will examine employment in more detail.Research shows that slight than 40% of employers would consider employing a person with a mental health issue (Rethink, 2009).Consequently the prejudice and discrimination people face as a result of a mental health diagnosis presents problems in itself. In 2002/ 2003The Citizens Advice Bureau conducted research regarding social exclusion and mental health and their results were stark. 60% of people with mental health problems gave up work as a result of discrimination, prejudice and stigma. 61% per cent of male adults with a psychiatric disorder are in regular or part-time employment. Whereas the figure is 75% of men with no psychiatric disorder (Mind,2010b). If an individual has maintained a job or found employment then if they are affected by relapses this again impacts financially. With these statistics in mind it is clear to see that many who experience mental health issues will in addition be affected by economic hardship. Living on state benefits and sometimes less, as a result of an inflexible benefit system, can similarly result in a vicious circle of deprivation and poverty in all aspects of their lives, not on ly economic but in health, social activity and participation.The social causation model defined within the social model needs to be understood by practitioners as it acknowledges the experiences of individuals, as well as being the springboard for challenging the socio political environment which contributes to social problems, which in turn impact on an individuals mental health. This is fundamental for practitioners as one of the key roles of social workers is to challenge and champion social and political change (Horner,2006).According to Rogers and Pilgrim (2006) race, gender and age are all areas of disadvantage than can be investigated via social causation. This would support the findings of several studies which highlight the relationship between some of the identified areas and poor mental health. Examples to illustrate these links are, Irish men have collar times higher psychiatric admission rates than the general population (Fitzptrick, 2005) women are more likely to be treated for mental health problems than men (Mental Health Foundation, no date) and in research by Beecham et al (2008) it was identified that fewer than 10% of older people with clinical depression were referred to specialist mental health services compared with about 50% of younger adults. These stark differentials question the basis of these statistical differences and one explanation is social causation.In recent geezerhood there has been a shift in Mental Health order. Although the Mental Health enactment 1983 remains the primary legislation, there has been the addition of the Mental skill pretend 2005 which provides a legal framework to protect individuals who lack, or may lack capacity. The Mental Health Act 2007 amended the MHA 1983 and the MCA 2005. Along with these amendments to legislation there has also been a radical shift in policy documents from central Government. These policy shifts demonstrate the need to understand mental health in a more holistic context. Th e emphasis is shifting from purely medical perspectives with a recognition of how the social perspective has an impact on a persons mental health well being. A plethora of policies from government such as Tackling Health Inequalities (DOH, 2001) Working Together UK Action Plan on Social Inclusion(DWP, 2008) and Child Poverty Review(H.M. Treasury,2004) have been designed to tackle social inequalities such as health, income, work and education as well as a recognition for the need for more person centred approaches to delivering services. This does not detract from the clear message from legislation that risk and public safety are of paramount importance. The debates about care or discover and rights versus risk are ever present particularly with high profile cases such as Christopher Clunis and Michael Stone were pivotal in the changes to the Mental Health Act in 2007. The Mental Health Alliance (2006) maintain that legislative reforms which enables individuals to access services w ithin the mental health arena when they need it, as distant to imposing treatment, would be a more viable option and address the issue of risk in a more proactive way.The Mental Health Act 1983 still remains the overarching legislation regarding mental health in the England today and is the only piece of legislation that permits the detention of an individual before they have committed an offence and purely on the basis that they might pose a threat to themselves or others(Golightly,2008).The changes in 2007 allowed for approved mental health professionals rather than the traditional approved social workers. One could argue that if this is eradication of the social worker role and the move to further medicalise mental health (as the approved mental health professional can be health background rather than social care).The Mental Capacity Act 2005 might be viewed by some as contradicting the Mental Health Act 1983. After all a person suspected of having a mental illness may fulfil th e incision 3 test of capacity under the Act, and under the principles of the act is able to make unwise decisions, but the Act makes no stipulation regarding these unwise decisions. understandably committing a criminal offence is an unwise decision and a person committing the offence could clearly know and understand their action and face consequences laid pig under criminal justice legislation. Under the Mental Health Act a person is not required to have committed an offence to be detained, a suspicion of possible harm to self or others is enough to warrant a section 2 estimation for involuntary admission. This arena has been intercommunicate with and the Mental Capacity Act 2005 amendment to the Mental Health Act 1983 whereby an individual cannot refuse treatment if that treatment is deemed necessary under the measure ups of the Mental Health Act in that the MHA effectively overrides the MCA if the person is or deemed to be mentally ill. This is a contradiction regarding any other forms of medical treatment for a physical condition such as treatment for cancer or radical surgery(if a person meets the capacity assessment criteria), a person can refuse treatment for any other physical health condition but not for mental illness as a person can be detained to authoritative treat.New Horizons is a cross government programme which was launched in 2000 which identified not only the need of improved mental health services but the recognition the importance of maintaining good mental health and well being for everyone and covers childhood to old age (DOH,2009). It clearly recognises the impact of social factors aiming to address social inequalities identifying health, education and employment as important factors in an individuals well being and the impact on mental health.The Mental Health Act 1983 is the primary legislation which covers the assessment, detention, treatment and rights of people with a mental health condition. Following the psychiatric model t he practitioner would need to make an assessment of Ahmeds functioning identify the signs and symptoms which he is exhibiting for Ahmed these would be his day to day functioning he has rent arrears, utilities have been cut off personal care evidence suggests he lives on takeaways social functioning he is a loner and he goes into the town centre shouting apparently aggressive thoughts he appears to be having delusions that his mother is not his historical mother, and possibly hallucinations evidenced with him shouting, but not directed at anyone. The psychiatric model uses judgements of normal which are not objective, but on agreed standards of normal within a heathen and social context (Esyenck,1994 and Giddens,1997). But the question has to be who is the predominant force in that society and how does this impact on individuals from differing cultural backgrounds in the teat of normality. Although the case study has not specified Ahmeds cultural background it is an area whic h needs delinquent consideration.There are discussions regarding psychiatry as being colour blind and culture blind. Fernando(2002) examines the rationale for these concepts in relation to hearing voices, and explains perhaps cultural stereotypes which do not consider multi cultural dimensions are responsible. Fernando(2002) draws upon the studies relating to high proportions of British African Caribbean men being labelled as aggressive, perhaps due to the appearance or interpretation of symptoms leading others to define the symptoms within the mental health arena (Nazroo and King, 2002). Fernando (2002) expounds further by explaining this could also be related to society norms. The norms are dictated by the predominant forces within society. When individuals do not conform to social norms they are subject to sanctions in order to ensure conformity this is evident within the legal justice system a person commits a crime a punishment a fine or community of interests service order o r prison sentence is served. The parallels for mental health could be seen that if a person does not conform then admission to infirmary, intervention and treatment may be viewed as the sanctions to deviating from those perceived norms. luck management is a highly politicised area with the primary objective in the political arena to manage risk, whilst improved outcomes for individuals appears to be in secondary (Holloway,1996). Holloway(1996) goes on to say in order to understand and therefore manage the risk then as a practitioner you need a very fine understanding of the individual. Good practice regarding risk management is about a clear animal foot for the decision and an expectation for the proposed outcome, as well as provision for change if the intended outcome does not occur (Petch,2001).A discussion with Ahmed regarding voluntary admission for assessment and treatment would be deemed appropriate given the assessment. The Mental Health Act 1983 clearly states in sectio n 131 that voluntary admission should always be used if the person is willing. Should Ahmed resist treatment and admission to hospital then it would be necessary to address the need for detention under section 2 of the act. This provision is made with the agreement of 2 doctors ideally one who knows Ahmed perhaps his GP, and an approved mental health professional (AMHP). Under the Mental Health Act 1983 section 2 allows involuntary admission to hospital for assessment and treatment. Under section 2 Ahmed does not have the right to refuse treatment. Once Ahmed is admitted to hospital then assessment for a diagnosis would be paramount.The two diagnostic and classification tools used in modern psychiatry are the DSM IV codes and ICD 10 codes (Bolton, 2008). Although there are differences in these codes, the premise for these codes and outcomes are the same. These codes map out the bio medical model, the reduction of the illness to signs and symptoms to which a head-shrinker can deter mine a diagnosis and treatment based on that diagnosis. Whilst this may be useful for organic brain disorders for the majority of mental health problems where there is no definitive biological condition, the diagnosis simply reflects the individuals reflections on how they think and feel. The treatment plan would be developed based on the assessment outcome (diagnosis). Often treatment ranges are limited with a high emphasis on dose interventions, where the primary objective is to stabilise Ahmeds mental health condition in an effort to return him to a functional state. This medicalised response and the use of drugs could be viewed as a means of social control (Rogers and Pilgrim, 2005).By drawing on the theory of social causation this would enable me to support Ahmed to analyse the issues he is confront in a non judgemental way. Oppression and discrimination is observed in the lives of people from marginalised groups (Dalrymple and Burke,1995) and as practitioners we have an obli gation to challenge discrimination and oppression. Personal experiences are clearly associated with social, cultural, political and economic divisions and therefore understanding these areas in context to the individual is vital in understanding and challenging the oppression and discrimination they may clangoring (Adams et al, 2002). The stigma attached from having mental health problems cannot be underestimated. Research by the Department of Health Attitudes to Mental Illness in 2007 showed that whilst many of the negative pre conceived ideas and beliefs held by society about people with a mental health illness were diminishing, but the changes year on year were not significant. This may be due to education and understanding of mental illness and the understanding of the effects of discrimination and stigma. The Time to Change Programme (2008) is by its own admission, nationally and globally the most ambitious plan to stamp out discrimination faced by people with mental illness. Stigma poses a threat to all aspects of an individuals life if diagnosed with a mental illness, they contribute to social isolation, distress and difficulties gaining and maintaining employment. In a survey by Crisp and Gelder (2000) discovered there were consistent themes of perceptions of people who had a mental illness. Some views were common amongst the several diagnoses, namely they were difficult to talk to and they were unpredictable to assumptions of being dangerous.Completing a Community Care Assessment in ossification with the NHS and Community Care Act 1990 would be necessary in order to identify Ahmeds needs and how those needs would be best provided for. The assessment would include discipline from Ahmed as well as significant others where applicable and determine need on a short and / or long term basis (Sharkey, 2007). The assessment does not detract from the need of some immediate intervention, to work directly with Ahmed to address some of the immediate issues su ch as his rent arrears (which would right off bring low the threat of eviction) and getting his utility services back in place. Acute and crisis services and intervention were designed to offer support in a less restrictive and stigmatising way than traditional formal of intervention such as compulsory admission (Golightly,2008).Crisis intervention is a model of intervention which ideally prevents the topographic point from deteriorating further and fixs on existing resources and strengths in order to improve the situation (Ferguson,2008). This could assist Ahmeds mental health and well being as well as his environment and other social factors i.e. relationship with mum and neighbours. The intervention allows a recent Cochrane review found that rest home care crisis treatment, coupled with an ongoing home care package, was a viable alternative to hospital admission for crisis intervention for people with serious mental illnesses and probably more cost effective (Joy at al, 2006 ).Working directly with Ahmed using a task centred approach would be ideal as it is a very practical based approach. The work is time limited, structured and problem focused(Parker and Bradley, 2007, p.93). An example for Ahmed might beOutcome Pay off rent arrears so no longer in debt.Rationale this would immediately reduce the risk of eviction as well as encouraging Ahmed to take responsibility for his situation in a supportive and empowering way.Steps scoff a payment plan with Ahmed that is manageable within current budget (10 every 2 weeks)Once plan agreed Ahmed to visit accommodate provider to agree payment plan and request an update every month on arrears.Pick up benefits every 2 weeks, on a Tuesday, and immediately pay 2 weeks rent at paypoint in post offices along with agreed 10 arrears and obtain receipt.For the purpose of this assignment I have listed some of the actions which could be identified in order to support Ahmed.Pay off rent arrears.Benefits assessment to ensure Ahmed is claiming his benefit entitlement.Tenancy support worker in order to support with tenancy related issues such as rent, utilities and maintaining a tenancy agreement.Support worker to assist with increasing his contact and reduce social isolation. This could be simply going out for a coffee or some other activity which Ahmed identified.To explore if Ahmed has concerns regarding psychiatry, and his reluctance to meet with the psychiatrist this is vital it may simply be he forgot about the appointment or further issues regarding his concept of psychiatry.To work with Ahmed to explore his thoughts regarding his mother and assess the foundation for his thoughts that she is not his mother.To gain understanding on any other significant relationships in the past (there is mention in the case study of children) and the possibility of re-connection with his children and wider family connections.Re-connection with community whether this would be utilising self help groups, classes w hich may hold a particular interest or active engagement in community/ voluntary projects to build self esteem and confidence and develop a sense of purpose and engagement.Explore training / employment optionsTo support Ahmed to begin a life reputation book or consider psychology intervention. To offer support to examine Ahmeds current strategies of coping recognising his abilities through the strength model and supporting him to identify any patterns and how to deal with them.To develop a contract for future work in order to be clear of professional boundaries and expectations from both parties and how intervention might look in the future should this be required.Should the circumstances not improve or continue to deteriorate then there is a possibility of seeking hospital admission either, voluntarily or in accordance with the Mental Health Act 1983.More people than ever are being detained in hospital under compulsory orders. Admissions to hospital under the Mental Health Act 19 83 have risen by nearly 30% in the past ex in England. According to a report from three national mental health charities, Rethink, Sane and the Zito Trust, this figure is a worrying reflection of the care for people with mental illness (Kmietowicz, 2004). A sobering thought for any professional. As a practitioner I have learnt that causes of mental health issues are often complex and can involve a combination of biological vulnerability, environmental factors, social stressors, social networks, supports and relationships, psychological orientations and learned behaviour. Coppock and Hopton (2000) state each perspective on mental distress and therapeutic intervention has its own internal logic(p.175) and stress the importance of recognising the alternatives, otherwise, practitioners are in danger of becoming a rigid in their practice, not work in a person centred way. Having a critical perspective and understanding of the variety of theoretical perspectives and approaches regarding mental health is beneficial. It is clear that these perspectives whether biomedical or social have added to our understanding of mental health. The relative merits of the various perspectives are constantly argued, most characteristically by pointing out the limitations of the differing perspectives. Such critiques can be productive but are only a step in a larger task to develop broader perspectives that can be productively incorporate the different useful insights reached from each of a variety of different points of view.A person centred approach to mental health would seem the optimum approach when examining mental health issues. It recognises the uniqueness of individuals and accounts for all the possible variables and their interactions from social causation, stress vulnerability, gender etc. which would enable practitioners to examine issues within a broader holistic context, preferably of rigid simplistic processes of bio medical model (Freeth, 2007).Word Count 4007

Eulers Totient Theorem

Eulers Totient TheoremSummary Euler Totient theorem is a generalized form of Fermats Little supposition. As such, it solely depends on Fermats Little Theorem as indicated in Eulers correction in 1763 and, later in 1883, the theorem was named after him by J. J. Sylvester. According to Sylvester, the theorem is basically about the alteration in similarity. The term Totient was derived from Quotient, hence, the function deals with division, just in a unique way. In this manner, The Eulers Totient function for any integer (n) disregard be demarcated, as the figure of positive integers is not greater than and co-prime to n.a(n) = 1 (mod n) found on Leonhard Eulers contributions toward the development of this theorem, the theory was named after him despite the fact that it was a generalization of Fermats Little Theory in which n is identified to be prime. found on this fact, some scholarly source refers to this theorem as the Fermats-Euler theorem of Eulers generalization.Introductio nI starting time developed an interest in Euler when I was completing a tender crossword the concealed message read Euler was the master of the crossword. When I first saw the inclusion of the name Euler on the list of prompt words, I had no option but to just go for it. Euler was a famous mathematician in the eighteenth century, who was acknowledged for his contribution in the math discipline, as he was trus bothrthy for proving numerous problems and conjectures. Taking the number theory as an example, Euler successively played a vital role in proving the two-squ are theorem as well as the Fermats small(a) theorem (Griffiths and Peter 81). His contribution also paved the way to proving the four-square theorem. Therefore, in this course project, I am going to focus on his theory, which is not known to umpteen it is a generalization of Fermats little theorem that is commonly known as Eulers theorem.TheoremEulers Totient theorem holds that if a and n are coprime positive integers , then since n is a Eulers Totient function.Eulers Totient solveEulers Totient Function (n) is the count of positive integers that are less that n and relatively prime to n. For instance, 10 is 4, since there are four integers, which are less than 10 and are relatively prime to 10 1, 3, 7, 9. Consequently, 11 is 10, since there 11 prime numbers which are less than 10 and are relatively prime to 10. The similar way, 6 is 2 as 1 and 5 are relatively prime to 6, but 2, 3, and 4 are not.The spare-time activity table represents the totients of numbers up to twenty.Nn21324254627684961041110124131214615816817161861918208Some of these examples seek to prove Eulers totient theorem.Let n = 10 and a = 3. In this case, 10 and 3 are co-prime i.e. relatively prime. Using the provided table, it is clear that 10 = 4. Then this relation can also be represented as follows34 = 81 1 (mode 10). Conversely, if n = 15 and a = 2, it is clear that 28 = 256 1 (mod 15).Fermats Little TheoryAccording to Liskov (221), Eulers Totient theorem is a simplification of Fermats little theorem and works with every n that are relatively prime to a. Fermats little theorem only works for a and p that are relatively prime.a p-1 1 (mod p)ora p a (mod p)where p itself is prime.It is, therefore, clear that this equation fits in the Eulers Totient theorem for every prime p, as indicated in p, where p is a prime and is given by p-1.Therefore, to prove Eulers theorem, it is vital to first prove Fermats little theorem.Proof to Fermats Little TheoremAs earlier indicated, the Fermats little theorem can be expressed as followsap a (mod p)taking two numbers a and p, that are relatively prime, where p is also prime.The set of a a, 2a, 3a, 4a, 5a(p-1)a(i) dig another set of number 1, 2, 3, 4, 5.(p-1a)(ii)If one decides to take the modulus for p, each segment of the set (i) will be appropriate to an item in the randomness set (ii). Therefore, there will be one on one correspondence between the two set s. This can be proven as lemma 1.Consequently, if one decides to take the product of the first set, that is a x 2a x 3a x 4a x 5a x . (p-1)a as well as the product of the import set as 1 x 2 x 3 x 4 x 5 (p-1). It is clear that both of these sets are congruous to one another that is, each component part in the first set matches another element in the second set (Liskov 221).Therefore, the two sets can be represented as followsa x 2a x 3a x 4a x 5a x . (p-1)a 1 x 2 x 3 x 4 x 5 (p-1) (mode p).If one takes out the factor a p-1 from the left-hand side (L.H.S), the resultant equation will be Ap-1 a x 2a x 3a x 4a x 5a x . (p-1)a 1 x 2 x 3 x 4 x 5 (p-1) (mode p).If the same equation is divided up by 1 x 2 x 3 x 4 x 5 (p-1) when p is prime, one will obtaina p a (mod p)ora p-1 1 (mod p)It should be clear that each element in the first set should correspond to another element in the second set (elements of the set are congruent). Even though this is not obvious at the first step, it can still be prove through trio logical steps as followsEach element in the first set should be congruent to one element in the second set this implies that none of the elements will be congruent to 0, as pand a are relatively prime.No two numbers in the first set can be labeled as ba or ca. If this is done, some elements in the first set can be the same as those in the second set. This would imply that two numbers are congruent to each other i.e. ba ca (mod p), which would mean that b c (mod p) which is not true mathematically, since both the element are divergent and less than p.An element in the first set can not be congruent to two numbers in the second set, since a number can only be congruent to numbers that differ by multiple of p.Through these three rules, one can prove Fermats Little Theorem.Proof of Eulers Totient TheoremSince the Fermats little theorem is a special form of Eulers Totient theorem, it follows that the two proofs provided earlier in this exploration a re similar, but slight adjustments need to be made to Fermats little theorem to justify Eulers Totient theorem (Krizek 97). This can be done by using the equationa n 1 (mod n)where the two numbers, a and n, are relatively prime, with the set of figures N, which are relatively prime to n 1, n1. n2.n n . This set is likely to drive home n element, which is defined by the number of the relatively prime number to n. In the same way, in the second set aN, each and every element is a product of a as well as an element of N a, an1, an2, an3ann.Each element of the set aN must be congruent to another element in the set N (mode n) as noted by the earlier three rules. Therefore, each element of the two sets will be congruent to each other (Giblin 111).In this scenario case, it can be said thata x an1 x an2 x an3 x . an n a x n1 x n2 x n3 x .n n (mod n).By factoring out a and an from the left-hand side, one can obtain the following equationa n 1 x n1 x n2 x n3 x .n n 1 x n1 x n2 x n3 x .n n (mod n)If this obtained equation is divided by 1 x n1 x n2 x n3 x .n n from both sides, all the elements in the two sets will be relatively prime. The obtained equation will be as followsa n 1 (mod n)Application of the Eulers TheoremUnlike other Eulers works in the number theory like the proof for the two-square theorem and the four-square theorem, the Eulers totient theorem has real applications across the globe. The Eulers totient theorem and Fermats little theorem are commonly used in decryption and encryption of data, especially in the RSA encryption systems, which protection resolves around big prime numbers (Wardlaw 97).ConclusionIn summary, this theorem may not be Eulers most well-designed piece of mathematics my favorite theorem is the two-square theorem by unnumbered descent. Despite this, the theorem seems to be a crucial and important piece of work, especially for that time. The number theory is still regarded as the most useful theory in mathematics nowadays. Thr ough this proof, I have had the opportunity to connect some of the work I have earlier done in discrete mathematics as well as sets relation and group options. Indeed, these two options seem to be among the purest sections of mathematics that I have ever studied in mathematics. However, this exploration has enabled me to explore the relationship between Eulers totient theorem and Fermats little theorem. I have also applied knowledge from one discipline to the other which has broadened my view of mathematics.Works CitedGiblin, P J. Primes, and Programming An Introduction to Number Theory with Computing. Cambridge UP, 1993. Print.Griffiths, H B, and Peter J. Hilton. A Comprehensive Textbook of Classical Mathematics A Contemporary Interpretation. London avant-garde Nostrand Reinhold Co, 1970. Print.Krizek, M., et al. 17 Lectures on Fermat Numbers From Number Theory to Geometry. Springer, 2001. Print.Liskov, Moses. Fermats Little Theorem. Encyclopedia of Cryptography and Security, pp. 221-221.Wardlaw, William P. Eulers Theorem for Polynomials. Ft. Belvoir Defense Technical Information Center, 1990. Print.

Just Mercy by Bryan Stevenson Review

Just Mercy by Bryan Stevenson check outBeacon Lights Book ReviewJust Mercy by Bryan StevensonEvery once in a while a hold up comes along that makes you think and even changes the way you meet previously looked upon a subject. Just Mercy is such a nurse. This is the true story of a young lawyers fight for arbiter on the part of more on death row. The author, Bryan Stevenson battles racial injustice and represents many poor, non-white, mentally ill and young offenders. Their stories are interspersed throughout the book as he recounts his defense of Walter McMillian, a black man on death row. The memoir reads like a legal thriller, juxtaposing his many triumphs and failures.Bryan Stevenson grew up poor in Delaware. His great-grandparents had been slaves in Virginia and this legacy of thrall influenced the way his grandparents raised their children and grandchildren. They particularly emphasized the importance of faith and education. Stevensons faith was cultivated in the Africa n Methodist Episcopal Church where he play the piano and sang in the choir. Stevenson attended Eastern College, a Christian institution outside Philadelphia, and then Harvard Law School. His focus to defend the poor began during college when he took an intensive class on race and poverty litigation. He was required to spend a month with an organization doing social justice work. They sent him to gallium to work with the Southern Prisoners Defense Committee where his first case required him to meet with a condemned man on death row.In the late 1980s, Stevensons legal firm first took up the cause of Walter McMillian, who was wrongfully convicted and sentenced to death for the murder of a white woman. The states case had many inconsistencies. They manufactured stories from witnesses who said they were with Walter when he perpetrate the crime and disregarded accounts from many eyewitnesses who said they were with Walter at a church fundraiser. The legal system was determined to find soulfulness to convict for this murder and discrete Walter would be prosecuted because of his affair with a prominent white woman (a crime during this time period). The exposition of this case opened my eyes to the unfortunate fact that since prosecutors and legal philosophy have legal immunity they can do considerable harm to innocent citizens when they are on the hunt for justice.A large portion of this book deals with the cases of poor black children sentenced to adult prisons and serving life sentences. Stevenson tells these stories very convincingly and sympathetically. He challenges their sentences because he says they are juveniles and his firm recognized the incongruity of not allowing children to smoke, drink, pose because of their lack of maturity and judgement while simultaneously treating some of the most at-risk, neglected, and impaired children exactly the same as full-grown adults in the criminal justice system. Circumstances that would bring a youth to be put in a situation where he felt his only option was to kill someone because he is not aware of his other options, should be recognized upon sentencing. One example is a young boy who shoots his mothers abuser. Yes, punishment needs to occur, but placing a young child in an adult prison is not always appropriate justice.Stevenson also defends many poor white women who have been convicted of the murder of their col crunchator or stillborn child. He tells the stories of pregnant women who are too poor to see a doctor or go to the hospital, and then unfortunately during labor deliver a stillborn child. These women are then arrested and charged with capital murder which is punishable by the death penalty.Not all of the characters in Stevensons book are sympathetic and his defense of them does not always seem to be justified. As a defense lawyer his heart may sometimes come in in the way of seeing their crimes objectively. In particular, he unsuccessfully defends a prisoner who commits the hein ous act of killing a child with a die meant for a neighbor.While justice has been denied for a large portion those in the prison system, the authors faith in both the power of redemption and justice, underlines his continued wish in the possibility of change. The true measure of our character, Stevenson writes, is how we treat the poor, the disfavored, the accused, the incarcerated, and the condemned we all need mercy, we all need justice, and perhaps we all need some measure of gratuitous grace.

Composting and the Benefits and Limitations of its Use as Soil Amendmen

Composting and the Benefits and Limitations of its Use as Soil Amendment Composting is widely-known as an environmentally sustainable method of recycling food scraps and garden/yard clippings. jibe to the United States Environment Protection Agencys (EPA) 1994 report entitled, devour Prevention, Recycling, and Composting, food discards constitute approximately 8 percent of municipal solid waste generated nationwide. A character study observed in San Francisco, California, reported that an estimated 31 percent of residential wastes and 19 percent of commercial waste generated is food waste. Composting is a viable behave to the food-waste problem. Composting not only reduces the count of waste, buy also contains chemical properties and other rich elements that benefit the soils quality, allowing farmers to use it as soil amendment. The following research bequeath examine the process of composting and its different variables in order to investigate its positive and negative affect s on the soil. Composting refers to the controlled decomposing of organic matter by microorganisms, mainly bacteria and fungi, that dishonour organic matter down into readily available nutrients. In truth, it relies on little to no human intervention which makes it fairly easy. There are literally dozens of different technologies that are currently used to create compost (Stickelberger, 1975, p.188). Professor David Bice of Carleton College utilizes a method known as vermicomposting. Dictated by the amount of space (he is limited to in his apartment), Professor Bice places his food scraps in a bucket where red-colored worms digest and convert the bio-waste into a fertilizer product. Therefore, selection of a system depends largely on pragmatic factors.... ...lized form of organic matter that improves the physical, chemical, and biological properties of soil.Works CitedStickelberger, D, 1975, Survery of city refuse composting. In Organic Materials and Fertilizers Rome, Italy, FAO S oils, Bulletin 27.Kapage, F.S.C.P, 1974, tropical Soils Classification, Fertility, and Management New York, St. Martin Press, 201p.Broadbent, F.E., 1987, Organic Matter . Minnesota Compost and Co-Compost Research Project, In USDA Yearbook of Agriculture U.S. Government Printing Office, Washington, D.C.Government Document, February 1994, Waste Prevention, Recycling, and Composting Options Lessons From 30 Communities U.S. Environmental Protection Agency, Washington D.C. 47p.Government Document, May 1994, Composting Yard Trimmings and Municipal Solid Waste U.S. Environmental Protection Agency, Washington D.C. 56-57p.

journalism Essay -- essays research papers

In my twenty years and some months existence in this world, Ive been fortunate enough to personify a secured disembodied spirit. I believe nutrient and shelter are two of the most important essentials in life, and Ive never had to worry about food not being on the table or if I had a place to sleep at night which is why I consider myself to vex a secure life. Volunteering at Simpson Housing helped me realize many things in life, and also made me wonder why some people are so fortunate in life while others struggle to survive in this world.Prior to Simpson Housing, I was vaguely familiar with the issue of homelessness. I only knew the al-Qaida of it, but never fully understood it. There are a lot of misconceptions and stereotypes about the homeless and Ive learned that you cant really judge until youve experienced it. You hear a lot of mischievously things about homeless people- theyre lazy, drug addicts, bums, freeloaders, etc Its easy to focus on the bad because you remember the bad more than the good. It must be hard for homeless people because they are pre-judged without even getting to be known. They get rejected in advance getting a chance. I will admit that I did believe some of the misconceptions of homeless people because I had atomic number 53 negative experience. When I was younger, my family and I utilize to go eat at Rainbow, a Chinese restaurant, in Minneapolis. We always went at night and on the way home, there was a disrobe where all the homeless people would camp out. I couldnt believe people had to live wish that. Ive had several encounters with homeless people where theyd come up to me asking for money until this once incident. I was with my dad and this lady and her son approached us asking for some help. I had always prone a dollar or two before, but I saw she had a son so I convinced my dad to spend them atomic number 23 dollars. They seemed to be really gracious of our donation and we felt really good about helping them. Fi ve minutes later, we saw the lady and her son turn on away in a brand new Toyota Camry. My dad and I were completely stunned. I was so angry. There are so many others that couldve used the money we had given. The lady took advantage of us, and completely had no morals whatsoever. However, that did not stop me from wanting to give help to the needy. Instead of giving them money, I give them food. I know its not exactly that same, but I still do feel that I am helping them. ... ... but I certain some people have no control over it and that really saddens me. My heart goes out to homeless children because they are so young. They have so much more to worry about when they should only be focusing on having fun as a child and getting their education. However quite of being able to focus on school, they have to focus on surviving. Life isnt fair, but then again what is in life? Situations like homelessness is not something many can touch base with, but it is something we can all take p art in to help reduce it. No one deserves to live a life where nothing at all is certain. With so many mistaken beliefs on homeless people, those who are fortunate in life need to realize that those who are homeless are strong in heart. They dont give up and they keep living each solar day in hope for a better tomorrow. Ive learned through volunteering at Simpson Housing is that you have to take the good with the bad and learn from it all. get dressedt let the bad hold you down and you should embrace it and turn it into something positive. Whatever may come your way, you should appreciate it because it only helps you grow into the person you are to become.