Mayo Clinic free essay sample

Strategic planning and evaluation is extremely complex for every organization. The Mayo Clinic is a not-for-profit medical organization that services three metropolitan areas: Scottsdale/Phoenix Arizona, Jacksonville Florida and Rochester Minnesota. It’s known for specialization in hard-to-treat diseases, and also known for their innovative and effective treatments for diseases that have gone undiagnosed or under-treated in the same patients with other doctors. Health care is the single most important and essential service that touches the lives of everyone worldwide today. The competition is fierce, and that is why the Mayo Clinic’s founders and co-founders have integrated strategic objectives that will shape and guide the direction of their future as they know this is crucial to the productivity and the longevity of their organization. Dr. William Worrall Mayo (a pioneering physician) established the very first Mayo Clinic in Rochester, Minnesota in 1863. Dr. Mayo had a zeal for medicine and considered practicing medicine to fall under the guidelines of what he felt to be a family tradition. We will write a custom essay sample on Mayo Clinic or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page In 1883 is son Doctor William James Mayo joined him and in 1888 is other son Doctor Charles Horace Mayo followed. Through watching their father practice medicine for years, is what too gave them a zeal for medicine and venture out and follow into his footsteps and practice medicine. It was in 1883 that a tornado swept through Rochester leaving in its wake, both fatalities and injuries. This unfortunate experience is what inspired Mother Alfred Moes, a nun, of the â€Å"Sisters of Saint Francis† teaching order, to request Dr. Mayo and sons alongside them, to build the first general hospital in Southeastern Minnesota. This was the world’s first private integrated group practice. â€Å"The 27-bed Saint Mary’s Hospital opened in 1889 as a result of this partnership. (Medical Foundation of Education and Research copyright 2001-2011). http://www. mayoclinic. org/careerawareness/mi-history. html It was in 1919, â€Å"that the Mayo brothers dissolved their partnership and turned the clinics name and assets, including the bulk of their life savings, to a private, not-for-profit, ch aritable organization now known as Mayo Foundation. † (Medical Foundation of Education and Research copyright 2001-2011). Dr. William W. Mayo felt deeply that they should give back to those individuals that gave to them, that started the organization; and that could only be accomplished through medical education. From this point on, the Mayo’s, their associates and all other potential Mayo Clinic physicians; could not receive a salary or profit personally from any proceeds established from the practice. Any income gained beyond this point from operating expenses, must be contributed to education, patient care and/or research. A board of governors and a committee system was established by the brothers to â€Å"present effective oversight of many aspects of Mayo life, thereby reinforcing the cooperative spirit of the founders. (Medical Foundation of Education and Research copyright 2001-2011). http://www. mayoclinic. rg/careerawareness/mi-history. html It was in the late 1980’s that the Mayo Clinic took the initial step to expand the organization beyond the state of Minnesota. In 1986 a clinic was established and launched in Jacksonville, Florida and again in 1987 in Scottsdale, Arizona. It was not until 1998 the Mayo Clinic reached their milestone by opening the Mayo Clinic Hosp ital located in Phoenix, Arizona. This two hundred bed facility was designed to incorporate technology into all aspects of patient care and experiences which required extensive and costly investments of information technology systems. The organization realized that â€Å"Technology was no longer a thing of the past that was once referred to as a â€Å"back of the office support enabler,† (Medical Foundation of Education and Research copyright 2001-2011). and that they had to strategically devise a plan to secure the future of the organization. http://www. mayoclinic. org/careerawareness/mi-history. html As the organization’s strategic appetite broaden for technology, their initiative to broaden their strategic direction did also because their completion deadline in late 2000 was fast approaching. Several Phoenix metropolitan area Mayo clinics were either consolidating or closing their practices. Senior leaders were very disturbed by this because this marked a change of the organizations strategic direction from the first 10 years of operations prior to the opening of the Mayo Clinic Hospital. The Chief Information Officer (CIO) partnered up with the physician chair of the IT oversight committee and conducted a situational analysis of the organizations components and map out a five year diagram of all the related human factors, physical factors, social factors, and economic factors that has come into lay as they attempted to fulfill the organizational goals and strategies; and modify them as they saw fit. The situational analysis consisted of evaluating the organizations management teams existing strategies, guidelines and procedures to ensure authentic comprehension of the organization’s objectives and that they are or were implemented appropriately. This analysis help ed the organization to identify and eliminate weak points within the preceding system. Together the CIO and the physician chair of the IT oversight committee developed a plan parallel to that of the division’s information system. Kranmer, Frey, Kirby, Lenko and Vrabel (2005) state that â€Å"The objectives of this team were to create a similar strategic roadmap that would not only create a technology vision and direction for the Arizona operations; it would clearly illustrate the importance of technology in supporting the broader organizational strategic plan. † Edell, Curtright and Stolp-Smith (2000) stated that â€Å"Managing and measuring performance become exceedingly complex as healthcare institutions evolve into integrated health systems comprised of hospitals, outpatient clinics and surgery centers, nursing homes, and home health services. They further state that, â€Å"Leaders of integrated health systems need to develop a methodology and system that align organizational strategies with performance measurement and management. To meet this end, multiple healthcare organizations embrace the performance-indicators reporting system known as a balanced scorecard or a dashboard report. This discrete set of macro level indicators gives senior management a fast but comprehensive glimpse of the organizations performance in meeting its quality, operational and financial goals. The leadership of outpatient operations for Mayo Clinic in Rochester, Minnesota, built on this concept by creating a performance management and measurement system that monitors and reports how well the organization achieves its performance goals. † The â€Å"scorecard† concept is how the Mayo Clinic in Rochester, Minnesota leadership management team monitored and reported how well the organization completed their performance goals. The Mayo Clinic’s vision, primary value, core principles, and day-to-day operations key performance indicators were monitored on a weekly, monthly or quarterly basis. January 2001 the leadership team found themselves in a crisis because the capital investment of the proceeding three years was focused on the hospital opening and the remediation of Y2K concerns. It was determined that many of (IT)’s customers had forgone using their more strategic information system in deference to the technological and organizational imperatives of the time. This caused for a demand for new systems and exceeds the available capital budget by more than 300 percent. Edell, Curtright and Stolp-Smith (2000) state that â€Å"Healthcare systems face strong pressures to improve clinical quality, enhance service, expand access, and reduce costs. Competitive pressures in the marketplace require healthcare systems to measure, monitor, and report system performance to maintain and expand a market base. Thus, those healthcare systems that are capable of dearly articulating and demonstrating the value of services provided enjoy a competitive advantage. They further state â€Å"As healthcare institutions evolve into integrated health systems comprising hospitals, outpatient clinics and surgery centers, nursing homes, and home health services, the task of measuring performance increases in complexity. Leaders of these institutions need to develop a methodology and system that align organizational strategies and core principles with performance measurement and management indicators. † â€Å"In the true business management sense, strategy is distingui shed by several key dimensions. (Moseley III, 2009). According to Moseley III (2009), â€Å"it may be easier to understand the concept of â€Å"strategic† planning by contrasting it with two other forms of planning – â€Å"operational† and† tactical. † As these operations combine, they will â€Å"merge into a seamless continuum of forward-looking activity intended to ensure the survival and growth of the organization (Moseley III, 2009). At this point, the key dimensions of the organizational strategy will become directly linked to the strategic mindset of the organization. It is my belief that key dimensions of the organization are relevant to having a strategic mindset because it is ultimately planned to over exceed the organizational goals which requires engaging and performing activities different of that of the competition. In order for your organization to stand out from the competition, communication must be persuasive and artistic. Organizational goals are set to â€Å"do something that is not being done at that very instance. † (Moseley III, 2009, p. 3). The strategic and planning processes derived by this rganization have transitioned from being irregular reactive exercises to becoming planned, judicious and practical components of the overall IT management plan. A major benefit derived from this process is the ability to demonstrate the strategic alignment of IT initiatives and projections. Plans are ineffectual if they are not carried out accordingly. In conclusion, the Mayo Clinic one of the most accredited quality standard organizat ions known today. They have provided quality health care for more than six million people since it was founded in 1883.

Chromatography and Solvents Essay Example

Chromatography and Solvents Essay Example Chromatography and Solvents Paper Chromatography and Solvents Paper Chromatography is a method of separating compounds and mixtures so that they can be identified and analyzed. The word chromatography means color writing. There are many kinds of chromatography such as the thin layer chromatography, Partition chromatography, Column chromatography, and Paper chromatography. Chromatography is important in the analysis of processes and materials such as environmental contamination, food, drugs, blood, petroleum products, and radioactive fission products. It has many uses in the rapidly evolving biotechnology industry. The chromatography sorbents help purify problems in the production of drugs. Equipment used for chromatography is essential for chemical laboratories today. With these devices, scientists can identify chemical compounds in complex mixtures such as smog, cigar smoke, and even coffee aroma. Chromatography could be used to show how much of one substance there is in a mixture. Solvents are used to separate mixtures. Some solvents that we see every day are nail polish remover, water, rubbing alcohol, and vinegar. In chromatography, the components go through 2 phases called the mobile phase and stationary phase. The stationary phase may be solid, liquid, liquid supported on a solid, or gel. They may be packed in a column, spread as a layer, or distributed as a film. The mobile phase may be gaseous or liquid. In paper chromatography, the filter paper is the stationary phase and the solvent is the mobile phase. The separation is achieved when the solutes in the mobile phase and stationary phase results in different retention lines for the different chemical compounds. The chromatographic system consists of 3 components which are solvents, soluble, and sorbents. Solvents are used to dissolve solutes to form a solution. Not all solvents have to be liquid and not all solutes have to be solid. Higher temperatures of the solvent usually increase the dissolving of the solute. One exception to this is that the solubility of gas in liquid usually decreases with temperature. If the components of this system react chemically with each other than the inert substance dispersing the reactants is the inert solvent. Chemical reactions will also dissolve more solutes. Water is an excellent solvent for ionic substances. It breaks down the ionic crystals and separates the component ions form each other. The water molecules form shells around the ions and keep them far apart. Covalently bonded molecules like organic compounds don’t dissolve well in water. They dissolve well in organic solvents. Some alcohols have hydrogen bonds so they dissolve in water. Rubbing Alcohol is useful as an antifreeze compound and solvent. It contains methanol which is produced from natural gases. Methanol is made from mixing hydrogen and carbon monoxide at high temperatures and pressure. The boiling point increases due to hydrogen bonding that occurs between hydroxyl groups. Acetone is a colorless, flammable, explosive liquid that contains a characteristic odor that can be detected at very low concentrations. 2008). (Chemical compound: CH3COCH3) Used for making nail polish remover, model airplane, and glue. It belongs to a family known as ketones. Ketones are a compound with carbonyl group (carbon and oxygen bonded together) attached to 2 carbon atoms, made of two propane molecules. Acetone may be present in the human body but only in small concentrations. Diabetic patients may have larger amounts. Exposure to Acetone should be avoided because it causes irritation in the eyes and throat. The vinegar is an organic compound that contains up to 5% Acetic Acid (has chemical compounds CH3COOH) and 95% water. Acetic acid is a clear colorless liquid with a pungent odor. It is soluble in alcohol, acetone, water, and other organic compounds. Vinegar has been used as a cleaning agent, printing of textiles, and as an acidifier to improve the flow of oil from wells. Neil Schlager (2006). Acetic acid is corrosive and prolonged exposure can cause irritation to throat, nose, and eyes. It can also cause headaches, confusion, chest tightness, and coughs. Salt (another name for NaCl sodium chloride) is made from a chemical reaction of an acid and a base. During this reaction, the acid and base are neutralized producing salt, water and heat. Lerner (2008). Table Salt (also NaCl) only has one positive ion. Salt is an important compound for preserving food and making soap. It is also very important in the making of chlorine and sodium. Water (H2O) is a chemical compound of hydrogen and oxygen held together by polar covalent bonds. Its polarity causes it to form hydrogen bonds. Hydrogen bonds are an attraction between slightly positive H atoms in a polar molecule with the slightly negative side of another polar molecule. Water molecules form 5 hydrogen bonds and have a high specific heat. Water has a wicking property called capillary action. Capillary action is the force that draws water out of the roots of plants and into the stems and leaves. Analyzing ink is important questioned documents that might be forged. It could be used to identify inks in forged checks, wills, or altered records. Ink may look the same but they have very different chemical compositions. Ink is made up of a combination of pigments and dyes, oils, and resins. Some inks are even made of soybeans. Inks may be analyzed by a destructive or nondestructive test. The nondestructive is analyzed first and is better because it keeps the paper intact. Micro spectrophotometry is the main method of nondestructive testing. It scans the ink in infrared and ultraviolet light to record its wavelengths of light it absorbs. Thin layer chromatography is used for destructive testing. A tiny sample of ink paper is punched out and placed on a strip of paper with other ink samples. Then the strip is placed into a solvent but it’s placed where the sample ink is dry. The solvent is drawn up through capillary actions and the sample spots move up with it. The end result is a pattern of colored spots where you can compare it with others to make identification.

A report on based on the company Gourmet burger kitchen Essay - 2

A report on based on the company Gourmet burger kitchen - Essay Example Not only the national government or the local government is taking steps in maintaining healthy food regulations but different regulatory bodies and trade unions are also taking steps in promoting and maintaining healthy environment and keeping the track of consumer rights. Switzerland is known to have a unique political system where they practice direct democracy; they have the most decentralized power frequent referendums and encourage participation from the citizens. But one of the most unique aspects in Switzerland government is that they have no political pressure groups leaders (CIA World fact Book, 2009). Due to this GKB and all other companies like to invest in Switzerland because all the companies are given a lot of leverage to operate independently and there is least interference from the national or local government bodies. But keeping in mind the rights of consumers Switzerland government has set proper food safety regulations. Thus it has implemented both GM food safety and labeling legislations. In 1995, Switzerland was the first country who implemented a labeling regime for GM food since then revision has been taken in this (Wugar, 2006, 1). Thus now when a new company has to start its new operation is has to follow a proper procedure, f irst it needs authorization from federal office of Public Health, then it needs to get registered and all the legal requirements need to be fulfilled. The regulations on food and commodities and other pertinent regulations make sure that proper implementation of food laws are enacted and thus the Federation keeps a proper check on food quality and standards (Rentsoh & Partner, 2009, 1). Switzerland is known to have the most stable political system and due to this all companies try to take their business in this country. Switzerland is very competitive in nature in terms of new investment and thus attracts many companies and business men in setting

Autism in a Child at School Essay Example | Topics and Well Written Essays - 2750 words

Autism in a Child at School - Essay Example These children are often wrongly dismissed by many teachers in ordinary schools as having normal behavioural problems and are not given the special kind of treatment and education that they need. Instead, they are treated just like other kids in most schools leading to poor performance on their part. Many a times, private schools refuse to admit children with autism giving reason that they are ill equipped to deal with autism in the classroom. The handful of schools that admit these special needs children are very expensive and have a limited capacity, meaning they can only accept a limited number of children (Cowly, 2010). It is therefore the mandate of teachers in special needs education and parents with an autistic child to ensure that they acquire quality education and stand a fair chance at life after school, and this is the subject of this research paper. The research discusses in depth different aspects of autism in children in school and is divided into different sections for comprehensiveness. First, it discusses the legal definition of special education needs. The second section talks about the role of the learning support worker/ teaching assistant regarding supporting an autistic child in school. Third, Workplace behaviour policy and procedure in schools that will ensure creation of quality environment for supporting children with autism in schools is discussed. ... Special Education Needs Special Needs Education refers to the process of providing education to students with special needs in the best possible way that recognizes and addresses the individual needs and differences of the students. The achievement of the objectives of this delicate task requires planning of individual and carefully monitored teaching procedures, carefully designed teaching materials and equipment, well thought out settings and any other measures that will help children with special needs to achieve the required level of confidence and self esteem to succeed in school work (Haddon, 2004). There is general agreement between professionals and parents that it takes a lot of hard work to help children with autism get the best out of the classroom. This is because every child with an autism spectrum disorder is unique, with various characteristics and styles of learning. This therefore requires an education curriculum that is wide enough to accommodate the whole spectrum. Effort must therefore be made to create these conditions that are not available in ordinary classrooms. Students with ASD will benefit more in an environment with additional educational services like use of unconventional teaching methodologies; use of technology developed for their aid and auxiliary facilities such resource centers. These measures are what set special education apart from general education, which is the type of learning in education centers for normal children. Special education has in the past been used to refer to a special instruction set or approach meant to enhance the learning process of special need children who are slow learners. Children with autism have however shown a high level of intellectual giftedness that usually surpasses that of ordinary

The Irrationality Of The Mathematical Constant E Mathematics Essay

The Irrationality Of The Mathematical Constant E Mathematics Essay This dissertation gives an account of the irrationality of the mathematical constant. Starting with a look into the history of irrational numbers of which is a part of, dating back to the Ancient Greeks and through to the theory behind exactly why is irrational. 1. Introduction: In this paper, I aim to look at some of the history and theory behind irrational numbers ( in particular). It will take you through from learning the origins of irrational numbers, to proving the irrationality of itself. The mathematical constant is a very important and remarkable number; it is sometimes referred to as Eulers number. It has many vital applications in calculus, exponential growth/decay and also compound interest. One of the most fascinating things however is taking the derivative of the exponential function; defined. The derivative of is simply, i.e. it is its own rate of change. An irrational number can be defined as any number that cannot be written as a fraction; that means to say any number that cannot be written in the form. 1.1 History of Irrational Numbers: The first proof of the existence of irrational numbers came a few centuries BC, during the time when a prevalent group of mathematicians/philosophers/cultists called Pythagoreans (after their leader and teacher Pythagoras) believed in the purity of expressions granted by numbers. They believed that anything geometric in the Universe could be expressed as whole numbers and their ratios. It is believed a Pythagorean by the name Hippasus of Metapontum discovered irrational numbers while investigating square roots of prime numbers; he found that he could not represent the square root of 2 as a fraction. Bringing his findings to his mentors (Pythagoras) attention brought the death sentence upon himself. As story has it, Pythagoras (who believed in the absoluteness of numbers) had him drowned to death. According to Plato (a prominent Greek philosopher and mathematician; 428/427 BC 348/347 BC), the irrationality of the surds of whole numbers up to 17 was proved by Theodorus of Cyrene. It is understood that Theodorus stopped at the square root of 17 due to the algebra being used failing. It wasnt until Eudoxus (a student of Plato) that a strong mathematical foundation of irrational numbers was produced. His theory on proportion, taking into account irrational and rational ratio featured in Euclids Elements Book V. The sixteenth to nineteenth century saw negative, integral and decimal fractions with the modern notation being used by most mathematicians. The nineteenth century was particularly important in the history of irrational numbers as they had largely been ignored since the time of Euclid. The resurgence in the scientific study of irrationals was brought upon by the need to complete the theory of complex numbers. An important advancement in the logical foundation of calculus was the construction of the real numbers using set theory. The construction of the real numbers represented the joint efforts of many mathematicians; amongst them were Dedekind, Cantor and Weierstrass. Irrational numbers were finally defined in 1872 by H.C.R. Mà ©ray, his definition being basically the same as Cantor suggested in the same year (which made use of convergent sequences of real numbers). Leonhard Euler paid particular attention to continued fractions and in 1737 was able to use them to be the first to prove the irrationality of and. It took another 23 years for the irrationality of to be proved, of which was accredited to Eulers colleague Lambert. The nineteenth century brought about a change in the way mathematicians viewed irrational numbers. In 1844 Joseph Liouville established the existence of transcendental numbers, though it was 7 years later when he gave the first decimal example such as his Liouville constant.Charles Hermite in 1973 was the first person to prove that was a transcendental number. Using Hemites conclusions Ferdinand von Lindemann was able to show the same for in 1882. 1.2 History of the Mathematical Constant: The number first arrived into mathematics in 1618, where a table in an appendix to work published by John Napier and his work on logarithms were found to contain natural logarithms of various numbers. The table did not contain the constant itself only a list of natural logarithms calculated from the constant. Though the table had no name of an author, it is highly assumed to have been the work of an English mathematician, William Oughtred. Surprisingly the discovery of the constant itself came not from studying logarithms but from the study of compound interest. In 1683 Jacob Bernoulli examined continuous compound interest by trying to find the limit of as tends to infinity. Bernoulli managed to show that the limit of the equation had to lie between 2 and 3, and hence could be considered to be the first approximation of. 1690 saw the constant first being used in a correspondence from Gottfried Leibniz to Christiaan Huygens; it was represented at the time by the letter. The notation of using the letter however came about due to Euler and made its first appearance in a letter he wrote to Goldbach in 17318. Euler published all the ideas surrounding in his work Introductio in Analysin infinitorum (1748). Within this work he approximated the value of to 18 decimal places; The latest accurate account of is to 1,000,000,000,000 decimal places and was calculated by Shigeru Kondo Alexander J. Yee in July 2010. 1.3 A few representations of e: can be defined by the limit: (1) By the infinite series: (2) Special case of the Euler formula: (3) Where when, (4) 2. The Proofs: 2.1 Proving the infinite series of e: In proof 2.2.2 we will use the fact that: (5) As this paper dedicated to, it would be useful to know where this equation comes from. The answer lies in the Maclaurin series (Taylor series expansion of a function centred at 0). (6) Let our, and we have that all derivatives of is equal to We now have that. (7) We now let and we have equation (5). 2.2 The irrationality of e and its powers. Continued fractions are closely related to irrational numbers and in 1937 Leonhard Euler used this link and was able to prove the irrationality of and. The most general form of a continued fraction takes the form: (6) Due to the complexity that can arise in using the format in equation (6), mathematicians have adopted a more convenient notation of writing simple continued fractions. We have that can be expressed in the following manner: (7) With the use of continued fractions it is relatively easy to show that the expansion of any rational number is finite. So it is obvious to note that all you would have to do to prove that a given number is irrational, would be to show its regular expansion not be finite. Using this tool we will now show the Eulers expansion for: We have: (8) Equation (8) shows, we now invert the fractional part: (9) Here we have, once again we invert the fractional part: (10) Hence, we continue in the same way to produce: (11) So. (12) So. (13) So. (14) So. (15) So. (16) So. Using the figures above provides the following result: (17) Observing equation (17) allows us to notice pattern and we can show this by re-writing in the following way: (18) Clearly it seems that the sequence will clearly increase and never terminate. Similarly Euler shows this in other examples using. (19) Equation (19) shows an arithmetic increase by 4 each time from the number 6 and onwards. Noticeably equation (18) and (19) do not provide proof that is irrational and are merely just observations. However Euler uses his previous work on infinitesimal calculus, which then proves this sequence is infinite. The proof that Euler uses is very long and complicated as it involves transforming continued fractions into a ratio of power series, which in turns becomes a differential equation of that he can transform into the Ricatti equation he needs. Since Eulers time mathematicians have found far more manageable and direct ways in proving the irrationality of. 2.2.1 Proving the irrationality of e: While Euler was the first to establish a proof of the irrationality of using infinite continued fractions, we will use Fouriers (1815) idea of using infinite series to prove more directly. Proof: Defining the terms: Using the Maclaurin series expansion we have: (20) Now lets define to be a partial sum of: (21) For we first write the inequality: (22) Equation (22) has to be positive as we stated to be the partial sum of, which is the infinite sum. Now well find the upper limit of equation (22): (23) Taking out a factor of: (24) Now as we are looking for an upper limit, we need an equation greater than equation (24): (25) We take note that the terms in the square bracket in equation (25) for the upper limit is a geometric series with. Right hand Side (RHS) of equation (25): (26) (27) (28) (29) We have: (30) Multiply through by: (31) Now lets assume i.e. is rational. Using the substitution implies: (32) Now by expanding the RHS gives us the following result: (33) (34) We note the following: is an integer. , this implies that divides into and hence is an integer. Each term within the square bracket is an integer; we know that can be divided by and upwards to and produce integer values. Therefore as all terms are integers, we have: (35) where is an integer value. Observe that by choosing any we have and furthermore. Using equation (31) we now obtain the following result: (36) (37) Equation (37) implies is not an integer. This is a contradiction to the result obtained in 1) and so therefore is proven to be irrational. 2.2.2 Proving the irrationality of ea: Proof 2.1 successfully shows how is irrational however, the proof is not strong enough to show the irrationality of. Using an example, we have the as a known irrational number, whose square is not. In order to show all integer powers (except zero) of are irrationals, we need a bit more calculus and an idea tracking back to Charles Hermite; where the key is located in the following lemma. Proof: Lemma: For some fixed, let: (38) The function is a polynomial of the form, where the coefficientsare integers. For we have The derivatives and are integers for all Proof: (see appendix) Theorem 2: is irrational for any integer. Proof: Take to be rational, where is a non-zero rational number. Let with non-zero integers and. being rational implies that is rational. This is a contradiction to theorem 2 and hence is irrational. Assume where are integers, and let be large enough that. State , (39) where is the function of the lemma. Note that can also be written in the form of an infinite sum as we see that any higher derivatives where for vanishes. We now want to obtain a first order linear equation using equation (39). We start by differentiating: (40) Now from observation we see that by multiplying equation (39) by and then eliminating the first term we end up with equation (40). (41) Equation (41) takes the form our required first order linear equation, which is solved in the following manner: First re-write in the standard form: (42) Next we find the integrating factor  µ to multiply to both sides of the equation: (43) From equation (43) we now have the following equation: (44) (45) Note the limit runs as stated in of the lemma. We now manipulate equation (45) by multiplying by so that we can apply of the lemma. (46) (47) We have that , so thereforeand hence: (48) As is just a polynomial containing integer values multiplying derivatives of, we can state using of the lemma that is an integer. Part of the lemma states . With this we can now estimate the range that lies within. Firstly we know that is a positive value and hence. For the upper limit we have: (49) Note that to find the upper limit we eliminate the integral and substitute the upper bounds for and. From before we have and also that we took n large enough so that, which can be re-written , which implies the following: (50) (51) Equation (51) states that cannot be an integer and hence contradicts Equation (48). Therefore we have that is proven to be irrational. 3. Further Work: Following on and further proving the irrationality of, would be to prove that is a transcendental number. Irrational numbers can be split into two categories algebraic and transcendental; hence transcendental numbers are numbers that are not algebraic. Algebraic numbers are defined as any number that can be written as the root of an equation of the form. A minimal polynomial is achieved when is the smallest degree possible for a given. The square root of 2 is an example of an irrational number, but also it is an algebraic number of degree 2, of which the minimal polynomial is simply. Euler in the late 18th century was the first person to define transcendental numbers, but the proof of their existence only came around in the papers of Liouvilles in 1844 and 1851. The number was the first important mathematical constant to be proven transcendental and was done so by Charles Hermite in 1873. The techniques Hermite used influenced many future mathematical works including the first proof of being transcendental by Ferdinand von Lindemann; also used in the creation of the Lindemann-Weierstrass theorem. Further work on transcendental numbers involving can be still seen today. Mathematicians knowis a transcendental number, but as of yet have not been able to prove this. 4. Conclusion: Overall, the main objective of this paper was to give an account of the irrationality of. This has been achieved and with it we have been able to see the progress from the first discovery of irrational numbers by the Pythagoreans of Ancient Greek, through to the work covered on Eulers number. References: Webpage Resources: Cook, Z. (2000), Irrational Numbers, The Guide to Life, The Universe and Everything, BBC [Online]. Available: http://www.bbc.co.uk/dna/h2g2/A455852, [Accessed: 6th January 2011]. OConnor, J.J and Robertson, E.F. (1999), Theodorus of Cyrene [Online]. Available: http://www-history.mcs.st-and.ac.uk/Biographies/Theodorus.html, [Accessed: 6th January 2011]. OConnor, J.J and Robertson, E.F. (1999), Eudoxus of Cnidus [Online]. Available: http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Eudoxus.html, [Accessed: 6th January 2011]. OConnor, J.J and Robertson, E.F. (2001), The number e, Number Theory [Online]. Available: http://www-history.mcs.st-and.ac.uk/HistTopics/e.html, [Accessed: 6th January 2011]. Russel, D. (2002), Hippasus Expelled!, Irrational Pythagoreans [Online]. Available: http://math.about.com/library/blpyth.htm, [Accessed: 6th January 2011]. Sondow, J and Weisstein, E.W. e. MathWorldA Wolfram Web Resource [Online]. Available: http://mathworld.wolfram.com/e.html, [Accessed: 6th January 2011]. Weisstein, E.W. Irrational Number, MathWorldA Wolfram Web Resource [Online]. Available: http://mathworld.wolfram.com/IrrationalNumber.html, [Accessed: 6th January]. Yee, A.J. (2010), e, Mathematical Constants Billions of Digits [Online]. Available: http://www.numberworld.org/digits/E/, [Accessed 6th January 2011]. Zongju, L. Shuxue Lishi Diangu (Historical Stories in Mathematics), Chiu Chang Publishing Company [Online]. Available: http://db.math.ust.hk/articles/calculus/e_calculus.htm, [Accessed 6th January 2011]. Arithmetic Sequences and Series, Arizona State University [Online]. Available: http://fym.la.asu.edu/~tturner/MAT_117_online/SequenceAndSeries/Geometric_Sequences.htm, [Accessed: 6th January 2011]. Online PDF Resources: Collins, DC. Continued Fractions, [Online]. Available: http://www-math.mit.edu/phase2/UJM/vol1/COLLIN~1.PDF, [Accessed 6th January 2011]. Conrad, K. (2005), Irrationality of, [Online]. Available: http://www.math.uconn.edu/~kconrad/math121/121piande.pdf, [Accessed: 6th January 2011]. Field, B. (2010), Irrational and Transcendental Numbers, page 23 [Online]. Available: http://maths.dur.ac.uk/Ug/projects/library/CM3/0910/CM3_BenField.pdf, [Accessed: 6th January 2011]. Sandifer, E. (2006), Who proved e is irrational?, How Euler Did it [Online]. Available: http://www.maa.org/editorial/euler/How%20Euler%20Did%20It%2028%20e%20is%20irrational.pdf [Accessed: 6th January 2011]. Online Video Resources: Adams, C, Garrity, T and Burger, E. (2006), Pi verses e, The Mathematical Association of America [Online]. Available: http://www.youtube.com/watch?v=whpAX30vjoE, [Accessed: 6th January 2011] Delaware, R. A Proof e is irrational, Proof, University of Missouri [Online]. Available: http://www.youtube.com/watch?v=FtIL7nGgDNM, [Accessed: 6th January 2011]. Book Resources: Aigner, M and Ziegler, G.M. Proofs from THE BOOK, Third Edition, [Berlin: Springer, 2004]. Dorrie, H and Translated by Antin, D. 100 Great Problems of Elementary Mathematics, THERE HISTORY AND SOLUTION, [New York: Dover Publications, Inc., 1965]. Sandifer, C.E. The early mathematics of Leonhard Euler, [USA: The Mathematical Association of America (Incorporated), 2007].

Kindergarten in Turkey :: Education

Living conditions, which are very poor in Turkey, affect the contentment of the people significantly. Hence, many women who have any children have to work to help family budget and for live in more comfort. Today, working outside is a fashion for women it gives women an economic liberty and respect. That is good for them however, from the side of many young children that is bad because they have to go kindergartens when their mothers go to work. Nowadays, the number of children who go to kindergartens is increasing rapidly. Unfortunately, many of them are growing up without their mother’s love. So sending children to kindergartens causes some problems which are so important like missing or hating mother and home, being a stressful person in early ages and so on. The major cause of hating mother is spending all childhood in nurseries. Today, we can see in news many teenagers are killing their mothers due to lack of mothers’ love. Their mothers are a normal person for them however we cannot deny that mothers are holly existences for us. So if there is not a necessity, women should not work outside or else, they should look after their children after the work. The other equally significant point is being a stressful person in the future life. Many scientists believe that living in a routine reason for stress. Moreover, in kindergarten children are getting used to a routine life. Therefore these young children meet stress in their early ages and they will more stressful people in their future lives because in nursery there is a hard and well disciplined education. In contrast to these many people claim that kindergartens make children more social in the society. However these claimants do not know that kindergartens cannot give a real parent’s love so if children do not have real love, they will not love their children so this will continue and love between children and parents will be end.

Cdr Professional Engineer

PROFESSIONAL ENGINEER Summary Statement These are the competency Units and Elements. These elements must be addressed in the Summary Statement (see Section C). If you are applying for assessment as a Professional Engineer, you will need to download this page, complete it and lodge it with your application. Competency Element |A brief summary of how you have applied the element |Paragraph in the career episode(s) | | | |where the element is addressed | |PE1 KNOWLEDGE BASE | | | |PE1. Knowledge of science and engineering | | | |fundamentals | | | |PE1. 2 In-depth technical competence in at least | | | |one engineering discipline | | | |PE1. Techniques and resources | | | |PE1. 4 General Knowledge | | | |PE2 ENGINEERING ABILITY | | | |PE2. Ability to undertake problem identification,| | | |formulation, and solution | | | |PE2. 2 Understanding of social, cultural, global, | | | |and environmental responsibilities and the need to| | | |employ principles of sustainable development | | |PE2 . 3 Ability to utilise a systems approach to | | | |complex problems and to design and operational | | | |performance | | | |PE2. Proficiency in engineering design | | | |PE2. 5 Ability to conduct an engineering project | | | |PE2. 6 Understanding of the business environment | | | |PE3 PROFESSIONAL ATTRIBUTES | | | |PE3. Ability to communicate effectively, with the| | | |engineering team and with the community at large | | | |PE3. 2 Ability to manage information and | | | |documentation | | | |PE3. Capacity for creativity and innovation | | | |PE3. 4 Understanding of professional and ethical | | | |responsibilities, and commitment to them | | | |PE3. Ability to function effectively as an | | | |individual and in multidisciplinary and | | | |multicultural teams, as a team leader or manager | | | |as well as an effective team member | | | |PE3. Capacity for lifelong learning and | | | |professional development | | | |PE3. 7 Professional Attitudes | | |