Biography of Srinivasa Ramanujan, Mathematical Genius

Biography of Srinivasa Ramanujan, Mathematical Genius Srinivasa Ramanujan (born December 22, 1887 in Erode, India) was an Indian mathematician who made substantial contributions to mathematics- including results in number theory, analysis, and infinite series- despite having little formal training in math. Fast Facts: Srinivasa Ramanujan Full Name: Srinivasa Aiyangar RamanujanKnown For: Prolific mathematicianParents’ Names: K. Srinivasa Aiyangar, KomalatammalBorn: December 22, 1887 in Erode, IndiaDied: April 26, 1920 at age 32 in Kumbakonam, IndiaSpouse: JanakiammalInteresting Fact: Ramanujans life is depicted in a book published in 1991 and a 2015 biographical film, both titled The Man Who Knew Infinity. Early Life and Education Ramanujan was born on December 22, 1887, in Erode, a city in southern India. His father, K. Srinivasa Aiyangar, was an accountant, and his mother Komalatammal was the daughter of a city official. Though Ramanujan’s family was of the Brahmin caste, the highest social class in India, they lived in poverty. Ramanujan began attending school at the age of 5. In 1898, he transferred to Town High School in Kumbakonam. Even at a young age, Ramanujan demonstrated extraordinary proficiency in math, impressing his teachers and upperclassmen. However, it was G.S. Carr’s book, A Synopsis of Elementary Results in Pure Mathematics, which reportedly spurred Ramanujan to become obsessed with the subject. Having no access to other books, Ramanujan taught himself mathematics using Carr’s book, whose topics included integral calculus and power series calculations. This concise book would have an unfortunate impact on the way Ramanujan wrote down his mathematical results later, as his writings included too few details for many people to understand how he arrived at his results. Ramanujan was so interested in studying mathematics that his formal education effectively came to a standstill. At the age of 16, Ramanujan matriculated at the Government College in Kumbakonam on a scholarship, but lost his scholarship the next year because he had neglected his other studies. He then failed the First Arts examination in 1906, which would have allowed him to matriculate at the University of Madras, passing math but failing his other subjects. Career For the next few years, Ramanujan worked independently on mathematics, writing down results in two notebooks. In 1909, he began publishing work in the Journal of the Indian Mathematical Society, which gained him recognition for his work despite lacking a university education. Needing employment, Ramanujan became a clerk in 1912 but continued his mathematics research and gained even more recognition. Receiving encouragement from a number of people, including the mathematician Seshu Iyer, Ramanujan sent over a letter along with about 120 mathematical theorems to G. H. Hardy, a lecturer in mathematics at Cambridge University in England. Hardy, thinking that the writer could either be a mathematician who was playing a prank or a previously undiscovered genius, asked another mathematician J.E. Littlewood, to help him look at Ramanujan’s work. The two concluded that Ramanujan was indeed a genius. Hardy wrote back, noting that Ramanujan’s theorems fell into roughly three categories: results that were already known (or which could easily be deduced with known mathematical theorems); results that were new, and that were interesting but not necessarily important; and results that were both new and important. Hardy immediately began to arrange for Ramanujan to come to England, but Ramanujan refused to go at first because of religious scruples about going overseas.  However, his mother dreamed that the Goddess of Namakkal commanded her to not prevent Ramanujan from fulfilling his purpose. Ramanujan arrived in England in 1914 and began his collaboration with Hardy. In 1916, Ramanujan obtained a Bachelor of Science by Research (later called a Ph.D.) from Cambridge University. His thesis was based on highly composite numbers, which are integers that have more divisors (or numbers that they can be divided by) than do integers of smaller value. In 1917, however, Ramanujan became seriously ill, possibly from tuberculosis, and was admitted to a nursing home at Cambridge, moving to different nursing homes as he tried to regain his health. In 1919, he showed some recovery and decided to move back to India. There, his health deteriorated again and he died there the following year. Personal Life On July 14, 1909, Ramanujan married Janakiammal, a girl whom his mother had selected for him. Because she was 10 at the time of marriage, Ramanujan did not live together with her until she reached puberty at the age of 12, as was common at the time. Honors and Awards 1918, Fellow of the Royal Society1918, Fellow of Trinity College, Cambridge University In recognition of Ramanujan’s achievements, India also celebrates Mathematics Day on December 22, Ramanjan’s birthday. Death Ramanujan died on April 26, 1920 in Kumbakonam, India, at the age of 32. His death was likely caused by an intestinal disease called hepatic amoebiasis. Legacy and Impact Ramanujan proposed many formulas and theorems during his lifetime. These results, which include solutions of problems that were previously considered to be unsolvable, would be investigated in more detail by other mathematicians, as Ramanujan relied more on his intuition rather than writing out mathematical proofs. His results include: An infinite series for Ï€, which calculates the number based on the summation of other numbers. Ramanujan’s infinite series serves as the basis for many algorithms used to calculate Ï€.The Hardy-Ramanujan asymptotic formula, which provided a formula for calculating the partition of numbers- numbers that can be written as the sum of other numbers. For example, 5 can be written as 1 4, 2 3, or other combinations.The Hardy-Ramanujan number, which Ramanujan stated was the smallest number that can be expressed as the sum of cubed numbers in two different ways. Mathematically, 1729 13 123 93 103. Ramanujan did not actually discover this result, which was actually published by the French mathematician Frà ©nicle de Bessy in 1657. However, Ramanujan made the number 1729 well known.1729 is an example of a â€Å"taxicab number,† which is the smallest number that can be expressed as the sum of cubed numbers in n different ways. The name derives from a conversation bet ween Hardy and Ramanujan, in which Ramanujan asked Hardy the number of the taxi he had arrived in. Hardy replied that it was a boring number, 1729, to which Ramanujan replied that it was actually a very interesting number for the reasons above. Sources Kanigel, Robert. The Man Who Knew Infinity: A Life of the Genius Ramanujan. Scribner, 1991.Krishnamurthy, Mangala. â€Å"The Life and Lasting Influence of Srinivasa Ramanujan.† Science Technology Libraries, vol. 31, 2012, pp. 230–241.Miller, Julius. â€Å"Srinivasa Ramanujan: A Biographical Sketch.† School Science and Mathematics, vol. 51, no. 8, Nov. 1951, pp. 637–645.Newman, James. â€Å"Srinivasa Ramanujan.† Scientific American, vol. 178, no. 6, June 1948, pp. 54–57.OConnor, John, and Edmund Robertson. â€Å"Srinivasa Aiyangar Ramanujan.† MacTutor History of Mathematics Archive, University of St. Andrews, Scotland, June 1998, www-groups.dcs.st-and.ac.uk/history/Biographies/Ramanujan.html.Singh, Dharminder, et al. â€Å"Srinvasa Ramanujans Contributions in Mathematics.† IOSR Journal of Mathematics, vol. 12, no. 3, 2016, pp. 137–139.â€Å"Srinivasa Aiyangar Ramanujan.† Ramanujan Museum Math Education Centre, M.A .T Educational Trust, www.ramanujanmuseum.org/aboutramamujan.htm.

The concept of organizational change within management theory Research Paper

The concept of organizational change within management theory - Research Paper Example Organizational change is a paradigm for addressing the impact of new external and internal forces, changes in culture and structure within an organization (Mills, 2003). Basically, organizational change deals with the change management’s human aspect. A methodical organizational change is favorable when change necessitates all the people in an organization to gain new skills, practices, and knowledge (Poole & Van De Ven, 2004). By appropriately establishing expectations and goals, using instruments to enhance communication and information dissemination and dynamically pursuing means to avoid misunderstanding, stakeholders are more predisposed to accept a change at the onset and remain steadfast to the change despite of any difficulties accompanying it. Meanwhile, if one were to look deeply after monitoring and examining several organizational changes, an array of goals would appear to exist. These goals could be implied or formally stated, or they could be embedded in the deci sions and responses of the management (Kamoche, Cunha, & Cunha, 2002). To the outsider, the general goals can be grouped under such categories as reduced turnover, reinforced innovation, new strategies, enhanced teamwork and cooperation, strengthened motivation, etc (Kamoche et al., 2002). Organizational changes are usually intended for these several common goals. Fundamental to these more apparent goals are generally two underlying purposes: (1) changes in employees’ behaviors and attitudes, and (2) changes in the adaptation level of an organization (Kezar, 2001). The first objective of organizational change, to realize transformations in patterns of behavior, becomes evident if one identifies that the adaptation level of the organization is not strengthened except if a large number of its people behave or act differently with regard to their tasks and their relationship to each other. An organization does not function mechanically; it operates through its people, and every organization possesses distinctive approaches to decision making (Kezar, 2001). Hence, any organizational change, regardless if it will be established through a training course or a new structural plan, is fundamentally trying to encourage employees to accept and implement new behavioral patterns and rudiments for performing tasks and relating to each other. Likewise, organizations are constantly trying to adapt themselves strongly and effectively to their immediate internal and external environment. Due to the fact that organizational management has no power to totally control its environment, particularly the external one, they are persistently obliged to initiate internal changes in the organization which permit them to deal more successfully with new challenges and problems of the external environment, such as difficult social demands, technological advances, heightened competition, and new government regulation (Murray & Richardson, 2002). Organizational changes are normally la unched in ‘response’ to demands from the external environment. Nevertheless, in several instances, changes are initiated in ‘expectation’ of future demands and problems. What Provokes Organizational Change? A fundamental fact of the twenty-first century is that managers and organizations as a whole are confronted with insistent pressures of change. Organizations are ever more

Health Assessment Research Paper Example | Topics and Well Written Essays - 1250 words

Health Assessment - Research Paper Example Sometimes, the condition is irreversible, and operation is the only resort to solve the problem. Nevertheless, with prompt medical treatment, proper diet and exercise, the disease could be controlled or even cured in time. This paper discusses nursing practices in dealing with patients with plantar fasciitis, a condition common to people who had history of heavy walking and running. The paper details the complaints of the client, subjective and objective data to be collected, rationale for collecting additional data, and health promotion strategies that a nurse can give to the client. The Patient’s Complaint Waking up with painful heel and finding it difficult to walk and climb down the stairs in the morning have become the usual scenarios in the life of Cynthia. At age 35, Cynthia wondered why she developed arthritis. She thought that the pain in her heel was due to arthritis, given the fact that arthritis is common among her father’s relatives. Her father has been suf fering from arthritis for nine years, and he is now 73. Cynthia first felt the pain three years ago when she started working as a freelance writer for several publishing companies. Working at home, she did not go out frequently and only did so when attending meetings, conferences and the like. She submitted write-ups through email, allowing her to stay at home without needing to dress up smartly. That time, Cynthia gained some weight, thus making her quite obese. She did not think of her ailment as permanent; she barely thought that she got the pain from walking as she did her shopping twice monthly. Three years passed and the pain occurred from time to time whenever she went out to do the grocery. Six months ago, she found a new job as a full-time office-based editorial manager. This time around, she has to wear office clothes and use shoes to pair with them. She has been using ballet flats for three months prior to the consultation. Thinking ballet flats look cute and feel comfort able, she bought three pairs of the shoes. Ballet flats are trendy; they are very popular especially among youngsters and are preferred by those who do walking most of the time. These shoes are very colorful and nice to wear because they are usually made of cotton or textile materials so the feet can breath even with long-time wear. The smooth material does not cause blisters unlike leather shoes. Most of all, ballet flats are cheap so one can practically change shoes everyday. Cynthia was attracted to this kind of shoes, not knowing that they could aggravate her condition. When she consulted with an orthopaedist, Cynthia was instructed to undergo x-ray of both feet to find out if bone spurs grew in her heels. The results are positive. Cynthia has inferior calcaneal exostoses or heel spurs on both feet. These results gave the doctor an impression that she has plantar fasciitis. Plantar fasciitis, otherwise known as â€Å"policeman’s heel,† is the painful condition of t he plantar fascia, the connective tissue found on the soul of the foot, usually at the heel part. According to Roxas (2005), the cause of this pain is multifactorial, including excessive mobility, wearing tough shoes, walking or running on hard surfaces, and being overweight. These characteristics of plantar fasciitis determine the additional data required to be collected. Additional Objective and Subjective Data to be Collected Identifying plantar fasciitis is easy in consideration of the

Resource File and Personal Theory Paper Essay Example for Free

Resource File and Personal Theory Paper Essay Behavior Person-Centered Theory is a theory that focuses on the individual person and the behaviors (appropriate and inappropriate) so that not only will the person be independent of self esteem issues but, he or she will learn behaviors that promote positive attitudes. Instead of just looking at the behaviors this theory, looks at the person as a whole (the behaviors positive and negative, his or her feelings about themselves and the people around him or her, and the triggers that make him or her behave in negative ways. I believe in this theory because it does not just focus on one aspect of the person such as the negative behaviors and triggers, it looks also looks at the positive behaviors and triggers. By doing this you are able to learn what makes a person react the way he or she does and if the actions are deliberate or if the actions are true reactions to the situations or stimuli. Some people have a tendency to show you what they think you want to see or hear (manipulation) but if you learn what actions trigger what reactions (good and bad) you can teach the individual how to avoid those situations or stimuli. The theorist and theory that I relate to the best is Yalom and the interpersonal group therapy. I relate to this theory because it focuses on problems in current relationships and situations while examining the ways in which those particular problems are reflected within the members of the group. It is always important for patients to know that he or she is not the only person going through the kinds of situations the patient may be facing. When a patient learns that he or she is not alone in the world (concerning the types of problems being faced) it allows the patient to better relate and discuss what it is he or she is going through and as a group solutions can be developed. What surprised me the most about the theories learned in class was that a single  theory can treat more than one problem or person. I always believed that everyone was subjected to the same theory no matter what the situation was. I was also surprised to learn that not all people are placed in in-patient facilities if the doctor feels that something else should be done. This was very apparent in the case where the lady whose husband was cheating on her, tried to kill herself numerous times and the doctor decided to treat her as an outpatient instead of committing her. Since being in this class, I have learned that not all theories apply to all people and situations. One theory can be used to treat a multitude of people and situations. Not all people are committed for actions some may deem psychotic it is up to the attending physician whether or not the person is committed to a facility.

Macbeth: Imagery Of Animal Behavior And Class Status Advances :: essays research papers

Macbeth: Imagery of Animal Behavior and Class Status Advances In Macbeth, the imagery of animals behavior and class status advances the theme of animals in relation to human characteristics. The examples discussed in my paper will make it quite clear that this imagery is evident, throughout the play.   Ã‚  Ã‚  Ã‚  Ã‚  In Act 1 sc. 3 line 8, the first witch chants and says that the sailor is the master of the Tiger. The witch is comparing the man to a Tiger. The tiger is a very good animal and is near the top of the Elizabethan World Picture. Hence the man is good. Furthermore the witch say's that she herself is like a rat without a tail. Thus she is missing something important. The witch is incomplete, just like the rat. Furthermore I believe she is hiding something because when you are missing something you are apt to be very self conscious and hide it. In addition the rat is veer low on the chain of being.   Ã‚  Ã‚  Ã‚  Ã‚  The next passage is Act 1 sc. 7 line 49. In this passage Lady Macbeth is quoted saying â€Å"like the poor cat I ‘th' adage† (1, vii., 49). That means â€Å" the cat who eats fish but will not get his feet wet † (Folgers, p 40). Lady Macbeth is telling Macbeth that he is like the cat because he wants to become king but he won't get his hands bloody. However Lady Macbeth would find someone else to get their feet wet, someone to do her dirty work.   Ã‚  Ã‚  Ã‚  Ã‚  In act 2 scene 4 line 15, the old man and Ross talk about the recent murder. The old man says that the killer, an owl made sure no one was looking and attacked the falcon and killed it. The owl, lower then the falcon on the chain of being usually eats mice, which is low on the hierarchy. But this time the owl eats the falcon whom is usually on the top of the hierarchy.   Ã‚  Ã‚  Ã‚  Ã‚  Later in the play during act 3 Macbeth talks bout the list of dogs and the list of men. On line 140 in sc.1 Macbeth compares the murders with the lowliest of dogs. In the next act, Act 4 three witches use very lowly animals to describe Macbeths kingship. In sc. 1 lines 1-30 the witches say that

Assignment: Fee Setting Essay

The government benefits seminar for children and families was a major success, so Advocates for Children will carry out a similar seminar in a nearby town. The executive director has decided that this second seminar should make the highest possible amount of money. For this reason, they will not offer a reduced fee schedule, and all attendees must pay the entire fee. This seminar will happen in a smaller room than the first one did, which can only leave space for 45 trainees, at most. Here is the seminar’s proposed budget: Proposed Seminar Budget 1. Conference room rental $175.00 $ 175.00 2. Audiovisual equipment Rental $75.00 3. 4 presenters @ $500 $2,000.00 4. 45 workbooks @ $15 $675.00 5. 45 lunches @ $12 $540.00 6. 45 coffees @ $3.50 $158.00 Subtotal $3,623.50 7. Indirect costs @ 25% of $3,622.50 $ 906.00 Subtotal $4,529.00 8. Profit margin @ 5% of $4,528.13 $ 227.00 Subtotal $4,756.00 You are the executive director. Following the checklist in Figure 11.1, perform all the computations necessary to set a fee. What will your fee be? What is your break-even point? What is your go/no-go decision point? Fixed Costs 1. Conference room rental $175.00 $ 175.00 2. Audiovisual equipment Rental 75.00 3. 4 presenters @ $500 2,000.00 4. Indirect costs @ 25% of $3,675.00 $ 906.00 5. Profit margin @ 5% of $4,594.00 $ 227.00 Total Fixed Costs $3,383.00 Variable Costs 6. 45 workbooks @ $15 $15.00 7. 45 lunches @ $12 12.00 8. 45 coffees @ $3.50 3.50 Total Variable Costs $30.50 Breakeven point I would put my breakeven and go/no go point at 30 attendees. I have set it lower to make up for margin or error, and when more than 30 people attend the profits will also increase. This is the revenue maximization strategy that I will use. XP= A+BX 30P= 3,383 + 30.50(30) 30P= 3,383 + 915 30P= 4,298 P= 143 *Fee will still be set within the standard bracket. Exercise 11.2 As the executive director of Advocates for Children, you have had a change of heart. You decide not to attempt to maximize revenues in this second seminar. You decide to exclude a profit margin in the fee computation, but you will include indirect costs. Additionally, the local United Way in the community hosting the seminar has guaranteed 45 participants. If fewer than 45 participants register for the seminar, the United Way will make up the difference. In exchange for this guarantee, the United Way has asked you to set the seminar fee as low as possible. Following the checklist in Figure 11.1, perform all the computations necessary to set a fee. What will your fee be? Fixed Costs 1. Conference room rental $175.00 $ 175.00 2. Audiovisual equipment Rental 75.00 3. 4 presenters @ $500 2,000.00 4. Indirect costs @ 25% of $3,675.00 $ 906.00 Total Fixed Costs $3,156.00 Variable Costs 5. 45 workbooks @ $15 $15.00 6. 45 lunches @ $12 12.00 7. 45 coffees @ $3.50 3.50 Total Variable Costs $30.50 45 participants 45P = 3156 + 30.50(45) 45P = 3,156 + 1373 (rounded-up) 45P = 4549 (rounded-up) (Divide both sides by 45) P = $101.00 (rounded-up) For 45 participants,the fee is $101.00 (100.63 if not rounded-up). * I chose to use the number 45 because the United Way has guaranteed that they will make up the difference if less than 45 people attend. Reference Martin, L. (2001). Financial management for human service administrators. Boston, MA: Allyn and Bacon.

Human Growth Hormone The Picture Of Dorian Gray

Human growth hormone | Who wants to live forever? | HGH for sale, HGH supplements, HGH pills, HGH for men, HGH for women, buy HGH 2017 at www.hghworld.us People have been searching for the eternal life forever, but the researchers agree: It does not exist. Nevertheless, many desperately try to fight against old age. Last new weapon is called human growth hormone - or just HGH (human growth hormone). The dream of eternal youth is reserved for the gods, but we humans have always sought immortality. Like Dorian in Oscar Wildes The Picture of Dorian Gray , giving her soul in exchange for eternal youth and beauty. Or Orlando in Virginia Wolf s novel of the same name, after order from Elizabeth I decides never to grow old and live for†¦show more content†¦But at some point even the most skilled plastic surgeons must throw the scalpel in the ring and let nature take over and what do you do? In the American magazine Vanity Fair, one could recently read a story about the latest in discipline to cheat death. For up to $ 10,000 a year, clinics can be treated with human growth hormone - human growth hormone or just HGH (human growth hormone) - either manually or with the help of doctors injecting into the body. The result should be unbelievable according to users: marked abs, less wrinkles, greater sex drive and much more energy. HGH (human growth hormone) - or just H, as the substance is called on street level - according to Vanity Fair, has begun to circulate among the A-list celebrities in Los Angeles. Especially among those who approach or just passed the 50 years. More than 50-year-old actors who still have marked abdominal muscles and visible veins on the upper arms are undoubtedly HGH (human growth hormone), says an anonymous movie agent, who allegedly represents at least one of the major Hollywood stars. Another notability in the City of England, the former model and actor, Alana Stewart, dares to showcase his use of HGH (human growth hormone). On her birth certificate, 1945 - in the Hollywood context, the Middle Ages and not