Add Math Project Essay Example

Add Math Project Essay Example Add Math Project Essay Add Math Project Essay Experience classroom environments which are Hellenizing, interesting and meaningful land hence improve their thinking skills. Experience classroom environments where knowledge and skills are applied in meaningful ways in solving real-life problems. Experience classroom environments where expressing ones mathematical thinking, reasoning and communication are highly encouraged and expected. Experience classroom environments that stimulates and enhances effective learning. Acquire effective mathematical communication through oral and writing, and to use the language of mathematics to express mathematical ideas correctly and precisely. Enhance acquisition of mathematical knowledge ND skills through problem-solving in ways that increase interest and confidence. Prepare ourselves for the demand of our future undertakings and in workplace. Realize that mathematics is an important and powerful tool in solving real-life problems and hence develop positive attitude towards mathematics. Train ourselves not only to be independent learners but also to collaborate, to cooperate and to share knowledge in an engaging and healthy environment. Use technology especially the CIT appropriately and effectively. Train ourselves to appreciate the intrinsic values of mathematics and to come more creative and innovative. Realize the importance and the beauty of mathematics. Acknowledgements First of all, I would like to say Illuminable to Allah for giving me the strength and health to do this project work. Also, I would like to say thanks to my Additional Mathematics teacher, Pun Intra Ross Lezzy Bin Zinnia Abiding for helping me by giving the rubrics and guidelines for this folio. Not forgotten my parents for providing everything such as money to buy anything that are related to this project work and their advice which is the most needed for this project such as internet, books and computers. They also supported me an encouraged me to complete this task so that I will not procrastinate in doing it. To my beloved friends, thanks for all the ideas, advices and help that you shared with me. Finally, I would like to say thanks for those who involved in the making of this folio. May God bless all your kindness. Thank you. Calculus Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of revues), and integral calculus (concerning accumulation of quantities and the areas under and between curves); these TV branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally considered to have been founded in the 17th century by Isaac Newton and Gottfried Leibniz, today calculus has widespread uses in science, engineering and economics and can solve many problems that algebra alone cannot. Calculus is a part of modern mathematics education. A course in calculus is a gateway to Other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called the calculus of infinitesimals, or infinitesimal calculus. The word calculus comes from Latin (calculus) and refers to a small stone used for counting. More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, calculus of variations, lambda calculus. Part 1 INTERNET REFERENCE BOOK Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into an array, now called a matrix which can be manipulated to find the of the system, if any.

The Biography of Edwin Hubble

The Biography of Edwin Hubble The astronomer Edwin P. Hubble made one of the most profound discoveries about our universe. He found the cosmos is much larger than the  Milky Way Galaxy. In addition, he discovered that the universe is expanding. This work now helps astronomers measure the universe. For his contributions, Hubble was honored by having his name attached to the orbiting Hubble Space Telescope.   Hubbles Early Life and Education Edwin Powell Hubble was born November 29, 1889, in the small town of Marshfield, Missouri. He moved with his family to Chicago when he was nine years old, and remained there to attend the University of Chicago, where he received a bachelor’s degree in mathematics, astronomy, and philosophy. He then left for Oxford University on a Rhodes Scholarship. Due to the dying wishes of his father, he put his career in the sciences on hold, and instead studied law, literature, and Spanish. Hubble returned to America in 1913 after the death of his father and began teaching high school Spanish, physics, and mathematics at New Albany High School in New Albany, Indiana. However, his interest in astronomy led him to enroll as a graduate student at the Yerkes Observatory in Wisconsin. His work there led him back to the University of Chicago, where he received his Ph.D. in 1917. His thesis was titled Photographic Investigations of Faint Nebulae. It  laid the foundation for the discoveries he later made that changed the face of astronomy. Reaching for the Stars and Galaxies Hubble next enlisted in the Army to serve his country in World War I. He quickly rose to the rank of major and was injured in combat before being discharged in 1919. He went immediately to Mount Wilson Observatory, still in uniform, and began his career as an astronomer. He had access to both the 60-inch and the newly completed 100-inch Hooker reflectors. Hubble effectively spent the remainder of his career there, where he also helped design the 200-inch Hale telescope. Measuring the Size of the Universe Hubble, like other astronomers, was used to seeing strangely shaped fuzzy spiral objects in astronomical images. They all debated what these things were. In the early 1920s, the commonly held wisdom was that they were simply a type of gas cloud called a nebula. These spiral nebulae were popular observation targets, and a lot of effort was spent trying to explain how they could form given the current knowledge of interstellar clouds. The idea that they were whole other galaxies was not even a consideration. At the time it was thought that the entire universe was encapsulated by the Milky Way Galaxy - the extent of which had been precisely measured by Hubble’s rival, Harlow Shapley. To get a better idea of the structure of these objects, Hubble used the 100-inch Hooker reflector to take extremely detailed measurements of several spiral nebulae. As he was observing, he identified several Cepheid variables in these galaxies, including one in the so-called Andromeda Nebula. Cepheids are variable stars whose distances can be precisely determined by measuring their  luminosity and their periods of variability. These variables were first charted and analyzed by astronomer Henrietta Swan Leavitt. She derived the period-luminosity relationship that Hubble used to discover that nebulae he saw could not lie within the Milky Way. This discovery initially met great resistance in the scientific community, including from Harlow Shapley. Ironically, Shapley used Hubble’s methodology to determine the size of the Milky Way. However, the paradigm shift from the Milky Way to other galaxies that Hubble was a tough one for scientists to accept. However, as time passed, the undeniable integrity of Hubble’s work won the day, leading to our current understanding of the universe. The Redshift Problem Hubbles work led him on to a new area of study: the redshift problem. It had plagued astronomers for years. Here is the gist of the problem: spectroscopic measurements of the light emitted from spiral nebulae  showed that it was shifted toward the red end of the electromagnetic spectrum. How could this be?   The explanation turned out to be simple: the galaxies are receding from us at high velocity. The shift of their light toward the red end of the spectrum happens because they are traveling away from us so fast. This shift is called the Doppler shift. Hubble and his colleague Milton Humason used that information to come up with a relationship now known as Hubble’s Law. It states that the farther away a galaxy is from us, the more quickly it is moving away. And, by implication, it also taught that the universe is expanding.   The Nobel Prize Edwin P. Hubble was honored for his work but unfortunately was never considered a candidate for the Nobel Prize. This was not due to a lack of scientific achievement. At the time, astronomy was not recognized as a physics discipline, therefore astronomers were not eligible. Hubble advocated to change this, and at one point even hired a publicity agent to lobby on his behalf. In 1953, the year Hubble died, astronomy was formally declared to be a branch of physics. That paved the way for astronomers to be considered for the prize. Had he not died, it was widely felt that Hubble would have been named that year’s recipient. Since the prize is not awarded posthumously, he did not receive it. Today, of course, astronomy stands on its own as a branch of science that also includes planetary science and space science. Hubble Space Telescope Hubble’s legacy lives on as astronomers continually determine the expansion rate of the universe, and explore distant galaxies. His name adorns the Hubble Space Telescope (HST), which regularly provides spectacular images from the deepest regions of the universe. Fast Facts about Edwin P. Hubble Born  November 29, 1889, Died: September 28, 1953.Married to Grace Burke.A well-known basketball player at the University of Chicago.Originally studied law, but studied astronomy in graduate school. Received Ph.D. in 1917.Measured the distance to the nearby Andromeda Galaxy using light from a variable star.Discovered that the universe is larger than the Milky Way Galaxy.Devised a system for classifying galaxies according to their appearance in images.  Honors: numerous awards for astronomy research, the asteroid 2068 Hubble and a crater on the Moon anmed for him, the Hubble Space Telescope named in his honor, U.S. Postal Service honored him with a stamp in 2008.   Edited by Carolyn Collins Petersen

Some Philosophy Questions Essay Example | Topics and Well Written Essays - 1500 words

Some Philosophy Questions - Essay Example However, Meno’s next proposal is that, virtue has the capability of exercising power over people. Socrates opposes this proposal on two grounds: first, it not honorable for children or slaves themselves to exercise power over people, and secondly, presiding over people is only virtuous if at all it is done justly. This opinion influences Meno to immediately consider virtue as being justice. But he then gives in to Socrates that integrity is a kind of virtue but not virtue itself. Since Meno is more competence, he attempts to classify virtue again, this time suggesting that it concerned with longing for good things and obtaining the power to protect them but provided that one does so justly (Plato 33-37). However, his definition again stumbles upon the predicament of using â€Å"justice† in defining virtue. So because of him being very talkative, he even starts to contrast Socrates to an animal with the name torpedo fish, claiming that it numbs anything it touches. This disturbs Socrates responding that learning is not just finding out something new, but rather recollecting something that the essence had the information about before birth, and has forgotten since then. We see him trying to review the clear picture of what he meant, by calling one of Meno’s slave boys, drawing a square containing sides of two feet, and then ask the boy to make calculation of how lengthy would be the face of a square, if it happened to contain twice an area belonging to the one he had just drawn. After the boy gets a wrong answer, Socrates helps him to recognize the correct answer without essentially explaining anything that would force the boy into solving the problem on his own. If the boy reaches into a conclusion on his own with no direct teaching, then he must have been summoning up something he already knew. Socrates proposes two hypotheses on the subject of virtue, in order to totally convince Meno. The first verbalizes that, if integrity is a category of knowledge, then teaching is a key factor and second, if it exists anything good that isn’t knowledge, the possibility is that virtue is not a class of knowledge (Plato 59-63). He later concludes that virtue is wisdom either in general or parts and therefore it cannot be something that people are born with. He also says that virtue is not necessarily a product of knowledge but of factual belief. And that it is a topic of being capable of giving a report of what people knows, just like it is reviewed by the slave boy with the mathematical proof. Question two Descartes totally agrees that mind is completely different from body by establishing two motive factors, the religious and the scientific motive that makes his argument called real distinction. The religious motivation provides a rational starting point for a trust in the soul’s immortality. The scientific motivation emphasis that the nature of mind is absolutely distinctive as of that belonging to the body, hence paving way for Descartes’ description called the new mechanistic physics. The argument therefore shows that there could be possibility for one existing without the other. In religious motivation, Descartes’ purpose of reviewing that human intelligence or soul is really different from body is to refute the irreligious people. This is because they only believe in mathematics and that they would not

Article Errors among Japanese Students Essay Example | Topics and Well Written Essays - 1000 words

Article Errors among Japanese Students - Essay Example It is relatable that the English articles 'a', 'an', 'zero', and 'the' often raise difficulty not to ESL/EFL learners alone, but even to learners of English as a first language. It is often found that the articles are a source of difficulty to learners as well as teachers of English as a second/foreign language and it is especially true about learners whose native languages do not have articles or do have articles or article-like morphemes which are used in ways that differ from English articles. An analysis of the morpheme acquisition by the learners of English as a foreign language confirms this difficulty with regard to the acquisition of English articles and it was found in a study by Brown (1973) that the articles 'a' and 'the' came at numbers nine and ten in the acquisition of fourteen morphemes. ... al errors in the use of indefinite articles and a focused study on the Japanese lower-intermediate tertiary level learners, as attempted in this paper, brings out some pertinent issues in the use of articles by EFL learners. One of the most obvious difficulties in the learning of English by the lower-intermediate tertiary level learners of Japan is the use of articles and an understanding of the language situation in the country provides the significant explanation for the type of difficulty with the use of articles. An important reason for the problems with the use of articles in Japanese context can be traced in the structure of the Japanese language along with other reasons. The Japanese students find it hard to follow the rules for the use of the article in English which are very complex. To explain the problem in linguistic terms, it will be particularly noted that there is no provision for the use of articles in the Japanese language. The absence of the article in Japanese raises serious trouble to the learners of English, especially in the early stages of EFL as in the case of the lower-intermediate tertiary level learners of Japan. It is also relatable in this context that Japanese language does not differentiate between singular and plural noun forms in grammar except in a few specific cases. This problem with regard to the concept of countability in grammar for the Japanese speakers also causes difficulty especially to the novice learners of English in the learning of English indefinite articles. The result of all these language differences in the use of articles is that the teacher of English in the lower-intermediate tertiary level introduces the articles to the learners as a totally new type of word and there is serious difficulty in the teaching of the

Sir Gawain And The Green Knight Essay -- essays research papers

Defining a True Hero Is a hero the one who decides to stand up when everyone else is only thinking about it? Is a hero the one who retains integrity rather than give in to the world’s everyday temptations? Is a hero the picture of courage, or an example of morals? These are the questions that arise after reading the epic story of Beowulf by an anonymous author, and the romantic tale of Sir Gawain and the Green Knight, also written by an anonymous author. The stories describe two very different heroes. Beowulf was undoubtedly a hero, but as time advanced and the world became more complicated, what constituted a hero became more shady; therefore, while he is not anything like Beowulf, Sir Gawain is also in fact a true hero. Beowulf is a hero. That is an undeniable fact. His heroic image stands out notably because Beowulf is what could be called an active hero while Sir Gawain plays the part of a passive hero, but still a hero nonetheless. Beowulf has one duty: he must fight and win. If he succeeds, he is a hero; if he fails he is simply a failure (except when he fails at defeating the dragon because he has already proved himself and goes with honor, which is different from initially failing). In the last lines of the story the author clearly acknowledges Beowulf’s overall triumph, "Telling stories of their dead king and his greatness, his glory, praising him for heroic deeds, for a life as noble as his name." Sir Gawain on the other hand ...

Explanatroy Synthesis – Black Hawk War

Talha Baig Dr. Amy Larsen English 1302 – UHD March 14, 2013 Explanatory Synthesis: â€Å"The Black Hawk War of 1832† Black Hawk was an Indian war chief who had a following of couple hundred Sauks Indians. Black Hawk and his followers fought against the Americans before the war of 1832 and were strictly against the expansion of Americans into their territory (Tena 2-3). The Indian war chief was born in Saukenuk and had been living there with his fellow Indians until the Americans came and forced them out of their land.Since Saukenuk was Black Hawk's hometown, he was determined to hold onto it and was ready to oppose Americans because he saw the Americans as a threat to his culture and land (John 3). His anger and disgrace towards the Americans eventually led to the Black Hawk war along with couple of other factors. The unjust treaty of 1804 was one of the main factors of the War and it made Black Hawk even more concerned about the Americans and the treaty also caused som e intertribal rivalries between different Indian tribes but even after that Black Hawk was hoping to avoid a war.It is known that the American soldiers who confronted Black Hawk allegedly fired the first shot, which started the Black Hawk war. The United States Government put forth many treaties to obtain the Land from the Indians but the unjust Treaty of 1804 is known as the main factor that led to the War of 1832. The way the signing of the this Treaty took place was very unlawful because most of the Indians who signed it were not really main authority holders of the Indian tribes and the signing of the treaty proceeded even though there were many Indians who were not ready to sell their lands over to the Americans (John 1).Some of the Indians did not even fully understood the conditions of the treaty and the worst part of this treaty was that it gave the land of the Saukenuk village over to the Americans, which made Black Hawk furious and bitter (Tena 3). Since even Black Hawk, w ho was a major Indian chief did not have the complete knowledge about the extent of the Treaty, it proves that the Treaty of 1804 was unlawful and unjust. After the Treaty of 1804, Black and other Sauks became extremely bitter and enraged towards the Americans. The Treaty also ended up causing some intertribal rivalries between the indian tribes.Black Hawk and his followers were not willing to accept the terms of the treaty of 1804 and wanted to resist the American ways but on the other hand some Indian tribes feared that they would stand no chance against the Americans and did what they were told by the Americans, which became the cause of tension between the Indians (John 2-3). One of the leaders who held a different point of view from Black Hawk was Keokuk, who was also the leader of Sauks indians and he had no intentions of resisting against the Americans ( Jane 4 ).The different point of views of the Indian tribes and the intertribal rivalries that the Treaty of 1804 stirred up caused Black hawk and his followers to go on a different path, which was to try and move back to the land where they all originally started from. That land was Illinois and the Americans had begin settling there. Black Hawk and his followers tried several times to retake their hometown but could not succeed and were attacked by the Americans, which led to the conflict known as the Black Hawk war.The Indian chief with his couple hundred followers decided to resist against the Americans and tried going back to where they started from, with the purpose of settling there (Jane 4). However, Black Hawk was still hoping to avoid getting into a war with the americans but in the end it was inevitable. The Americans always thought of the native Indians as savages, who killed a lot of Americans in the past. So when Black Hawk and his people were crossing the Mississippi River, they were attacked by the American soldiers and the Indians ultimately lost (Arnold 1).It is known that the Americans allegedly attacked and fired on the Indians first, which resulted in the Black Hawk war of 1832 and the capture of the Indian Chief; Black Hawk by the Americans. The road to the Black Hawk war of 1832 was paved by the unlawful treaty of 1804, which not just enraged Black Hawk but also caused a lot of intertribal rivalries between the Indians and further more the unjust actions of American soldiers brought upon the downfall of Black Hawk (Tena).One can easily blame the treaty of 1804 for ultimately dividing the indians and for their bitterness towards the United States government, since Black Hawk was just trying to protect the land and the culture of his people (John 3-4). Word Cited Tena L. Helton. â€Å"What the White â€Å"Squaws† Want from Black Hawk: Gendering the FanCelebrity Relationship. † The American Indian Quarterly 34. 4 (2010): 498-520. Project MUSE. Web. 14 Mar. 2013. Arnold Krupat. Patterson's Life; Black Hawk's Story; Native American Elegy. † Ame rican Literary History 22. 3 (2010): 527-552. Project MUSE. Web. 14 Mar. 2013. John K. Flanagan. â€Å"The Treaty of St. Louis and Black Hawk's Bitterness. † 21 N. Ill. U. L. Rev. 405. (2001 ): 2553 words. LexisNexis Academic. Web. 14 Mar. 2013. Jane Simonsen. â€Å"Descendants of Black Hawk: Generations of Identity in Sauk Portraits. † American Quarterly 63. 2 (2011): 301-335. Project MUSE. Web. 14 Mar. 2013.

A Few Good Men Legal Analysis - 796 Words

A Few Good Men Legal Analysis - Aakriti Gera A Few Good Men is a 1992 American legal drama directed by Rob Reiner. The story follows the court-martial of two U.S. Marines, who are charged with the murder of a fellow marine and the problems faced by the lawyers, of the accused, while preparing their defenses. The Marines are on a murder trial for carrying out a â€Å"code red† order. The movie refers to â€Å"code red† as a type of extrajudicial punishment used for an alleged crime or offense, which is carried out without a legal procedure. A young lawyer who lacks experience and enthusiasm defends the case. The lawyer immediately jumps to a bargain plea in order to settle the case quickly. In legal terms, a plea bargain allows a lawyer the freedom to negotiate on behalf of the client. In return, the client pleads guilty to one charge, which means that a second charge would be dropped. Such settlements seem quicker and easier, whilst still providing with the guilty verdict for the prosecution. The Marines are set to face charges of murder, conspiracy to commit murder and conduct unbecoming a marine. The movie highlights a few ethical issues. One talks about the ethical conduct, acting in accordance with orders and duties. The first scene of the movie shows such an order being carried out, hence the questions to be followed are as follows, and did Dawson and Downey do the correct by following such an order? As I watched the movie, I noticed that according to their duties they didShow MoreRelatedA Few Good Men Summary938 Words   |  4 PagesA Few Good Men Summary A few Good Men is a movie that presents strong a strong ethical dilemma. The story is about two Marines Pfc Downey( James Marshall), and Lanc Cpl. Dawson (Wolfgang Bodison) who are charged with the murder of another marine PFC Santiago. 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