Carl Friedrich Gauss Essay Example | Topics and Well Written Essays - 1000 words

Carl Friedrich Gauss - Essay Example Gauss represented a clear expression of a great mathematician of a small town called Gottingen. He is known in history for his remarkable geometrical discoveries. He is known for his discoveries in method of least squares, quadratic reciprocity, and non-Euclidean geometry. One of his greater works is also seen in astronomy. I totally agree with the works of Gauss on construction of polygons, least squares method, the fundamental theorem of algebra or the non-Euclidean's - differential geometry. Though he never published these discoveries anywhere but his work is highly remarkable. Gauss started with these discoveries at a very early age. He proved the construction of regular 17 sided polygons called heptadecagon. He proved that this can be constructed simply with the help of a ruler and a compass and thinks this is one of his greatest achievements in the history of geometry. Because as opposed to Kepler, Gauss proved that not only a triangle, square, pentagon, hexagon are constructible but then he proved it right that 17 sided figures can also be constructed with the equal lengths. He further added that 17 gon can be constructed using four quadratic equations (Swetz, 1994). One more important discovery of Gauss is the theory of least squares and normal distribution. He proved that every curve led to the least squares. He believed that the problems can be simplified by solving the errors evenly distributed. As a result, this gave the accurate estimates by solving the errors incurred in the equation. The construction was possible with trigonometric functions along with arithmetic and square roots. Gaussian distribution curve is a bell shaped curve used for normal distribution. In the Gaussian distribution, all the values combined give the value as 1. Gauss gave the fundamental theorem of algebra where he proved that any algebraic equation to the degree n, where n is a positive integer will have n number of roots. I totally agree with Gauss in his work on Disquisitiones Arithmeticae where he investigated the number theory within mathematics. Also, he made it possible to draw a circle into equal arch's just with the help of a ruler and a compass. In the number theory, he came up with an idea of congruence in numbers with the help of which infinite series of whole numbers can be broken into smaller chunks of numbers. This can e explained by taking an example: 700 - 400 = 300 right. Here the remainder is 300. This remainder can further be divided into smaller chunks of numbers like 100, 50, and 30 and so on. Here 700 and 400 are congruent to each other by modulo 100. This concept was very much popular among the digital watches. The gauss theory of numbers has its relevance even today and many great mathematicians of today hold this o pinion. It plays a crucial role in the Internet world today through security technologies (Struik 1987). In is theory of geometry, he never agreed to Euclidean's indeed known for his non-Euclidean geometry. He found that parallel postulate fails in the Euclid's geometrical theory that through a point which is not on the line, in this case either there is none or more than one parallel line. The basic difference between the Euclid and Non Euclid's theory on geometry was the nature of parallel lines. Non Euclid theory discovered the geometry of space. The non Euclidean's geometry studied Elliptic geometry

Cultural Diversity and Language Education Assignment

Cultural Diversity and Language Education - Assignment Example Spnish cme very esily to me becuse of ll the French I hd tken nd my strong desire to lern the lnguge. fter college, I trveled for yer in South meric, where I both reinforced my Spnish nd lso picked up Portuguese while visiting Brzil. When I returned from South meric I ws unsure wht I wnted to do, so I enrolled in bilingul techer eduction progrm sponsored by Title VII. yer of student teching nd bilingul methods courses certified me s bilingul techer. I becme bilingul techer out of my love for Spnish. I see the process of becoming bilingul s lifelong journey, one in which I m still involved. When I strted teching, I hd no ide tht bilingul teching ws so controversil, stigmtized, nd complex. For 6 yers, I struggled s Spnish-English bilingul elementry school techer in Oklnd, Cliforni. Prt of this struggle ws cused by lck of support from my principl nd collegues, who did not understnd the purposes of wht is needed to develop bilingulism. During tht time, I obtined mster's degree in curriculum nd bilingul eduction. t the clssroom level, despite my techer trining nd mster's degree, I still fced dily dilemms such s, "Wht should I do with 30 kids whose lnguge dominnce vries from Spnish to English nd ll the shdes in between" "Wht kind of curriculum should I use for Omr, who hs just come from Mexico to my fourth-grde clss nd doesn't know how to hold pencil becuse he hs never gone to school before" "How do I work with Guillermo, who is very bright, fully bilingul, finishes his work in 2 minutes, nd strts to red the encyclopedi becuse he's bored" "How do I tech my clss with inferior nd inpproprite Spnish mterils nd books" Somehow, I lerned to survive by creting my own mterils nd developing meningful lerning opportunities for students; by individulizing instruction; by hving students help one nother; nd by tking students out into the community nd bringing the community into the clss through trips, projects, nd guests. The effort to do this in n unsupportive environment ws t gret psychic expense tht cu sed me to burn out. I found myself becoming imptient with the children. I needed chnge. When the chnce cme to move to New York to pursue doctorte in curriculum nd bilingul eduction t Techers College Columbi University, I looked t it s n opportunity to begin to find nswers to these teching questions. From my teaching experience, I can say that second lnguge cquisition cn begin t ny ge nd hence t different levels of brin mturity nd cognitive development. It cn tke plce predominntly in forml lerning or during informl dy-to-dy communiction (depending on socil fctors, the level of cognitive development, nd previous eduction). The ge fctor is closely relted to the method of lnguge lerning due to the difference in the cognitive orgniztion of children's nd dults' lnguge cquisition. In orgnized lerning, for exmple, different types of prctice mteril nd lerning ids exploit different input nd processing modlities (visul, uditory, nd motor). First lnguge cquisition goes "hnd in hnd" with the development of cognitive bilities nd the construction