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Problem 4. Prove that (y^3+z^3 ) x^2+yz^4 is irreducible over C[x,y,z]. Also prove that (y^3+z^3 ) x^2+y^2 z^3 is irreducible. Assume that (y^3+z^3 ) x^2+yz^4=a*b. Then one of a or b is linear in x^2 and the other doesn’t have x^2 at all because the degree of the product is the sum of the two degrees. Now we write 〖a=cx〗^2+d, so c and d have only y’s and z’s. Then (y^3+z^3 ) x^2+yz^4=(〖cx〗^2+d)*b But now b*d=yz^4, and since C[y,z] is a unique factorization domain, b and d must be monomials.

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Decent EssaysOver time, Fox wanted a spin-off show and Futurama was born. Futurama extends the jokes that were used in the Simpsons to a higher-dimension. Many of the jokes in Futurama involve sophisticated relationships learned in multivariable calculus such as surface integrals and Mobius strips among other topics. The second half of the book focuses on these more advanced topics as portrayed in

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Decent EssaysMy favorite AP Calculus AB topic is solving limits. This is because limits are fairly simple to solve. AP Calculus AB was extremely difficult for me, so I was happy to find a topic that was somewhat easy for me to understand. I know that a limit is the value that a function or sequence approaches as the input or index approaches some x-value. To solve most limits, I had to use six basic properties of limits: the sum rule, the difference rule, the product rule, the constant multiple rule, the quotient

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Better EssaysThe major topics explored in Calculus C are largely defined by derivatives of vector-valued and parametrically defined functions, integration by partial fractions, improper integrals, series convergence (Taylor and Maclaurin), L’Hopitals Rule, and numerous applications. All of the following topics require a solid foundation in not only Calculus A but also Calculus B. Vector-valued functions include mathematical functions of one or more variables whose range is defined as a set of both multidimensional

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Decent Essaysand what I learned as well as my career. I was placed in Sharpstown International School, in which I was with Mr. O 'Heron. He taught both Pre-calculus and Calculus classes. Those two classes are for seniors and there may have been a few juniors in the pre-calculus class. There are in total four classes that I observed, one calculus and the rest pre-calculus. Activities Throughout the field, I barely engaged in any different activities, mainly observe the students. Though they did ask a few questions

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Decent EssaysLeonhard Euler was born on April 15, 1707, in Basel, Switzerland, Leonhard Euler was one of math's most pioneering thinkers, establishing a career as an academy scholar and contributing greatly to the fields of geometry, trigonometry and calculus. He released hundreds of articles and publications during his lifetime, and continued to publish after losing his sight. Euler showed an early aptitude and propensity for mathematics, and thus, after studying with Johan Bernoulli, he attended the University

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Decent EssaysIt was December and near the end of the first semester of my senior year. I sat next to my close friend Adrian as I helped him understand the last few AP Calculus lessons. The time had reached 4:30 P.M., and we’d been sitting together in Mr. Brink’s room after school for almost two hours. Mr. Brink sat at his desk while Adrian and I were at a different table. Only the three of us remained in the room. Eventually, Adrian started to pack up. I gave him a hug as he left, then sat back down. As I looked

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Decent EssaysPrior to taking Pre – Calculus I had taken College Algebra which has helped me tremendously with the objectives of Pre – Calculus. I learned basic algebra skills that helped me advance in solving the objectives needed for the advancement of the course. I am currently working for a construction framing business in which some math skills are required. I plan on obtaining a major in structural engineering and a minor in mechanical. The College Algebra class thought me how to add, subtract, divide

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Decent Essaysreceiving stickers and praise notes in elementary school to non-stop studying for an algebra test, I’ve always expected an A on my assignments. But then came junior year of high school. I had signed up for one of my school’s most demanding courses, AP Calculus AB. On the first day of class, the teacher explained the depth of the material we would be learning, telling us that it would cover a wide range of math, and showed us a brief introduction to it. He also mentioned that it was a course where we would

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Decent EssaysThe purpose of this project is to solve the game of Light’s Out! by using basic knowledge of Linear algebra including matrix addition, vector spaces, linear combinations, and row reducing to reduced echelon form. | Lights Out! is an electronic game that was released by Tiger Toys in 1995. It is also now a flash game online. The game consists of a 5x5 grid of lights. When the game stats a set of lights are switched to on randomly or in a pattern. Pressing one light will toggle it and the lights

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