Binomial theorem

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  • Pascal's Triangle Essay

    scholars around 2nd century BC-10th century AD. I will use the binomial expansions derived from Pascal’s triangle as an example and then illustrate the coefficients expansion in general. After that, I will introduce Jade Mirror of the Four Unknowns written by Zhu Shijie around 14th century AD. My focus will be his idea of using the “four unknowns” to convert a problem into a mathematical system of polynomial equations. Later on, I will also…

    Words: 1661 - Pages: 7
  • Hypergeometric And Negative Binomial Distribution

    HD is the exact number of “S” in a sample. Calculations were the earliest use; and I use the same example as above. According to scientists, “the representation H (x; n, M, N) is the proper way to show this distribution. In contrast, NBD is the amount of failures per each random trial, with successes being fixed. Today, measurement, counting, and data are some of the ways they are used. The number of students that a tutor helped to receive either a pass or fail is my example. Nb (x; r, p)…

    Words: 841 - Pages: 4
  • Mathematical Proof Analysis

    Mathematical proof is a method used in both primary and secondary schools at varying levels. Children should be able to justify and give reasons for a conjecture they have produced in order to validate a mathematical proof. There are various techniques that can be used to illustrate the nature of proof in schools. Mathematical proof is defined as a thorough and believable argument to support the truth of a prediction in maths, which turns the assumptions into valid conclusions (Haylock and…

    Words: 785 - Pages: 4
  • Interactional View And Genderlect Styles

    As we delve deeper into our theories on interpersonal communication, we begin to learn more about ourselves and how to interact with the people around us. Whether they are in our lives on a personal, professional or combined capacity. This week I have decided to look at the theories of Interactional View and Genderlect Styles (Griffin, 2015). When we study Interactional View, a theory developed by Paul Watzlawick, we can see how communication has shaped us into the people we are today.…

    Words: 972 - Pages: 4
  • Tom Stoppard's Representation Of Gender In Arcadia

    standard practices during the time period because he prefers pleasure from sex from unconventional methods over loyal monogamy. Septimus is academically tutoring Thomasina, but is also teaching her sex in a unique manner considering their time period. This introduces Thomasina’s desire for knowledge, but also how sex and mathematics can be a societal battle. Septimus then immediate contrasts sex to math in order to portray how even though they seem like binary oppositions, they are immensely…

    Words: 1006 - Pages: 5
  • Proof In VCE Mathematics Study

    that one of the central goals of school mathematics, notably at the upper secondary level, is the development of proof concepts (Coe & Ruthven, 1994). The incorporation of algebraic proofs in Victorian Mathematics education also refutes the criticism that the focus on algebraic proofs theme is sporadic at the secondary school level (Pedemonte, 2008). Many different methods of proof are stated in both the VCE Mathematics Study Design 2016-2018 and some VCE Mathematics textbooks: Specialist…

    Words: 1036 - Pages: 5
  • Standard Deviation In Statistics

    Probability Warning, quit reading now if you don’t want to learn about how important probability and different parts of it are. Still reading? By the end of this paper you will be able to identify what probability is and what the different parts are, how they can be applied in the real world, and why it is important in a career. Independent Events what are they? When two events are independent of each other hints the name, this means is that one event has no effect on the other event. An example…

    Words: 1005 - Pages: 5
  • Methane-To-Methanol Reaction Report

    A. Defining Reaction Mechanisms and Catalyst Structure The methane-to-methanol reactions that we aimed to evaluate consist of four critical steps starting from the initial reactants (CH4, NH4+, oxo): C-H activation followed by a hydrogen atom abstraction (HAA) from CH4 to form some combination of the hydrogenated complex, ammonium or ammonia, and a methyl radical; a radical rebound (RR) to form a methanol adduct and ammonium; methanol dissociation from the metal; and catalysis regeneration via…

    Words: 1109 - Pages: 5
  • The Einstein-Podolsky-Rosen Experiment

    action at a distance would describe all the uncertainties of quantum physics and would help us understand the unknowns of quantum mechanics. There have been varies experiments that support the claims of action at a distance and those who disagree and look to disprove this concept. One of the experiments that disproves the argument is the Einstein-Podolsky-Rosen experiment in short known as the EPR experiment. The correlation in this experiment mainly suggest that there are no influences between…

    Words: 1672 - Pages: 7
  • The Pythagorean Theorem: Euclidean Geometry

    Pythagorean Theorem The Pythagorean Theorem also known as Pythagoras’s theorem is a relation in Euclidean geometry that are the tree sides of a right triangle. It’s the sum of the areas of the two squares on the legs equals the area of the square on the hypotenuse. The equation use for it is A squared plus B squared equals C squared.The Theorem relates the lengths of the three sides of any right triangle. The theorem is named after the ancient Greek. There is evidence that indicates that…

    Words: 526 - Pages: 3
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