Binomial theorem

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…

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)…

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…

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…

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.…

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…

are people that will disagree and say that the reason of evolution is because with time our species became more observant and gained knowledge and just knew that these things would work then they created them. I believe that this is completely wrong I think that there needs to be a theory then experiments, that is the only way for evolution to work. People believe that the basis of math is based off of assumptions. And I completely agree because assumptions and theories to me are synonyms.…

These things don't exist in math. Math is full of "rules" that don't have exceptions. Things such as the Pythagorean Theorem will always work for right triangles. There will never be a right triangle where a^2 + b^2 does not = c^2. This is what I like about math. Math is a subject that I think would never Let me down ; It has no contradictions. It's something that's reliable and useful. I've learned that without math, life would be a cycle of events without reason. If I ever wonder why when I…

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…

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…