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Brief Summary of Historical Orientation of Mathematics

1 pages (250 words)

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... a brief summary of Historical Orientation of Mathematics combining Political Events, Cultural Events and Mathematical Ideas As far as the history of mathematics is concerned, the same can be traced back to 3000 BCE. The political and cultural events related with the evolution of mathematics bring quite a few significant things in perspective. The Base-60 place value system started to develop within Mesopotamia and the Egyptians used the base-10 for grouping different numbering systems. This was the time when Harappan civilization was getting its roots firm within India. By 2000 BCE, Pythagorean triples and quadratic equations had started to form important basis. In about a thousand years’ time, by...

Counting Systems

5 pages (1250 words)

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... of Counting Systems The first operation to be considered is numeration, which is defined in a rather modern vein as the representation of numbers by symbols. To fully appreciate the task the Treviso's author is undertaking in this section, one should understand the level of acceptance for the "Hindu-Arabic" numeral system that existed in Europe at this time (Al-Daffa, 1977).. The new numerals had been known in Europe from about 1000 A.D. yet they had not been universally accepted for use. Computing and the techniques of arithmetic still centered around the manipulation of counters and recording one's results with Roman numerals. There was a certain social status and prestige associated with the use...

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History of Mathematics High School Essay

2 pages (500 words)

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... Describe the system of rod numerals and its origin. Originally, the Ancient Chinese used the Rod numerals in doing computations. It was used before the invention of the abacus. Today, these can be seen in some Chinese markets in Hong Kong. Rod numerals or counting rods are short rods that are manipulated on top of a wooden table or counting board in doing the computations (Wikipedia). The way that a number is presented by counting rods is called the rod numeral system. The Chinese Rod Numeral System has only 9 numerals that can be represented in two ways depending on their position. It uses the decimal place value system for values greater than 10. The rods are placed in columns with the rightmost...

How concerns of commerce and business spur on the development of mathematics

9 pages (2250 words)
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... Concerns of Commerce and Business in Development of Mathematics The historical study of mathematics was more of an investigation about the original mathematical discoveries and ancient mathematical methods and other notations. In the old age, before the worldwide knowledge spread, developments towards mathematics were only within very few locales (Menninger 77). The oldest mathematical texts that were available included, the Rhind mathematical papyrus, which was of Egyptian mathematics between 2000-1800 BC, Plimpton 322 of Babylonian mathematics in 1900 BC and the Moscow mathematical papyrus in 1890 BC. These texts were all in accordance to the Pythagorean Theorem that is the oldest and known to...

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Ancient and Indigenous Mathematics

8 pages (2000 words)

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... and Indigenous Mathematics Introduction A brief and meaningful definition of mathematics is difficult yet it is also difficult to imagine a world without mathematics. Most histories of mathematics that have greatly influenced the growth and development of mathematics were written in the nineteenth century. At that time, there were two different developments that were taking place that directly affected both the content and balance of these books, particularly those produced in the United States and Britain (Graham, 2012).
The discoveries of ancient mathematics on clay tablets in Mesopotamia and papyri in Egypt pushed back the origins of written mathematical records by at least fifteen centuries. Ho...

1 pages (250 words)

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... Part a. In your own words, define the word “function.” Function refers to a relation madeby ordered pairs (x, y) composed of the domain (x-values) and the range (y-values) that have one-to-one correspondence with each other.
b. Give your own example of a function using a set of at least 4 ordered pairs.
Example: (1, -5) (3, 0) (5, 1) (7, 4)
c. Explain why your example models a function.
The given example models a function because the values of ‘x’ is in the set of ordered pairs are distinct so that there exists a unique ‘x’ that matches every ‘y’ in the range.
d. Give your own example of at least four ordered pairs that does not model a function.
Example: (8, -7) (...

2 pages (500 words)

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... Difference Between a Linear Equation and a Function. A linear equation, y = mx + b, refers to an equation which exhibits a linear relationship between the domain or set of x-values and the corresponding range or set of y-values. Linear equations are normally first degree with respect to both ‘x’ and ‘y’ except in case where x = constant in which the degree of ‘y’ is zero and ‘x’ remains the same at any value of ‘y’ and in case where y = constant in which the slope is zero as well as the degree of ‘x’. All linear equations are function.
Examples of a Linear Equation:
(a) y = 2x + 5 (b) y = -3x + 4
On the other hand, a function pert...

On the Numerical Solution of Black-Scholes Equation

3 pages (750 words)
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... Solution of Black-Scholes equation Introduction Black-Scholes model is used to describe behaviour of derivative instruments like call and put option. The model yields a partial differential equation called the Black-scholes equation which can reduced to the form of the famous heat equation. Partial difference equations can be solved using either Finite difference methods or Finite element methods. Both these methods make use of a discrete mesh and the values are calculated at the mesh points by iteration using known values. This paper discusses an alternative method which is meshless and is based on Radial Basis functions(RBF’s).It discusses the results obtained after using different sets of RBF’s...

Chaos theory Applications to PDEs (geometry design)

8 pages (2000 words)
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... of Chaos Theory in the Differential Equations Application of Chaos Theory in the Differential Equations Introduction The chaos theory in the finite dimensional dynamical systems is known to exist and it includes or leads to the development of discrete systems and maps of the ordinary differential equations. This theory has led to profound mathematical theorems that have numerous applications in different fields including chemistry, biology, physics, and engineering among other fields or professions (Wasow, 2002). However, the chaos theory of the partial differential equations has never been well-developed (Jordan and Smith, 2003; p. 55). Therefore, there has been a growing demand for the development ...

Mathematics Assignment

4 pages (1000 words)

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... Calculate the following: (a) 12.345 300.47) = 12.345 - 300.47 = -288.125 (b 111.3) - 17.08 = -111.3 - 17.08 = - 128.38 (c) 34.56 0.005)= - 0.1728
(d) (-123.046) (-7.04) = 123.046 7.04 = 17.478
2. Simplify the following:
(a) 3ab - 5ab + 4ab = -2ab + 4ab = 2ab
(b) 5x - 7xy + 3x + 4xy = (5x + 3x) + (4xy - 7xy) = 8x - 3xy = x(8 - 3y)
3. Calculate the following:
(a) 3ab * 5/2 ac2 = 15/2 a2bc2
(b) 3xy2z (-3/2 xz2) = 3xy2z * (-2/3 xz2) = -2y2 / z
4. Simplify the following:
(a) = = =
(b) = ==
5. Let p and q be the polynomials
p = 3x2 - 2x + 5; q = 5x - 4
Calculate:
(a) P + q = 3x2 - 2x + 5 + 5x - 4 = 3x2 + 3x + 1
(b) P - q = 3x2 - 2x + 5 - (5x -4) = 3x2 - 2x + 5 - 5x + 4 = 3x2 - 7x + 9
(c) P*q = (3...

On the geometry of piecewise circular curves T.F.Banchoff and P.J.Giblin, American Mathematical Monthly, (101),1994,403-416, In the plane a smooth piecewise circular curve is a curve made from arcs of circles such that at points where two arcs join the

6 pages (1500 words)

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... the plane a smooth piecewise circular curve is a curve made from arcs of circles such that at points where two arcs join the tangent lines agree. Properties of such curves are considered in this paper."
PIECEWISE CIRCULAR CURVES
Banchoff and Giblin define the piecewise circular curve thus: “A PC curve is given by a finite sequence of circular arcs or line segments with the endpoint of one arc coinciding with the beginning point of the next.”
Jaroslaw R. Rossignac and Aristides A. G Requicha view PCCs as “composed of line and arc segments and exhibit first-degree geometric continuity (GI), i.e., they have continuous unit tangent directions.”
These piecewise circular curves or PC curves have according...

Chemistry Practical Assignment - Copper carbonate

4 pages (1000 words)

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... Practical Assignment Introduction: Copper carbonate if heated will produce gas and by measuring the volume of gas, we can experimentally establish the correctness of both the equations provided to us.
The important thing for finding the correct equation is that the volume of one mole of gas at NTP is 22.4 liter and using this equation we can back calculate the mole or mass of carbon dioxide formed from the copper carbonate used for the experiment (Determining the Correct Equation for the Decomposition of Copper Carbonate, 2003) and hence find out the correctness of the eauation provided.
Equipment and Apparatus required for conducting the experiment: The following apparatuses are required to cond...

Understanding the definition of words

1 pages (250 words)

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... Part Discussion 1. In your own words, define the word “function.” Function pertains to a relation established by coordinates in ordered pairs (x, y) consisting of the domain (x-values) and the range (y-values) where each value of ‘y’ corresponds to a distinct value of ‘x’.
2. Give your own example of a function using a set of at least 4 ordered pairs.
Example: (4, -7) (0, -3) (1, 2) (3, 5)
3. Explain why your example models a function.
The given example models a function because for each unique value of ‘x’ in the domain, there corresponds a value of ‘y’ so that the relationship basically shows a one-to-one correspondence. No value of ‘x’ appears more than once in the examp...

Math Project

4 pages (1000 words)

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... Unit 4 Section Number: Instructions: Identify the document by typing your full and section number next to the yellow text. Re the file.
Type your answers next to the yellow text.
Unless otherwise stated, answers requiring decimal places should be rounded to two decimal places. This includes rounding dollar and cent amounts to the nearest cent.
To show your work, you will need to include
the algebra used to compute the solution to any equations
the formula with substituted values.
the final calculated answer with units.
To utilize the scientific calculator on your computer, do the following:
Open the calculator (if it is not in the accessories folder, then select Run from the Start menu)
Select Vie...

6 pages (1500 words)

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... Continuous flight Auger (CFA) is considered to be present between driven piles and drift shaft. This idea has a primaryattribute towards different lateral stress changes during times of installation of the various types of piles. In most cases especially during drilled shaft construction, soil stress seems to reduce or stay at the initial rate of excavation of a pile. When installing a driven pile, the process involved displaces the soil vertically and hence it raises the stress in the construction site or soil that surrounds it. It is highly important to note that the estimated static CFA capacity is achieved through methods that are developed for specific objects such as drilled shafts and driven...

Report

3 pages (750 words)

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... report Finding minima and maxima using Mathematical modeling College In this report mathematical modeling methods are going to be used to find the maximum and minimum heights for two roller coasters namely Feel the Fear and the Giant roller coaster. The same methods are to be applied in finding the maximum possible area of a fence enclosure and the dimensions of a snack bot those that yield maximum volume.
A step by step process is going to be used in the presentation of this report and the equations as well as the problems are going to be elaborately explained.
Introduction
Mathematical modeling is the process of describing a system using mathematical concepts and mathematical language. Mathematic...

Head Loss Fluid Mechanics

15 pages (3750 words)

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... Loss Fluid Mechanics Introduction Fluid flowing in pipes is usually turbulent. The flow is considered turbulent if the Reynolds value is greater than 4000. During the turbulent flow, the velocity distribution is relatively the same (or uniform) and the velocity profile is flatter in comparison to the laminar flow. It is important to note that there are pressure fluctuations and irregular velocity in turbulent flow. In turbulent flow, fluctuations in velocity influence the mean motion such that it causes additional shear resistance to the flow. The turbulent shear stress is composed of shear stress and viscous shear stress generated because of turbulence (Sawhney 2011, p629). Fluid flowing through a...

Using differentiation find the difference between maximum and minimum heights for both the roller coasters

3 pages (750 words)

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... Modeling Teacher’s Institute Mathematical Modeling Introduction Mathematical modeling is an approach to describe different phenomenon of nature, society and human activities using various mathematical formulas. Mathematical modeling describes real world issues. These issues may relate to science, engineering, economics, sports, financing and many other disciplines. Using mathematical formulas, people express the cause and effect relationship of a phenomenon. Mathematical modeling is nothing but finding relationship among different variables that describe a phenomenon or object (Simon Fraser University n.d.).
The process of mathematical modeling is like conducting a lab experiment in physics, ch...

Heat exchanger

8 pages (2000 words)

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... exchanger al affiliation The main aim of this experiment is to enable the familiarize with the shell and tube heat exchanger and to determine the overall efficiency of the current rates of different fluids. The experiment aims to determine the effect of changing current on the shell and tube heat exchanger efficiency and overall heat transfer. Moreover, this experiment aims to find out the temperature efficiency for co-current and counter current, the concurrent and the counter current operation overall heat transfer coefficient, the number of transfer units and the efficiency of the heat exchanger. In this experiment, the shell and tube exchanger that was used comprised of a number of tubes that...

Materials and Surface Engineering

5 pages (1250 words)

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... a) Modulus at the contact of two metals (Econ) is given by the following equation. Where E1 = Elastic modulus of metal; E2 = Elastic modulus ofmetal;
1 = Poisson’s ratio of metal 1 and
2 = Poisson’s ratio of metal 2
In this problem, as both the plates are of the same metal copper.
Therefore,
E1 = E2 = ECu = 140 GPa and
1 = 2 = Cu = 0.3
Therefore,
i.e. GPa
This means modulus at the contact is much smaller that modulus of a metal in a bulk.
Q1. b) Hardness of a metal (H) and its yield stress (y) are related by the following approximate relationship.
……………… (1)
The yield point is very near to the elastic limit of a metal and therefore, Hook’s law can be used to get strain at yield stress.
T...

Multiphoton Excitation for organic complex

48 pages (12000 words)

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... Introduction Recently, multiphoton induced emission is one of the hot research topics in near 20 years 9]. Therefore, there are many research groups which are drawing greater attention on organic material. The most common one is the organic material which consists of a typical Donor-acceptor D--A charge transfer structure. It processes a high nonlinear susceptibility. It also indicates that the material has high potential for nonlinear optic application. However, Donor-acceptor chromophores possessing a highly polarizable -conjugated system with highly two photon absorption active; but, it is not guaranteed that they will exhibit interesting and useful three photon absorption properties such as ...

Chemical Engineering Dissertaion. Designing a venturi scrubber

24 pages (6000 words)
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... Enginering Design of Venturi Scrubber 0 Introduction Contaminated gas is ushered into contact with curtains of liquid spray that is directed at right angles to gas flow after entering involute section. Scrubbed gasses proceed along the involute. The bulk of the liquid is separated and the remainder entrained as the droplets are removed as they enter the spin zone. The liquid reaches the bottom of the cone drain by force of gravity as the cleaned gases leave the scrubber at the outlet.
1.1 Principles
This gas scrubber accelerates the scrubber liquid, together with the air or gas exhaust stream, to high velocities and turbulence. This happens in the bottleneck of the venturi. Behind this bottleneck, t...

Tankless water heaters

10 pages (2500 words)

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... PROPOSAL Governor Rick Perry Texas Energy Conservation Office (SECO) {First Last} December 06, Re: New Residential Code Requirements for the Installation of Tankless Water Systems (Effective Date: January 01, 2015) Introduction Estimates for the year 2000 indicated that American households consumed 20% of the total energy consumption in the US (Stein & Meir, 2000). Estimates published by the Need Project (2012) reveal that in 2005 consumption by US households and the commercial sector combined for 42.1% of all the energy consumed in the US. According to the US Department of Energy (2012), the latest available data reveals that in 2005, American households spent US$201 billion on energy. Adomatis...

PETROLEUM ENGINEERING DESIGN PROJECT

18 pages (4500 words)

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... A study of formation damage in 10 Kilometer Well M-11 in the Wytch Farm Oil Field Wytch Farm Oil Field is considered as one of the largest oil fields in Europe. The oil field comprises of three major oil reservoirs. Due to the fact this oil field is associated with limestone and shale, its permeability is low such that if necessary action would have not been taken the reservoir might have been economically not viable, and exploitation might not been enhanced. In order to increase the permeability of one of the wells in Wytch Farm Oil Field, a horizontal well was developed. The development (particularly completion) of horizontal wells is usually associated with formation damage. In this research, the ...

Sir Isaac Newton as the Father of Modern Science in Scientific History

7 pages (1750 words)

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... HEAD: SIR ISAAC NEWTON: THE FATHER OF MODERN SCIENCE Sir Isaac Newton: the Father of Modern Science in Scientific History Date Sir Isaac Newton: the Father of Modern Science in Scientific History Introduction In scientific history Sir Isaac Newton is considered as the father of modern science because of his epoch-making and unique contributions to the science of physics and mathematics. Though in the field of physical science his predecessors have excelled in theoretical explanations of the behavior of the physical world, Newton provided theories a solid mathematical ground. He is mostly remembered because of his book “Philosophia Principia Mathematica” in which he explains the behaviors of moving...

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