The Mathematical Significance of Leon Mirsky
Leon Mirsky was born on December 19, 1918 in Russia. In 1926, The Mirsky family moved to Germany and seven years later in 1933, they were forced out of Germany and settled in Bradford, England. In 1936, he began studying for his Intermediate Exam at King's College in London. After his exam, he received a scholarship for a degree in math. Leon graduated in 1940 and went on to receive his Masters Degree and then a Ph.D. in 1949.

In his work towards a mathematics degree, Mirsky developed a great interest in the number theory and Mr. Edmund Landu, a proponent of the theory who wrote several papers on the subject in 1899. The Number Theory is a theory describing all of the properties of numbers, such as prime numbers, algebraic number fields, and quadratic forms.

Mirsky studied three major fields, the first being the theory of numbers, the second being linear algebra, and the third being combinatorics. In his first field of study, the theory of numbers, he studied numbers that are not divisible by the rth power of an integer. He also verified, with similar results, the representation of an odd integer as the sum of three primes. He also contributed to the Goldbach conjecture that any even number greater than two can be written as the sum of two prime numbers. He also added to the twin primes conjecture which says that twin primes are pairs to primes that are 2 apart. Examples of this are 41 and 43 as well as 5 and 7. The conjecture also states that pairs of such primes are infinite.

Mirsky also studied linear algebra on which he wrote several papers. Mirsky most notably wrote An Introduction to Linear Algebra (1955) as well as 35 other papers on the subject. His accomplishments in this field include proving the existence of matrices with eigenvalues and diagonal elements. His book, An Introduction to Linear Algebra covers information that includes determinants, vectors, matrices, linear equations and quadratic...

...Function
p(y) =
n
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p y (1 − p)n−y ;
Mean
Variance
MomentGenerating
Function
np
np(1 − p)
[ pet + (1 − p)]n
1
p
1− p
pet
1 − (1 − p)et
y = 0, 1, . . . , n
Geometric
p(y) = p(1 − p) y−1 ;
p
y = 1, 2, . . .
Hypergeometric
p(y) =
r
y
N−r
n−y
N
n
;
nr
N
n
r
N
2
N −r
N
N −n
N −1
y = 0, 1, . . . , n if n ≤ r,
y = 0, 1, . . . , r if n > r
Poisson
Negative binomial
λ y e−λ
;
y!
y = 0, 1, 2, . . .
p(y) =
p(y) =
y−1
r−1
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y = r, r + 1, . . .
λ
λ
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MATHEMATICAL STATISTICS WITH APPLICATIONS
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SEVENTH EDITION
Mathematical
Statistics with
Applications
Dennis D. Wackerly
University of Florida
William Mendenhall III
University of Florida, Emeritus
Richard L. Scheaffer
University of Florida, Emeritus
Australia • Brazil • Canada • Mexico • Singapore • Spain
United Kingdom • United States
Mathematical Statistics with Applications, Seventh Edition
Dennis D. Wackerly, William Mendenhall III, Richard L. Scheaffer
Statistics Editor: Carolyn Crockett
Assistant Editors: Beth Gershman, Catie Ronquillo
Editorial Assistant: Ashley Summers
Technology Project Manager: Jennifer Liang
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Marketing Assistant: Ashley Pickering
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Amidon-Brent
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Art Director: Vernon Boes
Print Buyer: Karen...

...The description of jails place in correction and its role throughout history
Jails were initiated before any other component within the correctional system such as prisons, probation, or halfway houses. These institutions are considered the front line of the correctional system because nearly every offender starts their journey through the system here. King Henry II ordered the first jail or gaols as they were known then, to be built in 1166. The purpose of these jails was to house displaced persons, the mentally ill, and the poor. The conditions within the jail were horrid, they were filled with violence, lack of sanitation, poor food, and lack of discipline. In 1773 John Howard, sheriff of Bedfordshire, was disgusted by these conditions and began inspecting other European jails to replicate a model for the operations for the jails in England. He began to work with members of the English House of Commons to create requirements (standards of operations) for English jails and prisons and the outcome was the Penitentiary Act of 1779. This Act stated jails must meet certain requirements such as (1) secure and sanitary structures (2) systematic inspections. (3) abolition of fees charged to inmates , and (4) a reformatory regime in which inmates were confined in solitary cells but worked in common rooms during the day ( Corrections: An Introduction 3e ) the U.S. colonies adopted to English model of a jail and began housing inmates, awaiting trial. The walnut street jail was...

...Critiquing the Mathematical Literacy Assessment Taxonomy: Where is the Reasoning and the Problem Solving?
Hamsa Venkat 1 Mellony Graven 2 Erna Lampen 1 Patricia Nalube 1
1 Marang Centre for Mathematics and Science Education, Wits University hamsa.venkatakrishnan@wits.ac.za; christine.lampen@wits.ac.za; patricia.nalube@wits.ac.za
2 Rhodes University
m.graven@ru.ac.za
In this paper we consider the ways in which the Mathematical Literacy (ML) assessment taxonomy provides spaces for the problem solving and reasoning identified as critical to mathematical literacy competence. We do this through an analysis of the taxonomy structure within which Mathematical Literacy competences are assessed. We argue that shortcomings in this structure in relation to the support and development of reasoning and problem solving feed through into the kinds of questions that are asked within the assessment of Mathematical Literacy. Some of these shortcomings are exemplified through the questions that appeared in the 2008 Mathematical Literacy examinations. We conclude the paper with a brief discussion of the implications of this taxonomy structure for the development of the reasoning and problem‐solving competences that align with curricular aims. This paper refers to the assessment taxonomy in the ...

...Significance of the study
Point of sale or POS systems are a necessary and invaluable part of most businesses. While they traditionally referred to an automated cash register, modern technology has seen that change to include a number of other elements that all make a business more efficient and easier to run.
Common POS systems include a computer, receipt printer, lockable cash drawer, a scanner to read the bar code, a magnetic swipe reader and a modem and pole display. Then there is the POS software. POS systems these days have come a long way from the early ones and do much more work. In fact they now do so much more that the POS element has now become just one more module in amongst many others, but it is none the less an important part of each business.
As well as actually allowing the customer to purchase goods, POS systems allow the business operator to do nearly everything from ordering and purchasing stock to generating reports on sales. As they continue to evolve, many more tasks can be done with POS systems, including the integration of e-commerce for online selling, electronic payment processing, integrated accounting, marketing, video surveillance, and much more.
Sales are the most important part of any business and so they come from customers, so POS systems should streamline the customer experience to make it as hassle free and pleasant as possible. For instance, POS systems for the restaurant business can enhance customer loyalty and...

...Mathematical Models
Contents
Definition of Mathematical Model Types of Variables The Mathematical Modeling Cycle Classification of Models
2
Definitions of Mathematical Model
Mathematical modeling is the process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon. It is a process that attempts to match observation with symbolic statement. A mathematical model uses mathematical language to describe a system. Building a model involves a trade-off between simplicity and accuracy. The success of a model depends on how easily it can be used and how accurate are its predictions.
3
Types of Variables
A mathematical model usually describes a system by a set of variables and a set of equations that establish relationships between the variables. The variables represent some properties of the system. There are four basic groups of variables:
– – – – Input variables Parameters Random variables Decision variables (output variables)
4
The Mathematical Modeling Cycle
Simplify Real World Problem
Interpret
Mathematical Model
Program
Conclusions Simulate
Computer Software
5
The Mathematical Modeling Cycle
1. Identify and understand the problem, draw diagrams 2. Define the terms in your problem 3. Identify...

...MATHEMATICAL METHODS
1. Finding An Initial Basic Feasible Solution:
An initial basic feasible solution to a transportation problem can be found by any one of the three following methods:
I. North West Corner Rule
II. The Least Cost Method
III. Vogel’s Approximation Method
1. North West Corner Rule
The North West corner rule is a method for computing a basic feasible solution of a transportation problem, where the basic variables are selected from the North-West Corner (i.e. top left corner).
The standard North West corner rule instructions are paraphrased below:
Steps:
Step 1. Select the north west (upper left hand) corner cell of the transportation table and allocate as many units as possible equal to the minimum between available supply and demand.
Step 2. Adjust the supply and demand numbers in the respective rows and columns.
Step 3. If the demand for the first cell is satisfied, then move horizontally to the next cell in the second row.
Step 4. If the supply for the first row is exhausted, then move down to the first cell in the second row.
Step 5. If for any cell, supply equals demand, then the next allocation can be made in either in the next row or column.
Step 6. Continue the process until all supply and demand values are exhausted.
2. The Least-Cost Method
The least-Cost Method is a method for computing a basic feasible solution of a transportation problem, where the basic...

...
Mathematical Happenings
Rayne Charni
MTH 110
April 6, 2015
Prof. Charles Hobbs
Mathematical Happenings
Greek mathematicians from the 7th Century BC, such as Pythagoras and Euclid are the reasons for our fundamental understanding of mathematic science today. Adopting elements of mathematics from both the Egyptians and the Babylonians while researching and added their own works has lead to important theories and formulas used for all modern mathematics and science.
Pythagoras was born in Samon Greece approximately 569 BC and passed away between 500 - 475 BC in Metapontum, Italy. Pythagoras believed that all things are numbers. He also believed that mathematics was and is the core of everything mathematical. He also believed that geometry is the highest form of mathematics and that the physical world could always be understood through the science of mathematics.
Pythagoreans have and will continue to give recognition to Pythagoras for 1) the angles of a triangle equaling to two right angles. 2) The Pythagoras theorem, which is a right-angled triangle, and the square on the hypotenuse equaling to the sum of the squares on the other two sides. This theory was created and understood years earlier by the Babylonians, however, Pythagoras proved it to be correct. 3) Pythagoras constructed three of the five regular solids. The regular solids are called tetrahedron, cube, octahedron, icosahedron, and dodecahedron. 4) Proving and...

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