Divisibility
In this section, we introduce the divisibility, prime numbers and the Division
Algorithm. Our focus is on understanding these concepts and the proofs that
establish the properties of divi
Alternative Induction Theorems
We define the greatest common divisor and least common multiple of more than
two integers recursively. That is, we define them for two integers, and then we use
these re
Mathematical Induction
Let us now consider the possibility of proving that all positive integers satisfy a
certain property. Since there are infinitely many positive integers, we cannot
possibly check
The Logic behind the Proofs
In this section, we go over the arguments we used to prove the statements of the
previous two sections. Note that we do not need to take a course to understand an
argument.
The Greatest Common Divisor
In the previous section, we considered the divisors of a single integer; in this
section, we study the divisors of two integers.
Definition 1.34. For a, b Z, an integer c i
Addition and Multiplication Axioms of Integers
In this section, we introduce proofs that involve addition and multiplication of the
integers. We are all familiar with the concepts defined in this unit
The Least Common Multiple
We now turn our attention to the multiples of pairs of integers.
Definition 1.46. For any integers a, b an integer m is a common
multiple of a and b if a| m and b| m; that is
The Fundamental Theorem of Arithmetic
We dedicate this section to proving the Fundamental Theorem of Arithmetic,
another theorem we can trace back to Euclids Elements. It explains the importance
of th
Finishing This Unit
1. Review the objectives of this unit and make certain that you are able to meet
all of them.
2. If there is concept, definition, example or exercise that is not yet clear to you,
Order Axioms of the Integers
In this section, we will freely use the results reached in the previous section,
including those in the exercises. That is, everything we learned about the integers in
the
75 / 88 Marks or 85.23%
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Keep up the great work
Bryan Foster
Les
Foster 1
Les Barnhouse
Math 215
20 Dec 2016
Assignment 5
9 / 15 Ma
66 / 70 Marks or 94.29%
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Les
Foster 1
Bryan Foster
Les Barnhouse
MATH 215
29 Jun 16
Assignment
67 / 70 Marks or 95.71%
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Review the final questions for some corrections
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Bryan Foster
Les
Foster 1
Les Barnhouse
MATH 215
04 Aug 16
Assignment
55 / 63 Marks or 87.30%
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Bryan Foster
Les
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Les Barnhouse
MATH 215
25 Dec 2016
Assignment 6
35
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Bryan Foster
Les
Foster 1
Les Barnhouse
MATH 215
16 Aug 16
Assignment #4
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1
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Bryan Foster
Les
Foster 1
Les Barnhouse
MATH 215
12 Jul 16
Assignment 2
Q
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Total Marks
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Please show all your work. Some questions require you to use graphs, tree
diagrams, formulas, and so on that are difficult or impossible to reprod
FORM FOR ESTIMATING MARKET SIZE
ESTIMATED TOTAL MARKET SIZE
1. DESCRIPTION OF PRINCIPAL MARKET
Estimated total sales in units
Estimated total sales in $000
Percent Change
201A-201B 201B-201C 201C-201D
Unit 1
Objective 1: Define physiology, and discuss the relationship between structure and function.
Homeostasis is the maintenance of a steady state in the body. Complementarity describes the
relation
ENVS461
Assignment II
Subject: Balance of Nature
Issue: Patterns in nature
Introduction:
From the early years of twentieth century ecology was seemed like a descriptive science
through which ecologist
ENVS461 Assignment I
1. The Development of Vegetation
By A. G. T. (Arthur Tansley)
A. In this excerpt, Professor Clementss main thesis is that, the plant formation is an
organism that can be considere
14
Loan Amortization: Mortgages
Point of Interest (Section 14.1)
Just When You Thought You Had It All Figured Out
1. Jeff is missing the point that his average investment (including interest earned)
Unit 1 Suggested Answers to Textbook Review Questions
Chapter 1
Questions for Review, page 17
1.
Examples of tradeoffs include time tradeoffs (such as studying one subject over
another, or studying at
Unit 4 Suggested Answers to Textbook Review Questions
Chapter 7
Questions for Review, page 166
1.
Buyers willingness to pay, consumer surplus, and the demand curve are all closely
related. The height
Worksheet 5: Competitive Profile Matrix
Factor
Market Position
1. What is their current
market share?
2. Has it been growing or
declining? To what
extent?
Strengths
3. What are their major
strengths?
Worksheet 2: What do you Plan to Sell?
Describe your proposed product/service offerings and who you see as your principal target
market for each offering or your whole line. If you have many products/
PRO FORMA INCOME STATEMENT WITH BREAKDOWN OF OPERATING EXPENSES
For the Year (date)
1. Gross Sales
Less: Cash Discounts
$
A. NET SALES
Cost of Goods Sold:
3. Beginning Inventory
$
4. Plus: Net Purchas
Worksheet 7: Outline for a Preliminary Marketing Plan
YOUR CONCEPT
Describe the principal concept underlying your product or service idea.
What is unique or distinctive about your idea? How does it di
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