Block II. Linear Systems Self-Test
1. A straight line passes through the points (2,5) and (1,7). What is the slope of the line?
2. Solve for w and z : w 2z 3 = 0
2w + 2z + 6 = 0
3. The following system of equations has how many solutions?
2x + 3y = 10
4x

Block I. Algebraic Self-Test
1. Solve the following equations:
a.
3 1 3x 2
x 2
4x
b.
6
7
2 1
12 x 6 x 3x 5
2. If an automobile averaged 40 miles per (mph) for 45 minutes and 50 mph for 1.5 hours,
how far did it travel?
3. Subtract (-2a + 7x 5c2) from (-

A Little Set Theory (Never Hurt Anybody)
Matthew Saltzman
Department of Mathematical Sciences
Clemson University
Draft: December 12, 2005
1
Introduction
The fundamental ideas of set theory and the algebra of sets are probably
the most important concepts a

ENM 503 Block 1 Algebraic Systems
Lesson 4 Algebraic Methods
The Building Blocks Numbers, Equations, Functions, and
other interesting things.
Did you know? Algebra is based on the concept of unknown values called
variables, unlike arithmetic which is base

ENM 503
Lesson 1 Models and Methods
The whys, hows, and whats of
mathematical modeling
A model is a
representation in
mathematical terms of
some real system or
process.
A Model Defined
A model is an object or concept that is used to
represent something e

ENM 503
Block 1 Algebraic Systems
Lesson 2 The Algebra of Sets
The Essence of Sets
What are they?
1
Set Theory
Theory: A formal mathematical system consisting
of a set of axioms and the rules of logic for deriving
theorems from those axioms.
Set theory

ENM 503 Block 1 Algebraic
Systems
Lesson 3 Modeling with Sets
Sets - Why do we care?
The Application of Sets a look ahead
1
Some Uses of Sets
Logic analyzing complex relationships
Optimization defining feasible regions
Modeling random processes
Probab

Engineering Analyses Methods
and Models (ENM 503)
Lesson 0 - Course Introduction
A preliminary course in the mathematical methods
and models used in the formulation and solution of
problems found in engineering management and
operations research
1
Course

ENM 503 Block 1 Algebraic
Systems
Lesson 5 Algebraic Models
Relive those old college algebra days when
solving an equation was childs play
1
The Road Ahead
is not always linear
Mall Mart Discount Stores
Modeling inventory
The algebra of high finances
Bre