**Course Description**

Matrices, systems of linear equations and inequalities, linear programming using

geometric and algebraic methods , set theory, probability, data analysis, and
game theory.

**Prerequisite: two years of high school algebra or Mathematics 105.**

**Text**

**No book required.**

Much of the work will be done on computers in the lab. However, each member of
the

class should have a calculator available for work in the classroom. A basic
calculator

would be sufficient; however, it would be advantageous if it is capable of
calculating

factorials , permutations, combinations, etc.

**Objectives**

Upon the completion of this course students will:

• Understand that in “ real world ” situations there may be many acceptable

approaches to solving a specific problem. Likewise, they will learn that there

are often multiple acceptable solutions and sometimes no acceptable solution.

• Be able to solve systems of linear equations and inequalities using paper and

pencil methods and/or function plotting software and inter pret the results .

• Be able to set up spreadsheets and demonstrate their “if…, then…”

capabilities.

• Demonstrate the application of matrices to “real world” situations.

• Be able to apply applicable emperical probability processes and compare the

results to results obtained by using mathematical probability.

**Course Overview and Objectives**

The overall scope of the course will of necessity be dependent on the present
abilities and

previous experience of the participants. The basic goal is to enable
participants to use

mathematics, when applicable, as a tool for problem solving and decision making
and to

help them recognize possible methods of solution. The emphasis will be on

understanding basic mathematical concepts and applications rather than on
mathematical

structure. The Curriculum and Evaluation Standards from the National Council of

Teachers of Mathematics will serve as a guide for many of the topics and methods

addressed in this course. Emphasis will be placed on modeling “real-world”
situations

using systems of equations and inequalities, data analysis, mathematical and
emperical

probability, and matrices to describe relationships and the use a variety of
methods to

solve problems, reach conclusions and interpret results. Students will
demonstrate an

ability to use paper and pencil methods of solutions for basic work; as topics
get more

advanced they will use function plotting software, data analysis software,
spreadsheets,

etc.

Participant’s progress and understanding will be assessed
through the use of quizzes,

worksheets, group projects , demonst ration of knowledge and/or skills, class
discussion

and tests.

Participants will be provided with a disk containing the function plotting
software and the

data analysis software.

**Grading:**

The final grade for the course will be based on the following: (Approximate)

In-class worksheets or group projects |
50 points each |

Quizzes |
50 points each |

Any test |
200 points |

The instructor will monitor participation in class discussion and group projects
and may

award points based on his observations.

Exercises related to material covered in the session may be presented as
take-home

worksheets. The purpose of homework is not for a grade, it is to help the
student realize

what he/she can do and what he/she might need help with. Questions related to
the

homework will be discussed before the quiz in each session.

Worksheets that are not completed by the end of a session may be taken home. The

completed worksheets will be due at the beginning of the next session.

Letter grades will be as signed based on the following:

A 92%-100% of total possible points

B 84%-91% of total possible points

C 72%-83% of total possible points

D 60%-71% of total possible points

**Attendance**

Each participant is expected to attend every session. Missing one session is

approximately equivalent to missing two consecutive weeks in a traditional
3-hour

course. Because of the nature of some of the group projects it is not possible
to make up

projects missed. In-class worksheets missed due to absence may be made up
outside of

class time. Quizzes and exams missed due to absence may be made up only if prior

arrangements have been made with the instructor or extraordinary circumstances
forced

missing of the quiz or exam. The final grade for a student who misses two
sessions will

be lowered one letter grade. If a student misses three or more sessions it is
un likely that

he /she will pass the course.

**OVERVIEW OF SESSIONS**

Following is the proposed schedule for each session. It may be necessary to
deviate from

the schedule based on the needs of the participants and/or time available.
Student

understanding of material and development of necessary skills is more important
than the

amount of material covered. For each session after the first there is a
possibility of a quiz

over material from the previous session.

Session 1:

Introductions Overview of course and discussion “real
world” problems as opposed to

contrived problems

Review of basics related to Cartesian coordinate system and linear relations

Introduce concept of functions and related notation and termino logy

Demo function plotting software (WinPlot)

Session 2:

Review topics from Session 1 and discuss any questions on
homework

Review systems of equations on the coordinate system

Discuss various paper-pencil methods to solve systems of linear equations

Demo use of WinPlot to solve systems of linear equations and beyond

In-class worksheet or group project

Session 3:

Review topics from Session 2 and discuss any questions on
homework.

Introduce concepts of linear programming

Discuss graphs of linear inequalities and systems of linear inequalities as

they relate to linear programming solutions

In-class worksheet or group project

Session 4:

Discuss questions over material from first three sessions

Mid-term exam or project

Introduce concept of matrices to represent data and discuss the algebra of

matrices

Session 5:

Review topics from Session 4 and discuss any questions on
homework

Demo use of spreadsheets or other software with matrices

Discuss real-world applications of matrices

In-class group project

Session 6:

Review topics from Session 5 and discuss any questions on
homework

Introduce basics of Set Theory, terminology, notation, Venn diagrams, etc.

Discuss counting principles and use of permutations and combinations

Session 7:

Review topics from Session 6 and discuss any questions on
homework

Discuss basics of both mathematical and emperical probability

In-class project using data collection and modeling using emperical

probability

Session 8:

Probability Project

Review material from first 7 sessions

Final exam or project