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 interpret 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, demonstration 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 assigned 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
unlikely 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 terminology
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
