Download Math 1218 - College of DuPage

College of DuPage
FY Fall/17
ACTIVE COURSE FILE
Curricular Area: Mathematics
Course Number: 1218
Title: General Education Mathematics
Semester Credit Hours: 3
Lecture Hours: 3
Lab Hours: 0
Clinical Hours: 0
This course is an IAI approved general education course: M1 904.
Changes from the present course must be accompanied by a yellow
Course Revision or Deletion Form.
Course description to appear in catalog:
Designed to fulfill general education requirements and not designed as a
prerequisite for any other college mathematics course. Focuses on
mathematical reasoning and the solving of real-life problems, rather than
routine skills. Logic and set theory will be studied. Two other topics from
the following list are to be studied in depth: counting techniques and
probability, game theory, geometry, graph theory, statistics, and
mathematics of finance. The regular use of calculators and/or computers
will be emphasized.
Prerequisite:
Math 0465 or Math 0482 (or college equivalent) with a grade of C or better
or a qualifying score on the mathematics placement test.
A.
General Course Objectives:
Upon successful completion of this course, students should be able to
do the following:
1.
2.
3.
4.
5.
Define the elements of a set
Count the elements of a set
Perform operations with sets
Construct Venn diagrams
Use mathematics to solve a variety of problems from the
following list:
a. Counting techniques and probability
b. Statistics
c. Game theory
d. Geometry
e. Graph theory
f. Mathematics of finance
5. Use problem-solving skills
6. Use technology in problem solving
B.
Topical Outline:
Three topics from the following are to be studied in depth, with Topic 1
required. The two additional topics may not include both Topic 2 and
Topic 3:
1.
Logic and set theory
a. Sets
b. Set operations
c. Venn diagrams
d. Number of elements in a set
e. Sets as a problem-solving tool
f. Statements
g. Truth tables
h. Compound statements
i. Euler diagrams
j. Valid arguments
2. Counting techniques and probability
a. The Fundamental Counting Principle
b. Permutations
c. Combinations
d. Miscellaneous counting methods
e. Sample spaces and probability
f. Computation of odds
g. Counting techniques and probability
h. Computation of probabilities
i. Conditional probability
j. Independent and dependent events
k. Mathematical expectation
3.
Statistics
a. Descriptive statistics
1) Collecting and describing data
2) Correlation and regression
b. Normal distribution
c. Statistical inference
1) Hypothesis testing
2) Confidence interval estimation
4. Game theory
a. Two-person games – constant sum
1) Pure strategies
2) Mixed strategies
b. Two-person games – variable sum
c. Larger games
d. Application of game theory
e. Theory of moves
f. Cyclic games
5. Geometry
a. Non-Euclidean geometry
1) Lobachevskian geometry
2) Riemannian geometry
3) Other non-Euclidean geometries
b. Fractal Geometry
1) Koch snowflake
2) Sierpinski gasket
3) Mandelbrot Set
c. Computer applications
1) Geometer’s sketchpad
2) Fractal generators
6. Graph theory
a. Euler circuits
b. Directed graphs
c. Hamiltonian circuits
d. Spanning trees
e. Critical paths
7. Mathematics of Finance
a. Interest
b. Annuities
c. Loans
d. Amortization
C.
Methods of Evaluating Students
Students will be evaluated by unit tests at appropriate intervals. Other
methods may include quizzes, homework, projects, and a comprehensive
final examination.
_______________________________
Initiator
Date
_______________________________
Sponsor
Date
_______________________________
Division Dean
Date
Textbook for Math 1218
Title:
Thinking Mathematically, 6th Edition
Author:
Robert Blitzer
Publisher:
Prentice Hall
Copyright: 2015
Topic
Chapter
Sections
Logic and Set Theory
2,3
All sections
Mathematics of Finance
8
Sections 8.2 – 8.6, 8.7, 8.8 (Section 8.1 is
optional)
Geometry
10
Section 10.7 (Other sections optional)
The Active Coursed File states “NonEuclidean Geometry”. Please see Active
Course File for topics to cover.
Graph Theory
14
All sections
Counting Techniques
and Probability
11
All sections
Statistics
12
All sections
In some instances, depending on the topic selected, the instructor may
have to provide supplemental material.
Use of Technology in Math 1218
Instead of relying on algorithms to solve problems encountered in this
course, computers and calculators should be used. The use of such
technology is an integral part of this course.
In all Mathematics courses, students with a documented learning disability
that specifically requires a calculator as determined by Health Services, will
be allowed to use a basic calculator for all test/quiz questions where
arithmetic calculations are not the main objective. The specific disability
must be verified with Health Services before the accommodation can be
made.