Basic Course Information
Schedule
Class Schedule: Wednesdays, 4:30
- 7:15 p.m., HH C-1
Instructor: B. Gold Office Location:
HH C-6 Office Telephone: 571-4451 E-mail Address:
bgold@monmouth.edu
Office Hours: Monday 1 – 2 p.m., Tuesday 4:30 – 5:30 p.m.,
Wednesday noon – 1 p.m., Thursday 4 – 5 p.m., Friday 12:30 - 1:30, or by
appointment or chance.
Catalog Description: This course gives the middle-school teacher a deeper understanding of topics from discrete mathematics which are taught in the middle school. This includes counting methods, graph theory, trees, networks, Pascal’s triangle, the binomial theorem, sequences, set theory, and recursion. We also discuss problem-solving heuristics.
Course Objectives: This course will
• Give students a deeper understanding of topics in discrete mathematics
taught at the K-12 level
• Introduce students to heuristics for problem-solving
• Give examples of how to use these concepts to develop classroom materials
to enhance student learning
• Introduce students to mathematical software available at the school
level for investigating discrete mathematics
• Involve students in problem solving activities via exploration and
experimentation to allow students to construct (and reconstruct) mathematics
understanding and knowledge
• Encourage visual reasoning as well as symbolic deductive modes of
thought (by incorporating models, concrete materials, diagrams and sketches)
• Introduce multiple strategies of approaching problems by discussing
and listening to how others think about a concept, problem, or idea
• Involve students in small group work and cooperative learning
• Help students become aware of their own mathematical thought processes
(and feelings about mathematics) and those of others
• Introduce students to multiple methods of assessment in mathematics
Learner Outcomes: Students will develop the ability to:
• Approach problems from multiple perspectives and help their students
become better problem solvers
• Use mathematical language to correctly state mathematical definitions
and theorems
• Begin developing mathematical proofs
• Use assorted counting techniques to solve problems
• Work with the assorted concepts from graph theory and apply them
to a range of problems, including map coloring, networks, traversing routes
• Relate those properties to mathematics taught in middle and high
school.
Methods of instruction: Each class will include answering questions from the previous class, lecture-discussion of the new mathematical topic of the day, one or more class activities to familiarize students with the material, a discussion of its connection to school mathematics, and some activities appropriate for use, at some grade level, with K-12 students. Some of the activities will involve use of appropriate computer software, both college level and K-12 level.
Required Texts: Alan Tucker, Applied Combinatorics; and George Polya, How To Solve It.
Course Requirements:
You should read the section(s) for the week prior to class.
In-class discussion and problem-solving:
Roughly 30% of each class will be spent on class discussion of advanced
concepts and their relationship to the school classroom, and 40% on group
problem-solving activities. Because in-class activities are such
an important part of the course, if you need to miss a class, please contact
me (preferably prior to the class, but in any case prior to the next class)
for ways to make up this work. This section of the grade comes primarily
from the weekly student activities you’ll design at the end of class, which
will be activities aimed at students in grades 6-12 which are based on
what was learned in class that week. These activities should be keyed
to helping students meet specific expectations in the NCTM Principles
and Standards for School Mathematics (PSSM).
Weekly homework assignments:
These assignments will reinforce the advanced mathematical concepts
learned in the class. Homework is due the week following discussion
of that section in class.
Reflective mathematics journal:
Weekly entries in these journals are to help students become aware
of their own mathematical thought processes (and feelings about mathematics).
I expect at least one entry per week, and will collect the journals one
week prior to midsemester and one week prior to the end of the semester.
You should reflect on what you found difficult and why, what you feel stretched
you, anything which seemed a waste of time and why, and anything else which
you believe will help you or me understand your mathematical growth during
the course.
In class examinations (2), Final Examination:
Examinations will cover correct use of mathematical terminology (especially
correct statement of definitions) and mathematical concepts studied.
Computer laboratory projects:
There will be 2 computer laboratory projects exploring computer software
which enhances students’ understanding of number concepts; these will be
done in class, with reflection on the uses, value, assessment mechanisms
and limitations of each after class
Curriculum project: 10%
Students will work in pairs beginning at mid-semester to develop week-long
curriculum projects which they will use with their classes and revise.
Methods of Evaluation and Grading Policy: 20% in-class work, 10% each in-class examinations (2), 20% final examination, 15% homework assignments, 5% journal, 10% computer projects, 10% curriculum projects.
Attendance Requirement: Attendance is very important, as
the ideas are not developed sufficiently fully in the text. Students missing
a class will be expected to consult with the professor about how to make
up the material.
Last date to Withdraw with automatic assignment of “W” grade:
Wednesday, November 5.
Statement on Academic Honesty: You are welcome to consult
others, whether students in the class or tutors in the Mathematics Learning
Center. However, whenever you have had assistance with a problem,
you are to state that at the beginning of the solution to the problem.
Unless it becomes excessive, there will be no reduction in credit for getting
such assistance. This policy applies to both individual and group
work. (Of course groups only have to acknowledge help from outside the
group.)
Examination Rules: No student is permitted to have at his or
her desk any books or papers that are not given out or expressly permitted
by the instructor. Possession of such material will be regarded as
evidence of intent to use the information dishonestly. No communication
between students during the examination is permitted. If there are
questions, or if there is a need for additional material, the instructor
should be asked. If there is a need for calculations or notes, they may
be written on the pages of the exam.
The following pledge must be signed and submitted with the examination:
“I, ____________________________, certify that I have read the above
rules for examinations, and that I have abided by them. By signing, I affirm
that I have neither given nor received aid during this examination, and
I understand that violation of this affirmation may result in suspension
or expulsion from Monmouth University.”
Statement on Special Accomodations: Students with disabilities
who need special accommodations for this class are encouraged to meet with
me or the appropriate disability service provider on campus as soon as
possible. In order to receive accommodations, students must be registered
with the appropriate disability service provider on campus as set forth
in the student handbook and must follow the University procedure for self-disclosure,
which is stated in the University Guide to Services and Accomodations for
Students with Disabilities. Students will not be afforded any special
accommodations for academic work completed prior to the disclosure of the
disability, nor will they be afforded any special accommodations prior
to the completion of the documentation process with the appropriate disability
office.
Outline of Course Content and Schedule:
Weeks 1-4: Logic, set theory, and recursion
For 9/10, read Appendix A.1 and the handout. Do problems (from
Appendix A.1) 1bcd, 2ace, 3, 5, 6, 7ac, 8, 10, 11ad, 12ac, 13, 16, 17b;
also, prove 11ad using the definitions of union and intersection.
For 9/17, read Appendix A.2. Do problems 18acd and 19 acd from sheet to be handed out 9/10, and from the handout 2.1 # 1acegik, 2ace, 3ace, 4ace, 5ace, 6ac, 7ace, 8ace; 2.2 # 2, 4, 9, 12, 18, 20a.
For 9/24, read second handout and section 7.1 through example 7, and
skim the first few pages of 7.3 so you have an idea what it’s about.
For homework, do A.2 # 1, 3, 7, 15, 17, and the following two problems
(using mathematical induction):
A. Prove Bernoulli’s inequality: If 1 + a > 0,
then (1 + a)n > 1 + na.
B. For all n > 1, prove 1/12 + 1/22
+ 1/32 + ... + 1/n2 < 2 - 1/n.
Weeks 5 – 9: Problem-solving heuristics and counting problems
For 10/1, read Polya’s How To Solve It. Do # 2, 3ac, 4a from
second handout; from 7.1 do #1, 3, 5; from 7.3, #1, 3ac
For 10/8, finish computer lab 1,
and read section 5.1 of the text. Do 7.1 #1, 3, 5; from 7.3, #1,
3ac. The first half of class will be our first
exam.
For 10/15, read sections 5.2 and 5.3. Do 5.1 # 1, 4, 5, 8, 11,
12. Bring in journals and class activities through 10/8’s class.
Semester project will be assigned.
For 10/22, read sections 5.4, 8.1. Do 5.2 # 2, 3, 5, 8, 11, 12;
5.3 # 2, 3, 5, 8, 9, 18.
For 10/29, read sections 1.1, 1.2. Do 5.4 # 2, 5, 15, 16; 8.1
# 2, 9, 13, 20.
Weeks 10 – 14: Graph theory, trees, and networks
For 11/5, read sections 1.3, 1.4. Do 1.1 # 1, 4, 15, 18, 32,
33, 34a; 1.2 # 2, 5ace, 6ace, 8.
For 11/12, read sections 2.1, 2.2. Do 1.3 # 1b, 2ac, 8a, 12;
1.4 # 1a, 3ace, 7ace, 8.
For11/19: We’ll do Computer lab
2. Semester project is due.
Read section 2.3. Do 2.1 # 1a, 2a, 4, 7; 2.2 # 1, 2ab, 3, 4ace.
For 12/3: Computer lab 2 is due; and we’ll have exam
2. Read 2.4; do 2.3 # 1ace, 2b, 7, 11, 12
For 12/10: Bring journals and class activities. Read 3.1,
3.2, 4.1. Do 2.4 # 1, 4; 3.1 # 1a, 2, 4, 5.
Due at the final exam or sooner: 3.2 # 1b, 2b, 4, 6, 12, 19;
4.1 # 2, 3ab, 4a.