Department of Mathematics
Math 29. Advanced
Problem Solving
Fall 2013
Course Syllabus
Time and Place: MWF 9:00 am-9:50 am, Lincoln
1135.
Instructor: Dr.
Adolfo J. Rumbos
Office: Mudd Science Library 106.
Phone/e-mail: ext. 18713 /
Office Hours: MWF 8:05 am-8:55 am, TR 9:00 am – 10:00am,
or by
appointment
Text: Quantitative Reasoning: Understanding
the Mathematical
Patterns in Nature
by Frederick P.
Greenleaf, Third Edition,
MacGraw-Hill,
2006
Courses Website: http://pages.pomona.edu/~ajr04747/
Course Description. The main goal of this
course is to enhance students' analytical and mathematical skills needed to
deal with a variety of problems that arise in the sciences. The best way to get better at problem solving
is to work on a lot of problems. In this
course we will be doing just that, in a cooperative environment. During each class, students will work in
groups on problems coming from modeling real-world situations in the context of
the physical, biological, social and environmental sciences.
Course Requirements.
1.
Group Problems. Students will be divided into groups and
given problem sets to work out in each class period. This is a collaborative effort, and everyone
must participate. The group work will
begin in class and continue outside of class in the mentor sessions. Each group is expected to work on all
problems in each problem set.
2.
Problem Solving Journals. Students
will neatly and carefully write up solutions to the in-class problems in a
special notebook, which we shall refer to as a Problem Solving Journal. This journal
notebook is to be separate from a notebook used for taking notes during
lectures and student presentations.
The journals
will be reviewed regularly throughout the semester in order to provide feedback
on your progress.
3.
Presentations. Students
will also be required to present to the class solutions to problems they have
already written up in their journals.
4.
Homework Assignments. At
each class meeting, homework assignments will also be given; these will be collected
on an alternate basis. The homework
assignments will be based on the mathematical topic covered during problem
solving sessions, as well as the assigned readings from the text.
5.
Exams. There
will be two tests throughout the semester (see attached Tentative Schedule of Topics and Examinations) and a final exam
scheduled for Tuesday, December 17, 2013
at 9:00 am.
Evaluation. Grades will be based on presentations
and solutions to assigned problems, two 50-minute examinations, and a final
exam. The overall score will be computed
as follows:
Problem solving journal 15%
Presentations 10%
Assignments 15%
Two 50-minute exams 40%
Final exam 20%
Rules for group work. Everybody
in each group is expected to participate in the process of coming up with
solutions to the in-class problems. Here
are some basic expectations regarding group work:
1.
Everyone
in the group must understand the statement of the problem. It is everybody’s responsibility to make sure
that everybody in the group understands what the problem is asking.
2.
Everybody
must participate in the problem solving process. This may involve asking clarifying questions,
suggesting approaches, performing all relevant calculations, etc.
3.
Everybody
must understand the solution to a given problem that the entire group has
figured out.
Expectations regarding write-ups. Even
though students work in groups in the process of coming up with solutions to
the problems, each student must write up solutions in the journals
individually. Each student must express
the solution in her or his own words.
These write-ups must be complete.
They must include a statement of the original problems, definition of
all the pertinent variables, and an explanation of the process leading to the
solution. A scattering of symbols,
formulas and calculations is not enough.
Math 29. Fall 2013
Tentative Schedule of Topics and
Examinations
Date Topic
W Sep. 4 Measurements and units.
F Sep. 6 Measurements and units.
M Sep. 9 Measurements
and units.
W Sep.
11 Solutions and dilutions.
F Sep.
13 Solutions and dilutions.
M Sep. 16 Solutions
and dilutions.
W Sep.
18 Estimations.
F Sep.
20 Estimations.
M Sep. 23 Estimations.
W Sep.
25 Relationships between
variables.
F Sep.
27 Relationships between
variables.
M Sep. 30 Relationships
between variables.
W Oct. 2 Relationships between variables.
F Oct. 4 Rates of growth and decay.
M Oct. 7 Rates of growth
and decay.
W Oct. 9 Rates of growth
and decay.
F Oct. 11 Rates of growth and decay.
M Oct. 14 Review
W Oct. 16 Exam 1
F Oct. 18 Triangulation, surveying
and mapping.
M Oct. 21 Fall
Recess.
W Oct. 23 Triangulation, surveying and mapping.
F Oct. 25 Triangulation, surveying and mapping.
M Oct. 28 Triangulation,
surveying and mapping.
W Oct. 30 Probability.
F Nov. 1 Probability.
Date Topic
M Nov. 4 Probability.
W Nov. 6 Expected
values.
F Nov. 8 Expected
values.
M Nov. 11 Expected
values.
W Nov.
13 Decision problems.
F Nov.
15 Decision problems.
M Nov. 18 Decision
problems.
W Nov.
20 Scales.
F Nov.
22 Scales.
M Nov. 25 Scales.
W Nov.
27 Scales.
F Nov.
29 Thanksgiving Recess.
M Dec. 2 Scales.
W Dec. 4 Review
F Dec. 6 Exam 2
M Dec. 9 Review
W Dec.
11 Review
Tu Dec. 17 Final Examination at 9:00 am