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Mathematics 102
Problem Solving
Spring Semester 2005
Instructor: Alan Stein
Meeting Times
MW 11:15-12:30 in Room 327.
![[TOP]](images/up.gif)
Textbook
Problem Solving by Vinsonhaler and DeFranco
Publisher: Thompson Learning
ISBN: 0-759-31013-0
This will be used in addition to numerous handouts. Note that its cost is nominal; the list price is just $12.95.
Additional References:
Effective Problem Solving by Marvin Levine.
Prentice Hall. ISBN 0-13-245481-5.
Thinking Mathematically by John Mason with Leone Burton & Kaye Stacey.
Addison-Wesley Publishing Company. ISBN 0-201-10238-2.
How to Solve It by G. Polya
Student Information Form
Please fill out the online
to help your instructor learn more about you. There is a bonus for filling out the form expeditiously and a penalty for delay. See the
form for specifics.
Class Mailing List
An Internet listserv mailing list has been set up for the use of this
class. The name of the list is WMA102-L@LISTSERV.UCONN.EDU. You
will automatically be signed up for the list when you complete the
. If you don't receive confirmation of your subscription within a day, please check with your instructor or fill out the form again.
It is expected that everyone in the class will
participate in the mailing list. Messages may be sent to everyone on the
mailing list in the same way any other email message is sent; just address
such messages to WMA102-L@LISTSERV.UCONN.EDU.
It is recommended that students check their email regularly. Your
instructor will use email to communicate with the entire class between
meetings as well as to communicate with individual students.
Goals:
The basic goal is to foster problem solving skills that can
be applied throughout the college experience and the rest of life.
Everything will take a back seat to that goal. Thus, some of the
general policies and proceedures that hold for other courses are not in
effect for this particular course.
Expectations:
You should expect to do a majority of your learning
outside the classroom, generally spending between six and nine hours a week
working on this class. Mathematics, like most subjects, is learned by
doing it, and we won't have time for you to do a lot of mathematics in
class. On the other hand, you are expected to come to class and you are
responsible for everything that happens in class whether you are there
or not. If you miss a class, you are expected to immediately find out what
happened either from me (email is wonderful for that) or from your
classmates. Most of all, it is expected that you will get excited about
what you are learning and to delight in your own, perhaps unexpected,
ability to solve intriguing problems.
Homework: Homework will be assigned,
collected and graded regularly. Homework is to be done outside of
class and we will not always devote class time to the discussion of
homework problems. Your written work is expected to be neat, accurate and
contain written explanations using full sentences and standard
English. All work must be shown; an answer without an explanation is not
worth any credit. It is your responsibility to get help if you can't
complete an assignment. You can come to my office, go to the Math Center,
work with other students, send me email, or use any reasonable, ethical and
legal method to figure out how to complete your assignments. No late
assignments will be accepted.
Assignments are due and will be collected at the start of class on the due date. They may also be submitted via email (to stein@math.uconn.edu) provided they are sent and received prior to the class meeting. Assignments submitted in class but after the general collection at the start of class or submitted by email but not received prior to the class meeting will be assessed a nominal one (1) point penalty.
After assignments are graded and returned, students may optionally redo them and have them regraded. To be regraded, they must be resubmitted, along with the original graded assignment, by the next session after the original submission was returned to the class. The two grades (for the original submission and the resubmission) will be averaged to obtain the grade to be recorded for the assignment.
If a student fails to submit an assignment when it is due, he or she may submit it at the time other students would be resubmitting the same assignment. In that case, it will be treated as if the original assignment was submitted on time and earned a 0. For example, a student who earns a perfect 10 after not submitting the original on time will have grades of 0 and 10 averaged and a grade of 5 will be recorded for the assignment. Note that not only is 5 greater than 0, but the assignment will be counted towards the requirement that at least 80% of the assignments for the semester be submitted.
There is no penalty for submitting an assignment before it is due.
Graded Assignments:
This listing of graded assignments is not necessarily complete.
| Number | Due Date | Exercises |
|---|
".$assignmentnumber." | ".$date." | ".$assignment." | ");
}
gradedassignment("1","Monday, January 31","One of 32, 33, 34");
gradedassignment("2","Monday, February 7","One of 35, 36, 37, 38");
gradedassignment("3","Monday, February 14","Crossword Puzzle Assignment");
gradedassignment("4","Wednesday, February 23","One of Bouncing Bishop, Commuter, Four Bean Heaps, Grilled Cheese");
?>
| 5 | Monday, February 28 | Organization Assignment - Part I |
| 6 | Monday, March 14 | Organization Assignment - Part II |
Show how you obtained your conclusion and demonstrate that it is correct.");
gradedassignment("8","Monday, March 28","Submit an interesting problem which may be amenable to the techniques studied in class. The problem should not be essentially the same as any in the textbook or the problem sets distributed in class");
gradedassignment("9","Monday, April 4
Extended to Wednesday, April 6","One of 102, 105, 106, 107");
gradedassignment("10","Monday, April 11","One of 146, 156, 157, 162");
gradedassignment("11","Monday, April 18","One of 123, 149, 164, 166");
gradedassignment("Extra Credit","Wednesday, April 27","One of 81, 101, 109, 110, 132, 141");
?>
Problem Collections:
Various collections of problems will be distributed during the course of the semester. These same problems may be downloaded here. The collections will be added to as the semester progresses. These collections are in PDF format.
| ".$setno.". | ".$setname." | \n");
}
}
setshow("1","Age",TRUE);
setshow("2","Planetary Voyage",TRUE);
setshow("3","Games",TRUE);
setshow("4","Brain Teasers",TRUE);
setshow("5","Intimate Engagement",TRUE);
setshow("6","Starting a Problem",TRUE);
setshow("7","Externalization",TRUE);
setshow("8","Organization - Matrix Problems",TRUE);
setshow("9","Organization",TRUE);
setshow("10","Organization - Counting",TRUE);
setshow("11","Visualization",TRUE);
setshow("12","Attack",TRUE);
setshow("13","Attack - Special Features",TRUE);
setshow("14","Attack - Special Features - Crytpoarithmetic",TRUE);
setshow("15","Attack - Go to the Extremes",TRUE);
setshow("16","Simplify the Problem",TRUE);
setshow("17","Hidden Assumptions",TRUE);
setshow("18","Attack - Conjecturing",TRUE);
setshow("19","Responses to Being Stuck",TRUE);
setshow("20","Cryptology",TRUE);
setshow("21","Dollar Auction Project",TRUE);
setshow("22","Student Contributed Problems",TRUE);
?>
Notes:
These brief notes may be of some assistance in putting the problem solving enterprise in perspective.
- Introduction
- PSSSP
- Phases of Work
- Adages
- Combinatorics
- Rubric: Stuck!, Aha!, Check and Reflect
Problem Solutions:
");
fref("math102/problemsolutions/".$problem,$name);
print("");
}
}
function showpdfsolution($problem,$name,$setvisible)
{
if ($setvisible)
{
print("- ".$name."
");
}
}
showsolution("planetaryvoyage","Planetary Voyage",FALSE);
showsolution("fourcities","Four Cities",FALSE);
showsolution("fredandfrank","Fred and Frank",TRUE);
showsolution("cartesianchase","Cartesian Chase",TRUE);
showsolution("knight","Chess Knight",TRUE);
showsolution("grilledcheese","Grilled Cheese",TRUE);
showsolution("combinationlisting","Listing Combinations",TRUE);
showsolution("coingrid","4×4 Grid of Coins",TRUE);
showsolution("lockers","Lockers",TRUE);
showpdfsolution("coconuts","Soldiers, Monkey and Coconuts",FALSE);
showpdfsolution("anthony","Anthony's Problem",FALSE);
showsolution("splittingsausages","Splitting Sausages",FALSE);
showsolution("gameofthirtyone","Game of Thirty-One",FALSE);
showpdfsolution("solutions128-130","Questions 128-130",FALSE);
showpdfsolution("solution-nim","Classification of positions in the game of Nim",FALSE);
showpdfsolution("solution-whythoff","Classification of positions in Whythoff's Game",FALSE);
?>
Group Projects:
You will be assigned several projects during the semester to be worked on
in groups. Projects will be graded on accuracy, creativity and
presentation. We will begin the projects in class, but additional time
outside of class will be required to complete them.
-- The first group project involves determining the most financially sensible option for making insurance payments. The Team Performance Agreement is due Wednesday, March 23, a preliminary, oral report will be made Wednesday, March 30 and the actual written report is due Wednesday, April 6.
Exams and Grading
There will be a midterm and final examination. The midterm will count for 100 points and the final will count for 150 points. There will be many homework assignments which will be graded; most will be worth 10 points but some will be worth more. There will be group projects, the value of each will be announced at the time of the assignment. At the end of the semester, the total number of points earned will be divided by the maximum number of possible points to determine the average for each student.
Since participation is so important in this course, in order to pass this course a student must complete, on time, at least 80% of the graded homework assignments.
Remember that no make-up for the midterm exam will be given.
The general principle for earning a grade for this particular course is the following.
- To pass, a student must at least pretend to be fascinated by the course.
- To earn a C, a student must actually appear to be fascinated by the course.
- To earn a B, a student must exhibit a modicum of success in solving problems.
- To earn an A, a student must exhibit a significant amount of success in solving problems.
Students demonstrate at least a pretense of fascination in a variety of ways, including: coming to every class on time and staying awake through the entire class; actively participating; asking and answering questions; bringing in problems they have run across outside of class; asking about problems on the various handouts even when they haven't been assigned; taking advantage of the various extra credit opportunities offered during the course of the semester; handing in all assignments on time; making the effort to expeditiously collect any assignment if not in class when it was returned.
In order to quantify the fascination exhibited, a number of extra credit opportunities will be afforded during the course of the semester, in addition to the up to ten point bonus available for simply filling out the Student Information Form quickly at the start of the semester. Exhibition of a lack of fascination will correspondingly be quantified through small penalties extracted when students submit assignments via email rather than in person. Periodically and randomly through the semester, the instructor will check his unclaimed papers file and any students who have papers in that file will be penalized.
Interactive Solutions
| ");
executecode($filename,$title);
print(" | ");
showcode($filename,$title);
print(" | ".$title." | ".$description." |
");
}
}
function executecode($filename,$title)
{
pref("math102/interactive/".$filename,$title);
print("SOLUTIONS");
}
function showcode($filename,$title)
{
print("
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