MCS  233: Discrete Math for Elementary Education
January 2007

 MCS-233 homepage Reading and homework assignments Peer review guidelines Prof. Barbara Kaiser Project Proof checklist Feedback Journals Homework guidelines

Course Information

Overview:    The word "discrete" means separate or distinct.  Discrete mathematics is the study of mathematical objects that consist of separate pieces.  This includes ssuch topics as elementary number theory, which is the study of the integers, graph theory, which is the study of relationships between finitely many objects, and combinatorics, which uses mathematical techniques to figure out how to count things without actually having to count.

Course Objectives:

• To develop the ability to think abstractly and creatively about mathematical and logical problems
• To develop problem-solving strategies
• To learn ways to communicate mathematics to a variety of audiences
• To identify and use different methods of mathematical proof
• To understand and use basic properties of the integers, especially prime numbers and modular arithmetic
• To explain and use the concepts of graphs and trees
• To solve problems using counting techniques and combinatorics
Prerequisites:  The formal prerequisite is MCS-121.  More to the point, you should be comfortable with thinking algorithmically, discovering patterns, and applying mathematical procedures to various types of problems.

Course web site:  The best source of information about this course is available at  www.gac.edu/~kaiser/mcs233/. There you will find a complete syllabus, course description, current homework assignments, and so on.

Books:   Discrete Mathematics with Graph Theory, second edition, by Goodaire and Parmenter.

This book is intended to be read thoroughly and thoughtfully.  For each class session, you are encouraged to read the pertinent portion of the text at least once  beforehand and at least twice afterwards.  Study the book with a pencil in hand.  Make notes in it.  Mark where you have questions.   Do NOT try the exercises without reading the text;  simply skimming the examples is not sufficient.   You will find that it will be  necessary to read the text several times before attempting any exercises.  To survive this course, you must learn how to read a math book!

Count  Down: Six Kids Vie for Glory at the World's Toughest Math Competition, by Steve Olson

This book describes several mathematically gifted high school students and discusses issues that are relevant to the mathematical education of all students.  It will be much easier to read than the textbook, and will provide us with some good questions about teaching and doing mathematics.

Classes:    Classes will be used for lectures, problem solving, discussions, and other fun activities.   You should prepare for classes by doing the reading beforehand (reading assignments are posted on the Web),  thinking about the problems in the text, and formulating questions of your own.  You should also participate as much as possible in class.  Class meetings are not intended to be a complete encapsulation of the course material.  You will be responsible for learning some of the material on your own.

Attendance, both physical and mental, is required.

To help me keep attendance and to check on your preparation, you will be expected to hand in a 3x5 index card at the beginning of each class period.  On this card, you should summarize  the most important points in the reading.  If you have questions on the reading, you should think carefully about the best way to phrase these questions and then write them on your card.  You can get three points per class - one for being there, one for your index card and one for participating in class.  If you are not in class, you will not get any points (even if you have a friend hand in a card).

Should you need to miss a class for any reason, you are still responsible for the material covered in that class. This means that you will need to make sure that you understand the reading for that day, that you should ask a friend for the notes from that day, and make sure that you understand what was covered. If there is an assignment due that day, you should be sure to have a friend hand it in or put it in my departmental mailbox (in Olin 324). You do not need to tell me why you missed a class unless there is a compelling reason for me to know.

We will be doing a lot of hands on activities in class, so you will need to bring scissors, colored pens or pencils, a hadfull of pennies and nickels, a glue stick, and a ruler or straightedge.  You will also find it handy to have a small stapler, paper clips, a package of 3x5 index cards, a two-pocket folder, and an eraser.

Problem solving journals:    You will be expected to keep a journal that helps you reflect on problem solving strategies and techniques, ways to improve your ability to solve mathematical problems, and ways to help others improve.  You will also be asked to respond to  the book Countdown.

Project:    Working in teams of two or three, you will design an activity that introduces students in grades K-8 to a concept in discrete mathematics.  You will write a description of what to do, produce the necessary materials, and write two descriptions of the mathematics behind the activity, one for fellow teachers and one for parents.  We will try out these activities in class; we may be able to try them out in the St. Peter schools.  All the activities will be collected into a book (or web page or both) for you to use as a teacher.

Homework
:  I will assign homework at the beginning of each chapter by posting them on the web. The problems will be designated as ``practice problems'', ``homework problems'' or ``honor problems''.

Practice problems are meant to give you practice solving, writing and reading mathematics.  For these problems, you will be assigned a partner.  You may work on the problems with anyone you like  except your partner. You should write up your solutions and give them to your partner for peer review.  These problems will not be handed in; however, you will be graded on how many you do and on the quality of your review.   Reading and evaluating others' work will greatly help your  performance on the other homework and on the tests.

Homework problems are homework problems which you hand in to me.  They will be graded on a scale of 0 - 10 per problem, where a 10 means that you've done a good job of solving the problem and writing the solution up clearly.  You are encouraged to work on doing these problems with one or two other students in the class; if you do so, then you should hand in a single set of solutions and the points will be given to all the students in the group.

Honor problems are problems that each of you must do individually.  You can think of these as miniature take-home tests; you are on your honor not to cheat by consulting other people or books.  You must write and sign the honor pledge on each of these assignments.

Academic Integrity  You are expected to to adhere to the highest standards of academic honesty, to uphold the Gustavus Honor Code and to abide by the Academic Honesty Policy. Copies of the honor code and academic honesty policy can be found in Academic Bulletin and in the Gustie Guide.

The first violation of the Honor Code will result in a score of 0 on the assignment in question and notification of the Dean of Faculty.  Further violations will result in failing the course.