INTRODUCTION TO ABSTRACT MATHEMATICS
MATH 222 – Spring 2007
Section 001
8:00—9:30
TR – Swart 2
TEXT:
An Introduction to Abstract Mathematics by R. J. Bond and W. J. Keane
INSTRUCTOR:
Dr. Hosien S. Moghadam
OFFICE:
Swart 105
PHONE:
424-0069, 424-7410
EMAIL:
moghadam@uwosh.edu
OFFICE HOURS:
TR:
9:40—11:10 AM
* Others by appointment
COURSE
COVERAGE:
Chapters 1 through 5 with some omissions and additions if necessary. Also
sections 6.1 and 6.2 if time permits. Topics to be covered are rules of logic
and mathematical reasoning, proof by induction, proof by contradiction,
direct proof, set theory and some operations on sets, functions and some of
their properties, binary operations and relations, an axiomatic approach to
the set of integers, congruence, countable and uncountable sets.
EXAMS:
90% of your grade
QUIZZES
10% of your grade
There will be three exams that will account for 90% of your final grade.
The dates will be announced a week in advance. No make-up exams except
for very special cases, and that will be handled on an individual basis and I
should be notified at least 24 hours in advance.
An optional comprehensive final exam may be given for improving your
grade or replacing the missing exam.
There will be some quizzes similar to your assignments and in class problem
solving and activities individually or in groups. Homework is given after
each lecture. Some homework and special assignments will be collected and
evaluated. I expect papers to be well written using the language of the
course, proper grammar and style.
GOALS AND
EXPECTATIONS:
The main objective of this course is to learn the fundamentals of abstract
mathematics and become comfortable with many concepts common to
different branches of mathematics. We will learn about the language of
proof, mathematical reasoning, and some of its various forms.
This course is taught with emphasis on problem solving, theorem proving,
generalizing, and making conjectures if possible. Upon successful
completion of this course, it is expected that you have been exposed, gained
experience, and improved in the following areas:
Communication, Problem Solving, and Connections.
GRADING:
Based on total points of 3 exams, quizzes, written works, class participation,
presentations, and attendance.
A ...... 91-100
AB ..... 86-90
B ........ 80-85
BC ..... 76-79
Scale
C .......67-75
D ......58-66
Please remember that you should attend class, study the text materials, and do the assigned problems in
order to learn and follow the lecture. I expect each student to be actively involved in class discussions,
group work, and class presentations. It is best to bring your work with you when seeking help from me.
COMMUNICATION:
Communicates effectively and efficiently whether individually or
collaboratively in both written and spoken discourse. Uses appropriate
mathematical language, symbolism, ideas, techniques, and models.
PROBLEM
SOLVING:
Uses problem solving strategies, algorithms, logic, and heuristic reasoning
to define, understand, and solve problems for which mathematical models
can be created.
CONNECTIONS:
Recognizes similar mathematical structures in different contexts; recognizes
relationships within and across the general content domains of discrete
mathematics, continuous mathematics, and probability. Recognizes and
appreciates the humanistic and historic aspects of mathematics.