Principles of Mathematics (32427) - Summer II 2004
M-F 11:40-13:50 in MAIN 205
- Instructor.
Dr. H. Knaust, Bell Hall 124, tel. 747-7002,
e-mail: helmut@math.utep.edu
- Office Hours.
M-F 11:00-11:30, or by appointment.
- Textbook.
Carol Schumacher, Chapter Zero, 2nd edition, Addison-Wesley, 2001.
The textbook is required at all class meetings.
- Prerequisites.
The course requires a certain level of mathematical maturity
that you should have gained by, for instance, having thoroughly and successfully
grappled with the concept of infinity in your Calculus II course
(which is the formal prerequisite for this course).
- Contents.
The course will hopefully "uncover" Chapters 0-5 of the textbook.
- Course Objectives. This is a Foundations course. This means that
hardly any prior knowledge is required. The class prepares you "do" mathematics on your own and
enables you take more advanced classes or read rigorous mathematical textbooks.
You should expect
(and I will expect) that you make considerable progress in the following areas:
- Make sense of an abstract definition by analyzing it carefully and constructing examples.
- Make sense of a mathematical statement and be able to bring to bear a variety of strategies for constructing its
proof.
- Be able to recognize a rigorous proof when you read one.
Conversely, be able to pick out the weak spot(s) in a less
rigorous argument. Be able to fill in details in a sketchy proof.
- Once you have devised a proof, be able to write it down in a
clear, concise manner using correct English and mathematical grammar.
- Be able to present and defend a proof to a group of your
peers.
- In-class Activities and Presentations. Mathematics is not a spectator sport.
I will call on students to give presentations of examples and exercises in the textbook. I will also regularly
ask for volunteers (or groups of volunteers) to present solutions to problems and proofs of theorems at the blackboard.
Your presentations are the most important part of the course.
Your chances of passing the course without spending a
significant amount of time on preparing in-class demonstrations are zero:
Your in-class work, evaluated for both quality and quantity, will account for
50% of your grade.
- Writing assignments. Occasionally, you will have short writing assignments.
These assignments will contribute 15% to your grade.
- Tests.
Two take-home exams will be given on the following dates:
- Handout: Wednesday, July 7; Return: Thursday, July 8
- Handout: Friday, July 16; Return: Tuesday, July 20
Make sure to reserve ample study time for the take-home exams on your calendar.
The take-home exams account for 15% and 20%, respectively, of your grade.
- Time Requirement.
I expect that you spend an absolute minimum of four to five hours a day
outside of class on reading the textbook, preparing for the next day, reviewing your class notes,
and completing assignments.
If you do not have time for such an intensive schedule, you must take the course some other semester.
- Attendance. Due to the course structure, attendance is mandatory. An unexcused absence will result in a
problem/theorem grade of 0 for the day of the absence. Four absences (excused or unexcused) will
lead to dismissal from the class with the grade of "F".
- Drop Policy.
The class schedule lists
Friday, July 9,
as the last day to drop with an automatic "W". After the deadline, you cannot drop the course.
- Information on the Web. This syllabus and ancillary material can be found on my homepage
http://helmut.knaust.info
.
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