Class: Mo-Fr, 3:00-4:20pm, Porter Hall 226 B
Website: http://www.contrib.andrew.cmu.edu/~dschlimm/80-110summer00
Instructor: Dirk Schlimm
Office: Baker Hall 148
Phone: 268-8573
Email: dschlimm@andrew.cmu.edu
Office hours: By appointment. The best way to contact me is via
email.
Course description: Although we spend the great bulk of our mathematical education learning how to calculate in a variety of ways, mathematicians rarely calculate anything. Instead they devote their time to clearly stating definitions, finding simple axioms, making conjectures about claims that might follow from these axioms, and then proving these claims of finding counterexamples to them. Although thinkers since Aristotle have devoted enormous time and energy to developing a theory of mathematical reasoning, it is only in the last century or so that a unified theory has emerged.
In this course, we not only consider the modern theory of mathematical reasoning, but we also consider several case studies in which a problem is simple to solve with mathematical reasoning but almost impossible to solve without it. For example, we consider how to compare the sizes of infinite sets, and how to solve the Monty Hall-Let's make a deal Problem. This allows you to get a feeling for the power of abstract reasoning, in particular when it's consequences are not so obvious at first sight, but can be validated by experience.
By learning a few facts about the evolution of mathematics from prehistory to modern times, and also by setting the relevant mathematical concepts into their historical context, you should be able to develop a basic understanding of the history of mathematics and of fundamental problems in the philosophy of mathematics. After all, this is a philosophy course!
Goals:
Homework: Usually short assignments are assigned during the week (Mondays, Wednesdays, and Fridays) which are due two work days later. Sometimes I will want you to write a short essay, but then you will have more time to complete it. Homeworks are returned with corrections within two days. Corrected assignments should be kept in the portfolio (see below).
Assignments can be redone within two days after I handed them back in order to obtain a better grade. This allows you to go over your work again and the opportunity to learn from previous errors. In some cases (e.g., when a proof should be presented), I will ask you explicitly to redo the assignment until no further corrections are necessary.
The assignments will be posted on the class web-site. It is your responsibility to obtain the assignment if you miss class. Attempting to give an excuse anywhere in the vicinity of: ``I didn't know there was an assignment,'' or ``I missed class and my friend gave me the wrong assignment'' will cause excessive irritation on the part of the instructor. You are free to collaborate on homework, but not to copy answers from friends. Assignments are due at the beginning of class on the date mentioned in the assignment, and have to be turned in on paper (except where explicitly mentioned). You may type them up or turn them in in legible handwriting. If you use a word-processor, make sure to use the spell-checker.
Portfolio: Students are expected to keep a portfolio about the contents of the class. This gives you the opportunity to organize the material presented in class in a neat and clear way. It will help you to keep track of where we are in the course. It will also make it easier for you to review the material and thereby help you to find out what you have really understood and what is not yet clear to you.
The portfolio should include:
You may use any type of paper you like, lined or unlined, and of any color it seems good to you to use. However, please use paper that has punched holes correctly placed for insertion in the binder, and please use full-size paper.
All materials for this course should be kept in the portfolio binder at all times. Use dividers to mark off each section. Please arrange them in the order mentioned above.
Remember: your portfolio is the embodiment of your work for this course. A complete and well presented portfolio virtually guarantees you a good grade. The opposite is also true.
The portfolio has to be handed in three times during the semester and will be returned with comments and a grade the next day of class. The grade will be based on completeness of content and clarity of exposition. What I will look for in particular is the following: Are all pages legible? Is the table of contents complete? Is there at least a page for each lecture? Are the main topics of each lecture summarized briefly? Are there personal remarks about interesting or puzzling points? Are all homeworks included (all versions of the ones which were redone)? (The content of the homeworks does not contribute to the portfolio grade, but to the grades for the homeworks.) Is the glossary complete? Are all terms in the glossary explained?
Exams: Two exams will be held during the course: on Monday, July 24, and Friday, August 11. They will cover the material up to the date of the exam. The final exam will be comprehensive.
It is possible to substitute an exam with a 5-10 page essay on a topic related to the course. If you want to take this option, talk to the instructor at least 10 days before the exam and discuss with him the topic you want to write about. You should present an outline of the essay one week before the exam date, and turn it in at the time of the exam. No extensions are granted. It is not possible to substitute the exam later than 10 days before the scheduled date of the exam.
Class participation: Class participation is expected. This includes showing up regularly (missing 1 or 2 classes is reasonable, missing 7 or 8 is not -- if you have to miss a class, please tell the instructor why), showing up prepared, making an effort to answer questions posed, contribute to class discussions, and present small problems in class. It is a well-known fact that active learning (e.g., participating in discussions) is much more effective than passive learning (e,g,. reading), thus you get more out of the course if you are actively involved.
The reading material only supplements the lectures, but cannot compensate for them. Most material covered in class will not be available otherwise. And although class participation will not be explicitly graded, the quizzes, which cover material presented in class and which are administered in class, do count towards your final grade.
Grading: The grade in this course depends on your continuous effort during the semester. The final grade will be based on five components according to the following weights:
18% Homeworks
18% In-class quizzes
18% Midterm
18% Final exam
28% Portfolio
Grades for homeworks, quizzes, exams, and portfolio will be on a scale between 0 and 10. The corresponding letter grades are: 10-9 A, 8-7 B, 6-5 C, 4-3 D, below 3 F.
Required text: The only required text is The Language of First-Order Logic by Jon Barwise and John Etchemendy which comes with the program Tarski's World for either PC or Mac. Please obtain this book by 10 July. If you have problems ordering it, I will be happy to assist you.
Additional texts will be handed out in class.