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Carnegie Mellon University, Department of Philosophy,
Summer 2000
The Nature of Mathematical Reasoning
Dirk Schlimm
Syllabus Update
Final instructions for portfolio
8/7/00
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:

Table of contents.

For each lecture:

a brief summary, containing the main concepts and ideas;

a few remarks about what you find interesting or puzzling.

Homeworks assigned in class.

Index of technical terms introduced in the course (for quick reference).

Reading material
The portfolio must be kept in a threering binder made for standard size
notebook paper (8 1/2 by 11 inches), preferably not more than 1 1/2
inches wide and
not less than 1 inch wide at the back. Your name should be clearly written
on the outside of the binder.
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 fullsize
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 on the day of the final exam and can be picked up the following week. 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 index complete? Are all terms in the index
referenced correctly?
Here's a list of terms I expect to find in the index:
 First half of course:
Archimedes, Aristotle, Euclid, Eudoxos, Hypatia, Thales, Plato, Pythagoras, commensurable, deductively valid, sound, deductive, inductive, formal, irrelevant, fallacious, Babylonians, Egyptians, proof of irrationality of the square root of 2, proof that there are infinitely many prime numbers, Thales' theorem, neolithicum, definition of even, notation, binary numbers, 7adic system, statement, proposition, premise, conclusion, inference rule, N, Q, R, constructive mathematics, reductio ad absurdum, indirect proof, proof by contradiction, objectivity, form of an argument.
 Second half of course:
11 function,
Axioms of probability,
Bayes' Theorem,
Cantor's diagonal argument,
Conditional probability,
De Morgan rule,
Georg Cantor,
George Boole,
Gerhard Gentzen,
Gottlob Frege,
Intuitionistic logic,
Knights and Knaves,
Kurt Gödel,
Law of total probability,
atomic sentence,
base case,
base clause,
cardinality,
completeness,
countable,
denumerable,
entailment,
expressively complete,
final clause,
formal language,
formula,
function,
induction hypothesis,
induction step,
inductive clause,
inductive/recursive definition,
injective,
interpretation,
mathematical induction,
molecular sentences,
names of syllogism,
natural deduction,
nonclassical logics,
propositional formula,
quantifier,
semantic method to check validity of arguments,
semantics,
sentential/propositional logic,
soundness,
syllogism,
syntax,
tautology,
terms in arithmetic,
truth table,
,
=.
 If you feel other terms should be added, include them in your index, too!
The final grade of the course will be based on five components
according to the following weights:
18% Homeworks
18% Inclass quizzes
18% Midterm
18% Final exam
28% Portfolio
[ 80110 home page
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© Dirk Schlimm, Last modified: August 4, 2000