Reading
In this class, we use the draft of a textbook by Paolo Aluffi
MODICUM MATHEMATICUM
As a supplementary material, the textbook by Richard Hammack
Book of Proof is recommended (a free electronic version of the book ia available
here ).
Course Objective
The primary goal of this class is to develop a way to approach mathematics as professional mathematicians do.
Most of the previous mathematical experience of the students is related to Calculus classes.
These classes are primarily directed to acquisition of tools.
For this reason, although very useful, Calculus classes tend to create a misleading impression about mathematics.
In this class we will learn that mathematics is not about specific tools, but about ideas and arguments. These ideas and arguments are frequently expressed as
proofs.
The class is designated as
writing-intensive. As a consequence, mathematical writing, and particularly, the writing of clear and correct proofs is a subject of emphasis.
The topics covered in this class consitute general mathematical literacy and are of substantial importance for most upper division mathematics proof-based courses. Specifically, the students will learn some language and terminology common throughout mathematics, basics of proof-building, and naive set theory. That will allow us to meaningfully address a question of the nature of an object as fundamental as real numbers. The class lays a foundation for learning core areas of mathematics including but not limited to algebra, analysis, and topology.
Grading Policy
The course contains a combination of concepts, ideas and techniques which the students must be able to apply in solving specific problems. Most of these problems require proving or disproving certain statements. Since this is a writing-intensive class, we simultaneously learn how to write mathematical texts.
At the end of the day, your grade will reflect your ability to solve specific problems. This assumes your ability to write down a simple proof so that it is mathematically and grammatically acceptable.
More specifically, the following rules are to be taken.
Final exam takes place according to the University final exams schedule, and will count for 30% of the final grade. The exam is cumulative (it covers all the material). There will be no make-ups for the final.
Four writing homework assignments count together for 40% of the final grade.
It will be possible to make up these assignments taking into the account my remarks and comments. For every assignment, two attempts will be given, and the score comes out as a maximum of the two.
Two midterm tests. The (average) grade for the tests counts for 30% of the final grade.
Regular homework assignments consist of problem sets marked as "Homework" in the textbook. It is assumed that
students are working on these problems as soon as the corresponding section is covered in class.
These assignments will never be collected and graded. However, those students who skip solving these problem sets
have pretty high chances to fail the class.