Math 403/603 Foundations of Math

Objectives. The main objectives of this course are:
  1. Learning to understand written theoretical mathematics
  2. Learning how to discover and write mathematical proofs
  3. Mastering conventions for mathematical oral and written communication
  4. Learning foundational concepts used throughout mathematics, including aspects of set theory, functions, and equivalence relations

At the end of the course you should know the main definitions and the main theorems we have covered, but more importantly, you should understand why the definitions and theorems are formulated in the way that they are, and what they mean. You should also know the proofs for the main theorems, as well as the kinds of reasoning that go into these proofs. A part of the second objective is developing the ability to understand and construct proofs. At the end of the course you should be able to analyze an unfamiliar proof, and either verify that the proof is valid, or find errors in it. You should also be able to construct your own proofs of new or unfamiliar results. In addition, you should know how to communicate your findings orally and verbally using accepted conventions and methods of the discipline of mathematics. 


Attendance.  Attendance in this course is expected, but not required or monitored; I will not keep track of days you miss class. However, you are responsible for anything presented in class, including announced schedule changes, modifications to assignments, and material that supplements what is in the text. Note also that the subjective component of your grade will take into account regular participation in class activities. Electing to skip these activities may lower your subjective grade.

Missed Exam Policy.   If you are forced to miss an in-class exam for reasons beyond your control (such as an illness, family emergency, etc.), a makeup may be arranged, but ONLY if I am informed in advance. I will NOT approve requests to reschedule an exam for reasons of convenience. For example, if you plan to travel during a school break and leave early or return late, that is not a valid reason to reschedule an exam. Similarly, avoidable conflicts for recreational, entertainment, social, or work activities are generally not valid reasons to miss an exam. The exam dates are listed on the overview webpage. Be sure to plan other activities around them.