Math 252 - Foundations of Higher Mathematics

Instructor: Brian Lins
Class Times & Location: MWF 1:30-2:20 Bagby 106
Office Hours: See my weekly schedule, and also by appointment.
Text: Number Theory Through Inquiry, by David C. Marshall, Edward Odell, and Michael Starbird.

Announcements

Here are review problems for the final exam.
Please order the course textbook (see link above) before classes start!

Course Description

The purpose of Math 252 is to teach the fundamental concepts and techniques of advanced mathematics. In this course we will use number theory as the vehicle for learning these skills. We will use an inquiry based approach. Instead of lectures, I will introduce new material by suggesting exercises and theorems, and it will be your job to try to prove them. You can only learn math by doing math! Among the topics we will cover are: Diophantine equations, prime numbers, modular arithmetic, Fermat's little theorem, and Euler's theorem. As time permits we may cover public-key cryptography, quadratic reciprocity, and/or Pythagorean triples. Occasionally we will detour to talk about important concepts and terminology from set theory and logic.

Tentative Schedule

The schedule below is tentative, and may be subject to change. Changes will be announced in class, and you are responsible for knowing about any changes even if you miss the class when they are announced.

Weekly schedule & homework

Attendance Policy

Attendance in this class is required. Repeated absences may result in a forced withdrawal from the course. You are responsible for any material you miss due to absence. Please let me know ahead of time if you know that you will not be able to attend class.

Grading Policy

The term grade will be based on the results of the examinations, the scores on written homework, and on class presentations. The grade is determined as follows:

Classroom Work & Presentations	10% points
Written Homework	40% points
Midterm 1	15% points
Midterm 2	15% points
Final Exam	20% points

Classroom Work & Presentations

Every class period, students will be asked to present solutions or attempted solutions to problems on the board. I will not grade these solutions on mathematical validity, only on the attempt.

Written Homework

There will be written homework assignments due every week. These homework assignments will be assigned from the book and from exercises we attempt in class. Half of the points for each homework assignment will be based on the mathematical validity of the work. The other half of the grade will be based on exposition and neatness. In order to receive full credit for the exposition portion of the grade, the write-up must satisfy the following criteria:

It must be neat, legible, stapled (if more than one sheet of paper), and have your name written clearly on top.
Individual problems must be clearly labeled and separated from other problems by at least a full line.
Each exercise must include a description of the problem to be solved (this may be copied directly from the exercise itself if it came from the book).
For proofs, all explanations must be written in complete sentences.
The end of any proof should be indicated with a Q.E.D. or a small square.

Late homework will not be accepted. You are permitted, and in fact encouraged to work together, but all homework assignments you submit must ultimately be your own work. I recommend that homework be typed. I may allow some homework assignments to be revised and resubmitted, but all resubmissions must be typed.

Exams

There will be two midterm exams and a cumulative final. The midterm exams will each count for 15% of the term grade and the final exam will count for 20% points. The exams may include both in-class and take home portions.