MATH 347: Fundamental Mathematics, Summer 2014
A.J. Hildebrand

Welcome

Welcome to Math 347! This course is an introduction to rigorous mathematical reasoning and proofs, and a preparation for upper level proof-based math courses such as Math 417 (Abstract Algebra) or Math 447 (Real Analysis). You will learn the fundamental concepts in mathematics such as sets, functions, and relations, how to construct a rigorous mathematical argument (a "proof"), and how to write up the argument in a clear and logically correct manner. Along the way, you will encounter many interesting, "cool" problems from a variety of areas of mathematics.

This course is both challenging and rewarding. It is unlike any other math course in that its focus is not on any particular mathematical subject, but rather on general mathematical concepts and abstract ideas, logical reasoning, and proofs. The emphasis is not on memorizing facts and formulas, but on learning precise mathematical thinking and logical reasoning. This course requires a serious investment of time and effort. For many students it is the most demanding math course they have taken so far. In fact, it had such a fierce reputation as a "make or break" course that there used to be T-shirts saying "I survived Math 347. And I can prove it."

This course is not for everybody, and you should not take it for the wrong reasons, e.g., because it happens to fit into your schedule, or because you need a couple more credit hours to satisfy graduation requirements. If you just want three hours of technical course work, there are many easier choices in the summer.

For those who are ready and willing to take on the challenge, the course offers many rewards. The analytical and logical skills you acquire in this course not only prepare you for advanced math courses, but are also useful in the real world. Knowing how induction really works, or getting comfortable with fearsome looking epsilon-delta definitions that you may have seen in calculus, but never really understood, can be deeply gratifying. You'll come across many interesting mathematical gems, logical puzzles, and challenging problems that one normally wouldn't see in other courses.

I will do my best to help you along the way and make this course an interesting, enjoyable, and worthwhile experience. Below is some basic information about the course; more information will be posted here as we move along. If you have any questions, concerns, or suggestions, feel free to contact me (email ajh@illinois.edu). I look forward to working with you over the coming eight weeks, and wish you an enjoyable, productive, and fulfilling, summer semester!

Course Basics

Exams, Grades, Course Policies

Class Diary

Daily class log with handouts, homework and reading assignments. Check this page daily.


Emergency Information.


Last modified: Wed 16 Jul 2014 09:17:40 PM CDT A.J. Hildebrand