Math 347 - Fundamental Mathematics: Syllabus
University of Illinois at Urbana-Champaign
Fall 2018
Instructor: Aron Heleodoro
Office: Altgeld 165
e-mail: aronah@illinois.edu
Lecture: MWF 3:00-3:50 pm
Office Hours: Th 4-5 pm or by appointment
Learning Goals:
•engage in an active learning experience and self-learning parts of the material;
•develop the habit of working with peers and discussing proof ideas before writing them down;
•grasp the essential differences between abstract mathematical subjects and previous mathematical
knowledge;
•achieve a good level of proficiency in self-learning and proof writing to be in condition to succeed in
further mathematics classes (e.g. Elementary Real Analysis and Intro to Abstract Algebra);
Objectives: The main goal of this course for students is to master the ability to write precise and good
proofs. The content used to achieve these goals is first a brief study proof techniques, which are then
extensively applied to different areas of mathematics. The course is naturally split into three parts:
1) introduction to basic set theory, proof methods, notably induction and a discussion of the concept of
cardinality;
2) a study of the real numbers, i.e. an introduction to real analysis;
3) an introduction to elementary number theory, i.e. a discussion of modular arithmetic.
Structure: There will be two different types of lectures alternated every week, unless an assignment is
taking place. The first type is a usual lecture where we might also discuss some exercises. The second type
is a flipped classroom, that is, students will be given a reading assignment before the class and on that day
they will come and start working on a worksheet. This is going to be a collaborative group activity where
students learn from each other.
Textbook: Mathematical Thinking: Problem-Solving and Proofs - Second Edition, John P. D’Angelo &
Doubles B. West. Note: Since half of the classes involve the students reading the material before coming to
class it is important that you have a copy of the book.
Assignments:
1
