Concepts of Mathematics

21-127 Concepts of Mathematics

Spring 2019

Sections 1 and 2

Class Info

Class times: Section 1: MWF 1:30pm - 2:20pm; Section 2: MWF 3:30pm - 4:20pm
Office Hours: MF 11:30am - 1:00pm

Textbook

We will be following Brendan Sullivan's book Everything You Always Wanted to Know About Mathematics (but Didn't Even Know to Ask), beginning with Chapter 3. Clive Newstead's text, An Infinite Descent Into Pure Mathematics, will be a secondary source. Most of the homework problems (and even some of the exam problems) will be drawn from one of these two textbooks. Both are available on the Canvas page for the course.

Course Description

This course introduces the basic concepts, ideas, and tools involved in doing mathematics. As such, its main focus is on presenting basic logic, and the methods of mathematical proof. These subjects are closely related to the application of mathematics in many areas, particularly computer science. Topics discussed include a basic introduction to elementary number theory, induction, the algebra of sets, relations, equivalence relations, congruences, partitions, and functions, including injections, surjections, and bijections. A basic introduction to the real numbers, rational and irrational numbers. Supremum and infimum of a set.

Grading

There will be weekly homework assignments (approximately two per week), two midterm exams, and a final exam. The lowest homework score and quiz score are dropped. The homework and tests will be weighted as follows in the final grade computation:

Homework (30%)
Quizzes (10%)
Midterm 1 (15%)
Midterm 2 (15%)
Final (15%)

Letter grade cutoffs will be determined at the end of the semester, but will not be more harsh than the standard cutoffs of 90% - 100% = A, 80% - 89.9% = B, etc.