Math 300A Winter 2011: Introduction to Mathematical Reasoning

Instructor: James King

Email: king@u.washington.edu Office: Padelford C440 Phone: 543-1915

Office Hours: Tues 1-2 and by appointment

Class Webpage: http://www.math.washington.edu/~king/coursedir/m300w11/

Class Email List: Email from this list will be sent to you with announcements. A test announcement will be sent the first week.

Nature and purpose of the Course: The catalog description of this course says this: “Mathematical arguments and the writing of proofs in an elementary setting. Elementary set theory, elementary examples of functions and operations on functions, the principle of induction, counting, elementary number theory, elementary combinatorics, recurrence relations.”

What the description does not say is that this course is intended to be a critical transition course between lower-division math courses that center more on “how to” and upper division courses that are more conceptual and abstract and more serious about the question “why?” Students who really learn the essential elements of this course should do much better in 400-level math courses and some 300 level courses with proofs, so it is important not only to make a good grade but to carry away the tools you will need.

Textbook and other resources: Basic Concepts of Mathematics and Logic by Michael C. Gemignani (Dover Press, ISBN 0-486-43506-7). The course will cover most of Chapters 1- 9 and some other material as well. There are a number of interesting free textbooks and sources on the web that will also be used to some extent by the class, and which individual students may find helpful as supplements.

Tests: There will be one midterm on Groundhog Day, February 2, and a Final Exam on March 16. There will also be a occasional quizzes (announced in advance) and occasional short in-class assessments (not announced in advance). The latter are for the instructor to get a sense of how the class is doing but also provide information for students on how they are doing.

Homework and in-class work: Even more than most math courses, Math 300 is not a spectator event. The goal is to build needed knowledge and skills, including the ability to write and explain as well as to read and understand. So there will be homework – some to be handed in on paper and some online – and also frequent class activities, some of which you will hand in for credit, sometimes for participation credit, sometimes to be graded. Because of the in-class work and the in-class assessments, it will be very hard to get a good grade in this course if one does not attend regularly.

On-Line Discussion: We will use Catalyst to include some assignments in the form of online discussion. More announced later.

Grading Formula: Homework: 15% – In-Class work 10% – Quizzes 10% – Midterm 25% – Final Exam 40%.

Reading Assignment for Week 1: Gemignani, Sections 2.1 and 2.2 for Monday, Sections 2.3 and 2.4 for Wednesday.

Online Assignment A due Friday 1/7 by midnight: See webpage for link. Do the reading first.

Written Homework 1 due Monday 1/10 in class: (1) Problem #4 in section 2.5, (2) Problem #6 in section 2.5, (3) Write the truth table for “if A then B”, (4) Write the truth table for “if ~ B then ~ A”.

FUTURE ASSIGNMENTS WILL BE ON THE WEBSITE, NOT ON HANDOUTS!