Math 300: Fundamental concepts of mathematics
Spring 2017

Instructor: Paul Hacking, LGRT 1235H, hacking@math.umass.edu
TA: Shelby Cox, shelbycox@umass.edu

Meetings
Classes: Tuesdays and Thursdays, 1:00PM--2:15PM, in LGRT 143.
Coseminar: Tuesdays 4:00PM-4:50PM, LGRT 1234; Wednesdays 4:00PM--4:50PM, LGRT 1114, and Wednesdays 5:00PM--5:50PM, LGRT 1114.
Office hours: Tuesdays 2:30PM--3:30PM and Wednesdays 2:00PM--3:00PM in LGRT 1235H (Paul Hacking); Wednesdays 3:00PM--4:00PM in LGRT 1117 (Shelby Cox).

Course text: Mathematical Reasoning: Writing and Proof, by T. Sundstrom, available for free download at the author's website here.

Prerequisites: Math 132.

Overview of course

The goal is that you learn to read, understand, and construct coherent, logically correct proofs, so that you may more easily make the transition from calculus to the more theoretical junior-senior courses, especially abstract algebra and modern analysis. Starting with explicit axioms and precisely stated definitions, you will systematically develop basic propositions about integers and modular arithmetic, induction and recursion, real numbers, infinite sets, and such other topics as time may allow. You will be provided with the needed background about logic, sets, and functions. For nearly every class you will create written mathematical proofs. You are expected to participate actively in class, including at the co-seminar.

Syllabus

We will cover Chapters 1--9 of the textbook.

Class log

Homework

There will be weekly homework, due at the beginning of Thursday's class. (First homework due Thursday 2/2/17.)

Homework sets

Exams

There will be two midterm exams and one final exam as follows:

Midterm 1: Tuesday 2/28/17, 7:00PM--8:30PM, in LGRT 206.
The syllabus for Midterm 1 is Sections 2.1, 2.2, 2.3, 2.4, 3.1, 3.2, and 3.3 of Sundstrom.
There will be a review session for Midterm 1 on Monday 2/27/17, 7:00PM--8:30PM, in LGRT 202.
Please try the review problems here before the review session.

Midterm 2: Tuesday 4/11/17, 7:00PM--8:30PM, in LGRT 206.
The syllabus for Midterm 2 is Sections 3.1, 3.2, 3.3, 3.4, 3.5, 4.1, 4.2, 4.3, 8.1, 8.2, and 8.3 of Sundstrom.
There will be a review session for Midterm 2 on Monday 4/10/17, 7:00PM--8:30PM, in LGRT 204.
Please try the review problems here before the review session.

Final exam: Wednesday 5/10/17, 10:30AM--12:30PM, in LGRT 143.
The syllabus for the final exam is Sections 2.1, 2.2, 2.3, 2.4, 3.1, 3.2, 3.3, 3.4, 3.5, 4.1, 4.2, 4.3, 5.1, 5.2, 5.3, 6.1, 6.3, 6.4, 6.5, 7.1, 7.2, 7.3, 8.1, 8.2, and 8.3 of Sundstrom. (See also the class log here.)
There will be a review session for the final exam on Tuesday 5/9/17, 7:00PM--8:30PM, in LGRT 204.
Please try the review problems here before the review session.

You are allowed one letter-size sheet of notes (both sides) for each exam. Calculators, additional notes, and the textbook are not allowed on exams and quizzes. You should bring your student ID (UCard) to each exam.

Grading

Your course grade will be computed as follows: Homeworks and quizzes 30%, Midterm exams 20% each, Final exam 30%.



This page is maintained by Paul Hacking hacking@math.umass.edu