Math 300.2: Fundamental concepts of mathematics
Fall 2017

Instructor: Paul Hacking, LGRT 1235H, hacking@math.umass.edu
TA: Gregory McGrath, gpmcgrath@umass.edu

Meetings
Classes: Mondays, Wednesdays, and Fridays, 11:15AM--12:05PM, in LGRT 143.
Coseminar: Tuesdays 4:00PM--4:50PM, 5:00PM--5:50PM, and 6:00PM--6:50PM in LGRT 1114.
Office hours: Mondays 2:00PM--3:00PM and Tuesdays 1:30PM--2:30PM in LGRT 1235H (Paul Hacking); Tuesdays 12:30PM--1:30PM in LGRT 1023 (Gregory McGrath).

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

Another useful text (not required) is An introduction to mathematical thinking, by W. Gilbert and S. Vanstone, Prentice Hall 2004. googlebooks.

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 Wednesday's class. (First homework due Wednesday 9/20/17.)

No late homework will be accepted. Instead, your two lowest homework scores will be dropped.

Homework sets

Exams

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

Midterm 1: Wednesday 10/11/17, 7:00PM--8:30PM, LGRT 143.
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 Tuesday 10/10/17, 7:00PM--8:30PM, in LGRT 143.
Please try the review problems here before the review session. Solutions pdf.

Midterm 2: Wednesday 11/15/17, 7:00PM--8:30PM, LGRT 143.
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, 8.3, 5.1, 5.2, and 5.3 of Sundstrom.
There will be a review session for Midterm 2 on Tuesday 11/14/17, 7:00PM--8:30PM, in LGRT 143.
Please try the review problems here before the review session. Solutions pdf.

Final exam: Wednesday 12/20/17, 10:30AM--12:30PM in LGRT 121.
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, 8.3, 9.1, 9.2, and 9.3 of Sundstrom.
There will be a review session for the final exam on Tuesday 12/19/17, 7:00PM--8:30PM, location TBA.
Please try the review problems here before the review session. Solutions pdf.

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