Math 321, Fall 2008

Syllabus & Homework

You should check this page frequently to obtain your homework assignments.

Course Syllabus

Our goal in Math 321 is to change the way you think about and approach mathematics. As a student in lower division courses you are mastering the techniques of Calculus. While you are encouraged to think critically about the course material, the emphasis is on acquisition of tools. In Math 321 we hope to prepare you for upper division courses, in which you begin to think about and approach mathematics more as a professional mathematician.

In keeping with the above stated goal, there is no set list of topics or syllabus for Math 321. That said, I expect we will cover most of the textbook, which includes topics that you very likely have never seen before:

These topics are essential for most upper division courses and it is important that you acquire some familiarity with them. That said and in keeping with the goal of the course, more important than what we cover is how we cover it.

Writing Intensive

Math 321 is classified as Writing Intensive. For us this means that your homework should be written in grammatically correct English sentences that clearly convey the relevant mathematics. As an example of what I am looking for, here is a solution to Question to Ponder #3 on p38.

Recall that every natural number factors as a product of primes, and that a natural number p is prime if it has no factors other than itself and 1. We are to prove there are infinitely many primes. We shall give a proof by contradiction.

Suppose there are finitely many primes. We list all the primes as p1, p2,..., pn. Set x=p1 p2 ... pn + 1 (the product of p1...pn plus 1) and observe that no pi is a factor of x. Now let q be a prime factor of x. Then q is a prime not appearing on the list, a contradiction.

Assignments

Homework problems marked in red will be collected. The initial submission of a homework problem is due one week after the problem is assigned. As described in the grading policy, I will write comments on your paper and return it. You should then revise your solutions and resubmit. Revisions are due one week after the homework is returned in class. I will then grade your solutions and return them to you.

Other problems will be discussed during the class period immediately following the one in which they are assigned.

Date Homework Comments Due
8/26 1.3.1, 1.3.2 and 1.3.3 ?? nothing
8/28 1.8.9, 1.8.10, 1.8.11, read 1.8.6 ?? nothing
9/2 1.12.1, 1.14.1, 1.14.4 read to p36 nothing
9/4 p37-38 #51,7 (hw1, due 9/11), 2.2.4, 2.6.1 read to p43, and p52-53 nothing
9/9 2.4.3, 2.4.4 (logic, too!), 2.4.7, 2.3.15 read 2.3.11-2.3.13, 2.3.5 nothing
9/11 2.4.5, 2.4.6 ?? hw1
9/16 2.4.9, 2.4.11, 2.5.7, p54-55 #52,6,83 (hw2, due 9/23) read 2.4.10-2.4.12 and 2.5 nothing
9/18 2.5.7 (please!) (re)read 2.5, especially 2.5.7; read 3.1 to p59 nothing
9/23 nothing new read 3,1 & 3.2 nothing
9/25 3.2.3, 3.2.6, 3.3.3, p64 #3, 3.3.2 (hw3, due 10/2) read 3.3 hw2, redo hw1
9/30 4.1.10, 4.2.4, 4.2.7 read 4.1, 4.2.1 to 4.2.10 nothing
10/2 4.2.4, 4.2.7, 4.2.10, 4.2.12, 4.2.13 read all of 4.2 hw3
10/7 4.2.17, 4.2.18, 4.2.21, 4.2.25, 4.2.26 (hw4, due 10/14) read a bit of 4.3 nothing
10/9 4.3.5 just try to understand 4.3.6, 4.3.9 & 4.3.17 nothing
10/14 4.3.23, 4.4.5 start reading 4.4 hw4, redo hw3
10/16 p97 #10,11 & 4.4.6, 4.4.9, (4.4.14, 4.4.15) read up to 4.4.16 redo hw2
10/21 p.100 #19 read up to 4.4.16, 4.4.23, 4.4.24, 4.4.27, 4.4.28 nothing
10/23 lemmas from class & 4.4.15 nothing new nothing new
10/28 nothing new nothing new redo hw4
10/30 study for the exam! practice exam here! review session Wednesday, 11/5, 3:30, Keller 401 study!
11/6 in class midterm exam midterm today midterm
11/13 5.1.4, 5.1.10, 5.1.11, 5.1.12, 5.1.14 read 5.1 & 5.2 take home midterm
11/18 5.1.10, 5.1.12, 5.1.14, 5.2.3, 5.2.4, 5.2.6, p.131 #3-7 read 5.2 & 5.3 nothing
11/20 5.3.5, 5.3.10, 5.4.10, p131 #5 (hw5 due 11/25) read 5.3 & 5.4 nothing
11/25 nothing - sorry, I forgot! Happy Thanksgiving! read 7.1 & 7.5 hw5
12/2 7.1.2, 7.1.6, final hw (due 12/11) read 7.1 & 7.5; start 7.2 up to 7.2.5 nothing
12/4 7.3.7, 7.3.9, 7.3.11, p177 #2 (hw6 due 12/9) read 7.2, 7.3 & 7.4 hw5 redo
12/9 practice final! review: 12/15, 10-11am, Keller 401 review: 12/17, 8-9pm, Keller 402 hw6
12/11 last day! course evaluations! study for the final! final 12/18, 12-2! final hw

[1] WARNING (for homework due 9/11): p37 #5 is false as stated. You should think carefully about why, and explain. Hint: it has to do with the quantification conventions discussed in the box on p14.

[2] Also convert the assertion to a logic statement and prove the logic statement using a truth table.

[3] Will giving examples be enough? Why or why not?