October's comments.
29 October. In Wednesday's class, we discussed Section 4.3, which is all about the laws of exponentiation. These laws are quite familiar, so we spent most of our time discussing how to verify them when the exponents are positive integers. We also discussed why we define the 0th power of any non-0 number to be 1, and why we do not define the 0th power of 0.

No new homework was assigned in Wednesday's class. However, students are reminded to read Section 5.1 for Monday's class.

23 October. This week, Thursday's office hours will be cancelled, and Wednesday's office hours will be extended to 2:30--4:30 PM. Tuesday's office hours will be 11 AM--12 n, as usual.

Thanks to Jillianne Whitfield for pointing out that I hadn't posted the final exam date on the course web page. As announced in class, the final will be December 18, 8--10 AM.

In today's class, we discussed Section 4.2 (on identities, properties, and rules), giving some examples and discussing how to prove (using the properties of arithmetic) and illustrate (with pictures, usually involving the rectangular array model) them. We built to a discussion of binomial multiplication and FOIL, and closed with a demonstration of how to multiply many-digit numbers using a limited-precision calculator.

For Wednesday's class, students should read Section 5.1.

Homework for today is Homework Set 18. However, students should change the words ``... as in Problem 7 ...'' in Problem 7 to read ``... as in Problem 6 ...'', and should delete the words ``(written in fraction form)'' from Problem 10(d).

19 October. Today's office hours will be held 2--3 PM, not 3--4 PM.
18 October. In today's class, we began our discussion of prealgebra -- essentially, algebra with emphasis placed on the fact that the algebraic expressions with which we are dealing should be regarded as standing in for specific, concrete numbers, and thus subject to the rules of arithmetic with which students are familiar. We briefly discussed when the use of letters for numbers is, and is not, appropriate in the statement and in the solution of a word problem, and saw several examples.

Since we did not have time to discuss the definitions in class, students should read carefully the definitions of expressions, equations, and identities in Section 4.1, making sure they understand the distinctions among the three.

Homework for today is set 16, except for problem 3, and set 17, except for problem 7. In addition to using the distributive algorithm in problem 17.8, students should also draw a picture to illustrate their conclusion.

11 October. In Monday's class, we finished up our discussion of the long division algorithm, reviewed briefly the important concepts for the exam, and practiced the familiar arithmetic algorithms (for addition, subtraction, and multiplication) in other bases. Although it is also possible to perform long division in other bases, we did not do so.

I have received permission from the instructor for Math 385 in Fall 2005 to make his first exam available on the web site. Although it is hoped that this practice exam will be helpful, no guarantee is given that the length or level of difficulty of this practice exam will be representative of those of our exam.

Homework for Monday (due October 18, after the break) is sets 14 and 15 from the text. Students should also read all of Chapter 4 before October 18.

8 October. In Wednesday's class, we began a discussion of the long division algorithm.

Homework for Wednesday was homework set 13.

3 October. In Monday's class, we discussed Sections 3.1 and 3.2, as well as part of Section 3.3. These sections discuss in detail the familiar algorithms of elementary school arithmetic. The idea in each case is to take a relatively complicated multi-digit operation (addition, subtraction, or multiplication, respectively), and break it down into many one-digit operations using the any-order and distributive properties.

I want to emphasise again the importance of doing the assigned reading before (and after, if necessary) each class. For Wednesday's class, students should read (or reread) Section 3.3 (which we have already begun), as well as Sections 3.4--3.6.

Homework for today is Sets 10--12 from the text.

Permanent version of this page created on 1 November 2006.