The goal of homeworks is practice on the topics covered in the text and
in class. If you’re unsure how to tackle one problem, look at the problems
nearby or at examples. One may be more clear to you and help you with
the assigned problem.
I have office hours now. Monday and Wednesday 1.30pm to 2.30pm (or
possibly later) in the Math Lab down the hall.
Be sure to read the entire problem. Many submissions contained only
partial answers even when it was clear you understood the mechanism.
With problems involving large numbers, expect most calculators and computer
software to break. Try to check results using properties of the input
numbers. For example the product of two numbers with units digit 1 also
has units digit 1. Or that the product of two d
digit numbers has either 2d
or 2d - 1
digits. (Think about long-hand multiplication to find these and other
properties.)
If there are questions about which problems were assigned or what the
problem is asking, contact me even if it’s the night before the homework
is due! I may not respond instantly, but it’s worth a shot.
Because there was apparent confusion over which problems were assigned,
I will start providing the homework on a separate page as well as directly
in the notes.
In general, writing out steps cushions the blow if the result is incorrect.
And writing out reasons helps even more. If your homework must be
late, reasoning in your own style and words shows you did not just
copy solutions. This class is as much about the method of thinking andcommunicating as it is about the final results!
Remember that homework is one 20% chunk. But there will be 14 or 15
assignments. Each is at most \mathop{\mathop{…}}
And if there are 10-20 problems per assignment, then each assignment is at
most\mathop{\mathop{…}}
This is another reason why homeworks are frequent. The impact of each
assignment is a little less when there are many.
Groups are fine, turn in your own work. Homework is due in or before class on
Mondays.
Following Pólya’s principles, write a careful solution for the following
problems:
From last week’s homework: Section 1.2, problems 9 and 49
From this week’s homework: Section 1.3, problem 40
For the write-up, use each of Pólya’s principles as a section heading. Begin
with a section on Understanding the Problem (or an equivalent phrase)
detailing what you have, what you want, and what (if any) relationships you
see immediately. Then under something like Devise a Plan, construct a
detailed plan. In Carry out the Plan, perform whatever operations are
required. Then under Examine Your Solution (or Look Back, etc.), check
your solution and rephrase it in English
Using whatever calculator or program
Compute 1∕7.
Write down the number exactly as displayed. Then subtract what
you have written from the calculator’s or program’s result. For a
calculator, divide one by seven and then subtract off what you see
without storing the result elsewhere. For a spreadsheet or other interface,
divide one by seven. Then compute 1∕7 - .14\mathrel{⋯}\kern 1.66702pt
for whatever was displayed. What is the result? What did youexpect? What result did others find?
Enter .1
into whatever device you use. Add .1
to it. Repeat eight more times, for a total of 10 ⋅ .1.
Subtract 1. What is the result? What did you expect? Whatresult did others find?
Note that you may email homework. However, I don’t use MicrosoftTM products
(e.g. Word), and software packages are notoriously finicky about translating
mathematics.
If you’re typing it (which I advise just for practice in whatever tools you use), you
likely want to turn in a printout. If you do want to email your submission, please
produce a PDF or PostScript document.