First of all, to maximize what you get out of lectures and section meetings,
it is strongly recommended that you read the sections in the book
before they are covered in class.
We will be going through the sections of Rosen's book in order,
until further notice.
By now, you should have read sections 1.1-1.8, 2.3-2.5, 3.1-3.5, 4.1-4.7, 5.1-5.6 in Rosen, and the Lenstra notes.
That's all the reading for the course.
The problems listed for a certain date below are due at the
beginning of your section on that date (always a Wednesday).
If you are using an edition of Rosen earlier than the 4th edition,
you may need to consult a friend's book to make sure that you are
doing the correct exercises.
September 5.
p.11: 4(f,g,h only), 8, 14, 20, 22(c), 30(d), 35, 40;
p.19: 6, 8(a,d), 10(a,d), 26, 28;
p.35: 22, 28(c), 34, 48(c), 50
Solutions
September 12.
p.45: 6, 7, 10, 14, 20, 26, 27 (find a procedure different from the book's solution, if you can)
p.54: 8, 14, 20, 30, 40
p.67: 12, 26, 28, 42, 56
Solutions
September 19.
p.79: 8, 10, 14(c,d), 18(c,d), 20, 32(a,d), 36, 42, 43
p.90: 8, 20, 22, 30, 36, 52, 60
p.96: 34, 38
Solutions (by J. Steever)
September 26.
p.125: 2, 10(e,f), 14, 15(d), 18, 22, 24(b), 28, 36, 42, 46(a), 48
p.135: 2(d), 6(a), 8(a), 10, 11(d)
Exercise A: Let n and b be positive integers, and assume b >= 2. Find a formula for the number of digits in the base b expansion of n. (Hint: use the floor function.)
Solutions
October 3.
p.148: 2(f), 8, 10, 15, 16, 22
p.182: 4, 22, 24, 32, 40, 42, 44(e), 52, 58, 66(a,e)
Solutions (Windows only?)
Solutions (non-Windows)
October 10.
p.149: 24
p.199: 6, 12, 28, 32, 40, 44, 48, 54
p.209: 3(d), 10, 22, 30, 40, 46
Solutions
October 17. No homework due: midterm week
October 24.
p.96: 30
p.218: 2, 4, 18
p.224: 4, 10, 12
p.228: 32, 50
p.242: 12, 14, 16, 18, 36, 52
Solutions
October 31.
p.242: 37, 38, 42, 48
p.248: 4, 10, 12, 30
p.258: 9, 16, 32, 40, 50
Solutions
November 7.
p.266: 6, 12, 33
p.284: 2, 16, 18
Lenstra notes: 1, 2, 3, 4, 5, 7, 17
Solutions
November 14.
p.266: 10, 16
p.285: 26, 44, 46
p.305: 37
Lenstra notes: 8, 12, 13, 15, 18(b,c), 19, 22, 24, 26
Solutions
November 21.
p.294: 4, 8, 12, 16(b,d), 20, 22, 29, 35, 38, 44, 46, 52
p.300: 1, 5, 14
Solutions
November 28.
p.317: 18, 20, 22, 36, 42
p.330: 2, 4(g), 20, 30, 32, 40
p.370: 16, 17
Solutions
December 5.
p.350: 6, 10(c,d,e), 24(a), 30, 34, 42, 46(a)
p.359: 6, 14, 24 (assume the coin is fair), 25
p.367: 10, 17, 22, 24, 26
Solutions
The reason for not listing all the homework assignments for the rest
of the semester is to make sure that they remain in sync with the
material being covered in lecture.
(If homework assignments were announced too far in advance,
I would eventually need to speed up or slow down lectures artificially,
and that would not be good.)
The problems assigned are sometimes not direct analogues
of any examples done in lecture or section.
This is intentional: the goal is not to train you to solve only
problems that match a certain template,
but rather to make you think more deeply about the subject,
so that you are prepared to solve
problems in your later courses or in the real world,
problems that may be different from anything you've seen before.
If you are having difficulty with a particular exercise in Rosen,
try a similar odd-numbered exercise and check the answer in the back
of the book.
Communicating effectively what you are doing is at least as important
as getting the right answer.
Remember to write in complete sentences on all except short answer questions.
The idea is to explain what you are doing as you go along,
both for your sake and for the reader's sake.
If you are unsure about what level of detail is appropriate,
use the examples in Rosen's text as a guide.
If you go to the mathematics library on the first floor of Evans Hall,
and check out a random book or journal article,
you will notice that mathematics
in the real world is almost always communicated in complete sentences.
The same is true of physics, engineering, computer science, and so on.
There is a reason for this:
words surrounding the equations, explaining what the
equations represent and what is being done to them,
make the logic of an argument clearer.
As with any form of writing,
it takes some practice to do this well,
to identify potential ambiguities
and to reword arguments so as to eliminate them:
even some professional mathematicians and scientists
have difficulty with this.
Finally, please remember to staple loose sheets!
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