The schedule of sections for M187 is to be taken seriously; that for M314 much less so.

Do note that in M187 problems are due two class sessions after they are assigned, whether I remember to write something about the due date or not. The due date is different only if I say so.

Also note that M314 problem sets are due one week from the date at which they appear in the calendar, unless a different due date is specifically posted.

** Monday January 15 :** MLK holiday

**Math 187:****Math 314:**

**Math 187:**sections 1-3

1.1 (for brief discussion in class; it's really a joke); 2.1, 2.2,2.6,2.7,2.8*,2.9.

**Math 314:**doesn't meet

**Math 187:**sections 1-3

3.1*, 3.2, 3.3*,3.4, 3.6, 3.9 (it's grotesque but it does make a logical point!)

**Math 314:**section 1

**Math 187:**sections 4-5

4.1*,4.2,4.3,4.4,4.5*,4.6

1.1-2 assignment due

**Math 314:**sections 1, 2

Homework 1 (complete): 1.1, 1.5, 1.8a, 1.10, 1.11. Write each proof carefully and clearly. Side assignment: rewrite every expression with … (ellipses) that you find in assigned problems using sigma notation. This does not mean that you have to use sigma notation in your proofs! 1.8b and 1.12 are likely class examples. EXTRA REMARKS: all proofs must be by math induction! Avoid using algebraic manipulations of sums of arbitrary length (with dots) other than pulling out one or two terms; don't factor them or multiply by constants, etc. These are really formal properties of sigma notation which should be proved...by mathematical induction (and don't use the formula for the sum of an arithmetic or geometric series).

**Math 187:**section 4

4.8,4.10*,4.12**,4.14*,4.15. Notice that I posted a proof from class on the main web page. I have rearranged the schedule a little, and it looks quite possible that further slowdowns may occur. We'll see.

1.3 assignment due

**Math 314:**section 2

**Math 187:**sections 5,6

5.1,5.4,5.5,5.7*,5.9*; 6.2* (just de Morgan's laws), 6.5, 6.9, 6.10, 6.11b, 6.11e*, 6.15a.

first 1.4 assignment due

**Math 314:**doesn't meet

**Math 187:**section 6

6.14,6.16,[6.17-19]**; I will post an additional worksheet here (as a PDF file); watch for it. When it is posted it will be here but as I write this I have not posted it yet. Please note that the handout WILL be graded; this will be true in general if I post handouts, unless I say otherwise.

second 1.4 assignment due

**Math 314:**section 3

**Math 187:**sections 10, 7

10.1*,10.2,10.4,10.5*; 7.4,7.5,7.6,7.7,7.9*,7.10 (I might reshuffle the section 7 problems a bit)

section 5-6 assignment due

**Math 314:**section 4

Homework 1 due; Homework 2 (complete): 2.5*, 2.6, 3.1, 3.3* (just v), 3.4* (just vii: they are wrong about v, which does not follow without the assumption that 0 and 1 are not equal!), 3.8* (something I will do later will give a hint about this), 4.1, 4.2, 4.3, 4.4 (these are really one big exercise). Be aware that I will certainly put 4.5 and 4.6 in the next set; they are worth trying.

**Math 187:**section 7,8

sorry about forgetting to post yesterday: you get an extra day to do it: 7.11*, 7.12,7.13,7.14*,7.15,8.1*,8.4,8.5*,8.8,8.9 (I think there is a typo in 8.9: I think the last one should be 1000!+1000, not 1000!+1002).

second section 6 assignment due (including worksheet); you may hand this in Tuesday as well since I suppressed questions on Friday. Note that the handout IS graded.

**Math 314:**section 4, 5

**Math 187:**section 9

see Wednesday

section 10 and first section 7 assignment due (second section 6 and handout also accepted).

**Math 314:**doesn't meet

**Math 187:**section 11

9.1,9.2*,9.3*,9.9,11.1*,11.16* (I want you to say if each statement is true or false, and if it is false give a counterexample; don't try to prove the true ones),11.18, 11.22** (just a Venn diagram is what I'm asking for but it is hard!)

**Math 314:**section 6 (we may return to this in detail at the end of the course if things go faster than I expect [hollow laughter])

**Math 187:**Test ITest I

Test I will cover sections 1-10 (only quite simple questions from section 9). Sample exams from previous semesters are here and here. Sorry about the glitch which removed them temporarily!

**Math 314:**Homework 2 due. Homework 3 (complete): 4.6, 4.8*, 4.10, 4.11 (this might require discussion), 4.15,4.16*,5.6* (remember that plus and minus infinity are now in play); I may post some problems related to section 6 but following my construction. The Feb. 2 lecture is posted here (PDF).

**Math 187:**section 13 (really we'll continue section 11)

11.5,11.9*,11.13 (hard),11.19*(discussed in class!)

second section 7 and section 8 problems due (extended because I posted them late).

**Math 314:**section 7

Homework 2 still accepted as on time! Notice that I have now starred problems in Homework 2 and 3 which I intend to mark.

**Math 187:**sections 14, 53

13.1,13.2*,13.3,13.7*,13.10,13.13*

section 9 and first section 11 set due

**Math 314:**doesn't meet

**Math 187:**sections 14,53

14.1*,14.4,14.5,14.6*,14.11,14.12,14.13*.

second section 11 problems due (do note that problems are due two class sessions after they are assigned whether I say anything about due dates or not).

**Math 314:**section 7, logic

**Math 187:**section 15

53.1,53.2*,53.3*,53.4,53.9,53.10 (in 9 and 10, no proofs; just think about whether they have the properties);54.1, 54.2*, 54.3.

section 13 problems due

**Math 314:**Test I is deferred for at least a week: it is now scheduled for Friday, February 23.

**Math 187:**section 15

15.1*,15.2*,15.4,15.7.15.8*,15.11,15.12*,15.13*.

section 14 (but not 53) problems due

**Math 314:**logic

**Math 187:**section 16

no new assignment

section 53/54 assignment due

**Math 314:**doesn't meet

Homework 4 (complete, I didn't add anything and actually this is plenty of work) will be formally due Wednesday (but note that only papers turned in by Tuesday morning will be guaranteed to be graded in time for the test Friday; I gather that the building will be locked on Monday): 7.3; 7.4; 8.1, 8.2*. Look at my main web page for other materials (manual of logical style and a sample exam).

**Math 187:**section 16

16.2, 16.3, 16.4*, 16.6*, 16.10 (there is a way to show this using the official definition of binomial coefficients; that is what they are looking for), 16.27*, 16.28*. Paper handout distributed: handout p. 209-210, 7*, 11, 12; p. 215-216, 1,2,9, 15*,16,19* (note that 215 and 216 are stapled in wrong order). All the handout problems are good for you!!!

section 15 due

**Math 314:**section 8, logic

**Math 187:**section 17

nothing due

**Math 314:**section 9

**Math 187:****Math 314:**holiday

**Math 187:**section 17

section 16 due

**Math 314:**doesn't meet

**Math 187:**section 18

handout due

**Math 314:**sections 9,10

**Math 187:**Test II**Math 314:**Test I (details of coverage to follow)section 10

**Math 187:**section 18

I really seem to have got ahead of the schedule: 19.1,19.3,19.4abdf*,19.5*,19.7,19.8*,19.11

**Math 314:**section 11

**Math 187:**section 19

**Math 314:**doesn't meet

**Math 187:**section 20-21

section 20/21: you have an extra day for this assignment. You are welcome to do section 20 problems using induction. 20.3, 20.4, 20.5, 20.6, 20.7; 21.3* all parts; 21.4* all parts; (21.8 acd)*, 21.10, 21.15.

section 19 due

**Math 314:**section 11

Homework 5, due next Wednesday: 8.3, 8.4, 8.5*, 9.1* (this is where you show *everything*), 9.4, 9.9*, 9.12*, 9.18. Please note that Dr. Kerr will be teaching the class Friday.

**Math 187:**section 20-21

**Math 314:**section 12

**Math 187:**section 20-21

**Math 314:**section 14

**Math 187:**section 22

**Math 314:**doesn't meet

**Math 187:**section 22

section 22: 22.1*, (22.2beik)*: because I didn’t post this until Friday morning, you have an extra day to do it.

section 20/21 due

**Math 314:**sections 14,15

Homework 5 due

**Math 187:**section 23

section 23: 23.1 (cdegi*), 23.2*. 23.3 23.4, 23.6, 23.9*

**Math 314:**section 15

**Math 187:**section 25

section 25.1*, 25.2, 25.4, 25.9a* (here a formal proof is expected),b,c; 25.10, 25.11, 25.12* (in 25.12, a completely formal proof is not needed; determine which of a b c are true statements and support your claims with examples, counterexamples, brief arguments or calculations)

**Math 314:**section 16 (Cantor's proof?)

**Math 187:**section 26

sections 22 and 23 due.

**Math 314:**doesn't meet

**Math 187:**section 26

**Math 314:**section 17

Homework 6, due Friday the 23d: I'm changing my strategy and writing a whole assignment here (and extending the due date). Of course we will not have covered all of this by the 14th; but it should all have been covered well before the 23d (I will of course modify it if we fall further behind): 9.12 (deferred from previous assignment); 10.2*, 10.6, 10.7 (it might not be clear what to do with this until after our section 11 discussion), 10.10, 10.11*, 11.2, 11.3*, 11.6 (a single word would help here -- what is it?), 11.7*, 11.9, 12.3*, 12.4*, 12.6. It is likely that Homework 7 will be assigned before the due date for Homework 6 (ideally I would like to post it on the 21st and make it due Wed after spring break). NOTE added March 19: the chapter 12 problems do not need to be changed: they depend on understanding the definitions of lim sup and lim inf, not on special stuff discussed in the section (not that this makes them easy).

**Math 187:**section 24

section 26: 26.1, 26.2, 26.3, 26.5*, 26.12, 26.16* parts 1 and 3 (we didn’t talk about inversions), 26.20 (hint: use even and odd permutations; individual moves are transpositions...)

**Math 314:**

**Math 187:**section 24

section 24, first assignment: 24.2, 24.3*, 24.4*, 24.7* (just for 9 numbers).

**Math 314:**section 18

**Math 187:**section 28

section 24 additional probs: 24.9*, 24.10*

section 26 due

**Math 314:**doesn't meet

**Math 187:**section 34

**Math 314:**section 18

**Math 187:**Test III**Math 314:**(Test II will be given on Friday of the first week after spring break, not before).section 19

Homework 6 due

**Math 187:****Math 314:**

**Math 187:****Math 314:**

**Math 187:****Math 314:**

**Math 187:****Math 314:**

**Math 187:**section 35

**Math 314:**section 19

**Math 187:**section 36

34.1*, 34.2, 34.4, 35.1, 35.2*, 35.11*, 35.12, 35.13 (might be hard), 35.16*

section 24 due (both parts)

**Math 314:**doesn't meet

**Math 187:**section 36

**Math 314:**section 20

**Math 187:**section 37

section 34 due

**Math 314:**Test II (this is the definitive date)section 23

**Math 187:**section 38

section 35 due

**Math 314:**section 24

**Math 187:**section 42

sections 36 and 37 are one assignment due Friday: 36.1 (acgiknpq)*,36.2,36.3(ac)*,36.4(bdf)*,36.13,36.14,37.1*,37.2*.

**Math 314:**doesn't meet

**Math 187:**section 45

**Math 314:**sections 24, 25

**Math 187:**section 45

Here is a worksheet on modular exponentiation and the Euler function, with assigned problems at the end.

section 36 and 37 assignment due

**Math 314:**section 25

Homework 7 (due next Monday): 14.2*, 14.3, 14.6, 14.12*, 14.13*, 15.1*, 15.4,15.6* (in part b, "observe" means "prove"), 15.7, 17.9*, 17.10ab*.

**Math 187:**section 46

**Math 314:**section 26

**Math 187:**section 46

Here find the RSA examples worksheet.

Euler function worksheet due

**Math 314:**doesn't meet

**Math 187:**section 47

**Math 314:**section 26,28

**Math 187:**section 48,49

homework due Tuesday: 46.1*, 46.2*, 46.3, 46.5, 46.12*, 46.13 (I did 12 and 13 in class; you should be able to reproduce my explanation); 47.1*, 47.3*, 47.4.

RSA worksheet due.

**Math 314:**section 28

Homework 8 (due next Wednesday): 17.3, 17.5*, 17.11*, 17.14, 18.2*, 18.4, 18.5, 18.6* (hint: use the IVT), 18.9*, 18.12.

**Math 187:**section 49

homework due Wednesday: 48.1*, 48.3,48.6,48.11**, worksheet p. 295, 15, 21, worksheet p. 309 3,7. Keep the worksheets; I may assign more problems from them for homework or review for this test.

**Math 314:**sections 29,30

Homework 7 due

**Math 187:**section 50

**Math 314:**doesn't meet

**Math 187:**section 51

Please notice the homework which (at least now) appears under Monday the 23d. It seems this may accidentally not have been posted until this morning (when I updated the schedule for the other class). Use these problems as test review work; I will accept them on Monday. Technology is wonderful -- when it works :-(

**Math 314:**section 31

**Math 187:**Test IV**Math 314:**Test III (there will certainly be a test this day) A REVIEW DOCUMENT for Test III is now found on my main page.

**Math 187:**section 52

**Math 314:**section 31

**Math 187:**section 52

last homework assignment: 51.13 (graph I put on board yesterday); 52.2, 52.6 (5-regular means that each vertex has degree 5), 52.11 (this is a direct application of Euler's formula); 49.1, 49.2, 49.5, 49.9, 49.13. Mostly this is food for thought if the topics interest you; I will be *quite* clear about what kinds of questions about these topics may appear on the final.

**Math 314:**doesn't meet

**Math 187:**review/overflow

**Math 314:**review/overflow

Homework 8 due; recommended for section 19, problems 19.1, 19.2.

**Math 187:**review

**Math 314:**review