Assignments will be posted here if they are problems from the book; if I prepare documents, they will be mentioned here but links will be on my main page. Assignments will not necessarily be announced in class; it is your responsibility to find them here.

If a due date is left out it is default (two class sessions after it is assigned in M187, one week after it is assigned in M311); a missing due date does not mean you are off the hook for the assignment...

M187 students, the schedule and assignments are lifted from the last time I taught the course and will be modified as we go along. Any zeroes that may appear are an artifact of the spreadsheet Im using to generate this web page; a zero just means "nothing there". Sections late in the course with no homework are ones I didnt get to last time –that particular class went very slowly, and its very likely that we *will* cover some of that material.

Please do not hesitate to send me email if you think an assignment should be here and it is not!

Math 187 meets in MG120 MTuWF 1:40-2:30 PM; final exam Wed May 9th 1-3 pm.

Math 311 meets in MG120 TuTh 8:15-9:30 AM; final exam Tues May 8th 8-10 am.

**Tuesday 17 January****Math 187:**2

2.1,2.2,2.4,2.6,2.7,2.8 (2.8 will require thought; there is a trick; this looks forward to things we will work on later).

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**Math 311:**1.2, 1.4 logical structure of Euclid's Elements (put a copy on reserve in the library)

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**Wednesday 18 January****Math 187:**2

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**Math 311:****Thursday 19 January****Math 187:**

**Math 311:**1.4, 1.5 Examination of some proofs in Euclid.

Homework 1: 1.6 exercises, page 10, problems 1,3,5,6 and either 9 (write a proof) or 11 (find the error in an incorrect proof). For problem 6 you will need a straightedge and compass.

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**Friday 20 January****Math 187:**3

3.1, 3.2, 3.3, 3.4, 3.6, 3.9

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**Math 311:****Monday 23 January**last day to add without permission number

**Math 187:**truth tables, logical notation

assignment is a worksheet

Section 2 homework due

**Math 311:****Tuesday 24 January****Math 187:**4

4.1, 4.3, 4.5, 4.7, 4.10, 4.13

Section 3 homework due

**Math 311:**2.2/2.3 incidence geometry

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**Wednesday 25 January****Math 187:**4

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Logic worksheet due

**Math 311:****Thursday 26 January****Math 187:**

**Math 311:**2.2/2.3 incidence geometry (continued)

Homework 2: exercises 2.4, p. 23, problems 1,3,5,7,10,11,12 plus an additional exercise stated on the class web page

Homework 1 due date

**Friday 27 January****Math 187:**5, 19 (there is not too much to say about 5, and I think parts of 19 should be covered earlier –this may end up taking two days. I will tell you what is due when at the end of class).

5.1, 5.3, 5.5 (there is a clever way to do this and a methodical way), 5.9; 19.1, 19.3, 19.4 bdg, 19.6.

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**Math 311:****Monday 30 January**add deadline, last day to drop without a W

**Math 187:**formal logic

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Section 4 due

**Math 311:****Tuesday 31 January****Math 187:**formal logic

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Sections 5 and 19 due

**Math 311:**2.5, logic

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**Wednesday 1 February****Math 187:**10

logic worksheet 2 is on the class web page (link near the syllabus on my main page); there is also a manual of logical style there which discusses the logical rules and gives examples to support what Im asking you to do on that sheet; also 10.1, 10.2, 10.4, 10.5 due Monday.

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**Math 311:****Thursday 2 February****Math 187:**

**Math 311:**2.5, logic

Homework 3 handout is on class web page.

Homework 2 due

**Friday 3 February****Math 187:**Final comments on section 10; start section 7

7.2,7.4,7.5,7.6,7.7,7.9,7.12,7.14

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**Math 311:****Monday 6 February****Math 187:**7,8

8.1, 8.4, 8.7, 8.8, 8.9.

Section 10 due

**Math 311:****Tuesday 7 February****Math 187:**9

9.1, 9.2, 9.3,9.7, 9.8

Logic worksheet 2 due

**Math 311:**feedback about 2.5 problems and H2 return

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**Wednesday 8 February****Math 187:**reviewed for exam

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Sections 7 and 8 due.

**Math 311:****Thursday 9 February****Math 187:**

**Math 311:**2.6: examples of proofs in incidence geometry; some proofs may be assigned as homework (and test prep) to be due after the exam.

Homework 4: section 2.6: write proofs of 2.6.3, 2.6.5, 2.6.7-9 (five proofs in all) in the style I used in class today.

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**Friday 10 February****Math 187:**Test I

**Math 311:****Monday 13 February****Math 187:**9,11

11.1 a-e, 11.3, 11.12, 11.16 (there will be another section 11 assignment) I checked these over and you should be able to do them using definitions of the operations and Venn diagram techniques discussed in class. I will talk tomorrow about how to write down a counterexample explicitly to something seen to be false from a Venn diagram. The proof is hard of course as always.

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**Math 311:****Tuesday 14 February****Math 187:**11

11.1fg, 11.5, 11.6, 11.7, 11.13*, 11.23, 11.25a

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**Math 311:**---

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Homework 3 due

**Wednesday 15 February****Math 187:**13

13.1, 13.2, 13.6, 13.9, 13.10*, 13.12, 13.13

Section 9 due

**Math 311:****Thursday 16 February****Math 187:**

**Math 311:**Test I

**Friday 17 February****Math 187:**14

14.1, 14.5, 14.8, 14.11, 14.12, 14.13.

first section 11 assignment due

**Math 311:****Monday 20 February**Presidents Day, no classes

**Math 187:**---

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**Math 311:****Tuesday 21 February****Math 187:**53-55

53.1, 53.3ace, 53.9, 53.10, 54.1, 54.2, 54.3, 55.2, 55.3. Hints may be given, don't hesitate to ask...

second section 11 assignment due

**Math 311:**---

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Homework 4 due

**Wednesday 22 February****Math 187:**15

15.1, 15.2, 15.3, 15.4, 15.9, 15.11, 15.13

Section 13 due

**Math 311:****Thursday 23 February****Math 187:**

**Math 311:**The Ruler Postulate

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**Friday 24 February****Math 187:**16

16.2, 16.3, 16.4, 16.6 (this is quite hard and requires careful attention), 16.10, 16.14, 16.27 (look at 16.28; we will do this in class)

Sections 14, 53-55 due

**Math 311:****Monday 27 February**drop deadline

**Math 187:**16 continued, discussion of counting of poker hands

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giving an extra day to work on 15...

**Math 311:****Tuesday 28 February****Math 187:**counting of poker hands might not be finished; 17

17.1, 17.2, 17.4, 17.5, 17.6.

Section 15 due

**Math 311:**The Ruler Postulate

Homework 5: exercises 3.2, page 45: 1 (hint: why does the RP imply that a line has infinitely many points?), 3 (just show it is a semimetric, you dont have to show the triangle inequality), 5, 6, 7, 14 (your reasoning should use the definition of absolute value and basic properties of order on real numbers), 16, 19, 21. All proofs in this section should use the official axioms from the book, not my alternative set in the notes. Be warned that while you have an extra day to do this, there is likely to be another set shortly with an overlapping time period...

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**Wednesday 29 February****Math 187:**18

counting problem worksheet

Section 16 due

**Math 311:****Thursday 1 March****Math 187:**

**Math 311:**---

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**Friday 2 March****Math 187:**extra counting

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**Math 311:****Monday 5 March****Math 187:**20/21

20.3, 20.4 (do these by math induction, not by least counterexample); 21: 21.3, 21.4 (all parts) – there will be another induction assignment.

17 due

**Math 311:****Tuesday 6 March****Math 187:**20/21

induction discussion continues...

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**Math 311:**---

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**Wednesday 7 March****Math 187:**---

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counting worksheet and first 20/21 assignment due

**Math 311:****Thursday 8 March****Math 187:**

**Math 311:**Homework 6 handout (mostly a practice test) is on the class web page. It is due Thursday (not Tuesday) after the test, to give reasonable time to work on problems which are not practice for the test.

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Homework 5 due

**Friday 9 March****Math 187:**Test II

**Math 311:****Monday 12 March****Math 187:**20/21

20.5 (you may use math induction to prove your result), 20.6, 21.8 all parts (Im likely to give some of these away tomorrow), 21.9 [hint: 21.9 involves thinking like that involved with Fibonacci numbers], 21.15 (I sketched how to do this in class, but write it out in detail). I'm giving an extra day for this assignment because some ideas will be introduced tomorrow, but start on it; the section 22 assignment will have the same due date.

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**Math 311:****Tuesday 13 March****Math 187:**test review, started 22

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**Math 311:**---

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**Wednesday 14 March****Math 187:**22

22.1ace, 22.2aefjk, 22.3ab

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**Math 311:****Thursday 15 March****Math 187:**

**Math 311:**Test II (rescheduled a week later)

**Friday 16 March****Math 187:**23

23.1acegi, 23.2, 23.3, 23.5abd,23.6. There will be another section 23 assignment.

Second 20/21 assignment due; this gives you an extra day, but don't relax; section 22 is likely due the same day.

**Math 311:****Monday 19 March****Math 187:**25

23.9, 25.1acegi,25.9a,25.10,25.11 (first think about finite sets; then think about the set of natural numbers, for which you will get a different answer);25.12a (it is: prove it is 1-to-1 then prove it is onto).

22 due

**Math 311:****Tuesday 20 March****Math 187:**26

26.1, 26.2abcd, 26.3, 26.5, 26.12, 26.16

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**Math 311:**---

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**Wednesday 21 March****Math 187:**34

34.1, 34.2, 34.4 (in 34.4 the statements they give are usually true – think about very exceptional cases)

23 and 23/25 assignments due

**Math 311:****Thursday 22 March****Math 187:**

**Math 311:**Homework 7, something fairly short to work on over break: problems 3,4,5,6 page 51. Don't hesitate to send me e-mail while I am in England; I have access to the internet and I will answer, but do remember that I am 8 hours ahead.

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Homework 6 due: actually, since I am out of town, it is just fine if you turn in H6 Tuesday after break. In addition (important) there is a typo in the last question: you are proving H=J not I=J; thanks to an alert student!

**Friday 23 March****Math 187:**35

35.1, 35.2 (I will show you how to do this tomorrow), 35.4 (I do not know the answer to this: experiment and see if you can find an answer – I will too), 35.11, 35.19, 36.1 bdfhjlnp (their notation is mysterious: the point is to do the indicated calculations in mod 10 arithmetic. They have put circles around the operation symbols to indicate that the operations are not quite the usual ones. The meaning of mod 10 division might take a little thought ).

26 due

**Math 311:****Monday 26 March**spring break

**Math 187:**

**Math 311:****Tuesday 27 March**spring break

**Math 187:**

**Math 311:****Wednesday 28 March**spring break

**Math 187:**

**Math 311:****Thursday 29 March**spring break

**Math 187:**

**Math 311:****Friday 30 March**spring break

**Math 187:**

**Math 311:****Monday 2 April****Math 187:**0

0

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**Math 311:****Tuesday 3 April****Math 187:**36

36.2, 3, 4, 14. I will have something to say about 14 on Friday, but do try it.

34 due

**Math 311:**---

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H6 still accepted

**Wednesday 4 April****Math 187:**36, 37

worksheet; 37.1, 37.3, 45.1, 45.2, 45.3 (I will give full answers to 37.3 on request)

35 due

**Math 311:****Thursday 5 April****Math 187:**

**Math 311:**---

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Homework 7 due

**Friday 6 April****Math 187:**review

0

First 36 assignment due

**Math 311:****Monday 9 April****Math 187:**---

36 worksheet due.

**Math 311:****Tuesday 10 April****Math 187:**Test III

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**Math 311:**Homework 8: section 3.4 problem 1 (this you should be able to work on now: think midpoint theorem); section 3.5 problems 1,3,5 (leaving the even problems for me to do in class). This will need the Thursday lecture –this is all due on the 19th.

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**Wednesday 11 April****Math 187:**38

sorry about the lack of section 38 homework: see tomorrow...

37 due.

**Math 311:****Thursday 12 April****Math 187:**

**Math 311:**---

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**Friday 13 April****Math 187:**42

38.2, 38.3, 38.9, 38.11 (for example, 3^2=9 and 4^2 = 16 are consecutive perfect squares), 38.12 (we did this at the beginning of the course!), 38.14, 38.15, 38.20 (hint: suppose that 2^{m/n} = 3; what absurd statement about whole numbers follows?). Watch the class web page for a brief worksheet of section 42 problems.

0

**Math 311:****Monday 16 April****Math 187:**45

45.1, 45.2, 45.3; probably also a worksheet of some sort, which will appear on the class web page.

0

**Math 311:****Tuesday 17 April****Math 187:**24

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**Math 311:**---

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**Wednesday 18 April****Math 187:**24

Section 24 probs 2,3,4,5,9,10, section 25 problem 9 (I did this in class, but write out your own version)

Section 38 due

**Math 311:****Thursday 19 April****Math 187:**

**Math 311:**---

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Homework 8 due

**Friday 20 April****Math 187:**46

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Section 42, 45 due

**Math 311:****Monday 23 April****Math 187:**46, 48

Section 46 probs 1,2,3,5,12,13,16,17; 48.1, 48.5, 48.11 (this is a counting puzzle). (if you pay attention, you will find that I have done some of these in class. But it is useful to write out certain proofs for yourself). I will post some extra problems on the class web page of kinds the book does not provide.

Section 24 due

**Math 311:****Tuesday 24 April****Math 187:**50

some problems on a handwritten sheet on the class page

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**Math 311:**Test III (Test IV (not a cumulative final) will be held in the final exam period)

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**Wednesday 25 April****Math 187:**test review

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**Math 311:****Thursday 26 April****Math 187:**

**Math 311:**Homework 9 (these are problems from the sections I expect to cover in the next week; the whole problem set is due at the final). 3.6.1, 4.1.1, 4.2.1 (hint: look at the second proof of the Isosceles Triangle Theorem), 4.2.2 (very like the proof of ASA: do NOT use sum of the angles of a triangle (because we dont know about it and it is not a theorem of neutral geometry anyway), 4.2.5, 4.3.3 (I'll do 4.3.2 in class), 4.4.1, 4.5.2 (which asks you to prove corollary 4.5.7, sorry about the misprint), 4.8.1 (you should be able to do 4.8.1 with nothing more than things you already know as I post this and the definition of defect of a triangle on page 98 (and algebra), even if we never get to section 4.8). You should not be worrying about a grade on this set; it will be checked off. Think of it as test prep. Complete solutions will be posted during the weekend before the final.

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**Friday 27 April****Math 187:**Test IV

**Math 311:****Monday 30 April****Math 187:**

**Math 311:****Tuesday 1 May****Math 187:**49

Section 49 problems 1,2,4,5,8,11,13 (hint: its not a tree (why); so it has a non cut edge. Cut that edge and do some counting. What do you get?) ,16b (there is a fairly easy way to do this—once you see something).

Section 46, 48 due

**Math 311:**---

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**Wednesday 2 May****Math 187:**51,52

last homework, due at final: 51.1 (they mean, find the smallest number of colors you need to color the graphs), 51.3 (hint: I mentioned this when I was talking about the definition of "bipartite"), 51.6, 51.8, 51.13 (hard; chromatic number is smallest number of colors needed), 52.2, 52.6 (five-regular means that every vertex is of degree 5),

Section 50 due

**Math 311:****Thursday 3 May****Math 187:**0

0

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**Math 311:**---

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**Friday 4 May****Math 187:**---

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Section 49 due; 51/52 due at final.

**Math 311:**