# Fall 2004 Calendar

This calendar covers both of my courses. It is now complete (but still always subject to change). I may or may not separate the two courses eventually.

The schedule now contains a daily schedule for Math 301: this might serve as a useful indication of what I expect to cover, but the details are subject to change.

I will post dates on which homework assignments are handed out, with links to the assignments themselves if they exist in online form, and dates on which they are due, and I may also use this (and/or the space in my web page pertaining to your class) as a place to post announcements for either class, so it is a good idea to keep an eye on this.

I will also use this as a convenient place to post readings for Math 497. I will post readings in the calendar under the date they are due to be read, rather than under the date when I assign them; this is not the way I did it the first time. Readings should be attacked as soon as they are posted; books should be on reserve in the library (on three hour reserve).

I don't discourage reading further in the books provided (including the ones not mentioned in any assignments yet...)

• Week 1:

• Monday, August 23:

Math 301: You must attend on one of the first two days or be administratively dropped; if you are unable to attend, contact me.

Math 301: section 1.1

Math 301 Assignment I (due Tuesday, August 31):

• 1.1, p. 13: 3,4,5,6,9,10,12,13,27,28.
• 1.2, p. 25: 1,2,3,4,7,10,11,12,24,29,30,31.
• 1.3, p. 37: 5,6,9,10,13,14,15,16,17,18.
• 1.6, p. 63: 3,4,5,6,11,12.

• Tuesday, August 24:

Math 301 and 497: You must attend on one of the first two days or be administratively dropped; if you are unable to attend, contact me.

Math 301: section 1.2

Math 497 question for Tuesday: How many natural numbers are there? (By "natural numbers" I mean the possible (finite) answers to "How many X's are there": 0,1,2...).

Math 497 reading: Morris Kline, Mathematical Thought from Ancient to Modern Times, pp. 1-37. Moore, The Infinite, pp. 1-26. Since the reserve in the library won't be set up for a week or so, I will distribute photocopies in class Tuesday. You can pick them up at my office if you want to get them earlier. Read these for Thursday.

• Wednesday, August 25:

Math 301: section 1.2 (1.6)

• Thursday, August 26:

Math 497: You must attend on one of the first two days or be administratively dropped; if you are unable to attend, contact me.

Note posted Aug. 25th: if you are finding the reading too long, you might find it useful to be aware that what I'm actually talking about on Thursday is early Greek mathematics (in particular, the proof that the square root of 2 is irrational and Zeno's paradoxes). Focus on the discussion of the Pythagoreans and Zeno, and read about the paradoxes of the infinite in the Moore selection, and you'll be fine for Thursday's discussion. One should at least skim the earlier history, but it's not that important.

Look under Tuesday for the reading for Tuesday; I'll put readings under the day they are due from now on.

• Friday, August 27:

Math 301: section 1.3

• Week 2:

• Monday, August 30:

Math 301: section 1.3 (1.6)

Math 301: Assignment II, due Sept. 8:

• 1.3, p. 37. probs 19, 20, 22, 25, 26, 27, 28, 33, 34.
• 1.4, p. 47. probs 5, 6, 7, 8, 11, 12, 15, 16, 19, 20, 25, 26, 29, 30, 31, 32.
• 1.5, p. 55. probs 2, 4, 6, 11, 12, 13, 14, 15, 16, 25, 26, 27, 33, 34.

• Tuesday, August 31:

Math 301: section 1.4

Math 301: Assignment I due.

Math 497: The reserved materials for this course in the library are available (ask for Holmes, Math 497). Tell me if you have trouble getting access to them.

Math 497: For today, read A. W. Moore, The Infinite, pp. 26-44 (this is the only required reading, except that you should finish the long reading assigned earlier if you haven't done so). Think about how the considerations of actual versus potential infinity relate to the paradoxes we discussed Thursday.

I recommend for today (and require by Thursday) the following readings from Kline, Mathematical Thought from Ancient to Modern Times: pp. 51-53 on Aristotle (definitions and axioms); pp. 56-68 on Euclid (this covers somewhat more than we will be talking about); pp. 173-77 on limitations of Greek mathematics. I'm giving more time on this because I didn't have it ready Thursday.

I have made a photocopied selection from Euclid, the Elements, book I, which is rather complicated to describe. This is available in my office if you want to come by and pick it up early; in any event I will hand it out in class on Tuesday. It also contains Hilbert's modern axiomatization of geometry for comparison.

I will be trying to get readings on the web at least a week before they are to be read from now on, because this is better for you and also better for my relations with the library :-)

• Wednesday, September 1:

Math 301: section 1.4 (1.6)

• Thursday, September 2:

Math 497: I require the readings from Kline recommended for Tuesday, and also Bertrand Russell, Introduction to Mathematical Philosophy, pages 1-28.

• Friday, September 3:

Add deadline. Last day to drop without receiving a W on transcript.

Math 301: section 1.5

• Week 3:

• Monday, September 6:

Labor Day Holiday -- no classes

• Tuesday, September 7:

Math 301: section 1.7

Math 301 Assignment III, due Sept. 14:

• section 1.7, p. 71, probs. 1,2,5,6,7,8,9,10,31,32.
• section 1.8, p. 79, probs. 5,6,9,10,11,12,17,25,26,27,28.

Math 497: no new reading for today. I expect that we will continue to discuss geometry -- Euclid and Hilbert. Make sure you pick up the reading from Russell originally assigned for last Thursday eventually (it's related to axiomatizing arithmetic), and watch this space: I might post more readings for the next Thursday.

Look over Hilbert's axioms and think about how they differ from Euclid's. We will talk a bit more about Pappus's proof of Euclid's Proposition V and whether triangles ABC and ACB are the same. I will try to prepare a proof of Euclid's Proposition I in Hilbert's system; wish me luck!

• Wednesday, September 8:

Math 301: section 1.8 (1.10)

Math 301: Assignment II due.

• Thursday, September 9:

Math 497: We are still talking about Hilbert's axioms for geometry; no further reading yet.

• Friday, September 10:

Math 301: Test I

• Week 4:

• Monday, September 13:

Math 301: section 1.9 (2.1)

Math 301: Assignment IV, due Tues. Sept. 21:

• 1.9, p. 90: 1-14, 37-40. (37-40 are calculator questions).
• 1.10, p. 99: 1,2,5,6.
• 2.1, p. 116: 1,2,5,6,7,22,23,25,26,27,28.
• 2.2, p. 126: 1,2,3,5,6,7,8,11,12,13,14,31,32.

• Tuesday, September 14:

Here is an updated version of my geometry axioms (Postscript) and the same geometry axioms (PDF)

Math 497: If you didn't make it today, please note that dates for Test I and the first essay assignment have both been delayed a week. This is partly because we've been going slowly and partly because we are losing a day on Thursday. We started talking about the Peano axioms for arithmetic today, so if you have not read the selections from Russell it would be a good idea to do so.

Math 497: ADVERTISEMENT: First meeting of the Philosophy Club is Wednesday, September 15, at the Idaho Pizza Company on Broadway. A flyer describes the question of the day.

Math 301: section 1.9 (2.1)

Math 301: Assignment III due.

• Wednesday, September 15:

Math 301: section 2.2

• Thursday, September 16:

Math 497: you should have discussed your first essay topic with me by now...

Math 497: I will not be on campus this day for personal reasons, so class is cancelled.

Both classes: I will not be on campus at all, so there is no 3 pm office hour either.

• Friday, September 17:

Math 301: section 2.2

• Week 5:

• Monday, September 20:

Math 301: sections 2.3

Math 301: Assignment V (due Sept. 28):

I did change in this assignment: we will not do 2.6.

• section 2.3: 2,4,6,8 (2-8 without calculator), 11,12,21,22,27,28,31,32.
• section 2.4: 5-10, 21, 23-24 (hard), 25.
• section 2.5: 1-4, 11, 12, 15, 16.
• section 2.6: I am not covering this, so you don't need to do 1-7 as originally posted.

• Tuesday, September 21:

Math 301: lab day

Here is the Maple file from the lab day.

Math 301: Assignment IV due today.

Math 497: Here are the promised notes on criteria for evaluating axioms and undefined notions (Postscript) and the same notes as a PDF file.

Math 497: Please be sure to discuss your essay topic with me sometime this week if you haven't already done so.

Math 497: today I'll talk about the Russell reading (pp. 1-28 in Introduction to Mathematical Philosophy, which is on reserve).

• Wednesday, September 22:

Math 301: section 2.4/5?

• Thursday, September 23:

Math 497: Test I is delayed one week, to Sept. 30.

Math 497: watch this space for two things before Thursday's class: I will post notes on the lecture Tuesday (which strayed into some minefields!) and I will also post some notes on topics for the exam (which will not be at the level of mathematical difficulty of the Tuesday lecture, I hasten to add!).

Math 497: Here are the promised notes on the Tuesday, Sept. 21 lecture (Postscript) and the same notes as a PDF file.

Math 497: Here are the promised notes for Test I preparation (Postscript) and the same notes as a PDF file.

I may also post some additional reading, but it is more likely that I will bring photocopies on Thursday.

• Friday, September 24:

Math 301: section 2.6?

Math 301: Assignment IV is graded and these papers (and older papers) are available outside my office door.

• Week 6:

• Monday, September 27:

Math 301: section 2.7?

Math 301: Assignment VI (due Tuesday, October 5):

• section 2.8: 3,4,7,8,9,10,11,12,23,24,25,26,31,32,33,34.
• section 2.9: 1,2,5,6,7,8,9,10,13,14,19,20,22,23.
• section 3.1: 1,2,9,10,13,14,17,18,23,24,25,27,30,42,43,44.
• Tuesday, September 28:

Math 301: section 2.8

Math 301: Assignment V extended one day.

• Wednesday, September 29:

Math 301: section 2.9

Math 301: Assignment V due (extended).

• Thursday, September 30:

Math 497: first essay assignment due date delayed one week.

Math 497: Test I (corrected date)

Math 497: Here are the promised notes for Test I preparation (Postscript) and the same notes as a PDF file.

Math 497: Test I will be graded before the drop deadline on Monday.

• Friday, October 1:

Math 301: section 3.1

• Week 7:

• Monday, October 4:

Math 301: section 3.2

Math 301: Assignment VII (due Wednesday or Friday next week):

• section 3.2, p. 199: 5-14 (use row operations), 16, 18, 20, 25, 26, 31-34, 37-39.
• section 3.3, p. 209: 1,2,5,6,11,12,15,16,19-22, 23, 24, 27-30.

• Tuesday, October 5:

Math 301: section 3.3

Math 301: Assignment VI due.

• Wednesday, October 6:

Math 301: section 3.3

Math 301: Homework 6 papers are all now entered in my gradebook and available outside my door.

• Thursday, October 7:

Math 497: Corrected due date for first essay assignment

Math 497: stuff to read (this assignment is now complete -- you don't really have to read all of this for Thursday, as there is quite a lot of it and we will doubtless take more than one day to go through it).

Euclid, The Elements, definitions of proportion from Books V and VII, and perhaps the proofs of some propositions early in Book VI (about similar triangles). I'll distribute photocopies of what we read, but if you can find a copy of the Elements...

Kline, Mathematics from Ancient to Modern Times, pp. 68-77 (discussion of the Euclid reading mentioned above), pp. 131-44 (classical arithmetic and algebra), pp. 183-99 (Hindus and Arabs), pp. 250-83 (enter the western Europeans!)

Surely we are not going to discuss all of this in one day; it's an agenda for some extended period of time.

You can if you wish look at Russell, Introduction to Mathematical Philosophy, pp. 63-76 for his development of integers, rationals, reals and complex numbers, but his terminology requires some explanation (which you might be able to figure out yourself by reading other parts of his book), and we won't get to modern constructions of number systems immediately.

• Friday, October 8:

Math 301: Test II

• Week 8:

• Monday, October 11:

Math 301: section 4.1

• Tuesday, October 12:

Math 301: section 4.1

Math 301: due date for Assignment VII will be delayed to either Wednesday or Friday depending on how long it takes me to finish up the determinant proofs.

• Wednesday, October 13:

Assignment VIII (due Wednesday, October 20):

There are a lot of problems from each of the two sections, but each section is scheduled to be covered in two days.

• section 4.1, p. 223: problems 1, 2, 5, 6, 7, 8, 11, 12, 13, 16, 17, 20, 21, 22, 25, 26, 27, 28, 29, 30, 32, 33.
• section 4.2, p. 234: problems 5, 6, 7-12, 15, 16, 21, 22, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38.

Math 301: section 4.2

• Thursday, October 14:

• Friday, October 15:

Math 301: section 4.2

Math 301: revised Assignment VII due date.

• Week 9:

• Monday, October 18:

Math 301: section 4.3

Math 301: Assignment IX, due Tuesday, October 26:

We are likely to be ahead of the official schedule by the end of the week. This is reflected in the sections covered in this assignment. If I turn out to be too optimistic, I'll adjust the due date for the assignment as needed. Some of this material should be familiar from sections 2.8 and 2.9.

• section 4.3, p 243: 11, 13, 14, 15, 16, 19, 20, 26, 31, 32, 33, 34.
• section 4.4, p. 253: 7, 8, 9, 10, 11, 12, 13, 14, 17, 25, 26, 27, 30, 31, 36.
• section 4.5, p. 260: 5, 6, 11-14, 21, 22, 23, 24, 26, 27, 28, 32, 33.

• Tuesday, October 19:

Math 301: lab day

Math 301: Here is the lab file. It contains the updates I added during the lab. The completed lab is due on the next lab day (Nov. 16). Completed labs should be submitted electronically (you can just send to "holmes", which will reach me on hal). If you don't know how to save Maple files or mail them from the lab machines, the lab monitors do know about such things.

• Wednesday, October 20:

Math 301: section 4.3

Math 301: Assignment VIII due.

• Thursday, October 21:

Math 497: You should have discussed your second essay topic with me by now...

• Friday, October 22:

Math 301: section 4.4

• Week 10:

• Monday, October 25:

Math 301: section 4.4 [actually, 4.6-7.]

Math 301: Assignment X, due November 2.

• 4.6 ("row space" is the only new topic in this section): 3, 4, 5, 6, 28, 29.
• 4.7: 5, 6, 7, 8, 15, 16, 19.
• 4.8: 7, 8, 9, 15, 16, 19, 20, 25, 26.
• 4.9: 6, 7, 15, 16, 17, 18.
• 5.1: 1, 2, 5, 6, 11, 14, 17, 18, 23, 24, 31, 32.

• Tuesday, October 26:

Math 301: section 4.5 [section 4.8]

Math 497: Take home quiz, due in class Thursday: find one real solution to x^3+3x^2-3x-11 = 0, using Cardano's method and showing all work. You should be able to find one real root without any use of complex numbers: this problem was deliberately reverse engineered to be doable (though the root you find is not rational). Notice that there are notes for this on my page (and above in this calendar). I will accept this on Thursday from anyone (even if you missed class Tuesday).

Assignment IX due.

Math 497: Here are notes on the cubic equation(Postscript) and the same notes as a PDF file. Thanks to a student who pointed out a typo (an incorrect minus sign).

• Wednesday, October 27:

Math 301: section 4.6 section 4.9]

• Thursday, October 28:

Math 497: Test II has been delayed 2 weeks

• Friday, October 29:

Math 301: section 4.7 [section 5.1]

• Week 11:

• Monday, November 1:

Math 301: section 4.8[5.1]

• Tuesday, November 2:

Math 301: section 4.9[5.1, 5.2]

Election Day: there are classes -- be sure to vote!

Math 497: Some historical reading for discussion of analytic geometry and the origins of the calculus. This is not all for one day! Kline, Mathematical Thought from Ancient to Modern Times:

pp. 270-274: various topics. Notice extension of binomial theorem to infinite series and the application of binomial coefficients to counting and probability.

pp. 278-282: algebra and geometry. Note discussion of algebra as an extension of logic relating to quantity (according to Descartes: this might be about p. 280, my notes being unclear) and the discussion of the state (rather the absence) of foundations of the subject, p. 282.

pp. 303-324: early coordinate geometry. Note on pp. 305-307, Cartesian mathematical philosophy... On pp. 311-312 comments by Descartes on objections of the Greeks to curves constructed with mechanical devices other than ruler and compass (he still has scruples about non-algebraic curves).

pp. 335-390, creation of calculus. (This is still ahead!)

• Wednesday, November 3:

Math 301: section 5.1

Math 301: Assignment X due.

Math 301: the test 3 review document is on my main page.

Math 301: Assignment XI, due Tuesday, November 9.

• section 5.2: 3-6, 13, 14, 15, 18, 19, 23, 24, 25, 27.
• section 5.3: 1-4, 5, 6, 7-10, 17, 18, 28, 29, 31, 32.
• Thursday, November 4:

Math 497: Here are notes on constructions of number systems in Postscript and PDF. I'm still working on these, but they already contain what is needed for the new take home quiz: express the commutative law of multiplication for positive rationals as a statement about natural numbers only, using the translation described in these notes. The construction notes are now considerably expanded (as of 1:30 pm Friday -- up to just before the constructions of complex numbers).

I am continuing to write more notes! This is taking longer than I expect -- it might be some time Sunday before I have full test study notes, but keep looking...

• Friday, November 5:

Math 301: Test III

• Week 12:

• Monday, November 8:

Math 301: section 5.2[5.5]

• Tuesday, November 9:

Math 301: section 5.3[5.4]

Math 301: Assignment XI due.

Math 301: Assignment XII, due Wednesday, November 17:

• section 5.5, p. 341: 1, 2, 3, 4, 9, 10 (more of 1-12 would do no harm), 13, 14, 15, 16, 25, 26.
• section 5.4, p. 333: 1, 2, 3, 4, 5, 6, 11, 12, 13, 14, 17, 22, 23.
• section 5.8, p. 368: 7-10, 19, 20.
• section 6.1, p. 382: 1, 2, 5, 6, 10, 11, 13, 14, 15-18, 23, 24, 26, 27, 28. I may provide extra problems on computing angles between vectors, on a worksheet.

The Test II review document is here, in Postscript and PDF. I have trouble viewing the PDF file in my browser, but downloading the file to my computer worked.

• Wednesday, November 10:

Math 301: section 5.4

• Thursday, November 11:

Armistice Day (there are classes -- but remember 11 AM, November 11, 1918. Those who forget history are condemned to repeat it.)

Math 497: Test II (corrected date)

Math 497: second essay assignment due date delayed

Math 497: ANNOUNCEMENT: I have consulted with almost all members of the class and arrived at the following change in the syllabus. There will be no final exam. In exchange for this, a presentation component is added to paper II: everyone should be prepared to present their second paper to the class for 15-20 min. Grading: 2/3 of grade is for the paper as paper. Of the remainder, most is for the presentation (it should be coherent and you should be ready to take questions) and a little is for attendance at your classmates' presentations. I will schedule your presentation when you come to discuss your topic with me. The final examination period is available for emergency use (no one will be scheduled in the final examination period at the outset, but makeups can happen then). If anyone does end up presenting in the final exam period, I would appreciate the presence of an audience!!! Two presentations per period in the four class periods after Thanksgiving break should give enough time...

• Friday, November 12:

Math 301: section 5.5

• Week 13:

• Monday, November 15:

Math 301: extra chapter 5 day -- applications or overflow.[section 6.1/6.2]

• Tuesday, November 16:

Math 301: lab day

Math 301: Assignment XIII (due Tuesday, November 23):

• section 6.2: 1-6, 9, 10, 11, 12, 13, 14, 17, 20, 25, 27, 28.
• section 6.3: 1, 2, 3, 4, 8, 9, 11, 12, 15, 16, 17, 18, 23, 24.
• (DEFERRED until next assignment: section 6.4: 3, 4, 7, 8, 9, 10, 13-16, 24.)
• Wednesday, November 17:

Math 301: section 6.1[6.2/6.3?]

Math 301: Assignment XII due.

• Thursday, November 18:

• Friday, November 19:

Math 301: section 6.1[6.3/6.4?]

• Week 14:

• Monday, November 22:

Math 301: section 6.2

• Tuesday, November 23:

Math 301: section 6.2

Math 301: Assignment XIII due (note that section 6.4 has been deferred to the next assignment).

Math 301: Assignment XIV, due Tuesday after break:

• section 6.4: 3, 4, 7, 8, 9, 10, 13-16, 24.
• section 6.5: 3-8, 11-14.

• Wednesday, November 24:

Thanksgiving Holiday

• Thursday, November 25:

Thanksgiving Holiday

• Friday, November 26:

Thanksgiving Holiday

• Week 15:

• Monday, November 29:

Math 301: section 6.3

• Tuesday, November 30:

Math 301: section 6.4

Math 301: Assignment XIV due.

Math 301: Assignment XV:

• section 6.6: 1-4, 7, 8, 11.
• section 6.7: 3-10, 13, 14, 15-18 (these four problems are formal algebra with the axioms), 21-26. I'll be talking about 6.7 for two days.

Math 497: Corrected due date for second essay assignment.

Math 497: Beginning of paper II class presentations: for explanation, see announcement under Nov. 11th entry

Math 497: paper presentation by Conklin. Math 497: I'm planning to talk about Cantor (set theory and infinite cardinal and ordinal numbers) and perhaps start on Hilbert's program today. In the last few lectures (and there are few!) I will be giving an overview of the modern view of foundations of mathematics -- this is _hard math_ which I am delighted not to be giving an exam on, but it should be fun to talk about.

One could read pp. 77-96 in Russell, Introduction to Mathematical Philosophy, and pp. 110-130 in Moore, The Infinite. Also Kline, Loss of Certainty, pp. 172-213. One will not have to have read this to understand my lecture (which is good, since I'm posting it rather late!)

• Wednesday, December 1:

Math 301: section 6.5

• Thursday, December 2:

• Friday, December 3:

Math 301: Test IV

The Test IV review document is here, in Postscript and PDF. Important additional remark: section 6.5 is not on the exam (deferred to the final).

• Week 16:

• Monday, December 6:

Math 301: section 6.5(6.6)

• Tuesday, December 7:

Math 301: section 6.7

Math 301: I will discuss the topic of Fourier series in section 6.8 today; this will be the last new material covered in the course. It is advisable to do problems 5-14 in section 6.8 (we will do some of these in class), but I'm not giving a formal assignment. Our remaining time will be spent reviewing for the final. I will attempt this week to return information about computer labs to everyone who has turned them in.

Math 497: presentation by Crawford on cellular automata (tentatively scheduled).

Math 497: Billy Hudson presentation of paper 2 scheduled.

• Wednesday, December 8:

Math 301: section 6.8

The Final Exam review document is here, in Postscript and PDF. You should be able to pick up the solution set to Test IV at my door by noon, as well.

Please note that I will not be in my office after noon today: I am ill and will be staying home. You can reach me by phone or e-mail, and I will be in tomorrow as usual.

• Thursday, December 9:

Math 497: Renne presentation (surreal numbers).

Math 497: Shultz presentation.

• Friday, December 10:

Math 301: review

• Final Exams:

• Math 301: Monday, December 13, 10:30 am -- 12:30 pm

Please note that the final exam is OPEN BOOK and OPEN NOTES. I think I mentioned this at the beginning of the class as my usual policy with regard to final exams, but I neglected to say anything about it during the last few days! Do not regard this as an excuse not to study; hunting for formulas in your book is not a good way to spend your time! Also, please drop me an e-mail if you read this (if you haven't already replied to e-mail from me on the same subject); I want to be certain that everyone knows this.

• Math 497: Tuesday, December 14, 1:00 pm -- 3:00 pm

No final exam -- paper II presentation makeups may happen in this period. See announcement under Nov. 11 entry. Math 497: It has been suggested that a final lecture with refreshments might happen during the final exam period! The instructor is in favor, as he'd like to do some wrapping-up -- what does everyone think?

Math 497: In fact, Shultz will be giving his presentation during the final exam period, so the class is expected to show up (reasonable excuses apply). Refreshments will be provided (I'll bring some and you are invited to do so as well).