BEGIN:VCALENDAR
METHOD:PUBLISH
PRODID:-//Apple Inc.//iCal 3.0//EN
CALSCALE:GREGORIAN
X-WR-CALNAME:Math 54
X-WR-RELCALID:F69EA5D2-BF53-4E33-A953-4471888F15A9
VERSION:2.0
X-WR-TIMEZONE:US/Pacific
BEGIN:VTIMEZONE
TZID:US/Pacific
BEGIN:STANDARD
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
DTSTART:19621028T020000
RRULE:FREQ=YEARLY;UNTIL=20061029T090000Z;BYMONTH=10;BYDAY=-1SU
TZNAME:PST
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
DTSTART:19870405T020000
RRULE:FREQ=YEARLY;UNTIL=20060402T100000Z;BYMONTH=4;BYDAY=1SU
TZNAME:PDT
END:DAYLIGHT
BEGIN:DAYLIGHT
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
DTSTART:20070311T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=2SU
TZNAME:PDT
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
DTSTART:20071104T020000
RRULE:FREQ=YEARLY;BYMONTH=11;BYDAY=1SU
TZNAME:PST
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
SEQUENCE:3
TRANSP:OPAQUE
UID:45315F6D-EED5-4D0C-9AE0-7237ED54E2FE
DTSTART;TZID=US/Pacific:20070213T135000
DTSTAMP:20070208T230439Z
SUMMARY:Special pre-exam Ken Ribet office hour
CREATED:20081120T045030Z
DTEND;TZID=US/Pacific:20070213T152000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:20
TRANSP:OPAQUE
UID:7DDB23C5-6CF6-4FF9-B299-750492475CD8
DTSTART;TZID=US/Pacific:20080123T151000
DTSTAMP:20080116T195215Z
SUMMARY:Math 54 lecture
CREATED:20081120T045035Z
DTEND;TZID=US/Pacific:20080123T160000
RRULE:FREQ=WEEKLY;INTERVAL=1;UNTIL=20080128T075959Z;BYDAY=MO,WE,FR;WKST=
 SU
END:VEVENT
BEGIN:VEVENT
SEQUENCE:12
DESCRIPTION:I've had only one lunch with students so far this semester. 
  I'm taking matters into my own hands and will simply invite myself.  I'
 ll announce the time and place and hope that students will show up.  I'l
 l be in front of Crossroads soon after 12:30PM on Monday.  We'll gather 
 up a group and go in for lunch.
UID:FC5E1FFA-18CF-47C7-819D-41C8117F159C
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20050919T123000
DTSTAMP:20050918T140843Z
SUMMARY:Crossroads lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20050919T133000
LOCATION:Crossroads DC
END:VEVENT
BEGIN:VEVENT
SEQUENCE:6
TRANSP:OPAQUE
UID:5E9E4B84-ADBD-404E-903E-C9A4A2CEC2D3
DTSTART;TZID=US/Pacific:20070209T122000
DTSTAMP:20070203T151456Z
SUMMARY:Clark Kerr Math 54 lunch
CREATED:20081120T045030Z
DTEND;TZID=US/Pacific:20070209T132000
LOCATION:Clark Kerr Campus
END:VEVENT
BEGIN:VEVENT
SEQUENCE:7
DESCRIPTION:Maybe the last 54 lunch of the semester!!
UID:A3261FBA-8513-4823-8AE1-8B10E4070FD5
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070509T124500
DTSTAMP:20070507T204403Z
SUMMARY:Crossroads DC lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20070509T134500
END:VEVENT
BEGIN:VEVENT
SEQUENCE:3
TRANSP:OPAQUE
UID:CBD3F3D3-F97E-4B10-80C4-679419FBF0C7
DTSTART;TZID=US/Pacific:20051212T130000
DTSTAMP:20051209T233628Z
SUMMARY:Clark Kerr DC lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20051212T140000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:23
TRANSP:OPAQUE
UID:76A33445-85C5-490C-B88E-333040941ED5
DTSTART;TZID=US/Pacific:20050829T141000
DTSTAMP:20050902T170949Z
SUMMARY:Math 54 Lecture
EXDATE;TZID=US/Pacific:20050905T141000
CREATED:20081120T045033Z
DTEND;TZID=US/Pacific:20050829T150000
LOCATION:100 Lewis
RRULE:FREQ=WEEKLY;INTERVAL=1;UNTIL=20050909T065959Z;BYDAY=MO,WE,FR;WKST=
 SU
END:VEVENT
BEGIN:VEVENT
SEQUENCE:19
DTSTART;TZID=US/Pacific:20050829T141000
DTSTAMP:20050828T223356Z
SUMMARY:Math 54 Lecture
DTEND;TZID=US/Pacific:20050829T150000
LOCATION:100 Lewis
DESCRIPTION:Course mechanics: lectures\, discussions\, quizzes\, homewor
 k\, exams\, office hours\, lunches\, our Head TA system.  The google dis
 cussion group (that you should subscribe to!).  The absolute importance 
 of attending lectures.  Stay awake\, pay attention\, turn off cell phone
 s.  No fooling around in class.  Yes\, you can interrupt with questions.
 \n\nOverview of linear systems and beginning of the discussion of Gaussi
 an elimination.\n\nHomework for this lecture: §1.1\, problems 1\, 2\, 3\
 , 4\, 10\, 11\, 14\, 19\, 20\, 21\, 22\, 29
UID:76A33445-85C5-490C-B88E-333040941ED5
TRANSP:OPAQUE
URL;VALUE=URI:http://math.berkeley.edu/~ribet/54/
CREATED:20081120T045033Z
RECURRENCE-ID;TZID=US/Pacific:20050829T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:22
DESCRIPTION:I think that we're pretty much OK with Gaussian elimination\
 , especially after the discussion sections on September 2.  Let's focus 
 on section 1.3.  We could conceivably touch on section 1.4.  I hope to t
 alk about matrix inverses and explain why matrix multiplication is assoc
 iative.\n\nWe've had no news about a room change as of this writing.  We
  have an excellent shot at a larger room\, but we're still in limbo.\n\n
 HW for this lecture is as follows:\nsection 1.2:15\,17\,19\,21 \nsection
  1.3:1\,2\,5\,7\,9\,11
UID:76A33445-85C5-490C-B88E-333040941ED5
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20050902T141000
DTSTAMP:20050902T170807Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045033Z
DTEND;TZID=US/Pacific:20050902T150000
LOCATION:100 Lewis
RECURRENCE-ID;TZID=US/Pacific:20050902T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:22
DESCRIPTION:We're going to be back with section 1.4\, which is a relativ
 ely long section.  We may move on to a bit of section 1.5\, so read that
  as well.\n\nHW for today's lecture:\nSection 1.3:15\,17\,19\,21\,23\,25
 \,33\nSection 1.4: 1\, 3\, 5\, 7
UID:76A33445-85C5-490C-B88E-333040941ED5
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20050907T141000
DTSTAMP:20050902T170949Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045033Z
DTEND;TZID=US/Pacific:20050907T150000
LOCATION:100 Lewis
RECURRENCE-ID;TZID=US/Pacific:20050907T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:20
DESCRIPTION:I will discuss the material in section 1.1 that I was hoping
  to discuss on Monday and then move on to sections 1.2 and 1.3.  We'll d
 o some Gaussian elimination and talk about matrix addition and multiplic
 ation.\n\nI think that I have a secret plan to get us into a larger lect
 ure room.  Even if you're not enrolled or on the waitlist\, stick around
  at least through Friday's lecture.\n\nHW for this lecture:\nsection 1.2
 \, problems 3\,5\,7\,9\,11
UID:76A33445-85C5-490C-B88E-333040941ED5
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20050831T141000
DTSTAMP:20050831T034732Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045033Z
DTEND;TZID=US/Pacific:20050831T150000
LOCATION:100 Lewis
RECURRENCE-ID;TZID=US/Pacific:20050831T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:4
TRANSP:OPAQUE
UID:DC897229-7DC0-49EE-9BAF-5C8759D25162
DTSTART;TZID=US/Pacific:20070516T140000
DTSTAMP:20070510T224444Z
SUMMARY:Math 54 office hour
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20070516T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:5
TRANSP:OPAQUE
UID:78029EA5-A949-4040-AF6B-FA2D329367A2
DTSTART;TZID=US/Pacific:20070518T123000
DTSTAMP:20070108T220744Z
SUMMARY:Math 54 exam
CREATED:20081120T045034Z
DTEND;TZID=US/Pacific:20070518T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:12
TRANSP:OPAQUE
UID:726D3A9D-B8F7-45CF-BF8D-786276E8AB67
DTSTART;TZID=US/Pacific:20070307T120000
DTSTAMP:20070228T045619Z
SUMMARY:Foothill DC Math 54 lunch
CREATED:20081120T045033Z
DTEND;TZID=US/Pacific:20070307T130000
LOCATION:Foothill DC
END:VEVENT
BEGIN:VEVENT
SEQUENCE:15
DESCRIPTION:Some students have been asking me to schedule a Math 54 lunc
 h outside of the DCs.  We have a number of Berkeley High students who ar
 e taking the course.  They have a short lunch hour and need to stay near
  Berkeley High.  I proposed La Cascada\, a Mexican place at 2164 Center 
 Street (near the Starbucks at the corner of Oxford and Center)\, and the
  proposal was accepted.  So let's do a lunch there.  At the request of t
 he Berkeley High students\, I declare the start time to be 11:40.\n\nLa 
 Cascada and Top Dog are next to each other and seem to share tables.  So
  you can get a hot dog if you don't like the fare at LC.  I personally l
 ike La Cascada's soup a lot\; it's full of cumin and tastes Indian to me
 .  Also\, La Cascada makes the best fish tacos on all of Center Street\,
  in my humble opinion\, anyway.
UID:9F2D2C86-975A-4ECC-9C38-36076A0507B2
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051109T114000
DTSTAMP:20051028T121912Z
SUMMARY:La Cascada Math 54 lunch
CREATED:20081120T045035Z
DTEND;TZID=US/Pacific:20051109T124000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:10
TRANSP:OPAQUE
UID:DE31F7DB-9720-4F18-B217-E3D5E371FD26
DTSTART;TZID=US/Pacific:20070402T123000
DTSTAMP:20070402T123439Z
SUMMARY:Foothill DC lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20070402T133000
LOCATION:Foothill
END:VEVENT
BEGIN:VEVENT
SEQUENCE:8
DESCRIPTION:Location TBA.  Where shall we go?  How about Clark Kerr or F
 oothill?  Send me e-mail if you want to come and have a preference.
UID:FDB93240-9469-488F-905D-063085D5CDD5
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051129T114500
DTSTAMP:20051128T235159Z
SUMMARY:Crossroads DC lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20051129T124500
END:VEVENT
BEGIN:VEVENT
SEQUENCE:8
TRANSP:OPAQUE
UID:47B285BF-A858-11D9-8ED7-0003939CD54A
DTSTART;TZID=US/Pacific:20051217T170000
DTSTAMP:20050816T160011Z
SUMMARY:Math 54 final exam
CREATED:20081120T045030Z
DTEND;TZID=US/Pacific:20051217T200000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:5
TRANSP:OPAQUE
UID:345C70F1-C884-40C7-84EE-4E9CBC46DE17
DTSTART;TZID=US/Pacific:20070129T150000
DTSTAMP:20070128T164651Z
SUMMARY:Ken Ribet office hour
CREATED:20081120T045030Z
DTEND;TZID=US/Pacific:20070129T163000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:12
TRANSP:OPAQUE
UID:5464866D-39E6-4445-93C5-7CB71DA308E2
DTSTART;VALUE=DATE:20070117
DTSTAMP:20070116T182948Z
SUMMARY:Discussion Sections
EXDATE;VALUE=DATE:20070219
EXDATE;VALUE=DATE:20070326
EXDATE;VALUE=DATE:20070330
EXDATE;VALUE=DATE:20070328
CREATED:20081120T045030Z
DTEND;VALUE=DATE:20070118
RRULE:FREQ=WEEKLY;INTERVAL=1;UNTIL=20070508;BYDAY=MO,WE,FR;WKST=SU
END:VEVENT
BEGIN:VEVENT
SEQUENCE:5
TRANSP:OPAQUE
UID:AAA4BEA1-E0F8-41D6-B54C-5EE5142D6971
DTSTART;TZID=US/Pacific:20070206T131000
DTSTAMP:20070202T214659Z
SUMMARY:Crossroads Math 54 lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20070206T141000
LOCATION:Crossroads
END:VEVENT
BEGIN:VEVENT
SEQUENCE:7
TRANSP:OPAQUE
UID:0A20AE60-9CF6-4C82-96C2-FAF8E9783F7F
DTSTART;TZID=US/Pacific:20070122T133000
DTSTAMP:20070122T174955Z
SUMMARY:Ken Ribet office hour
CREATED:20081120T045019Z
DTEND;TZID=US/Pacific:20070122T150000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:11
TRANSP:OPAQUE
UID:9F66C3FE-72E8-4E2D-B69E-8EDA75884C38
DTSTART;TZID=US/Pacific:20050922T124500
DTSTAMP:20050920T123629Z
SUMMARY:Unit 3 lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20050922T134500
LOCATION:Café 3
END:VEVENT
BEGIN:VEVENT
SEQUENCE:44
TRANSP:OPAQUE
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
DTSTART;TZID=US/Pacific:20070116T153000
DTSTAMP:20070418T013951Z
SUMMARY:Math 54
EXDATE;TZID=US/Pacific:20070327T153000
EXDATE;TZID=US/Pacific:20070329T153000
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070116T170000
RRULE:FREQ=WEEKLY;INTERVAL=1;UNTIL=20070509T065959Z;BYDAY=TU,TH;WKST=SU
END:VEVENT
BEGIN:VEVENT
SEQUENCE:42
DESCRIPTION:*** We are going to do course evaluations in class on Thursd
 ay\, April 26.  I'd like everyone to come and fill out a form.  If you l
 ike my teaching and my course\, I'd like to hear that.  If you don't\, I
  might as well get the news.  I put myself down for Math 54 next spring 
 (2008).  I will read your comments and keep them in mind next year.  Mak
 e your voice heard.  Influence the future.  ***\n\nSection 10.4 HW: 7\, 
 11\, 13\, 15\, 17\, 19\, 23(a)\, 31
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070426T153000
DTSTAMP:20070418T013709Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070426T170000
RECURRENCE-ID;TZID=US/Pacific:20070426T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:25
DESCRIPTION:We are going to be beginning our discussion of differential 
 equations.  This is partly a review of Math 1B.  Sections 3.1\, 3.2\, 3.
 3 and 4.1 of BD\, which is Boyce-DiPrima.  The homework from now on will
  be from BD.\n\nFor this lecture:\nSection 3.1: 1\, 7\, 11\nSection 3.2:
  1\, 3\, 13\, 14\, 19\, 21\, 23\nSection 3.3: 3\, 5\, 7\, 11
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070320T153000
DTSTAMP:20070317T173418Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070320T170000
RECURRENCE-ID;TZID=US/Pacific:20070320T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:20
DESCRIPTION:This lecture concerns section 3.7: rank\, nullity\, column s
 pace\, row space...  This is somewhat hard material\, and it takes some 
 time to get used to.\n\nHomework from Section 3.7 3\, 5\, 7\, 9\, 11\, 1
 3\, 15\, 17\, 21\, 23\n\nNote: this homework is due February 21
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070213T153000
DTSTAMP:20070204T220951Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070213T170000
RECURRENCE-ID;TZID=US/Pacific:20070213T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:41
DESCRIPTION:Homework for today:\nsection 10.2\, problems 1\, 3\, 13\, 14
 \, 15\, 16\, 17 and 18
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070419T153000
DTSTAMP:20070418T013456Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070419T170000
RECURRENCE-ID;TZID=US/Pacific:20070419T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:15
DESCRIPTION:The midterm covers all material that was treated in class th
 rough the lecture of February 8.  It does not cover material introduced 
 on February 13.  My policy is that students can bring in a single 2-side
  page (8 1/2 x 11 inches) of notes but can't refer to books.  Also: no e
 lectronic gadgets of any kind.  This includes calculators\, iPhones\, de
 dicated facebook devices\, etc.  As they say in the airline industry\, \
 "Anything with an on/off switch.\"
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070215T153000
DTSTAMP:20070110T212039Z
SUMMARY:Math 54 Midterm Exam
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070215T170000
RECURRENCE-ID;TZID=US/Pacific:20070215T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:23
DESCRIPTION:Sections 5.1 and 5.2 this week\n\nHW:\n\n5.1: 5\, 7\, 11\, 1
 3\, 15\, 17\, 19\, 20\, 25\, 31-39
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070306T153000
DTSTAMP:20070227T222307Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070306T170000
RECURRENCE-ID;TZID=US/Pacific:20070306T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:16
DESCRIPTION:You all have the unlucky situation of having to take a midte
 rm on the first classe after a week-long break.  I hope that you studied
  while you were on the beach in Baja!  As explained in class\, the exam 
 will cover everything in Hill but no differential equations.  Although t
 he exam is cumulative\, it stresses material that was not covered on the
  first exam.  The same rules apply: one page of notes\, no books or devi
 ces.
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070403T153000
DTSTAMP:20070325T145233Z
SUMMARY:Math 54 Midterm Exam
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070403T170000
RECURRENCE-ID;TZID=US/Pacific:20070403T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:30
DESCRIPTION:In this lecture\, we will do one or two more examples of red
 uction to row echelon form and then talk about the algebra of matrix add
 ition\, subtraction and multiplication.  Homework due next Monday (Janua
 ry 22):\n\nSection 1.2: 17\, 19\, 21\nSection 1.3: 2\, 4\, 5\, 7\, 8\, 9
 \, 13\, 15\, 21\, 33
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070118T153000
DTSTAMP:20070117T164851Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070118T170000
RECURRENCE-ID;TZID=US/Pacific:20070118T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:43
DESCRIPTION:Last day of class.  Wrap-up\, discussion of final\, problems
  from an earlier final\,...  Wild applause?  See you on the 18th
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070508T153000
DTSTAMP:20070418T013951Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070508T170000
RECURRENCE-ID;TZID=US/Pacific:20070508T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:21
DESCRIPTION:Fourth week of classes: More abstract concepts including sub
 spaces of vector spaces\, null spaces\, span and linear independence\; b
 asis and dimension.  This takes us through section 3.6\n\nHomework assoc
 iated with this lecture:\n\nSection 3.4: 1\, 5\, 11\, 17\, 19\, 25\, 31\
 , 33\, 39\, 43\n\nSection 3.5: 1\, 5\, 11\, 17\, 19\, 29
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070206T153000
DTSTAMP:20070204T220540Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070206T170000
RECURRENCE-ID;TZID=US/Pacific:20070206T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:28
DESCRIPTION:Sections 7.8\, 10.1 and 10.2 of BD were scheduled for this w
 eek\, but I lectured on section 7.8 on April 12.  Homework for this time
 :\n\nSection 7.8: 1\, 3\, 5\, 7\, 9\, 15\n\nSection 10.1: 1\, 3\, 7\, 9\
 , 15\, 17\, 19
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070417T153000
DTSTAMP:20070415T143131Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070417T170000
RECURRENCE-ID;TZID=US/Pacific:20070417T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:38
DESCRIPTION:Homework for this lecture:\n\nSection 3.3: 13\, 15\, 17\, 18
 \, 19 \nSection 4.1: 7\, 9\, 11\, 13\, 15\, 18\, 19
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070322T153000
DTSTAMP:20070317T173545Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070322T170000
RECURRENCE-ID;TZID=US/Pacific:20070322T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:17
DESCRIPTION:Second week of classes: Section 1.4.  In the both lectures\,
  we will discuss inverses and elementary matrices.\n\nHW due on Friday\,
  January 26:\n\nSection 1.3: 41\nSection 1.4: 1\, 3\, 5\, 7\, 9\, 11\, 1
 3\, 17\, 21\, 25\, 27
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070123T153000
DTSTAMP:20070121T155629Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070123T170000
RECURRENCE-ID;TZID=US/Pacific:20070123T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:42
DESCRIPTION:No homework due on May 7
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070503T153000
DTSTAMP:20070418T013839Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070503T170000
RECURRENCE-ID;TZID=US/Pacific:20070503T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:24
DESCRIPTION:Sections 5.3 and 5.4 of Hill.  This is likely to be our last
  week of linear algebra discussions.\n\nHW: section 5.3\, problems 1\, 3
 \, 5\, 7\, 11\, 13\, 17\, 19\, 21\, 27\, 28\, 29\, 31\, 32\, 33
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070313T153000
DTSTAMP:20070307T193927Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070313T170000
RECURRENCE-ID;TZID=US/Pacific:20070313T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:27
DESCRIPTION:Sections 7.5\, 7.6 and 7.7 of BD this week.\n\nHomework from
  section 7.5: 1\, 3\, 9\, 11\, 17\, 25\, 27\, 29\n\nand from section 7.6
 : 1\, 3\, 5\, 9\, 11(a)-(b)
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070410T153000
DTSTAMP:20070406T144903Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070410T170000
RECURRENCE-ID;TZID=US/Pacific:20070410T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:34
DESCRIPTION:KR back in town\, maybe suntanned.\n\nHomework for this lect
 ure:\n\nSection 3.8: 9\, 11\, 15\n\nSection 4.1: 1\, 3\, 7\, 9\, 13\, 19
 \, 25\, 29\, 31\, 35\, 37\, 41
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070222T153000
DTSTAMP:20070204T221609Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070222T170000
RECURRENCE-ID;TZID=US/Pacific:20070222T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:34
DESCRIPTION:Homework associated with this lecture:\n\nSection 3.5:  31 3
 3 \n\nSection 3.6: 3\, 5\, 9\, 17\, 24\, 27\, 29\, 33\, 37\, 40\, 43\, 4
 7 
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070208T153000
DTSTAMP:20070204T220749Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070208T170000
RECURRENCE-ID;TZID=US/Pacific:20070208T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:31
DESCRIPTION:HW due on Monday\, January 29:\n\nSection 1.4\, problems 29\
 , 35\, 37\, 39\, 41\, 45\, 46\, 47\n
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070125T153000
DTSTAMP:20070121T155746Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070125T170000
RECURRENCE-ID;TZID=US/Pacific:20070125T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:39
DESCRIPTION:Homework from section 7.6: 13(a)-(c)\, \n 28\n\nand from sec
 tion 7.7: 1\, 3\, 5\, 11\, 13\, 14\, 16
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070412T153000
DTSTAMP:20070406T145009Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070412T170000
RECURRENCE-ID;TZID=US/Pacific:20070412T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:16
DESCRIPTION:During this week we will discuss the mechanics of the course
  (lectures\, sections\, Head TA\, exams\, homework)\; linear systems\, G
 aussian elimination\; the algebra of matrices (including inverses)\; thi
 s will take us through section 1.3\n\nProblems for this lecture (due on 
 Friday in discussion):\n\nSectiion 1.1: 1\, 2\, 3\, 21\, 25\, 28\n\nSect
 ion 1.2: 1-6\, 8\, 10\, 12\, 16\, 18
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070116T153000
DTSTAMP:20070116T154653Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070116T170000
RECURRENCE-ID;TZID=US/Pacific:20070116T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:32
DESCRIPTION:Homework associated with this lecture:\n\nSection 3.2\, prob
 lems 21\, 25\, 29\, 36\, 37 \n\nSection 3.3\, problems 2\, 3\, 11\, 15\,
  23\, 25\, 27\, 34\, 35\, 37\, 38 \n
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070201T153000
DTSTAMP:20070129T045632Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070201T170000
RECURRENCE-ID;TZID=US/Pacific:20070201T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:19
DESCRIPTION:Third week of classes: The first three sections of Chapter 3
  of Hill.  We study vectors in 2-space\, 3-space and n-space.  Next\, we
  talk about general vector spaces.  The material is more abstract than w
 hat you might have bargained for\, so be prepared to think about the con
 cepts.\n\nHomework associated with this lecture:\n\nSection 3.1\, proble
 ms 7\, 9\, 11\, 20\, 22\, 30\, 37\, 39\, 43\, 49 and section 3.2 problem
 s 7\, 9\, 11\, 15\, 19\, 20
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070130T153000
DTSTAMP:20070128T170131Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070130T170000
RECURRENCE-ID;TZID=US/Pacific:20070130T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:36
DESCRIPTION:HW -- section 5.2\, problems 1\, 3\, 5\, 7\, 8\, 9\, 11(a)-(
 c)\, 19(a)-(c)\,  23\, 24\, 25\, 28\, 29\, 31\, 33\, 35
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070308T153000
DTSTAMP:20070227T222419Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070308T170000
RECURRENCE-ID;TZID=US/Pacific:20070308T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:31
DESCRIPTION:The last three lectures in the class are likely to be devote
 d to summing up section 10.5 and to review of the whole course.\n\nFor t
 his lecture\, there's the final homework\, from section 10.5: 1\, 2\, 3\
 , 5\, 7\, 8\, 9\, 10\, 11\, 21
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070501T153000
DTSTAMP:20070423T030100Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070501T170000
RECURRENCE-ID;TZID=US/Pacific:20070501T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:38
DESCRIPTION:HW from section 5.4: 1\, 3\, 5\, 7\, 11\, 13\, 15\, 19\, 21-
 25
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070315T153000
DTSTAMP:20070307T194105Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070315T170000
RECURRENCE-ID;TZID=US/Pacific:20070315T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:23
DESCRIPTION:sections 4.2\, 4.3 and 4.4 of the Hill book will be treated 
 this week.  Here's the homework for this lecture (sorry for the late pos
 ting):\n\n4.2: 1\, 3\, 6\, 9\, 17 \,21\, 25\, 31\, 32\, 33\n\n4.3: 1\, 3
 \, 5\, 7\, 13
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070227T153000
DTSTAMP:20070227T222025Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070227T170000
RECURRENCE-ID;TZID=US/Pacific:20070227T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:35
DESCRIPTION:Homework:\n\n4.3: 17\, 19\, 23\, 25\, 27\n\n4.4: 3\, 5\, 7\,
  11\, 17\, 19\, 21\, 23\, 27\, 28\, 29
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070301T153000
DTSTAMP:20070227T222135Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070301T170000
RECURRENCE-ID;TZID=US/Pacific:20070301T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:21
DESCRIPTION:This week: more on section 3.7\, and sections 3.8 and 4.1\n\
 nToday's lecture will be given by a guest lecturer because your usual in
 structor (KR) will be out of town for a couple of days.\n\nHomework for 
 this lecture:\n\nSection 3.7: 31\, 33\, 34\, 35\, 39\, 43\, 44\,45\n\nSe
 ction 3.8: 1\, 3\, 5
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070220T153000
DTSTAMP:20070204T221352Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070220T170000
RECURRENCE-ID;TZID=US/Pacific:20070220T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:30
DESCRIPTION:Sections 10.3\, 10.4 and 10.5 of BD this week.\n\n*** We are
  going to do course evaluations in class on Thursday.  I'd like everyone
  to come and fill out a form.  If you like my teaching and my course\, I
 'd like to hear that.  If you don't\, I might as well get the news.  I p
 ut myself down for Math 54 next spring (2008).  I will read your comment
 s and keep them in mind next year.  Make your voice heard.  Influence th
 e future.  ***\n\nHomework from section 10.3: 1\, 3\, 5\, 7(a)\, 9(a)\, 
 11(a)\, 17
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070424T153000
DTSTAMP:20070418T013608Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070424T170000
RECURRENCE-ID;TZID=US/Pacific:20070424T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:27
DESCRIPTION:More on section 4.1 and also section 7.1.  !!! I presented m
 aterial from section 7.7.\n\nHomework from section 7.1: 1\, 2\, 3\, 5\, 
 6\, 7(a)\, 15\, 16
UID:28407A3B-EB3D-4EEE-9C45-0EDE07FEC659
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070405T153000
DTSTAMP:20070408T225828Z
SUMMARY:Math 54
CREATED:20081120T045023Z
DTEND;TZID=US/Pacific:20070405T170000
RECURRENCE-ID;TZID=US/Pacific:20070405T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:1
DESCRIPTION:We haven't tried this time slot yet.  I hope that a bunch of
  you will turn out for the lunch.  If you don't have a meal contract\, t
 he rumor on the street is that it'll be easy to convince someone to swip
 e you in.
UID:DC13DEE1-45A0-4728-8C5C-BC7D77F521B2
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051011T114500
DTSTAMP:20051009T142957Z
SUMMARY:Math 54 lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20051011T124500
LOCATION:Foothill DC
END:VEVENT
BEGIN:VEVENT
SEQUENCE:14
DESCRIPTION:I had to cancel the lunch that I was planning for October 31
 .  So let's do November 1 instead.  Foothill: see you there!
UID:6147FB71-2AAE-4E0F-B80F-34EEA52CEBE1
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051101T130000
DTSTAMP:20051031T052352Z
SUMMARY:Foothill DC lunch
CREATED:20081120T045030Z
DTEND;TZID=US/Pacific:20051101T140000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:5
TRANSP:OPAQUE
UID:93DA1590-D60E-42F6-ABCA-A8EC808DAE84
DTSTART;TZID=US/Pacific:20070118T135000
DTSTAMP:20070115T223502Z
SUMMARY:Office hour
CREATED:20081120T045035Z
DTEND;TZID=US/Pacific:20070118T152000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:12
TRANSP:OPAQUE
UID:8BFE6A87-EE86-41E1-BDE5-6614118D53AC
DTSTART;TZID=US/Pacific:20051121T124500
DTSTAMP:20051116T042948Z
SUMMARY:Café 3 DC lunch
CREATED:20081120T045035Z
DTEND;TZID=US/Pacific:20051121T134500
END:VEVENT
BEGIN:VEVENT
SEQUENCE:18
TRANSP:OPAQUE
UID:934E991B-A858-11D9-8ED7-0003939CD54A
DTSTART;TZID=US/Pacific:20050824T141000
DTSTAMP:20050816T160248Z
SUMMARY:Math 54
EXDATE;TZID=US/Pacific:20050824T141000
EXDATE;TZID=US/Pacific:20050826T141000
CREATED:20081120T045035Z
DTEND;TZID=US/Pacific:20050824T150000
LOCATION:100 Lewis
RRULE:FREQ=WEEKLY;INTERVAL=1;UNTIL=20050829T065959Z;BYDAY=MO,WE,FR;WKST=
 SU
END:VEVENT
BEGIN:VEVENT
SEQUENCE:11
DESCRIPTION:I'll be having lunch with some students at Foothill on Septe
 mber 9.  Join us if you see us there!
UID:AE09C744-D922-498F-B6CA-D9722619BD98
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20050909T120000
DTSTAMP:20050909T010624Z
SUMMARY:Foothill lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20050909T130000
LOCATION:Foothill DC
END:VEVENT
BEGIN:VEVENT
SEQUENCE:9
DESCRIPTION:The Math Undergraduate Student Association organizes lunches
  for undergraduates\, grad students and faculty about once per month.  T
 he cost is quite nominal\; watch their Web site for details.  I have a m
 eeting from 12 to 1 but intend to come for the last half-hour.
UID:1F640D58-AD59-4CE0-86DD-684276E3A70D
TRANSP:OPAQUE
URL;VALUE=URI:http://musa.berkeley.edu/
DTSTART;TZID=US/Pacific:20050915T120000
DTSTAMP:20050911T213942Z
SUMMARY:MUSA lunch
CREATED:20081120T045021Z
DTEND;TZID=US/Pacific:20050915T133000
LOCATION:1015 Evans
END:VEVENT
BEGIN:VEVENT
SEQUENCE:9
DESCRIPTION:Definitely the last 54 lunch of the semester!!
UID:A0264295-D0B2-4616-8BF7-EEF4150DC12D
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070518T110500
DTSTAMP:20070518T040404Z
SUMMARY:Crossroads DC lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20070518T120000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:14
TRANSP:OPAQUE
UID:0EE2920E-05EA-40DB-A29E-38B5FCA2D9E3
DTSTART;TZID=US/Pacific:20050829T110000
DTSTAMP:20051013T032711Z
SUMMARY:K. Ribet office hour
EXDATE;TZID=US/Pacific:20050905T110000
CREATED:20081120T045021Z
DTEND;TZID=US/Pacific:20050829T123000
LOCATION:885 Evans
RRULE:FREQ=WEEKLY;INTERVAL=1;UNTIL=20051210T075959Z
END:VEVENT
BEGIN:VEVENT
SEQUENCE:12
TRANSP:OPAQUE
UID:0EE2920E-05EA-40DB-A29E-38B5FCA2D9E3
DTSTART;TZID=US/Pacific:20051021T110000
DTSTAMP:20051012T035653Z
SUMMARY:K. Ribet office hour
CREATED:20081120T045021Z
DTEND;TZID=US/Pacific:20051021T123000
LOCATION:885 Evans
RECURRENCE-ID;TZID=US/Pacific:20051017T110000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:14
TRANSP:OPAQUE
UID:0EE2920E-05EA-40DB-A29E-38B5FCA2D9E3
DTSTART;TZID=US/Pacific:20051024T101500
DTSTAMP:20051013T032714Z
SUMMARY:K. Ribet office hour
CREATED:20081120T045021Z
DTEND;TZID=US/Pacific:20051024T114500
LOCATION:885 Evans
RECURRENCE-ID;TZID=US/Pacific:20051024T110000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:5
TRANSP:OPAQUE
UID:1CA2225F-DE11-468C-B39F-15B647920A24
DTSTART;TZID=US/Pacific:20070313T124500
DTSTAMP:20070310T175218Z
SUMMARY:Crossroads DC Math 54 lunch
CREATED:20081120T045021Z
DTEND;TZID=US/Pacific:20070313T134500
LOCATION:Crossroads DC
END:VEVENT
BEGIN:VEVENT
SEQUENCE:4
TRANSP:OPAQUE
UID:2322C51E-4ABA-4CED-9EE3-DF4D4AD83562
DTSTART;TZID=US/Pacific:20051117T124000
URL;VALUE=URI:http://www.housing.berkeley.edu/dining/crossroads.html
DTSTAMP:20051107T192007Z
SUMMARY:Crossroads DC lunch
CREATED:20081120T045021Z
DTEND;TZID=US/Pacific:20051117T134000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:5
TRANSP:OPAQUE
UID:F4D5E28C-58EF-4A4A-96F8-9928A57EDDEB
DTSTART;TZID=US/Pacific:20051213T140000
DTSTAMP:20051211T195938Z
SUMMARY:Ribet office hours
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20051213T160000
LOCATION:885 Evans
END:VEVENT
BEGIN:VEVENT
SEQUENCE:4
TRANSP:OPAQUE
UID:8EEA8DF2-9016-4642-95DD-91CB056DFC00
DTSTART;TZID=US/Pacific:20070425T121000
DTSTAMP:20070412T215113Z
SUMMARY:Math 54 Foothill DC lunch
CREATED:20081120T045035Z
DTEND;TZID=US/Pacific:20070425T131000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:5
TRANSP:OPAQUE
UID:C04C20BA-188F-4067-8DD4-DFBBF2A7675C
DTSTART;TZID=US/Pacific:20051208T114000
DTSTAMP:20051207T052213Z
SUMMARY:La Cascada non-DC lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20051208T124000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:4
TRANSP:OPAQUE
UID:81FA78E0-4488-4DEA-8604-25DABB4A4356
DTSTART;TZID=US/Pacific:20070416T120000
DTSTAMP:20070409T235550Z
SUMMARY:Unit 3 DC lunch
CREATED:20081120T045035Z
DTEND;TZID=US/Pacific:20070416T130000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:6
TRANSP:OPAQUE
UID:4E715E41-3954-475E-97A7-1634A34562AE
DTSTART;TZID=US/Pacific:20051215T201500
DTSTAMP:20051211T200101Z
SUMMARY:GSI-led Review Session (10 Evans)
CREATED:20081120T045030Z
DTEND;TZID=US/Pacific:20051215T220000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:9
DESCRIPTION:The Math Undergraduate Student Association invites you to an
  \"all you can eat\" lunch in the math department comment room (1015 Eva
 ns).  There will be lots of yummy food including an increased vegetarian
  selection.  The cost is $3 per person.  You'll find math department fac
 ulty\, graduate students\, undergraduates and staff members.  I will be 
 there briefly at the beginning\; I have a lunch appoinment that day.
UID:CADEC51F-DD74-49AC-B815-231FBA04DBCB
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051108T113000
DTSTAMP:20051105T210015Z
SUMMARY:MUSA lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20051108T130000
LOCATION:1015 Evans
END:VEVENT
BEGIN:VEVENT
SEQUENCE:58
TRANSP:OPAQUE
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
DTSTART;TZID=US/Pacific:20050909T141000
DTSTAMP:20051016T003827Z
SUMMARY:Math 54 Lecture
EXDATE;TZID=US/Pacific:20051125T141000
EXDATE;TZID=US/Pacific:20051111T141000
EXDATE;TZID=US/Pacific:20050824T141000
EXDATE;TZID=US/Pacific:20050826T141000
EXDATE;TZID=US/Pacific:20050905T141000
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20050909T150000
LOCATION:155 Dwinelle
RRULE:FREQ=WEEKLY;INTERVAL=1;UNTIL=20051210T075959Z;BYDAY=MO,WE,FR;WKST=
 SU
END:VEVENT
BEGIN:VEVENT
SEQUENCE:36
DESCRIPTION:HW: section 3.7: 34\, 35\, 39\, 43\, 44\, 45\; 3.8: 1\, 3\, 
 5\, 9\n\nIf you found a California Water Polo fleece sweater in 155 Dwin
 elle on Monday\, please let me know.  Its owner asked me to ask you for 
 it.\n\nWe are going to finish up the material on CS(A)\, RS(A)\, NS(A) a
 nd relations among them.  We will then talk a bit about coordinates and 
 change of basis.\n\nThe URL for my radio appearance on Monday is http://
 www.kpfa.org/archives/index.php?arch=10447.  I hope that everyone had fu
 n as I dashed down to the station\, which is on MLK near University.
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051005T141000
DTSTAMP:20050914T003137Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051005T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051005T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:56
DESCRIPTION:Last week of classes\, folks.  We will discuss section 10.4 
 of B-D.  Homework for this section: 7\, 11\, 13\, 15\, 17\, 19\, 23(a)\,
  31
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051205T141000
DTSTAMP:20051202T144158Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051205T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051205T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:40
DESCRIPTION:Determinants.  Homework from section 5.1: 5\, 7\, 11\, 13\, 
 15\, 17\, 19\, 20\, 25.  Recall that this lecture will be given by GSI N
 athan H.  One thing that's clear is that we'll be taking on faith some o
 f the general properties of determinants that are not proved completely 
 until Math 110.  The properties that we need\, fortunately\, are pretty 
 obvious for matrices of small size\, where everything can be computed ex
 plicitly by hand.  Most phenomena that you'd want to explore can be seen
  already in determinants of matrices of size at most 3 or 4.  In actual 
 applications\, the matrices are likely to be huge\, and you'd be interes
 ted in finding efficient algorithms to compute things.\n\nIf I were givi
 ng the lecture\, I'd try to set out the major properties of determinants
  and explain how to compute determinants of size 1\, 2\, 3 and 4.  This 
 is one part of the course where you have to take some things on faith.  
 Complete proofs\, which are long but not conceptually hard\, are given i
 n Math 110.  Most books like to think of the determinant of an n x n mat
 rix as a function of n variables -- the variables are the columns of the
  matrix.  You can write down a quick list of the properties of this func
 tion of n variables that characterizes it completely.  This means that t
 here is at most one function that has all the properties on the list.  W
 hat's hard is to show that the function exists: you have to define the d
 eterminant of an n x n matrix and check that the function so defined has
  all the requisite properties.  The definition that's used is (c) in the
  big displayed box on page 325 of our book.\n\nYou then need to know a w
 hole bunch of things:\n\n1. det(A) is non-zero if and only if A has an i
 nverse.\n\n2. det(AB) = det(A)det(B)\n\n3. A matrix and its tranpose hav
 e the same determinant.\n\n4. Diagonal and upper-triangular matrices hav
 e determinants that are easy to compute.\n\nA consequence of all these f
 acts is \"Cramer's Rule\,\" which Nathan will explain in class on Monday
 .\n\nA good thing to know is the relation between the determinant and vo
 lumes.  This is relatively easy to see for 2 x 2 matrices and even for 3
  x 3 matrices.  The relation is as follows.  If the columns of A are vec
 tors v_1\,...\,v_n\, then you can look at the parallelepiped spanned by 
 the v_i.  This object consists of all linear combinations of the v_i whe
 re the coefficients are real numbers between 0 and 1.  The volume of the
  parallelepiped is the absolute value of the determinant.  The sign of t
 he determinant tells you how the v_i are \"oriented\".  I'll bet that yo
 u encounter this issue in Math 53 for 3 x 3 matrices.
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DTSTART;TZID=US/Pacific:20051017T141000
DTSTAMP:20051015T233248Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051017T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051017T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:29
DESCRIPTION:General vector spaces.  Lots of problems from this section (
 3.3): 2\, 3\, 11\, 15\, 23\, 25\, 27\, 34\, 35\, 37\, 38
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DTSTART;TZID=US/Pacific:20050919T141000
DTSTAMP:20050917T143009Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20050919T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20050919T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:35
DESCRIPTION:Matrices as linear transformations.  Lots of homework from s
 ection 4.1:  1\, 3\, 7\, 9\, 13\, 19\, 25\, 29\, 31\, 35\, 37\, 41.  Muc
 h of what is written in this section is material that I have touched on 
 in class already.  Still\, it's good to have everything in one place.  A
 lso\, we'll talk about how linear transformations are represented by mat
 rices\; this is a genuinely new topic.
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DTSTART;TZID=US/Pacific:20051007T141000
DTSTAMP:20051007T145737Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051007T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051007T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:40
DESCRIPTION:Eigenvalues and eigenvectors.  Don't forget today's DC lunch
  at noon in Unit 3.  Homework for today from section 5.2: 1\, 3\, 5\, 7\
 , 8\, 9\, 11(a)-(c)\, 19(a)-(c) 
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DTSTART;TZID=US/Pacific:20051021T141000
DTSTAMP:20051021T145325Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051021T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051021T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:36
DESCRIPTION:Least squares and orthogonal projections.  HW from section 4
 .3: 1\, 3\, 5\, 7\, 13\, 17\, 19\, 23\, 25\, 27
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DTSTART;TZID=US/Pacific:20051012T141000
DTSTAMP:20050914T003748Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051012T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051012T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:45
DESCRIPTION:Symmetric matrices.  The homework for section 5.4 consists o
 f problems 1\, 3\, 5\, 7\, 11\, 13\, 15\, 19\, 21-25.  This homework wil
 l be due in section on November 8.  There are a lot of problems\, so ple
 ase don't postpone them until the last minute.  Sorry for not getting th
 ese up sooner.
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DTSTART;TZID=US/Pacific:20051031T141000
DTSTAMP:20051103T105148Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051031T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051031T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:43
DESCRIPTION:We will start our discussion of symmetric matrices.  The hom
 ework for this lecture was posted in the notes for the previous lecture.
 
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DTSTART;TZID=US/Pacific:20051028T141000
DTSTAMP:20050914T004234Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051028T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051028T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:19
DESCRIPTION:I am going to be in New York on this day\, so please see me 
 no later than October 28 if you have special issues about the exam.  Thi
 s exam will cover everything in the course up to and including material 
 in the lecture on October 28.  The format and general rules will be the 
 same as for the first midterm.  The exam is in theory cumulative\, but i
 n practice will test almost exclusively material that was not covered on
  the first midterm.  I will emphasize issues and concepts that were disc
 ussed in class.  (If you've missed some lectures\, I advise you to look 
 at people's notes.)
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DTSTART;TZID=US/Pacific:20051102T141000
DTSTAMP:20051016T002543Z
SUMMARY:Math 54 Midterm
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051102T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051102T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:23
DESCRIPTION:The fundamental subspaces of a matrix.  Homework from sectio
 n 3.7: 3\, 5\, 7\, 9\, 11\, 13\, 15
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DTSTART;TZID=US/Pacific:20050930T141000
DTSTAMP:20051002T175736Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20050930T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20050928T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:39
DESCRIPTION:Still on determinants.  Hey\, it's great to be back in Berke
 ley!  I'm looking forward to seeing some of you at lunch today and all o
 f you in lecture afterwards.  Homework for today's lecture will be again
  from section 5.1: exercises 31\, 32\, and 33-39.  I plan to do some exa
 mples that show how to compute the determinants of large ugly matrices w
 ith relative ease.  Also\, I'll explain Cramer's Rule: what it is\, why 
 it's true\, how to use it.
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DTSTART;TZID=US/Pacific:20051019T141000
DTSTAMP:20051019T163849Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051019T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051019T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:52
DESCRIPTION:Section 7.7 of B-D.  Problems 1\, 3\, 5\, 11\, 13\, 14\, 16 
 of this section.  I'm pleased to see that the authors have finally come 
 around to the point of view that I've been advocating in lecture: the be
 st way to solve X'=AX is to write down exp(At) and be done with it.  Thi
 s perspective is really helpful when you deal with repeated eigenvalues 
 (as in section 7.8).  We saw this already a week or so ago when I took A
  to be a non-zero 2x2 matrix whose square is 0.
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DTSTART;TZID=US/Pacific:20051121T141000
DTSTAMP:20051119T214921Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051121T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051121T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:32
DESCRIPTION:Section 3.6: basis and dimension.  HW: section 3.5 #34 and s
 ection 3.6 problems 3\, 5\, 9\, 17\, 24\, 27\, 29\, 33\, 37\, 40\, 43\, 
 47 
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DTSTART;TZID=US/Pacific:20050926T141000
DTSTAMP:20050926T002703Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20050926T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20050926T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:27
DESCRIPTION:We are still discussing section 1.4 and\, in particular\, th
 e \"main theorem\" (1.50).\n\nWe will move directly to section 3.1 once 
 we have finished up with section 1.4.  This section is very geometric: i
 t concerns vectors in the plane and in 3-space.  I apologize in advance 
 for my inability to draw good diagrams in 3-space.\n\nHW: sections 1.4: 
 45\, 46\, 47
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DTSTART;TZID=US/Pacific:20050912T141000
DTSTAMP:20050912T024936Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20050912T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20050912T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:39
DTSTART;TZID=US/Pacific:20051014T141000
DTSTAMP:20051014T001415Z
SUMMARY:Math 54 Lecture
DTEND;TZID=US/Pacific:20051014T150000
LOCATION:155 Dwinelle
DESCRIPTION:Orthonormal bases and Gram-Schmidt.  We'll do the general st
 atements and then see how G-Schmidt works when we have an interesting in
 ner product involving integrals.  Homework from section 4.4: 3\, 5\, 7\,
  11\, 17\, 19\, 21\, 23\, 27\,\n28\, 29 
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URL;VALUE=URI:http://math.berkeley.edu/~ribet/54/Lunch/
CREATED:20081120T045031Z
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BEGIN:VEVENT
SEQUENCE:51
DESCRIPTION:Section 7.6 of B-D.  Problems 1\, 3\, 5\, 9\, 11(a)-(b)\, 13
 (a)-(c)\, 28.  You'll probably see me with a laptop again.
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DTSTART;TZID=US/Pacific:20051118T141000
DTSTAMP:20051118T001206Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051118T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051118T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:36
DTSTART;TZID=US/Pacific:20051003T141000
DTSTAMP:20051004T033717Z
SUMMARY:Math 54 Lecture
DTEND;TZID=US/Pacific:20051003T150000
LOCATION:155 Dwinelle
DESCRIPTION:Ranks.  As I explained in e-mail\, I'm going to be leaving t
 his lecture early in order to get down to KPFA\, where I'll be on the ai
 r at 3PM.  Grace Lyo\, a math graduate student\, will either do the whol
 e lecture or take over mid-way.  We already known that the dimension of 
 a finite-dimensional vector space is well defined and that linearly inde
 pendent sets of vectors in such spaces can be enlarged to make bases.  A
 lso\, spanning sets can be shrunk in order to get bases\; we throw out t
 he junk.\n\nOn Monday\, we will study the column and row spans of a matr
 ix.  The dimensions of these spaces are the column and row ranks of the 
 matrix.  Holy cow\, they're equal.\n\nWe're having a lunch at 12:15 on W
 ednesday.  Let's do it at Clark Kerr\; I've never had lunch there in my 
 life!  Who can come?  Send me e-mail if you expect to be able to attend.
   When we have 6-10 students\, it's really quite perfect.  If you live i
 n CKC\, please show me how great your DC is.\n\nHomework: Section 3.7\, 
 problems \, 17\, 21\, 23\, 31\, 33\n\nSummary of lecture:\n\nWe know tha
 t the dimension of a finite-dimensional vector space is a\nwell defined 
 quantity.  We know that linearly independent subsets in\nsuch a space ca
 n be enlarged to make a basis and that spanning sets\ncan be shrunk to m
 ake a basis (by throwing out garbage).\n\nLet A be an m x n matrix.  We 
 have considered already the set of all\nAx with x in R^n.  This is a sub
 set of R^m and in fact is a subspace\nof R^m as we have already discusse
 d.  Insight: this subspace is the\nsubspace of R^m that is spanned by th
 e n different columns of A.\nIndeed\, if x is the vertical column vector
  with components\n(a_1\,...\,a_n)\, then Ax is the linear combination of
  the columns of A\nwith coefficients equal to the a_i.  We call this sub
 space CS(A)\;\nit's the column span of A.  The dimension of this space i
 s called the\nrank of A.\n\nAnalogously\, we let RS(A)\, the row span of
  A\, be the span of the m\ndifferent rows of A.  It's a subspace of R^n.
   A big theorem\, which\nwe can't prove until later this week\, is that 
 CS(A) and RS(A) have\nthe same dimension!  For example\, consider a matr
 ix with 2 non-\nproportional rows and 88 columns.  The row rank (i.e.\, 
 dimension of RS\n(A)) is clearly 2.  It follows that the column span is 
 also of\ndimension 2.  Better\, take A to have three rows (and 88 column
 s)\,\nwith the first two rows non-proportional and the third row equal t
 o\nthe sum of the first two.  The row rank is 2.  The space CS(A) is a\n
 subspace of R^3\, and we know immediately that this subspace is of\ndime
 nsion 2.  Note that RS(A) = CS(A^t)\, where the \"t\" means\n\"transpose
 \".  This is obvious from the definition of tranpose\; it\ndoesn't have 
 any real content.\n\nBy the way\, it's useful to note that if V has dime
 nsion m and is W is\na subspace of V\, then W is a finite-dimensional ve
 ctor space with\ndimension at most that of V.  For the proof\, note that
  any set of m+1\nvectors of W is linearly independent (because it's line
 arly\nindependent when viewed inside V).  Take a finite set of linearly\
 nindependent vectors of W with maximum size\; call the size d and note\n
 d \\le m.  Then this set is a *basis* of W.  As we saw on Friday\, if\ni
 t didn't span W\, we could take a vector outside the span and get a\nlin
 early independent subset of W with d+1 vectors.\n\nTheorem: if B and A a
 re row equivalent\, then RS(A)=RS(B).\nRow equivalence means that we can
  get from A to B (and vice versa)\nwith a sequence of elementary row ope
 rations.  It suffices to take B\n= EA\, where E is an elementary matrix\
 , in proving this theorem.  We\nconsider the three different row operati
 ons and see in each case that\nthey don't change RS(A) when we do the op
 erations to A!\n\nSuppose now that A is given and that B is the row eche
 lon form of A.\nThere are m rows in B\, but some of them are identically
  0.  The\nothers have pivots.  Proposition: CS(B) has the non-zero rows 
 of B as\na basis.  This is pretty clear because if we have a linear\ncom
 bination of the non-zero rows that's equal to 0\, we can show that\neach
  coefficient is 0 (in turn) by looking at the pivots.\n\nAnalogous state
 ment: if A and B are row equivalent\, then NS(A) = NS\n(B)\; the two nul
 l spaces are equal.  Indeed\, we have B = CA\, where C\nis invertible.  
 It's clear that Bx = C(Ax) is 0 if and only if Ax is 0.\n\nNumerically\,
  we see that row equivalent matrices have equal\n\"nullity\" (the dimens
 ion of the null space) and row rank.\n\nIf B is in row echelon form\, th
 en the dimension of NS(B) is clearly\nthe number of \"free variables\". 
  This is the number of columns less\nthe number of pivots\; it's the num
 ber of columns that have no\npivots.  Hence the nullity of B is n - r(B)
 \, where \"r\" stands for\n\"row rank\".  Because the row rank and nulli
 ty are the same for A and\nB (when B is the row echelon form of A)\, we 
 get a great formula:\n\n    n = row rank of A + nullity of A\n\nwhen A i
 s an m x n matrix.\n\nTo complete this picture\, we have to prove (on We
 dnesday\, I imagine)\nthat the row and column ranks of A are equal.  In 
 other words\, RS(A)\nand CS(A) have equal dimension.  One is a subspace 
 of R^n and the\nother of R^m.  There is maybe no direct way to compare t
 he subspaces\,\nbut they are equal in a numerical sense.  We prove this 
 theorem in\nMath 110.  As I have told my Math 110 students\, the equalit
 y of row\nand column ranks is a hard enough statement that most math gra
 duate\nstudents and working mathematicians would have great difficulty\n
 coming up with a coherent proof if they were put on the spot to\npresent
  one.\n\nTo prove that RS(A) and CS(A) have equal dimension\, we prove t
 wo\nthings.  The first is that CS(A) and CS(B) have equal dimension\n(wh
 ere B is the row echelon form of A once again).  The second is\nthat CS(
 B) and RS(B) have equal dimension (namely\, the number of\npivots).\n\nF
 or the first assertion\, all that matters is that B and A are row\nequiv
 alent\, so that B = CA\, where C is an invertible square matrix of\nsize
  m.  The column span of B consists of all vectors C(v)\, where V\nis in 
 the column span of A.  If v_1\,...\,v_r is a basis of the column\nspan o
 f A\, then C(v_1)\,...\,C(v_r) span the column span of B and can\nalso b
 e seen to be linearly independent.  (We'll do all this on the\nboard.)  
 Hence the column spans of A and B have bases with the same\nnumber of el
 ements.  Thus their dimensions are equal.\n\nNow let's look at a B in ro
 w echelon form.  There are n columns\,\nwhere each column is a vector of
  size m.  However\, if d is the number\nof pivots\, d is the number of n
 on-zero rows.  In the columns\, the\nlast m-d entries are all 0.  Hence\
 , morally\, the columns have length\nd\; they just have some trash of le
 ngth m-d at the end.  We can think\nof the columns as being elements of 
 R^d.  If you want to say the\nthing exactly\, you should say that the co
 lumns are elements of the\nspace of those elements of R^m that are 0 out
 side the first d\nentries.  Because this space clearly has dimension d\,
  the column rank\nof B is at most d.  (A subspace of R^d has dimension n
 o bigger than d\nas we saw above.)  To prove that the column rank is exa
 ctly d\, it\nsuffices to find d linearly independent columns.  For this\
 , we select\nthe columns with pivots.  They are obviously linearly indep
 endent by\nthe same argument that is used to prove that the non-zero row
 s are\nlinearly independent.
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URL;VALUE=URI:http://www.kpfa.org/archives/index.php?arch=10447
CREATED:20081120T045031Z
RECURRENCE-ID;TZID=US/Pacific:20051003T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:35
DESCRIPTION:Inner products.  HW from section 4.2: 1\, 3\, 6\, 9\, 17\, 2
 1\, 25\, 31\, 32\, 33
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DTSTART;TZID=US/Pacific:20051010T141000
DTSTAMP:20051009T143500Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051010T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051010T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:29
DESCRIPTION:Section 3.2: n-dimensional Euclidean space.  Homework from t
 his section: 7\,9\,11\,15\,19\,20\,21\,25\,29\, 36\,37.  In the lecture 
 on Friday\, I started talking about general vector spaces (section 3.3).
   This is enormously important material.  You need to work with examples
  in order to come to grips with the definition.  It's important to see w
 hy the examples are really examples and also to see to what extent the e
 xamples can be perturbed a bit and still be examples of vector spaces.  
 Vector spaces abound\, but not everything that you stumble over is a vec
 tor space. 
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DTSTART;TZID=US/Pacific:20050916T141000
DTSTAMP:20050917T142901Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20050916T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20050916T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:55
DESCRIPTION:We move to chapter 10 of B-D.  Today's material will come fr
 om section 10.1.  Homework from this secion: 1\, 3\, 7\, 9\, 15\, 17\, 1
 9\n\nThere will be a DC lunch on Tuesday.  I'm looking for people to tel
 l me which DC to go to.\n\nWe will be doing course evaluations on Wednes
 day\, November 30.  I want everyone to come!!!\n\nMy Thursday office hou
 r will be 11 to 12:30 (same as Monday's office hours) because I have an 
 appointment earlier in the morning.
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DTSTART;TZID=US/Pacific:20051128T141000
DTSTAMP:20051127T223027Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051128T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051128T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:23
DESCRIPTION:We will continue with section 1.4 of Hill and talk about ele
 mentary matrices and invertibility.  This is important and hard material
 \, so be sure to read the section before class.\n\nHW section 1.4: 9\,11
 \,13\,17\,21\,25\,27\, 29\,35\,37\,39\,41
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DTSTART;TZID=US/Pacific:20050909T141000
DTSTAMP:20050908T151305Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20050909T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20050909T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:49
DESCRIPTION:Section 4.1 of B-D.  Homework from section 4.1: 7\, 9\, 11\,
  13\, 15\, 18\, 19.  This lecture is about nth order linear differential
  equations\, and it gives some general theorems about the existence and 
 uniqueness of solutions.  You'll now see Wronskians that are determinant
 s of n x n matrices.  The simplest case is that of homogenous equations 
 with constant coefficients.  These are treated in some detail in section
  4.2\, which we do not cover in Math 54.  (It might be covered some in M
 ath 1B.)  Instead\, we will jump to systems of first order equations in 
 which there are several functions of t and several differential equation
 s that constrain them.
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DTSTART;TZID=US/Pacific:20051109T141000
DTSTAMP:20051108T032633Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051109T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051109T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:30
DESCRIPTION:Subspaces\, span\, null spaces.  The problems from section 3
 .4 are as follows: 1\, 5\, 11\, 17\, 19\, 25\, 31\, 33\, 39\, 43.
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DTSTART;TZID=US/Pacific:20050921T141000
DTSTAMP:20050917T143117Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20050921T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20050921T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:51
DESCRIPTION:Section 7.5 of B-D.  Problems 1\, 3\, 9\, 11\, 17\, 25\, 27\
 , 29.  I may start discussing some of the material from Section 7.6 as w
 ell.  I hope to show you some direction fields from http://www.scottsarr
 a.org/applets/dirField2/dirField2.html.
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051116T141000
DTSTAMP:20051116T135111Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051116T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051116T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:56
DESCRIPTION:Section 10.3 of B-D: the Fourier convengence theorem.  Probl
 ems from 10.3: 1\, 3\, 5\, 7(a)\, 9(a)\, 11(a)\, 17.  I will actually di
 scuss little of the Fourier convergence theorem and instead do another e
 xample or two.  Section 10.4 seems to add little scientific content to w
 hat I've said in class already.  If things go well\, we may be finished 
 with 10.5 by Monday or Wednesday or next week\, which means that there w
 ill be time for a review and for answering questions.
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051202T141000
DTSTAMP:20051202T144444Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051202T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051202T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:26
DESCRIPTION:Lecture on section 3.1 and maybe some of section 3.2.  Homew
 ork: section 3.1: 7\, 9\, 11\, 20\, 22\, 30\, 37\, 39\, 43\, 49
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20050914T141000
DTSTAMP:20050912T025013Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20050914T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20050914T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:50
DESCRIPTION:Section 7.1 of B-D.  Homework from this section: 1\, 2\, 3\,
  5\, 6\, 7(a)\, 15\, 16.  As you probably noticed\, I went pretty fast d
 uring Monday's lecture and discussed a bunch of material in section 7.5.
   That's because the theoretical theorem in 7.1 is sort of boring and no
 t something that I thought that you'd want to hear about in a lecture.  
 I'll do more examples of section 7.5-type stuff on Wednesday.
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051114T141000
DTSTAMP:20051115T231611Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051114T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051114T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:54
DESCRIPTION:Section 7.8 of B-D.  Problems 1\, 3\, 5\, 7\, 9\, 15 from th
 at section.  In the lecture\, I discussed the equation X'=AX when A has 
 repeated eigenvalues.  Take the case where A is a 2x2 matrix\, and suppo
 se that its characteristic polynomial is the square of t-lambda.  If A i
 s diagonalizable\, it is already diagonal: it's simply lambda times the 
 2 x 2 identify matrix I.  Suppose that this is not the case.  Then the e
 igenspace for A corresponding to the eigenvalue lambda is 1-dimensional.
   Let v be a generator of this space.  In other words\, v is the unique 
 eigenvector of A\, up to multiplication by a constant.\n\nIn the lecture
 \, I explained why there is a vector w such that Aw = v.  My explanation
  involved the Cayley-Hamilton theorem\, a general theorem from Math 110 
 that is easily verified by hand for 2 x 2 matrices.  The vector w is not
  unique\; indeed\, we can always replace w by w + av\, where a is any sc
 alar.  Fix w (and keep v fixed as well).\n\nTwo fundamental solutions to
  X'=AX are X = exp(lambda.t)v\, which is familiar to us\, and the relati
 vely unfamiliar exp(lambda.t)(w+lambda.v).  I hope that I have the secon
 d one right -- and I think that I do -- but I couldn't remember it in le
 cture without looking at my notes.  I explained how to derive these two 
 solutions from the guiding idea that exp(At) is the golden matrix that g
 ives n fundamental solutions in one stroke when we have an n x n matrix.
   I also checked that both alleged solutions really are solutions.\n\nIf
  you missed the lecture\, you missed an important lecture.  It may not h
 ave been my best lecture\, but it probably wasn't bad.  It had informati
 on and a good example.\n\nHappy Thanksgiving to all!
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051123T141000
DTSTAMP:20051124T040559Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051123T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051123T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:58
DESCRIPTION:We finish up section 10.5 of B-D\, have a 10-minute review o
 f the whole semester\, and lay plans to meet again on the evening of Dec
 ember 17.  Wasn't this a great course?\n\nI want you to know that I've e
 njoyed Math 54 [so far\, at least -- I'm writing this note on October 15
 ].  You guys are great.  I hope our paths cross again in an upper-divisi
 on course.\n\nThe final exercises for 10.5 are 9\, 10\, 11\, 21
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051209T141000
DTSTAMP:20051202T144309Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051209T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051209T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:42
DESCRIPTION:Diagonalization.  I'm going to be speaking about section 5.3
 .  The homework problems from this section are 1\, 3\, 5\, 7\, 11\, 13\,
  17\, 19\, 21 (in connection with today's lecture) and 27\, 28\, 29\, 31
 \, 32\, 33 (in connection with Friday's).  The material in section 5.3 i
 s the last that midterm #2 will cover.
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051026T141000
DTSTAMP:20051026T024741Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051026T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051026T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:58
DESCRIPTION:Section 10.5 of B-D\; exercises 1\, 2\, 3\, 5\, 7\, 8.  As y
 ou know from Monday's lecture\, we have already gotten into section 10.5
 .  I will explain the essential ideas today and then will start a \"revi
 ew\" phase.  If you have some good Math 54 questions\, bring them to lec
 ture even today.  Perhaps I can collect a few for discussion on Friday i
 f I don't discuss all questions today.
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051207T141000
DTSTAMP:20051207T133038Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051207T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051207T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:42
DESCRIPTION:More on eigenvalues and eigenvectors.  Also\, something abou
 t diagonalization.  Homework for this lecture is again from section 5.2:
  23\, 24\, 25\, 28\, 29\, 31\, 33\, 35.\n\nNow here's the plan: Grace\, 
 who took over the lecture briefly on October 3\, would like to come back
  and lecture to you again.  (If you fall off a horse\, get right back on
 .)  She will talk about aspects of diagonalization (section 5.3) on Wedn
 esday\, October 26.\n\nOne of the key facts about diagonalization is tha
 t eigenvectors that are associated to distinct eigenvalues are linearly 
 independent.  The proof of the theorem (p. 349 of the book) is marked \"
 OPTIONAL\".  I plan to explain that proof on Monday (i.e.\, today\, from
  the point of view of the calendar)\, so please read the proof in advanc
 e and be prepared to listen carefully.\n\nI will also do some examples l
 ike those beginning around page 336.  The task has the following form: \
 "Find bases for the eigenspaces of the matrix A=....\"  You basically kn
 ow how to do this already because you know how to solve systems of linea
 r equations.
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051024T141000
DTSTAMP:20051022T223533Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051024T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051024T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:47
DESCRIPTION:Section 3.3 of B-D\; homework problems 3\, 5\, 7\, 11\, 13\,
  15\, 17\, 18\, 19.  Note that there is an MUSA lunch on Tuesday and an 
 off-campus Math 54 lunch on Wednesday (see calendar).  This particular l
 ecture wasn't especially good.  Maybe Wednesday's will be better!
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051107T141000
DTSTAMP:20051108T032127Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051107T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051107T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:19
DESCRIPTION:Covers everything through the lecture of September 23 (i.e.\
 , the first four weeks of this class).  Reminder: you can bring in one s
 tandard-sized sheet of notes\, written on both sides of the page.  No ca
 lculators or other electronic devices are permitted.  You do not need bl
 ue books: write directly on the exam.
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20050928T141000
DTSTAMP:20050925T225352Z
SUMMARY:Math 54 Midterm
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20050928T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20050930T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:31
DESCRIPTION:Section 3.5: linear independence\, problems 1\, 5\, 11\, 17\
 , 19\, 29\, 31\, 33
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20050923T141000
DTSTAMP:20050922T130149Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20050923T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20050923T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:55
DESCRIPTION:Section 10.2 of B-D.  This is our first lecture on Fourier s
 eries.  Problems from 10.2: 1\, 3\, 13\, 14\, 15\, 16\, 17\, 18\n\nWe wi
 ll be doing course evaluations today.  Please: make sure not to miss the
  lecture!  Tell your friends.
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051130T141000
DTSTAMP:20051127T223518Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051130T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051130T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:47
DESCRIPTION:We'll start the material from Boyce-DiPrima on this date.  M
 ath 49 students: you should definitely come to this lecture\, and I'd ad
 vise you to go to section on November 3.  There are now 14 lectures left
  in the class\, including today's.  Every class session counts.  That me
 ans\, in particular\, that I will be lecturing on new material on Novemb
 er 23 (sorry).\n\nToday's lecture will be on sections 3.1 and 3.2 of BD.
   Homework as follows: section 3.1\, 1\, 7\, 11 and section 3.2\, 1\, 3\
 , 13\, 14\, 19\, 21\, 23.  We go fast here because some material is revi
 ew from Math 1B. 
UID:6C90011E-6695-400B-AF1D-DE64571E5C85
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051104T141000
DTSTAMP:20051031T152817Z
SUMMARY:Math 54 Lecture
CREATED:20081120T045031Z
DTEND;TZID=US/Pacific:20051104T150000
LOCATION:155 Dwinelle
RECURRENCE-ID;TZID=US/Pacific:20051104T141000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:4
TRANSP:OPAQUE
UID:9F2AFA5A-F13D-4A38-9CED-F925C8C8B758
DTSTART;TZID=US/Pacific:20070417T124000
DTSTAMP:20070314T230555Z
SUMMARY:Foothill DC lunch
CREATED:20081120T045035Z
DTEND;TZID=US/Pacific:20070417T134000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:14
TRANSP:OPAQUE
UID:7CE75C45-CF85-4F8A-B065-2E2DA7652A4B
DTSTART;TZID=US/Pacific:20050901T100000
DTSTAMP:20051121T174958Z
SUMMARY:K. Ribet office hour
EXDATE;TZID=US/Pacific:20051124T100000
CREATED:20081120T045034Z
DTEND;TZID=US/Pacific:20050901T113000
LOCATION:885 Evans
RRULE:FREQ=WEEKLY;INTERVAL=1;UNTIL=20051210T075959Z
END:VEVENT
BEGIN:VEVENT
SEQUENCE:12
TRANSP:OPAQUE
UID:7CE75C45-CF85-4F8A-B065-2E2DA7652A4B
DTSTART;TZID=US/Pacific:20051104T100000
DTSTAMP:20051013T005839Z
SUMMARY:K. Ribet office hour
CREATED:20081120T045034Z
DTEND;TZID=US/Pacific:20051104T113000
LOCATION:885 Evans
RECURRENCE-ID;TZID=US/Pacific:20051103T100000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:15
TRANSP:OPAQUE
UID:7CE75C45-CF85-4F8A-B065-2E2DA7652A4B
DTSTART;TZID=US/Pacific:20051201T110000
DTSTAMP:20051124T040702Z
SUMMARY:K. Ribet office hour
CREATED:20081120T045034Z
DTEND;TZID=US/Pacific:20051201T123000
LOCATION:885 Evans
RECURRENCE-ID;TZID=US/Pacific:20051201T100000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:14
TRANSP:OPAQUE
UID:7CE75C45-CF85-4F8A-B065-2E2DA7652A4B
DTSTART;TZID=US/Pacific:20051028T110000
DTSTAMP:20051012T035623Z
SUMMARY:K. Ribet office hour
CREATED:20081120T045034Z
DTEND;TZID=US/Pacific:20051028T123000
LOCATION:885 Evans
RECURRENCE-ID;TZID=US/Pacific:20051027T100000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:1
DESCRIPTION:Come to Clark Kerr campus and have lunch with the professor.
 
UID:0C45635A-16A7-4B26-B6FF-009D95CD3FEE
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051005T121500
DTSTAMP:20051005T235600Z
SUMMARY:Math 54 lunch
CREATED:20081120T045019Z
DTEND;TZID=US/Pacific:20051005T131500
LOCATION:Clark Kerr DC
END:VEVENT
BEGIN:VEVENT
SEQUENCE:9
TRANSP:OPAQUE
UID:D6804CC8-86EB-4F3E-929F-FE322A232363
DTSTART;TZID=US/Pacific:20070126T103000
DTSTAMP:20070123T022336Z
SUMMARY:Ken Ribet office hour
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20070126T120000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:12
DESCRIPTION:Lunch at Crossroads today
UID:4D231A3C-EF38-4A3D-8A32-18BF7E9FB36B
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051019T120000
DTSTAMP:20051015T233400Z
SUMMARY:Math 54 Crossroads lunch
CREATED:20081120T045030Z
DTEND;TZID=US/Pacific:20051019T130000
LOCATION:Crossroads DC
END:VEVENT
BEGIN:VEVENT
SEQUENCE:1
TRANSP:OPAQUE
UID:0493F844-26E7-431E-8BD7-D3292F2FE32A
DTSTART;TZID=US/Pacific:20070510T140000
DTSTAMP:20070510T224441Z
SUMMARY:Math 54 office hour
CREATED:20081120T045019Z
DTEND;TZID=US/Pacific:20070510T153000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:22
DESCRIPTION:I have office hours on Monday until 12:30.  I will try to dr
 ag students over to Foothill after the office hour.  Please join us if y
 ou can.  Note that I will be back at Foothill the next day (Tuesday) at 
 11:45.
UID:2D5E138B-8903-496F-ABAA-E4E6FA0052F8
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051010T124500
DTSTAMP:20051009T143200Z
SUMMARY:Math 54 lunch
CREATED:20081120T045030Z
DTEND;TZID=US/Pacific:20051010T134500
LOCATION:Foothill DC
END:VEVENT
BEGIN:VEVENT
SEQUENCE:4
TRANSP:OPAQUE
UID:D6B9B74E-0676-4BCE-B745-AF50470B4415
DTSTART;TZID=US/Pacific:20070319T123000
DTSTAMP:20070313T211351Z
SUMMARY:Clark Kerr DC Math 54 lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20070319T133000
LOCATION:Crossroads DC
END:VEVENT
BEGIN:VEVENT
SEQUENCE:4
TRANSP:OPAQUE
UID:4F434E37-BB0F-41E0-B15A-F2F3C558C528
DTSTART;TZID=US/Pacific:20070426T124000
DTSTAMP:20070424T221209Z
SUMMARY:Math 54 Crossroads DC lunch
CREATED:20081120T045030Z
DTEND;TZID=US/Pacific:20070426T134000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:19
TRANSP:OPAQUE
UID:7064C817-FCDC-46D4-A8BF-D724DD8B820E
DTSTART;TZID=US/Pacific:20051215T114500
DTSTAMP:20051215T043312Z
SUMMARY:Foothill DC lunch
CREATED:20081120T045033Z
DTEND;TZID=US/Pacific:20051215T124500
END:VEVENT
BEGIN:VEVENT
SEQUENCE:13
DESCRIPTION:This will be my first DC lunch in many days.  Hoping for a b
 ig turnout!
UID:A3156B0D-B2E3-4C98-B86C-B466D0ED3A97
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070227T124000
DTSTAMP:20070214T222711Z
SUMMARY:Café 3 Math 54 DC lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20070227T134000
LOCATION:Unit 3
END:VEVENT
BEGIN:VEVENT
SEQUENCE:7
DESCRIPTION:Please join us on Friday at 12:30.  Don't be shy about comin
 g!
UID:ACD515CD-9F64-4AF3-B959-5F4EE6D62721
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20050930T123000
DTSTAMP:20050930T040740Z
SUMMARY:Crossroads lunch
CREATED:20081120T045036Z
DTEND;TZID=US/Pacific:20050930T133000
LOCATION:Crossroads DC
END:VEVENT
BEGIN:VEVENT
SEQUENCE:13
TRANSP:OPAQUE
UID:866CF66E-29F1-45F8-BC07-8212CBE47668
DTSTART;TZID=US/Pacific:20070205T144500
DTSTAMP:20070425T124201Z
SUMMARY:Ken Ribet office hour
EXDATE;TZID=US/Pacific:20070430T144500
EXDATE;TZID=US/Pacific:20070219T144500
EXDATE;TZID=US/Pacific:20070326T144500
CREATED:20081120T045035Z
DTEND;TZID=US/Pacific:20070205T161500
RRULE:FREQ=WEEKLY;INTERVAL=1;UNTIL=20070511T065959Z
END:VEVENT
BEGIN:VEVENT
SEQUENCE:14
DESCRIPTION:Note change of time and duration!!
UID:866CF66E-29F1-45F8-BC07-8212CBE47668
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20070416T164000
DTSTAMP:20070416T151527Z
SUMMARY:Ken Ribet office hour
CREATED:20081120T045035Z
DTEND;TZID=US/Pacific:20070416T180000
RECURRENCE-ID;TZID=US/Pacific:20070416T144500
END:VEVENT
BEGIN:VEVENT
SEQUENCE:10
DESCRIPTION:Clark Kerr is a classy complex with a great DC.
UID:8F80E32F-311A-415C-8B96-760AA42CFB34
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20051024T125000
DTSTAMP:20051022T001241Z
SUMMARY:Math 54 Clark Kerr lunch
CREATED:20081120T045035Z
DTEND;TZID=US/Pacific:20051024T135000
LOCATION:Unit 3 DC
END:VEVENT
BEGIN:VEVENT
SEQUENCE:9
TRANSP:OPAQUE
UID:AF0CCE5B-086A-4317-A895-A2CE6E442B33
DTSTART;VALUE=DATE:20050830
DTSTAMP:20050816T163806Z
SUMMARY:Math 54 Discussion Sections
EXDATE;VALUE=DATE:20051124
CREATED:20081120T045036Z
DTEND;VALUE=DATE:20050831
RRULE:FREQ=WEEKLY;INTERVAL=1;UNTIL=20051209;BYDAY=TU,TH;WKST=SU
END:VEVENT
BEGIN:VEVENT
SEQUENCE:14
TRANSP:OPAQUE
UID:0E380AA9-2A75-4A2F-89E3-005031577065
DTSTART;TZID=US/Pacific:20070201T135000
DTSTAMP:20070425T124207Z
SUMMARY:Ken Ribet office hour
EXDATE;TZID=US/Pacific:20070503T135000
EXDATE;TZID=US/Pacific:20070215T135000
EXDATE;TZID=US/Pacific:20070301T135000
EXDATE;TZID=US/Pacific:20070329T135000
CREATED:20081120T045019Z
DTEND;TZID=US/Pacific:20070201T152000
RRULE:FREQ=WEEKLY;INTERVAL=1;UNTIL=20070509T065959Z
END:VEVENT
BEGIN:VEVENT
SEQUENCE:13
TRANSP:OPAQUE
UID:0E380AA9-2A75-4A2F-89E3-005031577065
DTSTART;TZID=US/Pacific:20070223T135000
DTSTAMP:20070216T004758Z
SUMMARY:Ken Ribet office hour
CREATED:20081120T045019Z
DTEND;TZID=US/Pacific:20070223T152000
RECURRENCE-ID;TZID=US/Pacific:20070222T135000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:3
TRANSP:OPAQUE
UID:0EFEBF96-A579-4D77-97EC-BD3CB89C1CAF
DTSTART;VALUE=DATE:20070216
DTSTAMP:20070119T170638Z
SUMMARY:Last day for students to drop classes.
CREATED:20081120T045021Z
DTEND;VALUE=DATE:20070217
END:VEVENT
BEGIN:VEVENT
SEQUENCE:6
DESCRIPTION:I've had three lunches with students so far this semester.  
 We can do more!  I've enjoyed meeting the students who have come and hop
 e to meet many more of you.
UID:4386875B-8836-48C2-BC34-EBF5E8BBFF86
TRANSP:OPAQUE
DTSTART;TZID=US/Pacific:20050926T124000
DTSTAMP:20050923T005049Z
SUMMARY:Foothill lunch
CREATED:20081120T045030Z
DTEND;TZID=US/Pacific:20050926T134000
LOCATION:Foothill DC
END:VEVENT
BEGIN:VEVENT
SEQUENCE:3
TRANSP:OPAQUE
UID:4025F69A-09DB-4D25-B6B1-9A9B371D246B
DTSTART;TZID=US/Pacific:20051207T130000
DTSTAMP:20051201T011821Z
SUMMARY:Crossroads DC lunch
CREATED:20081120T045030Z
DTEND;TZID=US/Pacific:20051207T140000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:8
TRANSP:OPAQUE
UID:77A6406C-4F74-480A-84F8-10011794905F
DTSTART;TZID=US/Pacific:20070130T124000
DTSTAMP:20070128T164712Z
SUMMARY:Math 54 Foothill DC lunch
CREATED:20081120T045034Z
DTEND;TZID=US/Pacific:20070130T134000
END:VEVENT
BEGIN:VEVENT
SEQUENCE:7
TRANSP:OPAQUE
UID:2F591655-FF88-4C90-B66E-9C0EC66C35D5
DTSTART;TZID=US/Pacific:20070117T110000
DTSTAMP:20070115T223432Z
SUMMARY:Office hour
CREATED:20081120T045030Z
DTEND;TZID=US/Pacific:20070117T123000
END:VEVENT
END:VCALENDAR