<?php
 $db = array (
  '0405-1300_P5120147.jpg' => 
  array (
    'db_updated' => 1274053425,
    'comment' => 'Previous year\'s sylabus.',
  ),
  '0405-1300_P5120148.jpg' => 
  array (
    'db_updated' => 1274053425,
    'comment' => 'About This Class.',
  ),
  '0405-1300_P5120149.jpg' => 
  array (
    'db_updated' => 1274053425,
    'comment' => 'Math 131 Spring 1993 Reality.',
  ),
  '0405-1300_P5120150.jpg' => 
  array (
    'db_updated' => 1274053425,
    'comment' => '2004 Sep 9: Welcome, Brouwer, Functor.',
  ),
  '0405-1300_P5120151.jpg' => 
  array (
    'db_updated' => 1274053425,
    'comment' => '2004 Sep 14, 16.',
  ),
  '0405-1300_P5120152.jpg' => 
  array (
    'db_updated' => 1274053554,
    'comment' => '2004 Sep 21: Hausdorff, closure, products, metric spaces.',
  ),
  '0405-1300_P5120153.jpg' => 
  array (
    'db_updated' => 1274053691,
    'comment' => 'HW1.',
  ),
  '0405-1300_P5120154.jpg' => 
  array (
    'db_updated' => 1274053691,
    'comment' => '2004 Sep 28: Agenda.',
  ),
  '0405-1300_P5120155.jpg' => 
  array (
    'db_updated' => 1274053691,
    'comment' => '2004 Sep 28: Topologies on product spaces, metric spaces.',
  ),
  '0405-1300_P5120156.jpg' => 
  array (
    'db_updated' => 1274053691,
    'comment' => '2004 Sep 30, Oct 5: Clopen sets, connectedness.',
  ),
  '0405-1300_P5120157.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Oct 7, 12: Compactness, Zorn, AC, Tychonoff, Stone-Cech.',
  ),
  '0405-1300_P5120158.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Oct 14: Lims and ultrafilters.',
  ),
  '0405-1300_P5120159.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '1996 may 2: Completely regular spaces, Stone-Cech.',
  ),
  '0405-1300_P5120160.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '1996 May 5: Cont., Urysohn.',
  ),
  '0405-1300_P5120161.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 October 19: Stone Cech.',
  ),
  '0405-1300_P5120162.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 October 19: Stone Cech (2).',
  ),
  '0405-1300_P5120163.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Oct 21: More on Stone Cech, T4 and Urysohn.',
  ),
  '0405-1300_P5120164.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Oct 26: Urysohn and Tietze, compactness in metric spaces.',
  ),
  '0405-1300_P5120165.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '1993 April 21: Coverings, the fundamental group of the circle.',
  ),
  '0405-1300_P5120166.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Nov 1: Compactness in metric spaces.',
  ),
  '0405-1300_P5120167.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Nov 1,2: Baire spaces, nowhere diffable functions.',
  ),
  '0405-1300_P5120168.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Nov 4: Baire spaces, locally-compact spaces, the fundamental group.',
  ),
  '0405-1300_P5120169.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Nov 9: Coverings, the fundamental group of the circle.',
  ),
  '0405-1300_P5120170.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Nov 11, 16: Soft properies of pi_1.',
  ),
  '0405-1300_P5120171.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'Term Exam 1.',
  ),
  '0405-1300_P5120172.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'Term Exam 1 (2).',
  ),
  '0405-1300_P5120173.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Nov 18: Homotopy theory lite.',
  ),
  '0405-1300_P5120174.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Nov 23: Homotopy theory lite.',
  ),
  '0405-1300_P5120175.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Nov 25, 30: Borsuk-Ulam, Van-Kampen.',
  ),
  '0405-1300_P5120176.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Dec 2: Van-Kampen',
  ),
  '0405-1300_P5120177.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2004 Dec 7: Van-Kampen.',
  ),
  '0405-1300_P5120178.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'Hatcher\'s page 58.',
  ),
  '0405-1300_P5120179.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'Covering Spaces in One Swoosh.',
  ),
  '0405-1300_P5120180.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'Covering Spaces in One Swoosh (2).',
  ),
  '0405-1300_P5120181.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'Covering Spaces in One Swoosh (3).',
  ),
  '0405-1300_P5120182.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'Errata to Munkres\' Book.',
  ),
  '0405-1300_P5120183.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Jan 4: Hatcher\'s page 58 and Covering Spaces in One Swoosh.',
  ),
  '0405-1300_P5120184.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2002 HW 3.',
  ),
  '0405-1300_P5120185.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2002 HW 4.',
  ),
  '0405-1300_P5120186.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2002 HW 5.',
  ),
  '0405-1300_P5120187.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2002 HW 6.',
  ),
  '0405-1300_P5120188.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Jan 6: Covering Spaces in One Swoosh.',
  ),
  '0405-1300_P5120189.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Jan 11: Covering Spaces in One Swoosh.',
  ),
  '0405-1300_P5120190.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Jan 13: The universal cover.',
  ),
  '0405-1300_P5120191.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Jan 18, 20: End of coverings and beginning of homology.',
  ),
  '0405-1300_P5120192.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Jan 25: The very basic of homology, invariance under homotopy.',
  ),
  '0405-1300_P5120193.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Jan 27: Homotopy, the long exact sequence of a quotient.',
  ),
  '0405-1300_P5120194.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Feb 1: Short and long exact sequences.',
  ),
  '0405-1300_P5120195.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2002 May 23: ... excision.',
  ),
  '0405-1300_P5120196.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'Formulas for the barycentric subdivision.',
  ),
  '0405-1300_P5120197.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Feb 3: ... excision.',
  ),
  '0405-1300_P5120198.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2002 May 28: Excision, simplicial spaces.',
  ),
  '0405-1300_P5120199.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2002 May 28: the barycentric subdivision.',
  ),
  '0405-1300_P5120200.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Feb 8: Excision.',
  ),
  '0405-1300_P5120201.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Feb 10: Khovanov homology.',
  ),
  '0405-1300_P5120202.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'The barycentric subdivision.',
  ),
  '0405-1300_P5120203.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Feb 22: simplicial spaces, geometric realization, simplicial homology.',
  ),
  '0405-1300_P5120204.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Feb 22: simplicial spaces, geometric realization, simplicial homology (2).',
  ),
  '0405-1300_P5120205.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Feb 24: cont.',
  ),
  '0405-1300_P5120206.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'About this class.',
  ),
  '0405-1300_P5120207.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Comp sylabus.',
  ),
  '0405-1300_P5120208.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 March 1: Degrees.',
  ),
  '0405-1300_P5120209.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 March 3: More on degrees.',
  ),
  '0405-1300_P5120210.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 March 8: Local formulas for degrees, linking numbers.',
  ),
  '0405-1300_P5120211.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 March 10, 15: H(RP^n).',
  ),
  '0405-1300_P5120212.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 March 17, 22, 24: Mayer-Vietoris, R^n theorems.',
  ),
  '0405-1300_P5120213.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 March 8: Term Exam 2.',
  ),
  '0405-1300_P5120214.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 March 8: Term Exam 2 (2).',
  ),
  '0405-1300_P5120215.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 Sketch of the last two weeks.',
  ),
  '0405-1300_P5120216.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'H(Sigma_2).',
  ),
  '0405-1300_P5120217.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 March 29: Cohomology.',
  ),
  '0405-1300_P5120218.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 March 31, April 5: Misc.',
  ),
  '0405-1300_P5120219.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 A Cup Product Example.',
  ),
  '0405-1300_P5120220.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'Genus 2 by Mister Bailey, HW12.',
  ),
  '0405-1300_P5120221.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => '2005 A Cup Product Example, enlarged.',
  ),
  '0405-1300_P5120222.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'Genus2Bailey.',
  ),
  '0405-1300_P5120223.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'The Final Exam.',
  ),
  '0405-1300_P5120224.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'The Final Exam (2).',
  ),
  '0405-1300_P5120225.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'The Final Exam (3).',
  ),
  '0405-1300_P5120226.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'A Sample Final Exam.',
  ),
  '0405-1300_P5120227.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'A Sample Final Exam (2).',
  ),
  '0405-1300_P5120228.jpg' => 
  array (
    'db_updated' => 1274142896,
    'comment' => 'A Sample Final Exam (3).',
  ),
  '0708-1300_P5060001.jpg' => 
  array (
    'db_updated' => 1274052623,
    'comment' => '2000 Oct 29: Course intro, the implicit function theorem.',
  ),
  '0708-1300_P5060004.jpg' => 
  array (
    'db_updated' => 1273340569,
    'comment' => '2000 Oct 29: Course intro, the implicit function theorem (2).',
  ),
  '0708-1300_P5060005.jpg' => 
  array (
    'db_updated' => 1273340569,
    'comment' => '2007 Sep 11: Course intro, differentials.',
  ),
  '0708-1300_P5060006.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 Sep 11: Course intro, differentials (2).',
  ),
  '0708-1300_P5060007.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 Sep 13: The implicit function theorem.',
  ),
  '0708-1300_P5060008.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 Sep 13: The implicit function theorem (2).',
  ),
  '0708-1300_P5060009.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2000 October 31: Functional structures, etc.',
  ),
  '0708-1300_P5060010.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2000 November 5: Manifolds.',
  ),
  '0708-1300_P5060011.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 September 18: Inverse and implicit, manifolds.',
  ),
  '0708-1300_P5060012.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 September 18: Inverse and implicit, manifolds (2).',
  ),
  '0708-1300_P5060013.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 September 20: Continuation.',
  ),
  '0708-1300_P5060014.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2000 November 12: Tangent vectors.',
  ),
  '0708-1300_P5060015.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2000 November 12: Tangent vectors, immersions, local structure.',
  ),
  '0708-1300_P5060016.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 September 25: Two definitions of manifolds, tangent vectors.',
  ),
  '0708-1300_P5060017.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 September 27: Tangents, Hadamard\'s lemma.',
  ),
  '0708-1300_P5060018.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2000 November 19: Immersions, submerssions, local structure.',
  ),
  '0708-1300_P5060019.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2000 November 21: Regular points, Sard\'s theorem, transversallity.',
  ),
  '0708-1300_P5060020.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 2: Immersions, submerssions, local structure.',
  ),
  '0708-1300_P5060021.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 2: Immersions, submerssions, local structure (2).',
  ),
  '0708-1300_P5060022.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 4: Local structures, Sard\'s theorem.',
  ),
  '0708-1300_P5060023.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 9: Sard\'s, transversallity.',
  ),
  '0708-1300_P5060024.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 9: Sard\'s, transversallity (2).',
  ),
  '0708-1300_P5060025.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 11: Intro. to Sard, the Cantor Aerogel.',
  ),
  '0708-1300_P5060026.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 11: Intro. to Sard, the Cantor Aerogel (2).',
  ),
  '0708-1300_P5060027.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 11: Intro. to Sard, the Cantor Aerogel (3).',
  ),
  '0708-1300_P5060028.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 11: Intro. to Sard, the Cantor Aerogel (4).',
  ),
  '0708-1300_P5060029.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 11: Intro. to Sard, the Cantor Aerogel (5).',
  ),
  '0708-1300_P5060030.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2000 November 26: More local structure.',
  ),
  '0708-1300_P5060031.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2000 December 3: Whitney\'s theorem.',
  ),
  '0708-1300_P5060032.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2000 November 28: Transversallity, Whitney, partitions of unity.',
  ),
  '0708-1300_P5060033.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 16: Proof of Sard.',
  ),
  '0708-1300_P5060034.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 16: Whitney.',
  ),
  '0708-1300_P5060035.jpg' => 
  array (
    'db_updated' => 1273341642,
    'comment' => '2007 October 18: Whitney, partitions of unity.',
  ),
  '0708-1300_P5060036.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2007 October 18: Whitney, partitions of unity (2).',
  ),
  '0708-1300_P5060037.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => 'Fubini from Guillemin-Pollack, HW3.',
  ),
  '0708-1300_P5060038.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => 'NSERC proposal material.',
  ),
  '0708-1300_P5060039.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2007 October 23: A Peano Curve.',
  ),
  '0708-1300_P5060040.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2007 October 23: A Peano Curve (2).',
  ),
  '0708-1300_P5060041.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2007 October 23, 25: Peano, Whitney, classification of surfaces.',
  ),
  '0708-1300_P5060042.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2007 October 30: Smooth retracts, smooth Brouwer, smooth approximation.',
  ),
  '0708-1300_P5060043.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => 'November 2007: Term Exam 1 planning.',
  ),
  '0708-1300_P5060044.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2007 November 1: Tubular neighborhoods.',
  ),
  '0708-1300_P5060045.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2007 November 1: Proper implies closed.',
  ),
  '0708-1300_P5060046.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => 'HW4.',
  ),
  '0708-1300_P5060047.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => 'On TE1.',
  ),
  '0708-1300_P5060048.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => 'Large Stokes\'.',
  ),
  '0708-1300_P5060049.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2000 December 31: Stokes\', differential forms.',
  ),
  '0708-1300_P5060050.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2001 January 16: Differential forms, R^3, pullbacks.',
  ),
  '0708-1300_P5060051.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2001 January 19: Pullbacks, integration.',
  ),
  '0708-1300_P5060052.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2001 January 21: The three dimensional theorems, Stokes\'.',
  ),
  '0708-1300_P5060053.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => 'November 2007: Term Test.',
  ),
  '0708-1300_P5060054.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => 'November 2007: Term Test (2).',
  ),
  '0708-1300_P5060055.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2007 November 6, 8, 13: Stokes\', contractibility of S^infinity.',
  ),
  '0708-1300_P5060056.jpg' => 
  array (
    'db_updated' => 1273342644,
    'comment' => '2007 November 20, 22: d, integration, orientation, Stokes\'.',
  ),
  '0708-1300_P5060057.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => 'A Planimeter.',
  ),
  '0708-1300_P5060058.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2007 November 27, 29: The planimeter, R^3, Maxwell.',
  ),
  '0708-1300_P5060059.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '1996 November 21: Maxwell.',
  ),
  '0708-1300_P5060060.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2001 January 23: The planimeter.',
  ),
  '0708-1300_P5060061.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => 'Feynman\'s Classical',
  ),
  '0708-1300_P5060062.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => 'Handout: A',
  ),
  '0708-1300_P5060063.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => 'HW6.',
  ),
  '0708-1300_P5060064.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => 'HW6 (2).',
  ),
  '0708-1300_P5060065.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2007 December 6: Homotopy for differential forms.',
  ),
  '0708-1300_P5060066.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2002 March 12: The fundamental group.',
  ),
  '0708-1300_P5060067.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2002 March 14: The lifting property, basic properties of the fundamental group.',
  ),
  '0708-1300_P5060068.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2002 March 19: More properties, Van-Kampen.',
  ),
  '0708-1300_P5060069.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2002 April 11: Covering spaces.',
  ),
  '0708-1300_P5060070.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2004 November 11, 16.',
  ),
  '0708-1300_P5060071.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2004 November 18: Homotopy theory light.',
  ),
  '0708-1300_P5060072.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '1996 June 9: The fundamental group of the circle.',
  ),
  '0708-1300_P5060073.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2005 November 22, 24: Almost all functions are bad, fundamental groups.',
  ),
  '0708-1300_P5060074.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2005 November 29, December 1: The fundamental group, covering spaces.',
  ),
  '0708-1300_P5060075.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2008 January 8: The fundamental group, the circle.',
  ),
  '0708-1300_P5060076.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2008 January 10: The circle, covering spaces.',
  ),
  '0708-1300_P5060077.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2004 November 23: More homotopy theory light.',
  ),
  '0708-1300_P5060078.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2004 November 25, 30: Borsuk-Ulam, Van-Kampen.',
  ),
  '0708-1300_P5060079.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2004: December 2: Van-Kampen.',
  ),
  '0708-1300_P5060080.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2004 December 7: Proof of Van-Kampen.',
  ),
  '0708-1300_P5060081.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2005 December 6: Borsuk-Ulam, topological groups, homotopy light, Van-Kampen.',
  ),
  '0708-1300_P5060082.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2005 December 8: Surfaces, Van-Kampen examples.',
  ),
  '0708-1300_P5060083.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2008 January 15, 17: Liftings in covering spaces, applications, Van-Kampen.',
  ),
  '0708-1300_P5060084.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2008 January 22, 24: Applications and proof of Van-Kampen.',
  ),
  '0708-1300_P5060085.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2006 January 10: Van-Kampen and applications.',
  ),
  '0708-1300_P5060086.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2006 January 12, 17: Applications and proof of Van-Kampen.',
  ),
  '0708-1300_P5060087.jpg' => 
  array (
    'db_updated' => 1273344303,
    'comment' => '2006 January 19: Covering maps.',
  ),
  '0708-1300_P5060088.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2006 January 24: Coverings, the lifting criterion.',
  ),
  '0708-1300_P5060089.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 January 29: Two covering spaces.',
  ),
  '0708-1300_P5060090.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 January 29: 14 covering spaces.',
  ),
  '0708-1300_P5060091.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 January 29: Coverings, the lifting criterion.',
  ),
  '0708-1300_P5060092.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2006 January 26: Classification by the fundamental group, the universal cover.',
  ),
  '0708-1300_P5060093.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2006 February 1: The universal covering space.',
  ),
  '0708-1300_P5060094.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 February 5: The covering space handout.',
  ),
  '0708-1300_P5060095.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 February 5: The covering space handout (2).',
  ),
  '0708-1300_P5060096.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 February 5: The covering space handout (3).',
  ),
  '0708-1300_P5060097.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 February 5: The covering space handout (4).',
  ),
  '0708-1300_P5060098.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 January 31, February 5, 7: Covering spaces.',
  ),
  '0708-1300_P5060099.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2002 May 2: Simplicies and the boundary map.',
  ),
  '0708-1300_P5060100.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2002 May 7: Simplicies, homology, functoriallity.',
  ),
  '0708-1300_P5060101.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2002 May 9: Cont.',
  ),
  '0708-1300_P5060102.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2006 February 2: More on thefundamental theorem of covering spaces.',
  ),
  '0708-1300_P5060103.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2006 February 7, 9, 14: Basic homology',
  ),
  '0708-1300_P5060104.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 February 12: Homology, the Abelianization of homotopy.',
  ),
  '0708-1300_P5060105.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 February 12, 14: Homology, the Abelianization of homotopy (2).',
  ),
  '0708-1300_P5060106.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2007 February 11: Term Exam 2.',
  ),
  '0708-1300_P5060107.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2007 February 11: Term Exam 2 (2).',
  ),
  '0708-1300_P5060108.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2002 May 14: The prizm, short to long exact sequences.',
  ),
  '0708-1300_P5060109.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2005 January 25: Homology, homotopy invariance.',
  ),
  '0708-1300_P5060110.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2005 January 27: The prizm, short to long exact sequences.',
  ),
  '0708-1300_P5060111.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 February 26: A Homology Theory is a Monster.',
  ),
  '0708-1300_P5060112.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 February 26: A Homology Theory is a Monster (2).',
  ),
  '0708-1300_P5060113.jpg' => 
  array (
    'db_updated' => 1273346619,
    'comment' => '2008 February 28: Exactness.',
  ),
  '0708-1300_P5060114.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 4: Long exact sequences, excision.',
  ),
  '0708-1300_P5060115.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 6: Proof of excision.',
  ),
  '0708-1300_P5060116.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 6: Proof of excision (2).',
  ),
  '0708-1300_P5060117.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 11: Proof of excision.',
  ),
  '0708-1300_P5060118.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 11: Proof of excision (2).',
  ),
  '0708-1300_P5060119.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 13: The homology of spheres.',
  ),
  '0708-1300_P5060120.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 18: Degrees.',
  ),
  '0708-1300_P5060121.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 18: Degrees (2).',
  ),
  '0708-1300_P5060122.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 20: CW spaces and homology.',
  ),
  '0708-1300_P5060123.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 20: Degrees.',
  ),
  '0708-1300_P5060125.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 25: CW spaces and homology.',
  ),
  '0708-1300_P5060126.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 25: CW spaces and homology (2).',
  ),
  '0708-1300_P5060127.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => 'HW12.',
  ),
  '0708-1300_P5060128.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => 'Topological Pathologies in R^3.',
  ),
  '0708-1300_P5060129.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => 'Planning, the key diagram for CW.',
  ),
  '0708-1300_P5060130.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => 'The key diagram for CW.',
  ),
  '0708-1300_P5060131.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2008 March 27: Things we skip, pathologies.',
  ),
  '0708-1300_P5060132.jpg' => 
  array (
    'db_updated' => 1273347400,
    'comment' => '2005 March 10, 15: CW, RP^n.',
  ),
  '0708-1300_P5060133.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => '2005 March 17, 22, 24: Mayer-Vietoris, Jordan\'s curve theorem, Borsuk-Ulam.',
  ),
  '0708-1300_P5060134.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => '2005(?) March 30, April 4: Borsuk-Ulam.',
  ),
  '0708-1300_P5060135.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => '2005(?) April 6: Invariance of domain, Borsuk-Ulam.',
  ),
  '0708-1300_P5060136.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => '2008 April 1: Invariance of domain, Borsuk-Ulam.',
  ),
  '0708-1300_P5060137.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => '2008 April 1: R^n theorems.',
  ),
  '0708-1300_P5060138.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => '2008 April 3: Borsuk-Ulam, the necklace theorem.',
  ),
  '0708-1300_P5060139.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => '2008 April 8: de-Rham cohomology and singular homology.',
  ),
  '0708-1300_P5060140.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => '2008 April 8: de-Rham cohomology and singular homology (2).',
  ),
  '0708-1300_P5060141.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => '2008 April 10: de-Rham cohomology and singular homology.',
  ),
  '0708-1300_P5060142.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => 'The Final Examination.',
  ),
  '0708-1300_P5060143.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => 'The Final Examination (2).',
  ),
  '0708-1300_P5060144.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => 'The Final Examination (3).',
  ),
  '0708-1300_P5060145.jpg' => 
  array (
    'db_updated' => 1273349447,
    'comment' => 'Annotated Term Test.',
  ),
  '0708-1300_P5060146.jpg' => 
  array (
    'db_updated' => 1274052328,
    'comment' => 'Annotated Term Test (2).',
  ),
  '94-117_PC300690.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Course description.',
  ),
  '94-117_PC300691.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Information sheet.',
  ),
  '94-117_PC300692.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Particle in harmonic oscillator.',
  ),
  '94-117_PC300693.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Particle in harmonic oscillator (2).',
  ),
  '94-117_PC300694.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Particle in harmonic oscillator (3).',
  ),
  '94-117_PC300695.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Particle in harmonic oscillator (4).',
  ),
  '94-117_PC300696.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Particle in harmonic oscillator (5).',
  ),
  '94-117_PC300697.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Feb 2: first class.',
  ),
  '94-117_PC300698.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Gaussian integration.',
  ),
  '94-117_PC300699.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'The Fourier transform.',
  ),
  '94-117_PC300700.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Feb 4 evaluation.',
  ),
  '94-117_PC300701.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Feb 4: Path integrals for the harmonic oscillator.',
  ),
  '94-117_PC300703.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Another evaluation.',
  ),
  '94-117_PC300704.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'HW1: Fourier analysis.',
  ),
  '94-117_PC300705.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Feb 7: Fourier analysis.',
  ),
  '94-117_PC300706.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Feb 9: To Schroedinger\'s equation.',
  ),
  '94-117_PC300707.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => '22b of Apr 27, 1992; Least action, a particle in E&M fields.',
  ),
  '94-117_PC300708.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => '22b of Apr 29, 1992: Maxwell\'s equations.',
  ),
  '94-117_PC300709.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'Feb 11: Differential forms.',
  ),
  '94-117_PC300710.jpg' => 
  array (
    'db_updated' => 1262224537,
    'comment' => 'HW2: Maxwell, Lorentz transformations, free Schroedinger.',
  ),
  '94-117_PC300711.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => '115 of Nov 27, 1991: Euler-Lagrange.',
  ),
  '94-117_PC300712.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => 'Feb 16: Maxwell.',
  ),
  '94-117_PC300713.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => '115 of Dec 2, 1991: Power lines.',
  ),
  '94-117_PC300714.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => '115 of Dec 4, 1991: The brachistochrone.',
  ),
  '94-117_PC300715.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => 'The brachistochrone.',
  ),
  '94-117_PC300716.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => 'Feb 18.',
  ),
  '94-117_PC300717.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => 'Evaluation.',
  ),
  '94-117_PC300718.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => '115 of Dec 6, 1991: The isoperimetric inequality.',
  ),
  '94-117_PC300719.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => 'Feb 23: Lagrange multipliers.',
  ),
  '94-117_PC300720.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => 'Euler-Lagrange following Itzykson-Zuber.',
  ),
  '94-117_PC300721.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => '115 of Dec 9, 1991: The Hamiltonian formulation.',
  ),
  '94-117_PC300722.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => 'Feb 24: Planning.',
  ),
  '94-117_PC300723.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => '115 of Dec 11, 1991: Poisson brackets, Noether\'s theorem.',
  ),
  '94-117_PC300724.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => 'Feb 28: The Hamiltonian formulation, quantization.',
  ),
  '94-117_PC300725.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => 'March 2: Symplectic geometry.',
  ),
  '94-117_PC300726.jpg' => 
  array (
    'db_updated' => 1262225287,
    'comment' => 'March 4: Symplectic geometry.',
  ),
  '94-117_PC300727.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'March 7.',
  ),
  '94-117_PC300728.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'HW2 Solution.',
  ),
  '94-117_PC300729.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'HW2 Solution (2).',
  ),
  '94-117_PC300730.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => '115 of Dec 16, 1991: Noether\'s theorem.',
  ),
  '94-117_PC300731.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Noether\'s theorem.',
  ),
  '94-117_PC300732.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'March 9: Poisoon brackets, Noether.',
  ),
  '94-117_PC300733.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'March 11: Noether.',
  ),
  '94-117_PC300734.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Hamilton-Jacobi.',
  ),
  '94-117_PC300735.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Hamilton-Jacobi (2).',
  ),
  '94-117_PC300736.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'March 14 HW: Hamilton-Jacobi.',
  ),
  '94-117_PC300738.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'March 14: Hamilton-Jacobi.',
  ),
  '94-117_PC300739.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'March 14: Hamilton-Jacobi (2).',
  ),
  '94-117_PC300740.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'March 16: Legendre\'s transform.',
  ),
  '94-117_PC300741.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'March 18: Second variations.',
  ),
  '94-117_PC300742.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Suggested topics for projects.',
  ),
  '94-117_PC300743.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'March 21 HW.',
  ),
  '94-117_PC300744.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'March 21: Second variations.',
  ),
  '94-117_PC300745.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'March 23: Second variations.',
  ),
  '94-117_PC300746.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'First page of Mermin\'s paper.',
  ),
  '94-117_PC300756.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Apr 4: Non-Commutative Probability.',
  ),
  '94-117_PC300757.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Apr 4: Non-Commutative Probability (2).',
  ),
  '94-117_PC300758.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'First page of my NCP paper.',
  ),
  '94-117_PC300763.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'The Heisenberg inequality (a page from my paper <a href=http://www.math.toronto.edu/~drorbn/papers/NCP/>Two Examples in Non-Commutative Probability</a>).',
  ),
  '94-117_PC300764.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Apr 6: Non-Commutative Probability.',
  ),
  '94-117_PC300765.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'April 8: Non-Commutative Probability.',
  ),
  '94-117_PC300766.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Apr 11 HW: Non-Commutative Probability.',
  ),
  '94-117_PC300767.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Apr 11: Non-Commutative Probability.',
  ),
  '94-117_PC300768.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Planning.',
  ),
  '94-117_PC300769.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'The Stone - von-Neuman Uniqueness Theorem.',
  ),
  '94-117_PC300770.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'The Stone - von-Neuman Uniqueness Theorem (2).',
  ),
  '94-117_PC300771.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'The Stone - von-Neuman Uniqueness Theorem (3).',
  ),
  '94-117_PC300772.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'The Stone - von-Neuman Uniqueness Theorem (4).',
  ),
  '94-117_PC300773.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'The Stone - von-Neuman Uniqueness Theorem (5).',
  ),
  '94-117_PC300774.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Apr 13: The Heisenberg inequality, SvN uniqueness.',
  ),
  '94-117_PC300775.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Apr 18: SvN uniqueness.',
  ),
  '94-117_PC300776.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Apr 20: SvN uniqueness, dynamics.',
  ),
  '94-117_PC300777.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Apr 20: creation and annihilation.',
  ),
  '94-117_PC300778.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Hermite.',
  ),
  '94-117_PC300779.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Hermite (2).',
  ),
  '94-117_PC300780.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Apr 22: The harmonic oscillator.',
  ),
  '94-117_PC300781.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Creation and annihilation.',
  ),
  '94-117_PC300782.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Apr 27: Rotations and spin.',
  ),
  '94-117_PC300783.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => '???',
  ),
  '94-117_PC300784.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Apr 29: Rotations and spin.',
  ),
  '94-117_PC300786.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'Linking numbers.',
  ),
  '94-117_PC300787.jpg' => 
  array (
    'db_updated' => 1262226768,
    'comment' => 'May 6: Perturbation theory.',
  ),
  '9596-Topology_P1010683.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'Syllabus.',
  ),
  '9596-Topology_P1010686.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'March 3: Continuity, topology, basis.',
  ),
  '9596-Topology_P1010687.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'HW1.',
  ),
  '9596-Topology_P1010688.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'March 7: Order topology, products, subset topology.',
  ),
  '9596-Topology_P1010689.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'March 10: Closed sets and proerties.',
  ),
  '9596-Topology_P1010690.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'HW2.',
  ),
  '9596-Topology_P1010691.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'March 14: Open sets and interiors, T2.',
  ),
  '9596-Topology_P1010692.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'March 17: Conditions for continuity, infinite products, metrics.',
  ),
  '9596-Topology_P1010694.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'HW3.',
  ),
  '9596-Topology_P1010695.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'HW3 (2).',
  ),
  '9596-Topology_P1010696.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'March 21: Products and metrizability, sequences and convergence.',
  ),
  '9596-Topology_P1010697.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'March 24: Convergence, connectedness.',
  ),
  '9596-Topology_P1010698.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'March 28: Connectedness in prodcuts, path connectedness.',
  ),
  '9596-Topology_P1010699.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'April 24: Intersections of open dense sets.',
  ),
  '9596-Topology_P1010700.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'April 18: Intersections of open dense sets, connectivity.',
  ),
  '9596-Topology_P1010701.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'April 21: Compactness.',
  ),
  '9596-Topology_P1010702.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'HW5.',
  ),
  '9596-Topology_P1010703.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'HW7.',
  ),
  '9596-Topology_P1010704.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'April 28: Tychonoff, Stone-Cech.',
  ),
  '9596-Topology_P1010705.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'April 28: Tychonoff, Stone-Cech (2).',
  ),
  '9596-Topology_P1010706.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'May 2: Urysohn, completely regular spaces, more on Stone-Cech.',
  ),
  '9596-Topology_P1010707.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'May 5: Urysohn, Stone-Cech, Lims.',
  ),
  '9596-Topology_P1010708.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'HW8.',
  ),
  '9596-Topology_P1010709.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'HW8 (2).',
  ),
  '9596-Topology_P1010710.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'HW9.',
  ),
  '9596-Topology_P1010711.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'HW9 (2).',
  ),
  '9596-Topology_P1010712.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'May 9: Normal spaces, proof of Urysohn.',
  ),
  '9596-Topology_P1010713.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'May 12: Compactness in metric spaces.',
  ),
  '9596-Topology_P1010714.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'May 26: Surfaces, the classification theorem.',
  ),
  '9596-Topology_P1010715.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'May 30: Quotient spaces, surfaces by identifications.',
  ),
  '9596-Topology_P1010716.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'June 2: Proof of the classification theorem.',
  ),
  '9596-Topology_P1010717.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'June 2: Proof of the classification theorem (2).',
  ),
  '9596-Topology_P1010718.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'June 6: Euler characteristics, groups.',
  ),
  '9596-Topology_P1010719.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'June 9: Groups, the fundamental group, the fundamental group of the circle.',
  ),
  '9596-Topology_P1010720.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'HW11.',
  ),
  '9596-Topology_P1010721.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'HW10.',
  ),
  '9596-Topology_P1010722.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'June 13: Brauer, the fundamental group of the circle.',
  ),
  '9596-Topology_P1010723.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'June 16: More on fundamental groups, Van-Kampen.',
  ),
  '9596-Topology_P1010724.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'June 20: Van-Kampen examples and proof.',
  ),
  '9596-Topology_P1010725.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'Moed B.',
  ),
  '9596-Topology_P1010726.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'Moed B (2).',
  ),
  '9596-Topology_P1010727.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'Moed A.',
  ),
  '9596-Topology_P1010728.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'Moed A (2).',
  ),
  '9596-Topology_P1010729.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'Grade histogram.',
  ),
  '9596-Topology_P1010730.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'Moed B grading key.',
  ),
  '9596-Topology_P1010731.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'Moed Meyukhad.',
  ),
  '9596-Topology_P1010732.jpg' => 
  array (
    'db_updated' => 1283910467,
    'comment' => 'Evaluation results.',
  ),
  '9697-Mechanics_PC300788.jpg' => 
  array (
    'db_updated' => 1262280959,
    'comment' => 'Course description.',
  ),
  '9697-Mechanics_PC300789.jpg' => 
  array (
    'db_updated' => 1262280959,
    'comment' => 'Course plan.',
  ),
  '9697-Mechanics_PC300790.jpg' => 
  array (
    'db_updated' => 1262280959,
    'comment' => 'Oct 17: ???',
  ),
  '9697-Mechanics_PC300791.jpg' => 
  array (
    'db_updated' => 1262280959,
    'comment' => 'Euler-Lagrange as in Itzykson-Zuber.',
  ),
  '9697-Mechanics_PC300792.jpg' => 
  array (
    'db_updated' => 1262280959,
    'comment' => 'Oct 24: Basic calculus of variations.',
  ),
  '9697-Mechanics_PC300793.jpg' => 
  array (
    'db_updated' => 1262280959,
    'comment' => 'Oct 24: Basic calculus of variations (2).',
  ),
  '9697-Mechanics_PC300795.jpg' => 
  array (
    'db_updated' => 1262281296,
    'comment' => 'HW1: Basic calculus of variations.',
  ),
  '9697-Mechanics_PC300796.jpg' => 
  array (
    'db_updated' => 1262281296,
    'comment' => 'Oct 31: Symmetries and conservation laws.',
  ),
  '9697-Mechanics_PC300797.jpg' => 
  array (
    'db_updated' => 1262281296,
    'comment' => 'Nov 7: The Hamiltonian.',
  ),
  '9697-Mechanics_PC300798.jpg' => 
  array (
    'db_updated' => 1262281296,
    'comment' => 'HW2: Hamiltonians.',
  ),
  '9697-Mechanics_PC300799.jpg' => 
  array (
    'db_updated' => 1262281296,
    'comment' => 'Review of differential forms.',
  ),
  '9697-Mechanics_PC300800.jpg' => 
  array (
    'db_updated' => 1262281296,
    'comment' => 'Nov 14: Symplectic geometry, Poisson brackets.',
  ),
  '9697-Mechanics_PC300801.jpg' => 
  array (
    'db_updated' => 1262281296,
    'comment' => 'Nov 21: The Maxwell equations.',
  ),
  '9697-Mechanics_PC300802.jpg' => 
  array (
    'db_updated' => 1262281296,
    'comment' => 'Feynman\'s equations of classical physics.',
  ),
  '9697-Mechanics_PC300803.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'HW3: Symplectic geometry, Poisson brackets.',
  ),
  '9697-Mechanics_PC300804.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'HW4: Maxwell and special relativity.',
  ),
  '9697-Mechanics_PC300805.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'Nov 28: Probability theories.',
  ),
  '9697-Mechanics_PC300806.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'The 3/4,3/4,3/4,0 square.',
  ),
  '9697-Mechanics_PC300807.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'Planning.',
  ),
  '9697-Mechanics_PC300808.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'Dec 5: Quantization of the harmonic oscillator.',
  ),
  '9697-Mechanics_PC300809.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'First page of Feynman\'s Quantum',
  ),
  '9697-Mechanics_PC300815.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'Dec 6: The CCRs and von-Neuman\'s uniqueness.',
  ),
  '9697-Mechanics_PC300816.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'Lemmas for von-Neuman\'s uniqueness.',
  ),
  '9697-Mechanics_PC300817.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'Jan 2: Term summary, von-Neuman\'s uniqueness.',
  ),
  '9697-Mechanics_PC300818.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'Jan 9: Presenting path integrals.',
  ),
  '9697-Mechanics_PC300819.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'Pricing of options.',
  ),
  '9697-Mechanics_PC300820.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'Term 2 course description.',
  ),
  '9697-Mechanics_PC300821.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'First page of Telfer\'s paper.',
  ),
  '9697-Mechanics_PC300822.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'Plans.',
  ),
  '9697-Mechanics_PC300823.jpg' => 
  array (
    'db_updated' => 1262282176,
    'comment' => 'Constants and units according to Encarta.',
  ),
  '9697-Mechanics_PC300824.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'Constants and units according to Encarta (2).',
  ),
  '9697-Mechanics_PC300825.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'Constants and units according to Encarta (3).',
  ),
  '9697-Mechanics_PC300826.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'Jan 16: Path integrals to canonical quantization.',
  ),
  '9697-Mechanics_PC300827.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'Feb 19: Energy levels from uncertainty.',
  ),
  '9697-Mechanics_PC300828.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'Feb 23: Lehavi on planetary orbits.',
  ),
  '9697-Mechanics_PC300829.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'Feb 23: Lehavi on planetary orbits (2).',
  ),
  '9697-Mechanics_PC300830.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'Feb 23: Lehavi on planetary orbits (3).',
  ),
  '9697-Mechanics_PC300831.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'Kepler\'s laws.',
  ),
  '9697-Mechanics_PC300832.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'Feb 27: Bohr\'s model, basic E&M.',
  ),
  '9697-Mechanics_PC300833.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'March 2: More E&M, Schroedinger\'s hydrogen atom.',
  ),
  '9697-Mechanics_PC300834.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'March 6: more Schroedinger, SO(3).',
  ),
  '9697-Mechanics_PC300835.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => '117 of Apr 27, 1994: Rotations and spin.',
  ),
  '9697-Mechanics_PC300836.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => '117 of Apr 27, 1994: Rotations and spin (2).',
  ),
  '9697-Mechanics_PC300837.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'March 9: Irreps of SO(3).',
  ),
  '9697-Mechanics_PC300838.jpg' => 
  array (
    'db_updated' => 1262282763,
    'comment' => 'March 13: Irreps of SO(3), solving Schroedinger\'s hydrogen atom.',
  ),
  '9697-Mechanics_PC300840.jpg' => 
  array (
    'db_updated' => 1262283083,
    'comment' => 'March 16: Schroedinger\'s hydrogen atom, errors.',
  ),
  '9697-Mechanics_PC300841.jpg' => 
  array (
    'db_updated' => 1262283083,
    'comment' => 'March 16: Schroedinger\'s hydrogen atom, errors (2).',
  ),
  '9697-Mechanics_PC300842.jpg' => 
  array (
    'db_updated' => 1262283083,
    'comment' => 'March 20: The errors.',
  ),
  '9697-Mechanics_PC300843.jpg' => 
  array (
    'db_updated' => 1262283083,
    'comment' => 'March 30: Klein-Gordon and towards Dirac.',
  ),
  '9697-Mechanics_PC300844.jpg' => 
  array (
    'db_updated' => 1262283083,
    'comment' => 'Apr 6: Clifford algebras.',
  ),
  '9697-Mechanics_PC300845.jpg' => 
  array (
    'db_updated' => 1262283083,
    'comment' => 'Apr 10: Dirac\'s equation.',
  ),
  '9697-Mechanics_PC300846.jpg' => 
  array (
    'db_updated' => 1262283083,
    'comment' => 'Apr 13: Dirac\'s equation.',
  ),
  '9697-Mechanics_PC300847.jpg' => 
  array (
    'db_updated' => 1262283083,
    'comment' => 'May 1: Dirac\'s equation.',
  ),
  '9697-Mechanics_PC300848.jpg' => 
  array (
    'db_updated' => 1262283083,
    'comment' => 'May 4: Dirac\'s equation.',
  ),
  '9697-Mechanics_PC300849.jpg' => 
  array (
    'db_updated' => 1262283083,
    'comment' => 'First page of Bjorken & Drell, Sections 1 & 4.',
  ),
  '99-Mechanics_PC300863.jpg' => 
  array (
    'db_updated' => 1262302642,
    'comment' => 'Course description.',
  ),
  '99-Mechanics_PC300864.jpg' => 
  array (
    'db_updated' => 1262302642,
    'comment' => 'Questionaire.',
  ),
  '99-Mechanics_PC300865.jpg' => 
  array (
    'db_updated' => 1262302642,
    'comment' => 'First page of particle',
  ),
  '99-Mechanics_PC300870.jpg' => 
  array (
    'db_updated' => 1262302642,
    'comment' => 'Safire of NYT on The Lagrangian Codes.',
  ),
  '99-Mechanics_PC300871.jpg' => 
  array (
    'db_updated' => 1262302757,
    'comment' => 'Safire of NYT on The Lagrangian Codes (2).',
  ),
  '99-Mechanics_PC300872.jpg' => 
  array (
    'db_updated' => 1262302757,
    'comment' => '96 Oct 24: Calculus of variations.',
  ),
  '99-Mechanics_PC300873.jpg' => 
  array (
    'db_updated' => 1262302757,
    'comment' => '96 Oct 24: Calculus of variations (2).',
  ),
  '99-Mechanics_PC300874.jpg' => 
  array (
    'db_updated' => 1262302757,
    'comment' => '96 Oct 24: HW1.',
  ),
  '99-Mechanics_PC300875.jpg' => 
  array (
    'db_updated' => 1262302757,
    'comment' => 'Euler-Lagrange following Itzykson-Zuber.',
  ),
  '99-Mechanics_PC300876.jpg' => 
  array (
    'db_updated' => 1262302911,
    'comment' => 'Apr 11: Euler-Lagrange, the isoperimetric inequality.',
  ),
  '99-Mechanics_PC300877.jpg' => 
  array (
    'db_updated' => 1262302911,
    'comment' => 'Apr 25: First page of special relativity handout by Lawrence.',
  ),
  '99-Mechanics_PC300887.jpg' => 
  array (
    'db_updated' => 1262302911,
    'comment' => 'Review of differential forms.',
  ),
  '99-Mechanics_PC300888.jpg' => 
  array (
    'db_updated' => 1262302911,
    'comment' => 'Equations of Classical Physics according to Feynman.',
  ),
  '99-Mechanics_PC300889.jpg' => 
  array (
    'db_updated' => 1262303523,
    'comment' => 'May 23: A particle in an E&M field.',
  ),
  '99-Mechanics_PC300890.jpg' => 
  array (
    'db_updated' => 1262303523,
    'comment' => '1996 Nov 21: Maxwell equations.',
  ),
  '99-Mechanics_PC300891.jpg' => 
  array (
    'db_updated' => 1262303523,
    'comment' => '1996 Nov 7: The Hamiltonian.',
  ),
  '99-Mechanics_PC300892.jpg' => 
  array (
    'db_updated' => 1262303523,
    'comment' => 'The 3/4,3/4,3/4,0 square in quantum probability.',
  ),
  '99-Mechanics_PC300893.jpg' => 
  array (
    'db_updated' => 1262303523,
    'comment' => 'First page of Feynman\'s Quantum',
  ),
  '99-Mechanics_PC300899.jpg' => 
  array (
    'db_updated' => 1262303523,
    'comment' => 'First page of Mermin.',
  ),
  '99-Mechanics_PC300904.jpg' => 
  array (
    'db_updated' => 1262303523,
    'comment' => '1996 planning page.',
  ),
  '99-Mechanics_PC300905.jpg' => 
  array (
    'db_updated' => 1262303523,
    'comment' => '1996 Dec 5: Canonical quantization of the harmonic oscillator.',
  ),
  '99-Mechanics_PC300906.jpg' => 
  array (
    'db_updated' => 1262303523,
    'comment' => '1996 Dec 6: The Heisenberg picture, von-Neuman uniqueness.',
  ),
  '99-Mechanics_PC300907.jpg' => 
  array (
    'db_updated' => 1262303523,
    'comment' => '1997 Jan 2: Summary, von-Neuman uniqueness.',
  ),
  '99-Mechanics_PC300908.jpg' => 
  array (
    'db_updated' => 1262303523,
    'comment' => '1997L Lemmas for von-Neuman uniqueness.',
  ),
  '99-Mechanics_PC300909.jpg' => 
  array (
    'db_updated' => 1262303523,
    'comment' => 'June 13: Misc.',
  ),
  '99-Mechanics_PC300910.jpg' => 
  array (
    'db_updated' => 1262303756,
    'comment' => '1996 Nov 28: The quantum probability story.',
  ),
  '99-Mechanics_PC300911.jpg' => 
  array (
    'db_updated' => 1262303756,
    'comment' => 'June 20: Wave packets etc.',
  ),
  '99-Mechanics_PC300912.jpg' => 
  array (
    'db_updated' => 1262303756,
    'comment' => 'Plot of the free propagator.',
  ),
  '99-Mechanics_PC300913.jpg' => 
  array (
    'db_updated' => 1262303756,
    'comment' => 'Plot of the free propagator (2).',
  ),
  '99-Mechanics_PC300914.jpg' => 
  array (
    'db_updated' => 1262303756,
    'comment' => 'June 27: Quantum politics.',
  ),
  '99-Mechanics_PC300915.jpg' => 
  array (
    'db_updated' => 1262303756,
    'comment' => 'June 27: Philosophical issues of quantum mechanics.',
  ),
  '99-Mechanics_PC300916.jpg' => 
  array (
    'db_updated' => 1262303756,
    'comment' => '???',
  ),
  '99-Mechanics_PC300917.jpg' => 
  array (
    'db_updated' => 1262303756,
    'comment' => 'The final exam.',
  ),
)
?>