{"ImageComments" -> {"0708-1300_P5060001.jpg"->"2000 Oct 29: Course intro, the implicit function theorem","0708-1300_P5060004.jpg"->"2000 Oct 29: Course intro, the implicit function theorem (2)","0708-1300_P5060005.jpg"->"2007 Sep 11: Course intro, differentials","0708-1300_P5060006.jpg"->"2007 Sep 11: Course intro, differentials (2)","0708-1300_P5060007.jpg"->"2007 Sep 13: The implicit function theorem","0708-1300_P5060008.jpg"->"2007 Sep 13: The implicit function theorem (2)","0708-1300_P5060009.jpg"->"2000 October 31: Functional structures, etc","0708-1300_P5060010.jpg"->"2000 November 5: Manifolds","0708-1300_P5060011.jpg"->"2007 September 18: Inverse and implicit, manifolds","0708-1300_P5060012.jpg"->"2007 September 18: Inverse and implicit, manifolds (2)","0708-1300_P5060013.jpg"->"2007 September 20: Continuation","0708-1300_P5060014.jpg"->"2000 November 12: Tangent vectors","0708-1300_P5060015.jpg"->"2000 November 12: Tangent vectors, immersions, local structure","0708-1300_P5060016.jpg"->"2007 September 25: Two definitions of manifolds, tangent vectors","0708-1300_P5060017.jpg"->"2007 September 27: Tangents, Hadamard's lemma","0708-1300_P5060018.jpg"->"2000 November 19: Immersions, submerssions, local structure","0708-1300_P5060019.jpg"->"2000 November 21: Regular points, Sard's theorem, transversallity","0708-1300_P5060020.jpg"->"2007 October 2: Immersions, submerssions, local structure","0708-1300_P5060021.jpg"->"2007 October 2: Immersions, submerssions, local structure (2)","0708-1300_P5060022.jpg"->"2007 October 4: Local structures, Sard's theorem","0708-1300_P5060023.jpg"->"2007 October 9: Sard's, transversallity","0708-1300_P5060024.jpg"->"2007 October 9: Sard's, transversallity (2)","0708-1300_P5060025.jpg"->"2007 October 11: Intro. to Sard, the Cantor Aerogel","0708-1300_P5060026.jpg"->"2007 October 11: Intro. to Sard, the Cantor Aerogel (2)","0708-1300_P5060027.jpg"->"2007 October 11: Intro. to Sard, the Cantor Aerogel (3)","0708-1300_P5060028.jpg"->"2007 October 11: Intro. to Sard, the Cantor Aerogel (4)","0708-1300_P5060029.jpg"->"2007 October 11: Intro. to Sard, the Cantor Aerogel (5)","0708-1300_P5060030.jpg"->"2000 November 26: More local structure","0708-1300_P5060031.jpg"->"2000 December 3: Whitney's theorem","0708-1300_P5060032.jpg"->"2000 November 28: Transversallity, Whitney, partitions of unity","0708-1300_P5060033.jpg"->"2007 October 16: Proof of Sard","0708-1300_P5060034.jpg"->"2007 October 16: Whitney","0708-1300_P5060035.jpg"->"2007 October 18: Whitney, partitions of unity","0708-1300_P5060036.jpg"->"2007 October 18: Whitney, partitions of unity (2)","0708-1300_P5060037.jpg"->"Fubini from Guillemin-Pollack, HW3","0708-1300_P5060038.jpg"->"NSERC proposal material","0708-1300_P5060039.jpg"->"2007 October 23: A Peano Curve","0708-1300_P5060040.jpg"->"2007 October 23: A Peano Curve (2)","0708-1300_P5060041.jpg"->"2007 October 23, 25: Peano, Whitney, classification of surfaces","0708-1300_P5060042.jpg"->"2007 October 30: Smooth retracts, smooth Brouwer, smooth approximation","0708-1300_P5060043.jpg"->"November 2007: Term Exam 1 planning","0708-1300_P5060044.jpg"->"2007 November 1: Tubular neighborhoods","0708-1300_P5060045.jpg"->"2007 November 1: Proper implies closed","0708-1300_P5060046.jpg"->"HW4","0708-1300_P5060047.jpg"->"On TE1","0708-1300_P5060048.jpg"->"Large Stokes'","0708-1300_P5060049.jpg"->"2000 December 31: Stokes', differential forms","0708-1300_P5060050.jpg"->"2001 January 16: Differential forms, ${\\mathbb R}^3$, pullbacks","0708-1300_P5060051.jpg"->"2001 January 19: Pullbacks, integration","0708-1300_P5060052.jpg"->"2001 January 21: The three dimensional theorems, Stokes'","0708-1300_P5060053.jpg"->"November 2007: Term Test","0708-1300_P5060054.jpg"->"November 2007: Term Test (2)","0708-1300_P5060055.jpg"->"2007 November 6, 8, 13: Stokes', contractibility of $S^\\infty$","0708-1300_P5060056.jpg"->"2007 November 20, 22: $d$, integration, orientation, Stokes'","0708-1300_P5060057.jpg"->"A Planimeter","0708-1300_P5060058.jpg"->"2007 November 27, 29: The planimeter, ${\\mathbb R}^3$, Maxwell","0708-1300_P5060059.jpg"->"1996 November 21: Maxwell","0708-1300_P5060060.jpg"->"2001 January 23: The planimeter","0708-1300_P5060061.jpg"->"Feynman's Classica","0708-1300_P5060062.jpg"->"Handout: ","0708-1300_P5060063.jpg"->"HW6","0708-1300_P5060064.jpg"->"HW6 (2)","0708-1300_P5060065.jpg"->"2007 December 6: Homotopy for differential forms","0708-1300_P5060066.jpg"->"2002 March 12: The fundamental group","0708-1300_P5060067.jpg"->"2002 March 14: The lifting property, basic properties of the fundamental group","0708-1300_P5060068.jpg"->"2002 March 19: More properties, Van-Kampen","0708-1300_P5060069.jpg"->"2002 April 11: Covering spaces","0708-1300_P5060070.jpg"->"2004 November 11, 16","0708-1300_P5060071.jpg"->"2004 November 18: Homotopy theory light","0708-1300_P5060072.jpg"->"1996 June 9: The fundamental group of the circle","0708-1300_P5060073.jpg"->"2005 November 22, 24: Almost all functions are bad, fundamental groups","0708-1300_P5060074.jpg"->"2005 November 29, December 1: The fundamental group, covering spaces","0708-1300_P5060075.jpg"->"2008 January 8: The fundamental group, the circle","0708-1300_P5060076.jpg"->"2008 January 10: The circle, covering spaces","0708-1300_P5060077.jpg"->"2004 November 23: More homotopy theory light","0708-1300_P5060078.jpg"->"2004 November 25, 30: Borsuk-Ulam, Van-Kampen","0708-1300_P5060079.jpg"->"2004: December 2: Van-Kampen","0708-1300_P5060080.jpg"->"2004 December 7: Proof of Van-Kampen","0708-1300_P5060081.jpg"->"2005 December 6: Borsuk-Ulam, topological groups, homotopy light, Van-Kampen","0708-1300_P5060082.jpg"->"2005 December 8: Surfaces, Van-Kampen examples","0708-1300_P5060083.jpg"->"2008 January 15, 17: Liftings in covering spaces, applications, Van-Kampen","0708-1300_P5060084.jpg"->"2008 January 22, 24: Applications and proof of Van-Kampen","0708-1300_P5060085.jpg"->"2006 January 10: Van-Kampen and applications","0708-1300_P5060086.jpg"->"2006 January 12, 17: Applications and proof of Van-Kampen","0708-1300_P5060087.jpg"->"2006 January 19: Covering maps","0708-1300_P5060088.jpg"->"2006 January 24: Coverings, the lifting criterion","0708-1300_P5060089.jpg"->"2008 January 29: Two covering spaces","0708-1300_P5060090.jpg"->"2008 January 29: 14 covering spaces","0708-1300_P5060091.jpg"->"2008 January 29: Coverings, the lifting criterion","0708-1300_P5060092.jpg"->"2006 January 26: Classification by the fundamental group, the universal cover","0708-1300_P5060093.jpg"->"2006 February 1: The universal covering space","0708-1300_P5060094.jpg"->"2008 February 5: The covering space handout","0708-1300_P5060095.jpg"->"2008 February 5: The covering space handout (2)","0708-1300_P5060096.jpg"->"2008 February 5: The covering space handout (3)","0708-1300_P5060097.jpg"->"2008 February 5: The covering space handout (4)","0708-1300_P5060098.jpg"->"2008 January 31, February 5, 7: Covering spaces","0708-1300_P5060099.jpg"->"2002 May 2: Simplicies and the boundary map","0708-1300_P5060100.jpg"->"2002 May 7: Simplicies, homology, functoriallity","0708-1300_P5060101.jpg"->"2002 May 9: Cont","0708-1300_P5060102.jpg"->"2006 February 2: More on thefundamental theorem of covering spaces","0708-1300_P5060103.jpg"->"2006 February 7, 9, 14: Basic homolog","0708-1300_P5060104.jpg"->"2008 February 12: Homology, the Abelianization of homotopy","0708-1300_P5060105.jpg"->"2008 February 12, 14: Homology, the Abelianization of homotopy (2)","0708-1300_P5060106.jpg"->"2007 February 11: Term Exam 2","0708-1300_P5060107.jpg"->"2007 February 11: Term Exam 2 (2)","0708-1300_P5060108.jpg"->"2002 May 14: The prizm, short to long exact sequences","0708-1300_P5060109.jpg"->"2005 January 25: Homology, homotopy invariance","0708-1300_P5060110.jpg"->"2005 January 27: The prizm, short to long exact sequences","0708-1300_P5060111.jpg"->"2008 February 26: A Homology Theory is a Monster","0708-1300_P5060112.jpg"->"2008 February 26: A Homology Theory is a Monster (2)","0708-1300_P5060113.jpg"->"2008 February 28: Exactness","0708-1300_P5060114.jpg"->"2008 March 4: Long exact sequences, excision","0708-1300_P5060115.jpg"->"2008 March 6: Proof of excision","0708-1300_P5060116.jpg"->"2008 March 6: Proof of excision (2)","0708-1300_P5060117.jpg"->"2008 March 11: Proof of excision","0708-1300_P5060118.jpg"->"2008 March 11: Proof of excision (2)","0708-1300_P5060119.jpg"->"2008 March 13: The homology of spheres","0708-1300_P5060120.jpg"->"2008 March 18: Degrees","0708-1300_P5060121.jpg"->"2008 March 18: Degrees (2)","0708-1300_P5060122.jpg"->"2008 March 20: CW spaces and homology","0708-1300_P5060123.jpg"->"2008 March 20: Degrees","0708-1300_P5060125.jpg"->"2008 March 25: CW spaces and homology","0708-1300_P5060126.jpg"->"2008 March 25: CW spaces and homology (2)","0708-1300_P5060127.jpg"->"HW12","0708-1300_P5060128.jpg"->"Topological Pathologies in R^3","0708-1300_P5060129.jpg"->"Planning, the key diagram for CW","0708-1300_P5060130.jpg"->"The key diagram for CW","0708-1300_P5060131.jpg"->"2008 March 27: Things we skip, pathologies","0708-1300_P5060132.jpg"->"2005 March 10, 15: CW, ${\\mathbb R}P^n$","0708-1300_P5060133.jpg"->"2005 March 17, 22, 24: Mayer-Vietoris, Jordan's curve theorem, Borsuk-Ulam","0708-1300_P5060134.jpg"->"2005(?) March 30, April 4: Borsuk-Ulam","0708-1300_P5060135.jpg"->"2005(?) April 6: Invariance of domain, Borsuk-Ulam","0708-1300_P5060136.jpg"->"2008 April 1: Invariance of domain, Borsuk-Ulam","0708-1300_P5060137.jpg"->"2008 April 1: ${\\mathbb R}^n$ theorems","0708-1300_P5060138.jpg"->"2008 April 3: Borsuk-Ulam, the necklace theorem","0708-1300_P5060139.jpg"->"2008 April 8: de-Rham cohomology and singular homology","0708-1300_P5060140.jpg"->"2008 April 8: de-Rham cohomology and singular homology (2)","0708-1300_P5060141.jpg"->"2008 April 10: de-Rham cohomology and singular homology","0708-1300_P5060142.jpg"->"The Final Examination","0708-1300_P5060143.jpg"->"The Final Examination (2)","0708-1300_P5060144.jpg"->"The Final Examination (3)","0708-1300_P5060145.jpg"->"Annotated Term Test","0708-1300_P5060146.jpg"->"Annotated Term Test (2)"}
}