Dror Bar-Natan: AcademicPensieve: Classes: 0708-1300:

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0708-1300_P5060001.jpg
2000 Oct 29: Course intro, the implicit function theorem

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2000 Oct 29: Course intro, the implicit function theorem (2)

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2007 Sep 11: Course intro, differentials

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2007 Sep 11: Course intro, differentials (2)

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2007 Sep 13: The implicit function theorem

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2007 Sep 13: The implicit function theorem (2)

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2000 October 31: Functional structures, etc

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2000 November 5: Manifolds

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2007 September 18: Inverse and implicit, manifolds

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2007 September 18: Inverse and implicit, manifolds (2)

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2007 September 20: Continuation

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2000 November 12: Tangent vectors

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2000 November 12: Tangent vectors, immersions, local structure

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2007 September 25: Two definitions of manifolds, tangent vectors

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2007 September 27: Tangents, Hadamard's lemma

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2000 November 19: Immersions, submerssions, local structure

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2000 November 21: Regular points, Sard's theorem, transversallity

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2007 October 2: Immersions, submerssions, local structure

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2007 October 2: Immersions, submerssions, local structure (2)

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2007 October 4: Local structures, Sard's theorem

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2007 October 9: Sard's, transversallity

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2007 October 9: Sard's, transversallity (2)

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2007 October 11: Intro. to Sard, the Cantor Aerogel

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2007 October 11: Intro. to Sard, the Cantor Aerogel (2)

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2007 October 11: Intro. to Sard, the Cantor Aerogel (3)

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2007 October 11: Intro. to Sard, the Cantor Aerogel (4)

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2007 October 11: Intro. to Sard, the Cantor Aerogel (5)

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2000 November 26: More local structure

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2000 December 3: Whitney's theorem

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2000 November 28: Transversallity, Whitney, partitions of unity

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2007 October 16: Proof of Sard

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2007 October 16: Whitney

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2007 October 18: Whitney, partitions of unity

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2007 October 18: Whitney, partitions of unity (2)

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Fubini from Guillemin-Pollack, HW3

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NSERC proposal material

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2007 October 23: A Peano Curve

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2007 October 23: A Peano Curve (2)

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2007 October 23, 25: Peano, Whitney, classification of surfaces

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2007 October 30: Smooth retracts, smooth Brouwer, smooth approximation

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November 2007: Term Exam 1 planning

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2007 November 1: Tubular neighborhoods

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2007 November 1: Proper implies closed

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HW4

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On TE1

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Large Stokes'

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2000 December 31: Stokes', differential forms

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2001 January 16: Differential forms, ${\mathbb R}^3$, pullbacks

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2001 January 19: Pullbacks, integration

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2001 January 21: The three dimensional theorems, Stokes'

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November 2007: Term Test

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November 2007: Term Test (2)

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2007 November 6, 8, 13: Stokes', contractibility of $S^\infty$

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2007 November 20, 22: $d$, integration, orientation, Stokes'

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A Planimeter

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2007 November 27, 29: The planimeter, ${\mathbb R}^3$, Maxwell

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1996 November 21: Maxwell

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2001 January 23: The planimeter

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Feynman's Classica

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Handout:

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HW6

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HW6 (2)

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2007 December 6: Homotopy for differential forms

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2002 March 12: The fundamental group

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2002 March 14: The lifting property, basic properties of the fundamental group

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2002 March 19: More properties, Van-Kampen

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2002 April 11: Covering spaces

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2004 November 11, 16

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2004 November 18: Homotopy theory light

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1996 June 9: The fundamental group of the circle

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2005 November 22, 24: Almost all functions are bad, fundamental groups

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2005 November 29, December 1: The fundamental group, covering spaces

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2008 January 8: The fundamental group, the circle

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2008 January 10: The circle, covering spaces

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2004 November 23: More homotopy theory light

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2004 November 25, 30: Borsuk-Ulam, Van-Kampen

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2004: December 2: Van-Kampen

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2004 December 7: Proof of Van-Kampen

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2005 December 6: Borsuk-Ulam, topological groups, homotopy light, Van-Kampen

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2005 December 8: Surfaces, Van-Kampen examples

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2008 January 15, 17: Liftings in covering spaces, applications, Van-Kampen

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2008 January 22, 24: Applications and proof of Van-Kampen

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2006 January 10: Van-Kampen and applications

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2006 January 12, 17: Applications and proof of Van-Kampen

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2006 January 19: Covering maps

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2006 January 24: Coverings, the lifting criterion

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2008 January 29: Two covering spaces

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2008 January 29: 14 covering spaces

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2008 January 29: Coverings, the lifting criterion

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2006 January 26: Classification by the fundamental group, the universal cover

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2006 February 1: The universal covering space

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2008 February 5: The covering space handout

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2008 February 5: The covering space handout (2)

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2008 February 5: The covering space handout (3)

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2008 February 5: The covering space handout (4)

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2008 January 31, February 5, 7: Covering spaces

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2002 May 2: Simplicies and the boundary map

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2002 May 7: Simplicies, homology, functoriallity

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2002 May 9: Cont

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2006 February 2: More on thefundamental theorem of covering spaces

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2006 February 7, 9, 14: Basic homolog

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2008 February 12: Homology, the Abelianization of homotopy

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2008 February 12, 14: Homology, the Abelianization of homotopy (2)

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2007 February 11: Term Exam 2

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2007 February 11: Term Exam 2 (2)

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2002 May 14: The prizm, short to long exact sequences

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2005 January 25: Homology, homotopy invariance

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2005 January 27: The prizm, short to long exact sequences

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2008 February 26: A Homology Theory is a Monster

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2008 February 26: A Homology Theory is a Monster (2)

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2008 February 28: Exactness

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2008 March 4: Long exact sequences, excision

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2008 March 6: Proof of excision

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2008 March 6: Proof of excision (2)

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2008 March 11: Proof of excision

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2008 March 11: Proof of excision (2)

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2008 March 13: The homology of spheres

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2008 March 18: Degrees

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2008 March 18: Degrees (2)

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2008 March 20: CW spaces and homology

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2008 March 20: Degrees

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2008 March 25: CW spaces and homology

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2008 March 25: CW spaces and homology (2)

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HW12

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Topological Pathologies in R^3

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Planning, the key diagram for CW

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The key diagram for CW

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2008 March 27: Things we skip, pathologies

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2005 March 10, 15: CW, ${\mathbb R}P^n$

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2005 March 17, 22, 24: Mayer-Vietoris, Jordan's curve theorem, Borsuk-Ulam

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2005(?) March 30, April 4: Borsuk-Ulam

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2005(?) April 6: Invariance of domain, Borsuk-Ulam

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2008 April 1: Invariance of domain, Borsuk-Ulam

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2008 April 1: ${\mathbb R}^n$ theorems

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2008 April 3: Borsuk-Ulam, the necklace theorem

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2008 April 8: de-Rham cohomology and singular homology

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2008 April 8: de-Rham cohomology and singular homology (2)

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2008 April 10: de-Rham cohomology and singular homology

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The Final Examination

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The Final Examination (2)

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The Final Examination (3)

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Annotated Term Test

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Annotated Term Test (2)

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