| Begge sider forrige revisjon
Forrige revisjon
Neste revisjon
|
Forrige revisjon
Neste revisjon
Begge sider neste revisjon
|
tma4190:2019v:start [2019-02-11]
glenmw [Tabell] |
tma4190:2019v:start [2019-04-12]
glenmw [Lecture Plan] |
| This is a rough outline of the course structure that will be updated throughout the semester. | This is a rough outline of the course structure that will be updated throughout the semester. |
| |
| ^ Week ^ Topic ^ Reference ^ Exercises ^ Notes ^ | ^ Week ^ Topic ^ Reference ^ Exercises ^ Notes ^ |
| | 2.1 | Introduction | | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Week01.pdf|Notes 1]] | | | 2.1 | Introduction | | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Week01.pdf|Notes 1]] | |
| | 2.2 | Topology of Rn | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise01.pdf|Set 1]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Week02.pdf|Notes 2]] | | | 2.2 | Topology of Rn | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise01.pdf|Set 1]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Week02.pdf|Notes 2]] | |
| | 3.1 | Subspaces, connectedness | | | | | | 3.1 | Subspaces, connectedness | | | | |
| | 3.2 | Cut points, compactness | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise02.pdf|Set 2]] | | | | 3.2 | Cut points, compactness | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise02.pdf|Set 2]] | | |
| | 4.1 | Smooth manifolds, tangent spaces | GP 1.1 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture05-hand.pdf|Notes 3]] | | | 4.1 | Smooth manifolds, tangent spaces | GP 1.1 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture05-hand.pdf|Notes 3]] | |
| | 4.2 | Tangent spaces | GP 1.2 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise03.pdf|Set 3]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture06-hand.pdf|Notes 4]] | | | 4.2 | Tangent spaces | GP 1.2 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise03.pdf|Set 3]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture06-hand.pdf|Notes 4]] | |
| | 5.1 | Inverse function theorem | GP 1.3 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/CoordinateChartSupplement.pdf|Supplement]] | | | 5.1 | Inverse function theorem | GP 1.3 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/CoordinateChartSupplement.pdf|Supplement]] | |
| | 5.2 | Submersions | GP 1.4 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise04.pdf|Set 4]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture07-hand.pdf|Notes 5]] | | | 5.2 | Submersions | GP 1.4 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise04.pdf|Set 4]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture07-hand.pdf|Notes 5]] | |
| | 6.1 | Fundamental theorem of algebra | GP 1.4 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/FundamentalTheoremAlgebra.pdf|Notes 6]] | | | 6.1 | Fundamental theorem of algebra | GP 1.4 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/FundamentalTheoremAlgebra.pdf|Notes 6]] | |
| | 6.2 | Transversality | GP 1.5 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise05.pdf|Set 5]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture09-10.pdf|Additional FTA notes]] | | | 6.2 | Transversality | GP 1.5 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise05.pdf|Set 5]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture09-10.pdf|Additional FTA notes]] | |
| | 7.1 | Transversality and homotopy | GP 1.6 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture10-hand.pdf|Notes 7]] | | | 7.1 | Transversality and homotopy | GP 1.6 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture10-hand.pdf|Notes 7]] | |
| | 7.2 | Transversality and homotopy | GP 1.6 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise05.5.pdf|Set 6]] | | | | 7.2 | Transversality and homotopy | GP 1.6 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise05.5.pdf|Set 6]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture12-hand.pdf|Notes 8]] | |
| | 8.1 | Sard's theorem, Morse functions | GP 1.7 | | | | | 8.1 | Sard's theorem, Morse functions | GP 1.7 | | | |
| | 8.2 | Sard's theorem, Morse functions | GP 1.7 | | | | | 8.2 | Sard's theorem, Morse functions | GP 1.7 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise06.pdf|Set 7]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture13-hand.pdf|Notes 9]] | |
| | 9.1 | Midterm | | | | | | 9.1 | Midterm | | | | |
| | 9.2 | Embeddings in Rn | GP 1.8 | | | | | 9.2 | Embeddings in Rn | GP 1.8 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise07.pdf|Set 8]],[[http://folk.ntnu.no/glenmw/IntroTopology2019/MobiusBand.pdf|Prob 4]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture15.pdf|Notes 9]] | |
| | 10.1 | Manifolds, partitions of unity | GP 1.8 | | | | | 10.1 | Abstract Manifolds, Projective Space | GP 1.8 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture16.pdf|Notes 10]] | |
| | 10.2 | Manifolds with boundary | GP 2.1 | | | | | 10.2 | Partitions of Unity | GP 1.8 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise09.pdf|Set 9]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture17.pdf|Notes 11]],[[http://folk.ntnu.no/gereonq/TMA4190V2018/TMA4190_Lecture16.pdf|P.O.U. supplement ]] | |
| | 11.1 | Brouwer Fixed-point theorem | GP 2.2 | | | | | 11.1 | Manifolds with boundary | GP 2.1 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture18.pdf|Notes 12]] | |
| | 11.2 | Transversality | GP 2.3 | | | | | 11.2 | Brouwer Fixed-point theorem, Transversality | GP 2.2, 2.3 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise10.pdf|Set 10]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture19.pdf|Notes 13]] | |
| | 12.1 | Transversality | GP 2.3 | | | | | 12.1 | Transversality | GP 2.3 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture20.pdf|Notes 14]] | |
| | 12.2 | Mod 2 intersection theory | GP 2.4 | | | | | 12.2 | Mod 2 intersection theory | GP 2.4 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise11.pdf|Set 11]] | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture21.pdf|Notes 15]] | |
| | 13.1 | Winding number, Jordan-Brouwer | GP 2.5 | | | | | 13.1 | Winding number, Borsuk-Ulam theorem | GP 2.5, 2.6 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture22.pdf|Notes 16]] | |
| | 13.2 | Borsuk-Ulam theorem | GP 2.6 | | | | | 13.2 | Lecture cancelled | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise12.pdf|Set 12]] | | |
| | 14.1 | Orientations | GP 3.2 | | | | | 14.1 | Orientations | GP 3.2 | | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Lecture23-24.pdf|Notes 17]] | |
| | 14.2 | Oriented intersection number | GP 3.3 | | | | | 14.2 | Oriented intersection number | GP 3.3 | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Exercise13.pdf|Set 13]] | | |
| | 15.1 | Oriented intersection number | GP 3.3 | | | | | 15.1 | Lefschetz fixed-point theory | GP 3.4 | | | |
| | 15.2 | Lefschetz fixed-point theory | GP 3.4 | | | | | 15.2 | Poincare-Hopf index theorem | GP 3.5 | | [[https://www.maths.ed.ac.uk/~v1ranick/papers/francisweeks.pdf|Conway's ZIP proof]] | |
| | | Poincare-Hopf index theorem | GP 3.5 | | | | |
| | | | | | | | |
| | | | | | | | |
| |
| |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Quiz01.pdf|Quiz 1]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Quiz02.pdf|Quiz 2]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Quiz03.pdf|Quiz 3]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Quiz04v2.pdf|Quiz 4]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Quiz05v2.pdf|Quiz 5]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Quiz06v2.pdf|Quiz 6]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Midterm1.pdf|Midterm]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Quiz07.pdf|Quiz 7]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Quiz08.pdf|Quiz 8]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Quiz09.pdf|Quiz 9]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Quiz10.pdf|Quiz 10]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Quiz11.pdf|Quiz 11]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/Quiz12.pdf|Quiz 12]], |
| | [[http://folk.ntnu.no/glenmw/IntroTopology2019/CourseContentOutline.pdf|Course Content Outline]] |
| |
| ===== Reference Group ===== | ===== Reference Group ===== |