| Math 343 | Topics in Analysis | Spring 2000 | |
| MONDAY | WEDNESDAY | FRIDAY | |
| JANUARY 24--28 | Introduction, Review of set theory | Review of the real line 1.1 -- 1.5 | Review of the real line 1.1 -- 1.5 |
| Jan 31--Feb 4 | Euclidean space, structures 1.6 | Metric spaces 1.7 | Open sets 2.1 |
| FEBRUARY 7--11 | Interior of a set , Closed sets 2.2 --2.3 | Accumulation points, Closure 2.4 --2.5 | Boundary of a set 2.6 |
| 14--18 | Sequences 2.7 | Completeness 2.8 | Compactness 3.2 |
| 21-25 | Heine Borel 3.2 --3.3 | Path connected sets 3.4 | Connected sets 3.5 |
| Feb 28 -- March 3 | Continuity 4.1 | Continuity 4.1 | Images of compact and connected sets, 4.2, 4.4, 4.5 |
| MARCH 6--10 | Images of compact and connected sets, 4.2, 4.4, 4.6 | Operations on Continuous functions 4.3 | Quotient and subset topology |
| March 11--19 | RECESS | ||
| 20-24 | Vector Fields in R^2 Take home midterm starts | Index of a vector field | Brouwer fixed point theorem |
| 27-31 | Spaces of conts functions 5.5 Take home midterm ends | Spaces of continuous functions 5.5 | Survey of Fourier Analysis 10.1 --10.2 |
| APRIL 3 -- 7 | Derivatives 6.1 | Matrix representation 6.2 | Continuity of differentiable maps 6.3 --6.4 |
| 10 --14 | Chain rule 6.5 | Contraction Mapping Principle (and ODEs) 5.7 | Inverse Function Theorem 7.1 |
| 17 -- 21 | Inverse Function Theorem 7.1 | Implicit Function Theorem 7.2 | Manifolds |
| 24 -- 28 | Vector fields on surfaces | Euler Characteristic | Poincaré-Hopf Theorem |