Your instructor:| Name: | Dr. Paulo Lima-Filho | E-mail: | plfilho@math.tamu.edu | |
|---|---|---|---|---|
| Office: | Milner Hall, Room 306 | URL: | http://www.math.tamu.edu/~Paulo.Lima-Filho | |
| Phone: | 845-5298 (office)
845-7554 (Math. Dept.) |
|||
Textbook:- Topology and Geometry, by Glen E. Bredon, Graduate Texts in Mathematics 139, Springer-Verlag;
- Topology, A first course, (for reference only) by James Munkres, Prentice-Hall.
Brief course description:- Contents: (3 credits)
- This is the first semester of a one year course designed to provide a modern introduction to Topology. The whole course is basically divided into three parts: General Topology, an introduction to Differential Topology and an introduction to Algebraic Topology.
- In General Topology we cover the basic notions of topological spaces and subspaces and their basic attributes, such as the notions of connectivity and connected components, separation and countability axioms. Quotient spaces, nets and convergence, compactness and local compactness, products, Tychonoff theorem; metrization theorems. Paracompactness and basic notions in homotopy theory.
- In Differential Topology, we cover basic notion of differentiable manifolds theory, examples, vector fields and tangent bundles; Sard's theorem; immersions and submersions; embedding theorems; transversality and Pontryagin-Thom theory.
- The last portion of the course will cover basic notions of Algebraic Topology, by first discussing the fundamental group and classification of covering spaces; Seifert-Van Kampen theorem and various computations. Then we proceed to introduce homology and cohomology theories and their axioms; CW-complexes and cellular homology; Mayer-Vietoris sequence; classical applications, such as Borsuk-Ulam theorem, Generalized Jordan curve theorem and Lefschetz-Hopf index theorem. Differential forms and DeRham cohomology for manifolds are then discussed, along with a discussion of the relation to singular cohomology.
Schedule of classes:- Mondays, Wednesdays and Fridays, ZACH 127A, 11:30am--12:20pm.
Test dates and grading policies:- Exam #1 : will take place on October 1st during class time; worth 100 points.
- Exam #2 : will take place on November 5th; worth 100 points.
- Final Exam : will be given in the last week of classes; worth 200 points.
- Assignments : Various assignments will be given along the semester and they are due one week after the respective hand out day. The totality of assignments will be worth 200 points.
- Grading : Total # points: 600. Grades will be curved in standard fashion.
- Exams, projects and assignments are activities to be performed individually by each student.
- Any violation of this policy or any cases of scholastic dishonesty will have severe and undesirable consequences for the perpetrators.
Makeup Exams:- will be given only in case of an absence authorized under University Regulations (Section 15 thereof). A note from your doctor or academic advisor is necessary. If you know in advance that you will miss an exam, please contact me beforehand, via e-mail.
Miscellaneous notes:- See my MATH 636 Home page in the Web for details on homework and projects.
