### Dr. Sarah's Math 4710/5710 Class Highlights Fall 2003 Page Also see the Main Class Web Page

Tues Dec 2 Compactness

Thur Dec 4 Compactness
Tues Nov 25 Finish up connectedness and path connectedness.
Tues Nov 18 Review Klein bottle, torus and projective plane with manipulatives, and finish 2.6

Thur Nov 20 Connectedness
Tues Nov 11 Finish 1.7 and begin 2.6

Thur Nov 13 Take test and Continue 2.6.
Tues Nov 4 Continue 1.7

Thur Nov 6 Continue 1.7
Tues Oct 28 Test 2 and Oral Test Continued

Thur Oct 30 Oral Test Continued.
Tues Oct 21 Continue 1.7
Tues Oct 14 Oral Test

Tues Oct 16 Begin 1.7.
Tues Oct 7 Selections from 1.6 and 5.1 (convergence, Hausdorff, and T_1 spaces).

Thur Oct 9 Finish Hausdorff and T_1 spaces, including an intro to the Zariski topology and p. 159 13 a and d.
Tues Sep 30 Section 1.4 continued

Thur Oct 2 Finish 1.4 and WebCT test.
Tues Sep 23 Finish section 1.3 and begin section 1.4.

Thur Sep 25 Section 1.4 continued
Tues Sep 16 Begin section 1.3.

Thur Sep 18 Continue section 1.3.
Tues Sep 9 Finish Patty section 1.1 and begin section 1.2. Go over portions of problem set 1.

Thur Sep 11 Go over basic definitions. Section 1.2.
Tues Sept 2 Patty section 1.1 continued.

Thur Sept 4 Convocation
Tues August 26 Syllabus and fill out Information Sheet. What is topology?. Selections from history of topology including Euler and the Konigsberg bridges (groups present solutions to what happens if you remove a bridge), and Euler characteristic. Hand out Proof-Writing Samples and review proof-writing via intro to Minesweeper proofs. Review the Proof-Writing Checklist Mathematical abbreviations. Hand out Problem Set 1.

Thur Aug 28 Finish mathematical abbreviations. Review of the principal of mathematical induction and its proof. Motivate the importance of continuity. History of calculus and how the lack of rigour necessitated the development of analysis and topology. Given the epsilon-delta definition of f continuous at x_o, try to prove that f(x)=|x| is continuous at x_o real. Notice that we need | |x|-|y| | < or = |x-y|, so we prove this. If time remains, Begin Patty section 1.1.