### 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.