5nov07 Revised. 

Note: For a variety of good reasons we are adding one week to 
      the expositions, problems and quizzes of Tondeur Chapter 1.

Syllabus Math 403 "Advanced Topics in Geometry" Fall 2007 
Text: P. Tondeur, Vectors and Transformations in Plane Geometry.
Supplements: G. Francis, A Toplogical Picturebook, Chapter 3.
             M. Hvidsten, Geometry with Geometry Explorer (GEX)
Instructor: George Francis, section D1, 11MWF.

See also http://new.math.uiuc.edu/math403/ 
for calendar, updates, notes and frequently asked questions (FAQ). 

Key: Day-Week labels. Text sections in [x.y]. Exercises in <x.y>.  

W1 Introductory Lecture and Course Outline.
   Hw-F1: Read Tondeur [1.5] and try exercise <1.6>.

F1 [1.6] Discuss Hw-F1. 
   Lesson: Parallelograms. Do <1.7, 1.8> in class.
   Hw-M2: Exercises <1.7, 1.8> written up neatly and try <1.9>.

M2 [1.7] Discuss Hw-M2. 
   Lesson: Centroid Theorem.
   Hw-F2: <1.10, 1.11, 1.12, 1.13>. 
   Note: We skip [1.8, 1.9 and 1.10].

W2 [1.11] Lesson: Barycentric Coordinates.
   Discuss exercises <1.17, 1.18>, write up solution in your Journal.

F2 [1.12] The Theorems of Ceva and Menelaus. Guest Lecture..
   Discuss HW-F2, 
   Hw-F4: <1.20, 1.21, 1.22, 1.23>.

M3 Labor Day. 

W3 Return and discuss Hw-M2.

F3 Discuss Hw-F2, begin on Ceva.

M4 [1.12] Ceva's Theorem proved with barycentric coordinates.

W4 [1.12] Menelaus' Theorem 
   Lesson: Equivalence of Ceva and Menelaus.

F4 Discuss: HW-F3.

M5 Quiz 1 (20 minutes)

   Lesson: Introductory Lecture on Plane Transformation Groups. 

   Note: We postpone [1.13] on Desargues and Pappus until we 
         treat the projective plane and linear perspective.
   Note: We next cover selections from Tondeur Chapter 2 and 3
         because Ch2 in its entirety is too difficult at this time,
         and Ch3 in its entirety is redundant plane vector calculus.
   Note: Use webnotes: "Dilatations, Euler's Line and Feuerbach's Circle."

W5 Court's Proof of the Euler Line Theorem (Euclidean Geometry).
   Discuss HW-F3 and Quiz.
   HW-W6: Dilatation Notes exercises <D1,D2>

F5 Construct <D1, D2> in the Lab using KSEG.
   Lesson: Transformations of the plane; translations. 
   HW-M7: <D3, D4, D5>.

F5 Computer Lab. Lesson on Ceva, Menelaus and Euler's Line.
   Complete lesson at home using GEX or KSEG or GSP.
   HW-F6: Write up lab report on exercises <D1, D2>. 

M6 Lesson: Central dilatations, reflections, involutions.
   HW-F5: <D5, D7, D8>.

W6 Discuss HW-M5.
   Lesson: Geometric properties of central dilatations.
   
F6 Lesson: Proof of Euler's Theorem using transformations.

M7 Discuss HW-F5.
   Lesson: Proof of Feuerbach's Nine Point Circle.
   Note: this completes the work tested on Midterm F7.

W7 Discussion of work to date. 

F7 Midterm (50 minute exam).

Weeks 8-10 Drawing in Linear Perspective [Class notes.] 

M8 Kepler's ideal points and lines. 
   Due M9: Problems on Desargues and Pappus w. Ideal Points

W8 Elements of Perspective Drawing. Alebrti's Veil.
   Quadrilateral to horizon with vanishing points.

F8 KSEG lab.  

M9 Horizon and Zenith, Eypoint, Alberti's Triangle.
   Thales' Theorem, Pythagorean Theorem and Geometric Mean. 
   Due W9: Eypoints from where a quad is a square in perspective. 

W9 3-point Perspective. 
   Due F9: Complete a given edge to a cube in 3-point perspective.

F9 Peeping House (more 3-pt perspective)
   Due M10: Build a paper peeping house for a perspective cube. 

(tentative)

M10 Sines, Periferal Angle Theorem, Cross Ratio, Perspective Ruler.
   Due W10: 

W10 2-point perspective. Plan and Elevation. 
   Due F10: Perspective Church.

F10 KSEG Lab. Be prepared to demonstrate constructions to date

Week 11 Finish homework portfolio. Propose semester project on 
    perspective.  

Weeks 12-15 Euclidean Isometry Groups [Tondeur Chapter 4]. 

Tondeur Chapter 4. There are class notes that will be handed out.
      For the following "daily" homework, the first problem is solved
      in part in the back of the book. Work on this problem will be 
      marked "present" for the time being. I may look at this later in
      the semester.

      The second problem, not solved in the back, will be graded for 10pts.
      

due W12    Ex 4.1 as corrected in class. 
           Ex 4.2 graded for 10pts.

due F12    Ex 4.3 Solution is in the back of the book. Marked present.
           Ex 4.4 graded for 10points.

due M13    Ex 4.5 Solution is in the back of the book. Marked present or not.
           Ex4.6  grade this (10points) and return W13

There will be an assignment due W13 and F13. I will announce it here by M13. 


Final, 8-11 Wednesday December 2007 (W16).