Last edited 28may13


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Syllabus "Post-Euclidian Geometry"
 
 netMA402 Summer 2013 


Note: This syllabus for the 8 week online NetMath
course is based on 45 class periods in the regular in-class semester course. 

Instructions 
This file is frequently updated. Check the date and reload your browser

pages each time you visit. Note the convention that "F1" means
"Friday of Week 1", while "C2" refers to the second lesson in Cartesian
Geometry. Label all course submissions by this week-day code. For full 
credit submit work as directed when it is due according to this syllabus.
Square brackets mark the sections in Hvidsten's textbook which most closely 
correspond to the lesson.  This syllabus overrides all other instructions, 
in case of an inadvertent conflict. 
Online students, please this syllabus to pace your study of the course.
It is based on a one semester course with two weekly lectures and one lab/quiz
per week.  Its adaptation to distance-education requires 
modifications which are announced separately.  Update this page before each reading.

Geometry and the Axiomatic Method [Hvidsten Chapter 1] 
\begin{itemize}
\item M1 Introduction and Advice for Completing the Course  
\item T1 [1.1, 1.2] Lesson A1:  Greek Geometry from Thales to Pappus  with filecard. 
\item W1 Lesson A2:  Exterior Angle Lab  I  Introduction to Geometry Explorer (GEX2.0) with filecard. Lab report is due in two weeks. 
\item R1 Lesson A3:  Axiomatic Systems in Geometry   
\item F1 [1.4] Lesson A4:  Toy Axiom System  better known as Finite Geometries. With filecard.
\item S1 Catch-up and Virtual Office.
\item M2 Submit  HomeworkM3 on axiomatic systems on Moodle. Do Hvidsten 1.5.4, 1.5.5., 1.5.6, 1.5.7 as directed. 
\item T2 Submit the Census Filecard . Questions 1 and 5 pertain only to online students.
\item W2 [1.5] Lesson A6: Models of Axiomatic Systems .
\item R2 Review and  Sample Quiz 
\item F2 QuizA. This quiz tests lessons A1-A6 and elementary skills GEX2.0. Be sure to bring your Journal to class with you. For online students, follow the directions for quizzes.  
\item S2 Catch-up and Virtual Office.
\end{itemize} 
Euclid's Geometry [Hvidsten Chapter 2] 
\begin{itemize}
\item  M3 [2.1] Lesson E1 on Absolute Geometry  with filecard. 
\item  T3 [2.2] Lesson E2 on Euclid's Parallel Postulate   with filecard.
\item W3 [2.3] Lesson E3 on John Playfair's Axiom  and its equivalents. Filecard TBA.
\item R3 Submit  Homework on Euclid's Parallel Postulate as posed in Lesson E2. 
\item F3 Lesson E4 on the Pythagorean Theorem  as Euclid proved it. With filecard.
\item S3  Review and catch up and Virtual Office.  
\item M4 QuizE . This is an in-class quiz testing lessons
E1--E4 on Euclid's geometry. Online students, follow directions on quizzes.
\end{itemize}
 Cartesian Geometry a.k.a. Analytic Geometry.
\begin{itemize}
\item T4   [2.5] Lesson C1 on  Similarity , ladder lemma, AAA, and simSAS. 
\item W4     Lesson C2  on  Cartesian Geometry as Model for Birkhoff's Axioms  
\item W4     Lesson C3, a remediation on  Circular Numbers  needed for Birkhoff's Protractor Axiom.
\item R4     Submit  HomeworkF6  on Birkhoff's Axioms. 
\item F4     Advice on preparing for the  Midterm 
\item S4     Virtual Office sessions in preparation to the Midterm. 
This ends the first half of the course.
\item M5-S5  The 2-hour proctored Midterm  must be taken in week 5 of this
course. Proctor information must be complete by one full week prior (eg M4) to taking the exam. 
\end{itemize}



 Part II of the Course 

The second 4 weeks of this course deals with the modern approach to 
geometry in terms of Transformation Groups, in particular the group of 
Moebius Transformation and its subgroups. The Syllabus will be filled 
in as lessons become ready and relevant. Please consult the Syllabus 
daily and be sure to update your browser.

\begin{itemize}
\item M5  Overview of Lessons on Models, Part I.
\item T5 [3.5] The Complex Plane and 
Euler's Theorem. Filecard Z1 questions due.  
\item W5 Q/A on Problems 3.5.1 -- 3.5.5 in Hvidsten.  
\item R5 Lesson on  Moebius Transformations  with filecard Z2.
\item F5 Quiz on complex numbers and plane geometry. (10 minutes)
\item S5 Catch-up and Virtual Office.
\item M6 Start on lesson on  Cross Ratios 
\item T6 Lesson on  Cross Ratios  with filecard Z3
\item W6  Discussion of the Exercises 8.2.1-15
\item R6 Homework M10 due. Submit Exercises 8.2.8, 8.2.2, and 8.2.3, and 
the two extensions.  
\item F6  Supplement 
as discussed in the session.
\item S6 Catch-up and Virtual Office
\item M7 Lesson on  Hyperbolic Group  with filecard H1.
\item T7 Lesson on  Hyperbolic Distance  with filecard H2.
\item W7 Lesson on  Hyperbolic Translation  with filecard H3.
\item R7 Supplementary lessons and catch up snow day. 
\item F7 Sample Quiz  on Moebius Transformations.
\item S8 Virtual Office preparation for the final.
\end{itemize}

 Review and Finals Week  
 Note. You may not take the final examination unless you have completed all
required work. A limited form of accommodation in special circumstances can be arranged with the
Professor of this course. Graduate students can obtain extensions according to the rules of the
Illinois Graduate College. Undergraduate students must also contact their departmental avisors for 
extensions. Non-degree seeking undergraduates may make private arrangements with the Professor.  

\begin{itemize}
\item M8 Review of course, preparation for the final.
\item R8 Review of course, essay topics for the final.
\itme F8 Final Examination as scheduled by the University.
\item W8-M8 The 3 hour proctored Final Examination 
must be taken between W8 and S9. Any final not in hand on M10 may not be ready
in time for an ontime submission of your grade. 
\end{itemize}


 The following sections are not part of the online, Summer 2013 syllabus of this course. 

 Area of all Ideal Triangles is $\pi$  
\begin{itemize}
\item M12 Gauss' theorem on areas (see notes) 
\item W12 Gauss' theorem cont'd
\item F12 Review of Lessons H1,H2,H3 (sample quiz).
\item M13 QuizH  
\item W13 Gauss' theorem concluded.
\end{itemize}
 Nano-Introduction to the Geometry of Fractals  
\begin{itemize}
\item M14 Fractal dimensions and Sierpinsky's Triangle. 
\item W14 Turtle Geometry 
\item F14 Recursion and Lindenmeyer Systems
\end{itemize}
 Review Week  
\begin{itemize}
\item M15 Review of course, preparation for the final.
\item W15 Review of course, essay topics for the final.
\item R16 Final Exam 
\end{itemize}




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