Estimated Schedule for Math 360
Spring 2007
last update: Jan 23

Unless otherwise stated, homeworks are due on Thursdays.  Chapters and exercise numbers refer to the third edition of the text. 

Week
Topics
Reading
Homework and projects due
1/22 Introduction.
Euclid's geometry  		Chapter 1
1/29 Euclid's geometry   Chapter 1 Chapter 1: Exercises 1, 2, 3, 4. Mayor Exercise 1.
To think about (but not submit) Exercises 8 and 11.
2/5 Logic and Incidence Geometry Chapter 2 Chapter 2, Exercises 1,2,3,4 and 5
Prove that the square root of 10 is not rational. Click here for a list of the logic rules in PDF.
2/12 Interpretation of Axioms Systems, Models,
Affine and Projective Planes
 Chapter 2 Chapter 2: Translate Prop. 2.2 and 2.3 (pag 51) to "shash" geometry and prove them (everything in shash terms)
Exercises 6 (Only Prop. 1,4,5), Exercise 7, and Exercise 8.
2/19 Hilbert's Axioms: Betweenness and Congruence. Chapter 3 Chapter 2: Exercise 9 (20 points), Exercise 10 (20 points), Exercise 11.
(Remember to justify your answers.)
Extra credit: Exercise 12.
2/26 Guest lecturer: Dennis Sullivan Chapter 3: 1, 6, 15, 20, 24, 28
For a list of Axioms and Propositions in PDF format click here , use right click on list.pdf, and save it.
3/5 Hilbert Axioms:  Continuity and Parallelism - Neutral Geometry
 Chapter 3, 4 Given in class. It is here in jpeg format.  
3/12 Review (3/13 ) -Midterm! (3/15)
No homework !
Practice problems for the midterm:
1. Chapter 1, Problems 1, 2, 3.
2. Chapter 2, Problems 7, 10, 11.
3. Chapter 2, Problem 8, 9.
4. Chapter 3, Problems 1, 2,  6.
Here there are solutions to some of the exercises (in Word)
3/19 Neutral Geometry - Sketchpad
 Chapter 4 Chapter 3: Problems 33 and 34
For the interpretation given  in Project 2 (Chapter 3) prove that the following axioms are correct statements (10 points each):
  1. Incidence Axiom 3
  2. Betweeness Axiom 3
  3. Congruence Axiom 2
  4. Elementary Continuity Principle.
Midterm statistics are here
3/26 Neutral Geometry
 Chapter 4  Geometer's sketchpad exercises click here.
Read the  Final Report Proposal and the Sketchpad Project. 

4/2
Spring Break

4/9 History of the parallel postulate Chapter 5 Final Report Proposal due ("worth" is ten points of HW)
Chapter 4: Problems 1, 3, 15.
4/16 The discovery of non-euclidean geometry Chapter 6 SketchPad Project due
Chapter 4: Problems 4, 5, 6
4/23 The discovery of non-euclidean geometry Chapter 6 Chapter 4: Problem 10.
Chapter 5: Problem 8
Chapter 6:  Problems 2, 3, 5, 14
•Extra credit (deadline at the end of the course).
–Chapter 4: Problems 8 and 9
–Chapter 5: Problem 1
4/30 Independence of the parallel postulate - Review
 Chapter 7 Practice exam
 Final Report Due 
Final exam: Tuesday May 15th, 11 to 1:30 in 4-130, Math Tower