MATH 403 C13, Fall 2005. Euclidean Geometry.

Textbook. Vectors and transformations in plane geometry, Philippe Tondeur.

For those who have not obtained the textbook yet, a copy of the book is available on the reserve in the Altgeld Hall library, during the regular library hours.

• Read and understand sections 1.1-1.5.
• hw1 Exercises 1.3, 1.4, 1.5, 1.6. Due Wednesday, Aug 31.
• hw2 Bottom of page 7, prove that the lines do not intersect; Exercises 1.7, 1.8, 1.9, 1.11.
• hw3 Ex. 1.10, 1.12, 1.13,1.15; due Wednesday Sept 14.
• hw4 Prove the lemma: If l is a line passing through two distinct points A and B, then l=l_AB.
  Prove the corollary: If two lines l and l' pass through the same pair of distinct points, then l=l'.
  Ex. 1.17 (do not use the answer in the book, use the definition of lines and parallel lines). Due Wednesday, September 21.
• hw5 Ex. 1.20, 1.23. Due Wednesday, September 28.
• hw6 Prove that if f:A->B is a bijection, then there exists a bijection g:B->A such that fg=identity and gf= identity. (This implies the existence of inverses in T=T(V).)
  Also Ex. 2.1, 2.2. Due Wednesday Oct. 19.
  
• hw7 Ex. 2.8, 2.9, 2.10. Due Wednesday Oct. 26. Hint for 2.8: first show that, given a bijection f, there is exactly one function g as in hw6 above; that is, the inverse of f is unique. That is, given a bijection f, there exists a unique g such that fg=identity and gf= identity. Then use this to show that alpha^-1 beta^-1 is the inverse of beta apha.
  Hint for 2.10: use compositions of the three central reflections about A',B',C', and look for their fixed points. What is a composition of three central reflections? What are fixed points of a central reflection?
  
• hw8 Suppose Z'(dot)Z=0 and Z"(dot)Z=0, where Z, Z' and Z" are non-zero. Show that Z' and Z" are proportional (parallel).
  Also Ex. 2.11, 2.12. Due Wednesday Nov 2.
  
• hw9 Use the proof of Theorem 1.4 to show that delta_G,-2 (A')=A and delta_G,-1/2 (A)=A'.
  Show that if delta is a central dilatation, and A and B are distinct points, then delta maps l_AB to l_{delta(A)delta(B)}. (One can also see that these two lines are parallel. The same holds for translations as well.)
  Also Ex. 3.4. Due Wednesday Nov 9.
• hw10 Ex. 3.7, 3.9, 3.11. Due Wednesday Nov 16.
• hw11 Ex. 4.1,4.2,4.4. Due Wednesday Nov 30.

What to prepare. As a general rule, quizzes and exams will be based on the material discussed in class and in the homework assignments that were before the date of the exam. This includes definitions and proofs of theorems. We generally follow the book, but I will often present more details in class than the book provides. So read the book and your class notes. The quizzes will concentrate on, but not be limited to, the material that was covered since the last quiz/exam. You are expected to learn and know all the material starting from the beginning of the course. Journals can be used only for the final exam, but it is a good idea to write things in the journal regularly. Using your journal makes it easier to prepare for quizzes/exams.

Exams. The midterm exam was on Wednesday, October 12. The median was 31 out of 40, mean 75.6%=30.24 . The curve used for exam: perfect score 40, A 32, B 27, C 22, D 17. This means that the interval from 32 to 40 is subdivided into three equal parts corresponding to A-, A, A+, respectively; and similarly for B,C,D.
You can check your current grade for this course. The expression ex:34<37/40 means that you received 34 points out of 40 for the exam, and it was rescaled to 37 because of the curve used. 37/40=92.5% corresponds to A- in the overall curve A 90%, B 80%, C 70%, D 60%.

The final exam did take place in the regular lecture room, from 8:00am to 11:00am, Saturday, December 17, 2005, as described in Final Exams Schedule. The median was 88 and the mean was 85.7%. The curve used for the final exam was A 90, B 80, C 65, D 55.

Grades. Homework 15%, quizzes 15%, projects 20%, midterm 20%, final 30%. A journal can be used for the final exam. It must be bound like a book, no spiral. Make notes in the journal at home, not in class. On the front write your name, MATH 403, Fall 2005, and also the word "journal". Only hand-written notes. No additional sheets. I will ask you to turn in the journal once or twice during the semester.

The grades for the project will not appear on the web until everyone has done it. Talk to me during the office hours if you would like to know the grade.

Questions. It is absolutely important that you ask questions, during the class and at the office hours. If at some point you realize that you were lost for a week, it is because you have not asked a question a week ago.

More information will appear here as we proceed.

Math Contests at Illinois
Informational Meeting
Thursday, Sept. 29, 5 pm -- 6 pm
245 Altgeld Hall
http://www.math.uiuc.edu/contests.html