Math 531: Foundations of Geometry.

Section 001

Fall 2011

University of South Carolina


      Instructor  
      Matthew Boylan  
  Office     LeConte 402  
  E-mail     boylan@math.sc.edu  
  Office hours     Mon. 12:30 - 1:30  
  Weds. 10 - 11  
  Thurs. 10 - 11  
  and by appointment  

  • University of South Carolina Mathematics Department .

  • Course information :

  • Prerequisite : Math 241.

  • Text : Geometry for College Students, by Isaacs, American Mathematical Society Pure and Applied Undegraduate Texts Vol. 8.

  • Objectives : Students will master concepts and solve problems on Euclidean geometry including properties of lines, circles, triangles, and other geometric figures.

  • Class meeting schedule :

      Lecture     MWF     9:05 - 9:55     LeConte 310  

    In accordance with official USC policy, a grade penalty of up to 10% may be assessed for any student missing more than 3 classes during the semester. Roll will be taken at the beginning of each class.

  • Exam schedule : (3 in-class exams and a cumulative final.)

      Exam 1:     Wednesday     September 21     9:05 - 9:55     LeConte 310  
      Exam 2:     Wednesday     October 26     9:05 - 9:55     LeConte 310  
      Exam 3:     Monday     November 21     9:05 - 9:55     LeConte 310  
      Final Exam:     Monday     December 5     9:00 - 12:00     LeConte 310  

  • Homework : Homework will be assigned each week and collected. A minimum requirement for success in this course is doing and understanding all assigned homework. You must do whatever it takes to meet this requirement. Do not hesitate to ask questions on the difficult problems.

  • Grading :

          Points/650     % of grade  
      Three hour exams:     100 pts. x 3     15% x 3  
      Final exam:     200 pts.     30%  
      Homework:     150 pts.     25%  
      Total:     650 pts.     100%  

    Extra credit will not be offered.

    Letter grades will be assigned according to the following approximate scale unless otherwise noted:

      A     B     C     D     F  
      90 - 100     80 - 90     70 - 80     60 - 70     0 - 60  

    Note: The deadline to drop without a WF is Thursday, October 13.

    Make-up policy Neither missed quizzes nor missed exams will be made up. Exceptions may be made for exams missed due to documented illness/family emergency.

  • Other policies : Electronic devices such as cell phones and blackberries are to be turned off or put on silent or vibrate mode during class meetings. Visible use of such devices during lecture is very distracting.

    Quiz and exam grades may be discussed only up to 7 days after being returned.

    If you plan to leave class early, the correct procedure is to inform me before the lecture begins. Early departures disrupt lecture unless this procedure is followed.

    Do not be late to lecture. If you know that you will arrive late, the correct procedure is to inform me ahead of time; students arriving late should discretely find an open seat. Late arrivals disrupt the lecture unless this procedure is followed.

  • Other help resources : Math Lab (free drop-in tutoring at various locations on campus, including LeConte 105), Private tutors , Math library .

  • Syllabus (which contains all of the above information): (pdf) ; addendum .

  • Lectures and Homework :

    Lectures Homework
      Dates     Sections     Topics     Problems     Due date  
      August  
      Week 1     19     F     1A, 1B    
      Congruent Triangles.  
     
      1B:   1, 3, 5, 7, 8.  
      Solutions.  
      8/29.  
      Week 2     22     M     1B    
       
     
           
      24     W     1B    
       
     
           
      26     F     1C    
      Angles and parallel lines.  
     
           
      Week 3     29     M     1D    
      Parallelograms.  
     
      1D:   4, 6, 7, 8, 9, 10; challenge: 12, 13.  
      Solutions.  
      9/7.  
      31     W     1D    
       
     
           
      September  
      2     F     1E    
      Area.  
     
      1E:   1, 3.  
      Solutions.  
      9/16.  
      Week 4     5     M        
      No class.  
     
      Labor Day.      
      7     W     1E    
       
     
           
      9     F     1F    
      Circles and arcs.  
     
      1F:   1, 2, 6, 7, 10; challenge: 5, 9, 12, 14.  
      Solutions.  
      9/16.  
      Week 5     12     M     1G    
      Polygons in circles.  
     
      1G: 2 or 3. Solutions.     10/5.  
      14     W     1H    
      Similarity.  
     
      1H:   3, 5, 6, 8; challenge: 1, 4, 7, 11.  
      Solutions.  
      10/5.  
      16     F     1H    
       
     
           
      Week 6     19     M     1H    
       
     
           
      21     W        
      Exam I.  
      Review.  
      Blank exam.  
      Solutions.  
     
     
      Covers: 1B, 1C, 1D, 1E, 1F.  
     
       
      23     F     1H    
       
     
           
      Week 7     26     M     2A    
      The circumcircle.  
     
      1, 3; challenge: 4, 5;  
      Solutions.  
      10/14.  
      28     W     2B    
      The centroid.  
     
      1, 3; challenge: 2, 5;  
      Solutions.  
      10/14.  
      30     F     2C    
      The Euler line, orthocenter, and nine-point circle.  
     
     
      1, 3; challenge: 2, 5.  
      Solutions.  
     
      10/24.  
      October  
      Week 8     3     M     2C    
       
     
           
      5     W     2C    
       
     
           
      7     F     2C    
       
     
           
      Week 9     10     M     2D    
      Computations.  
     
     
      1, 3; challenge: 2.  
      Solutions.  
     
      10/24.  
      12     W     2D    
       
     
           
      14     F     2E    
      The incircle.  
     
     
      1, 3; challenge: 2, 4, 5;  
      Solutions.  
     
      11/4.  
      Week 10     17     M     2E    
     
           
      19     W     2E    
       
     
           
      21     F        
      No class.  
     
      Fall break.      
      Week 11     24     M     2F    
      Exscribed circles.  
     
     
      1; challenge: 2;  
      Solutions.  
     
      11/4.  
      26     W        
      Exam II.  
      Review.  
      Blank exam.  
      Solutions.  
     
      Covers: 1G, 1H, 2A, 2B, 2C, 2D.      
      28     F     3B    
      The butterfly theorem.  
     
           
      Week 12     31     M     3B    
       
     
           
      November  
      2     W     3C    
      Cross ratios.  
     
     
      2, 4, 8; Challenge: 1, 5, 7, 10.  
      Solutions.  
     
      11/18.  
      4     F     3C    
       
     
           
      Week 13     7     M     3C    
       
     
           
      9     W     4A    
      Ceva's Theorem.  
     
     
      2, 3; Challenge: 4.  
      Solutions.  
     
      11/18.  
      11     F     4A    
       
     
           
      Week 14     14     M     4B    
      Interior and exterior cevians.  
     
     
      1, 2.  
      Solutions.  
     
       
      16     W     4C    
      Ceva's Theorem and angles.  
     
           
      18     F        
      Exam III Review.  
     
           
      Week 15     21     M        
      Exam III.  
      Review.  
      Blank exam.  
      Solutions.  
     
      Covers: 2E, 2F, 3B, 3C, 4A.      
                 
      No class.  
     
     
      Thanksgiving holiday: 11/23 - 11/27.  
     
       
      Week 16     30     M     4C    
       
     
           
      December  
      2     W     4D    
      Menelaus' Theorem.  
     
     
      1, 2, 3, 4.  
      Solutions.  
     
       
      4     F     4D    
       
     
           
      Finals week     5     M        
      Final Exam, 9 - 12.  
      Review.  
      Blank exam.  
      Solutions.  
     
     
      Cumulative.