21 B
Mathematics Math21b Spring 2007
Linear Algebra and Differential Equations
Course Head: Oliver Knill
Office: SciCtr 434

The Final 21b Examtook place Friday, Mai 18 at 2:15 PM in Science Center B. The average of the exam was 78/100.
  • All students enrolled in the course are required without exception to attend the exam administered by the FAS Exams Office. Students not present at this exam will receive a grade of ABS for the course.
  • Instructors may not approve or administer a makeup exam to any student absent from the exam. Makeup exams may only be approved by the Administrative Board for undergraduates or the Deputy Registrar for graduate students, Special Students, or cross-registered students and will be administered by the FAS Exams Office during the scheduled makeup exam period.

2. Midterm:Tue 4/10 7-8:30pmHall C
The second hourly covered the material from week 5-8. It was a relatively tough exam: the maximum was 92, the average was 71 points. The standard deviation was 12.
The week Tue Apr 3 to Tue Apr 10 was Pesach Holiday (=Passover), a 1 week holiday which we usually ignore when looking for exam dates since it is impossible to exclude an entire week. For students who observe this holiday, the makeup date is 9:00 PM the same day. (Candle lighting time is 8:03 PM on April 10, 2007 in Cambridge, MA, so that 9 PM should work). Qualified out of sequence exams have to take place on the exam Tuesday in the afternoon as usual. Please inform the course head early. Note the out of sequence policy at the bottom of this page.

1. Midterm:Wed 3/7 7-8:30pmHall C
  • The first hourly covered material from the first 4 weeks. The average was 77 points. The standard deviation was 10. The exam is returned in class on Thursday 3/8 or Friday 3/9.

Errata: (the files were updated at the time indicated near the erratum)
  • March 6: 5 PM by Ruvani Fonseka: Exam 2, TF problem 10, typo: A67 should be A2. Exam 1, TF problem 6, the answer is false: 2x2 matrix with 1 in the bottom left entry and 0s everywhere else has zeros in the diagonal but rank 1.
  • March 5: 8 PM by Lauren Luther: Exam 2, Problem 10, typo: T e1 = e1 = [-2, -1] not [-1,-2]. The explanation was otherwise correct.
  • March 5: 6 PM by Hann-Shyuin Yew: Exam 2, TF problem 12. The explanation was wrong.
  • March 5: 7 AM by Arda Ayvaz: Exam 2, Problem 3a: (-5,5,-1) is the solution. Problem 7, typo x+2 should be replaced by x2 in the solution.
  • March 3: 3 PM by Nike Sun: Exam 1, TF 7: the explanation was incorrect March 5: the answer is FALSE: The matrix with 1 in the lower side diagonal and 0 else is not included and has rank 2.
  • March 3: 10 AM: Exam 1, TF 16: the problem had dealt with 2x2 matrices. We changed I2 to In now to make it more general. The answer and explanation is unchanged.

Official policy at Havard is that "out of sequence midterm exams" are only offered for students observing religious holidays. We sometimes can accomodate students who happen to have an important sports event at the same time (it must be an actual game or tournament) or a concert or theater event (regular practice or rehearsals of course do not qualify to miss the exam). In case of a qualifying conflict, contact the course head to see whether it is possible to arrange the exam earlier at the same day. We will need a letter from your coach or director. The request has to come at least a week before the exam.
Please send questions and comments to
Math21b | Oliver Knill | Spring 2007 | Department of Mathematics | Faculty of Art and Sciences | Harvard University