Feedback is important in education. It is commonly believed that immediate feedback is very important. That is why instructors stay often late at night grading students’ assignments – to make sure that the students get their feedback as early as possible. However, surprisingly, experiments show that in many cases, delayed feedback is more efficient that the immediate one. In this paper, we prov...

Students’ performances in introductory programming courses show large variation across students. There may be many reasons for these variations, such as methods of teaching, teacher competence in the subject, students’ coding backgrounds and abilities, students’ self-discipline, the teaching environment, and the resources available to students, all of which can affect student performance and ou...

(This can be shown using a basis argument, which would amount to what most of you wrote anyway.) Thus, given S ∈ L(V ) such that imS ⊆ imT , we can define R = (T |W )−1S, from which it follows TR = S. Conversely, if S = TR, then since linear operators preserve inclusion and R(V ) ⊆ V , we have S(V ) = (TR)(V ) ⊆ T (V ); that is, imS ⊆ imT . 2. Let T be a linear operator on V with distinct eigen...

Answer: Long-term storage of keys, specially in disk, must take into account handling of backups and possible direct access to the underlying media. Therefore, keys’ long term storage should take place in encrypted format. For instance, an administrative password may be used to encrypt the keys. Even better, keys could be encrypted using an administrative key that is physically protected in phy...

0 (r sin θ + z)r dz dr dθ (b) Let T be the solid ball of radius 1 centered at (2, 0, 0). Set up, but do not evaluate, a triple integral in spherical coordinates which computes the moment of inertia of T around the z-axis. Hint: First consider the change of variables u = x − 2, v = y, w = z. Solution. After the change of variables, the sphere takes the form u+v+w = 1, and the z-axis becomes the ...

∙ A function is a rule that assigns to each objects in a set A exactly one object in a set B. The set A is called the domain of the function. The set of assigned abjects in B is called the range. ∙ (Domain Convention) If a formula (or several formulas) is used to define a function f , then we assume that the domain of f to be the set of all numbers for which f(x) is defined. ∙ A demand function...

Physics Department Physics 8.07: Electromagnetism II December 18, 2012 Prof. Alan Guth FORMULA SHEET FOR FINAL EXAM Exam Date: December 19, 2012 ∗∗∗ Some sections below are marked with asterisks, as this section is. The asterisks indicate that you won’t need this material for the quiz, and need not understand it. It is included, however, for completeness, and because some people might want to m...