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UPenn - ESE - 535
ESE535Day 20 Preclass ExerciseSpring 2008Consider the following Routing Graph:c1 c4Ac21c54AB25Bc3c6C36C1. For each of the following connection, list all possible Paths:Connection Src Stg 1 Stg 2 Dst A A AA A A
UPenn - ESE - 535
ESE535Day 13 Preclass ExampleSpring 2008Consider the following covers.Delay=1 Width=1Delay=1 Width=1Delay=1 Width=3AB1. What is the delay for each of the two covers?AB2. Consider the following 1D layouts for these two covers.
UPenn - ESE - 535
ESE535 University of Pennsylvania Department of Electrical and Systems Engineering Electronic Design Automation ESE535, Spring 2008Spring 2008Assignment #6BWednesday, April 9thDue: Monday, April 21st, beginning of class. Resources You are fre
UPenn - ESE - 535
ESE535Day 19 Preclass ExerciseSpring 2008Consider the following 1D placement for the logic: A = i0*i1; B = A+i2; C = i0*i3; D = B+C; o4 = Dinputs (i0,i1,i2,i3) on this sideoutput (o1) on this sideAAssume:BCD Input pins are on the
UPenn - ESE - 535
ESE535Day 5 Preclass ExampleSpring 2008Consider the following FSM:ST1 0Current State ST1 ST1 ST2 ST2 ST3 ST3 Next State ST2 ST3 ST2 ST1 ST3 ST11 ST3 0 0 1Input 0 1 0 1 0 11ST2(Note: Diagram and state transition table should represe
UPenn - ESE - 535
ESE535Day 14 Preclass ExampleSpring 2008Consider the following circuits:AA BB1. If the delay of each gate is 1, what is the delay of each of the circuits?2. Now, consider the delay of each gate to be a random variable that takes on the
UPenn - ESE - 535
ESE535 University of Pennsylvania Department of Electrical and Systems Engineering Electronic Design Automation ESE535, Spring 2009Spring 2009Assignment #1Wednesday, January 23Due: Monday, February 2, beginning of class. Resources You are fre
UPenn - ESE - 535
ESE535Day 12 Preclass ExampleSpring 2008Consider the following two layouts.ABCDEFAFBECD1. Convince yourself these two cases represent dierent layouts of the same circuit. 2. Assuming a squared wire-length cost metrics,
UPenn - CLASS - 222
Problem Set #4 ECON 222 Each of the following questions is worth 20 points. You can work in groups, but each person should hand in their own answers. These problems are designed to help you practice for the nal. 1. In the binary logit model with an i
UPenn - CLASS - 222
name: Final Exam ECON 115Each of the following questions is worth 20 points. Together with the take-home question, the exam will total 100 points. You have two hours to write this exam and you are welcome to use your notes. Please write your answer
UPenn - CLASS - 222
Problem Set #2 ECON 222 Due Date: Feb. 20, 2007 Each question is worth 20 points. 1. Download the dataset airfare.raw and the description of the data in arefare.des from the class webpage http:/athena.sas.upenn.edu/~petra/econ222.htm and for this pro
UPenn - CLASS - 721
Final Exam ECON 721, Spring Semester 1998 This is a 24 hour take-home exam. It is due within 24 hours of picking up the exam. You are welcome to use your notes and consult any references/text books that you want, but you are asked to work independent
UPenn - CLASS - 222
name:_ Makeup Midterm Exam ECON 115 Spring, 2004Answer 4 of the following 5 questions. Each question is worth 25 points. Please write your answers in the space provided and using the extra blank sheets provided. 1. Suppose you want to model the dec
UPenn - CLASS - 222
name:_ Midterm Exam ECON 115 Spring, 2004Answer 4 of the following 5 questions. Each question is worth 25 points. Please write your answers in the space provided and using the extra blank sheets provided. 1. Suppose you are interested in studying s
UPenn - CLASS - 133
name: Econ 133: Midterm Exam Spring Term, 2003 True, False Questions (60 points total, 10 points each) Please answer 6 of the following 7 questions with True (T) or False (F) and give brief justication for your answer, verbally and/or graphically. Us
UPenn - CLASS - 222
name:_ Final Exam ECON 115 Spring, 2004 Please answer 4 of the 5 questions. Each question is worth 20 points (and the take home problem is worth another 20 points, for a total of 100). 1. Suppose you are estimating the relationship between adult weig
UPenn - CLASS - 222
Lecture Notes #1: Review of Matrix AlgebraECON 222 Spring, 2007This note describes how vectors and matrices are used as a means of storing information. It also describes dierent types of operations that can be performed on vectors and matrices. Eva
UPenn - MATH - 432
Solutions to homework 2 4.5#2 One-pile game with the following rules: You may remove (1) any number of chips divisible by three provided it is not the whole pile, or (2) the whole pile, but only if it has 2 (mod 3) chips. The terminal positions are z
UPenn - MATH - 104
For each of the following problems, first sketch a graph of the curves (or, better, use Maple to plot them), write out a definite integral which computes the area of the region bounded by the curves and, if you can, evaluate the integral: The area i
UPenn - MATH - 104
Examination 2 Answer Key Part 1: Multiple Choice 1. c 2. f 3. b 4. g7. b13. h14. aPart 2: Free Response 1. a) Hes dead, Jim. b) yes (with Ts = 20 and a temperature of 55 degrees when coee has cooled)Part 3: Maple 1. d 2. plot({2 sinh(x), (
UPenn - MATH - 104
Week of 1/12/09 1/19/09 1/26/09 2/2/09 2/9/09 2/16/09 2/23/09 3/2/09 3/9/09 3/16/09 3/23/09 3/30/09 4/6/09 4/13/09 4/20/09 4/27/09 5/4/09 5/11/09Notes Sections Classes begin 1/14 Review No class 1/19 Review 6.1-6.2 6.3, 6.5; 8.1 8.2, 8.3, 8.4 Exam
UPenn - MATH - 240
MATH 240, HOMEWORK 6(1) Evaluate the following double integral in iterated form: 1 dy]dx 1 + y4 0 x Hint: The following identity may be useful: y 1 1 1 ] = [ 4 2 2+ 1+y 2 2 1+y 2y 1 + y 2y (2) Consider the vector eld [ F(x, y, z) =< (2x + y)ex
UPenn - MATH - 104
MATH 104 HW 10CLAY SHONKWILER8.4 2. Does the following series converge or diverge?en .n=1Answer: We can re-write the series as n=11 e1 en1,which is a geometric series with a = r = 1 , so the series converges to e1 e11 e=
UPenn - MATH - 603
ALGEBRA HW 7CLAY SHONKWILER1 Which of the following rings R are discrete valuation rings? For those that are, nd the fraction eld K = frac R, the residue eld k = R/m (where m) is the maximal ideal), and a uniformizer . For the others, explain why
UPenn - MATH - 603
ALGEBRA HW 1CLAY SHONKWILER1 Which of the following R-modules are nitely generated? Which are free? Which are R-algebras? Among the R-algebras, which are nitely generated as R-algebras? (a): R = Z, M = Z/5 Z/7 Answer: M is certainly nitely genera
UPenn - MATH - 501
GEOMETRY FINALCLAY SHONKWILER1. Advanced Calculus Prove the following result: Theorem 1.1. Let U Rn+1 be a non-empty open set and let f : U R be a smooth function and suppose S = f 1 (c) is a non-empty subset such that f (q) = 0 for all q S. No
UPenn - MATH - 500
TOPOLOGY TAKE-HOMECLAY SHONKWILER1. The Discrete Topology Let Y = {0, 1} have the discrete topology. Show that for any topological space X the following are equivalent. (a) X has the discrete topology. (b) Any function f : X Y is continuous. (c)
UPenn - MATH - 661
DIFFERENTIAL GEOMETRY HW 3CLAY SHONKWILER32. Determine the dihedral angles of the dodecahedron. Answer: Let v be a vertex of the dodecahedron. Since the dodecahedron is regular, the choice of v general. Three sides intersect at v; call them S1 , S
UPenn - MATH - 503
ALGEBRA HW 4CLAY SHONKWILER1 Prove that the number of non-isomorphic one-dimensional representations of a nite group G is |G|/|[G, G]|, where [G, G] denotes the commutator subgroup. Proof. Suppose : G C is a one-dimensional representation of G.
UPenn - MATH - 500
TOPOLOGY FINALCLAY SHONKWILER1. Hausdorff Spaces Let X be a Hausdor space. Show that for any nite collection of points {x1 , . . . , xn } in X there are neighborhoods U1 , U2 , . . . Un of x1 , x2 , . . . xn respectively such that Ui Uj = if i =
UPenn - MATH - 603
ALGEBRA HW 6CLAY SHONKWILER1 (a): Let R be a Noetherian ring, I the set of ideals of R, and I0 a subset of I. Let P be a property that ideals in I0 may or may not have. Suppose that one can show the following condition: (1) I I0 , if every ideal
UPenn - MATH - 502
ALGEBRA HW 2CLAY SHONKWILER1.7.22 Show that the group of rigid motions of an octahedron is isomorphic to a subgroup of S4 . Deduce that the groups of rigid motions of a cube and an octahedron are isomorphic. Proof. Label each face of the octahedro
UPenn - MATH - 360
Let > 0. Consider the following series:S=n=1(1)n1 . nDetermine when S converges and when S absolutely converges.1
UPenn - MATH - 170
16) Consider a mathematical model given byPn+1 = Pn 3What are the equilibrium and are they stable or unstable? The following is the graph of y =x y=x 3a) The stable equilibriums are: x = 0, x = -1, x = 1. There are no unstable equilibrium. b) Th
UPenn - MATH - 170
Math 170 Midterm Formula SheetOctober 28, 200811 PROPERTIES OF GCD AND FACTORIZATION21Properties of gcd and FactorizationDenition 1.0.1. Recall a natural number is one of {0, 1, 2, 3, }. Denition 1.0.2. Recall an integer is one of {
UPenn - MATH - 170
1(Math 170) Homework 1:Due September 16, 2007Exercise 1: Out of sight but not out of mind. The infamous band Slippery Even When Dry ended their concert and checked into the Fuzzy Fig Motel. The guys in the band (Spike, Slip, and Milly) decided to
UPenn - MATH - 170
1Instructions Write all answers in capital letters in the spaces provided on the next page! Do not remove this answer sheet from the rest of the exam. All problems are worth the same amount. Problems marked with (EC) are extra credit. There is
UPenn - MATH - 170
1Instructions Write all answers in capital letters in the spaces provided on the next page! Do not remove this answer sheet from the rest of the exam. All problems are worth the same amount. Problems marked with (EC) are extra credit. There is
UPenn - MATH - 170
1Instructions Write all answers in capital letters in the spaces provided on the next page! Do not remove this answer sheet from the rest of the exam. All problems are worth the same amount. Problems marked with (EC) are extra credit. There is
UPenn - MATH - 170
1(Math 170) Homework 2:Due September 23, 2008Exercise 1: Part (a): Dene using just recursion and multiplication the function which takes a natural number n and returns 2n . Part (b): Dene using just recursion and multiplication the function which
UPenn - MATH - 170
1(Math 170) Homework 3:Due October 2, 2008Exercise 1: Prove there is no largest odd number (hint use proof by contradiction) Exercise 2: Find the greatest common divisor of 7920 and 8316 (hint 7920 = 24 32 5 11 and 8316 = 22 33 7 11) Exerci
UPenn - MATH - 170
1(Math 170) Homework 9:Due November 20, 2008Exercise 4: Heart of Mathematics Chapter 2.2 Exercise 7 Exercise 4: Heart of Mathematics Chapter 2.2 Exercise 8 Exercise 5: Heart of Mathematics Chapter 2.2 Exercise 10 Exercise 6: Heart of Mathematics
UPenn - MATH - 10
1Denition of Real NumbersThe goal of the presentation is to discuss dierent denitions of the real numbers. Your presentation should include at least An explanation of what the Cauchy Sequences are. An explanation of what Dedekind cuts are. A di
UPenn - MATH - 170
1Denition of Real NumbersThe goal of the presentation is to discuss dierent denitions of the real numbers. Your presentation should include at least An explanation of what the Cauchy Sequences are. An explanation of what Dedekind cuts are. A di
UPenn - MATH - 170
1Algebraic and Transcendental NumbersThe goal of the presentation is to discuss logarithms and exponentials. Your presentation should include at least A discussion of what an Algebraic Number is A discussion of what a Transcendental Number is A
UPenn - MATH - 170
1August Mobius and Mobius StripsThe goal of the presentation is to discuss August Mobius. Your presentation should include at least A discussion of who Mobius was and his life. An explanation of what a Mobius strip is. A discussion of what it m
UPenn - MATH - 170
1Primeality Tests and Finding PrimesThe goal of the presentation is to discuss methods to test if a number is prime and for nding prime numbers. Your presentation should include at least A discussion of the Sieve of Eratosthenes An explanation a
UPenn - MATH - 12
1John Horton ConwayThe goal of the presentation is to discuss John Conway. Your presentation should include at least A discussion his life. A Conway chained arrow notation. A discussion of what it means to be non-associative. A discussion of t
UPenn - MATH - 170
1John Horton ConwayThe goal of the presentation is to discuss John Conway. Your presentation should include at least A discussion his life. A Conway chained arrow notation. A discussion of what it means to be non-associative. A discussion of t
UPenn - MATH - 170
1Zenos ParadoxesThe goal of the presentation is to discuss Zenos Paradoxes. Your presentation should include at least A discussion of who Zeno was. A discussion of Zenos three paradoxes, including a discussion of what they are and how they are r
UPenn - MATH - 170
1Carl Friedrich GaussThe goal of the presentation is to discuss Carl Friedrich Gauss. Your presentation should include at least A discussion of who he is. A discussion of the type of polygons he was able to construct using just a compass and str
UPenn - MATH - 12
1Cellular AutomataThe goal of the presentation is to discuss Cellular Automata. Your presentation should include at least A discussion of what cellular automata is. A discussion of the game of life (by Conway) An explanation of a 1 dimensional
UPenn - MATH - 170
1Cellular AutomataThe goal of the presentation is to discuss Cellular Automata. Your presentation should include at least A discussion of what cellular automata is. A discussion of the game of life (by Conway) An explanation of a 1 dimensional
UPenn - MATH - 170
1Blaise PascalThe goal of the presentation is to discuss Blaise. Your presentation should include at least A discussion of who he is and his religious/philosophical beliefs. A discussion of how him and Fermat discovered probability. A discussio
UPenn - MATH - 170
1Amalie Emmy NoetherThe goal of the presentation is to discuss Amalie Emmy Noether. Your presentation should include at least A discussion of who Amalie Emmy Noether was including a brief history of her life. A discussion of what an ascending/de
UPenn - MATH - 170
1Sir Isaac NewtonThe goal of the presentation is to discuss Isaac Newton. Your presentation should include at least A discussion of who Newton was. A discussion of his life. A discussion of his laws of gravity A brief discussion of his discove
UPenn - MATH - 170
1Peano ArithmeticThe goal of the presentation is to discuss Peano arithmetic. Your presentation should include at least A discussion of the the axioms of Peano arithmetic. Its relationship with induction (which axiom(s) allows proof by induction
UPenn - MATH - 170
1Vigenre cipherThe goal of the presentation is to explain and discuss the Vigenre cipher. Your presentation should include at least A discussion the history of the cipher. An explanation of how it is implemented (both in terms of the Vigenre tab
UPenn - MATH - 170
1Rene DescartesThe goal of the presentation is to discuss Rene Descartes. Your presentation should include at least A discussion of who he is. A discussion analytic geometry A discussion of the dualism In addition you should include at least on
UPenn - MATH - 12
1Bertrand RussellThe goal of the presentation is to discuss Blaise. Your presentation should include at least A discussion of who he. A discussion of Russells Paradox A discussion of the Principia Mathematica. In addition you should include at