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- Title: AnswerExercise32Page109
- Type: Notes
- School: UMBC
- Course: CS 203
- Term: Fall
Coursehero >> Maryland >> UMBC >> CS 203
Path: UMBC >> CS >> 203 Fall, 2005
Path: UMBC >> CS >> 203 Fall, 2005
Path: UMBC >> CS >> 203 Fall, 2005
Path: UMBC >> CS >> 203 Fall, 2005
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Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 441 Spring, 1995
Path: UMBC >> CS >> 441 Spring, 1995
Path: UMBC >> CS >> 441 Spring, 1995
Path: UMBC >> CS >> 643 Spring, 2004
Path: UMBC >> CS >> 643 Spring, 2004
Path: UMBC >> CS >> 643 Spring, 2004
Path: UMBC >> CS >> 643 Spring, 2004
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Path: UMBC >> CS >> 653 Spring, 2001
Path: UMBC >> CS >> 653 Spring, 2001
Path: UMBC >> CS >> 653 Spring, 2001
Path: UMBC >> CS >> 653 Spring, 2001
Path: UMBC >> CS >> 653 Spring, 2001
Path: UMBC >> CS >> 653 Spring, 2001
Path: UMBC >> CS >> 653 Spring, 2001
Path: UMBC >> CS >> 653 Spring, 2001
Path: UMBC >> CS >> 653 Spring, 2001
Path: UMBC >> CS >> 653 Spring, 2001
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
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Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 442 Fall, 2001
Path: UMBC >> CS >> 203 Fall, 2005
Path: UMBC >> CS >> 203 Fall, 2005
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 641 Fall, 2000
Path: UMBC >> CS >> 643 Spring, 2004
Path: UMBC >> CS >> 643 Spring, 2004
Path: UMBC >> CS >> 643 Spring, 2004
Path: UMBC >> CS >> 691 Spring, 2000
Path: UMBC >> CS >> 691 Spring, 2000
Path: UMBC >> CS >> 691 Spring, 2000
Path: UMBC >> CS >> 691 Spring, 2000
Path: UMBC >> CS >> 203 Fall, 2005
Path: UMBC >> CS >> 441 Spring, 1995
Path: UMBC >> CS >> 441 Spring, 1995
Path: UMBC >> CS >> 441 Spring, 1995
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to Answer Exercise 32 on Page 109 Let f be a function from a set A to a set B, and let S and T be subsets of A. Answer to part a) Proposition 1 f (S T ) = f (S) f (T ) Proof. y f (S T ) x [(x S T ) (y = f (x))] x {[(x S) (x T )] (y = f (x))} x {[(x S) (y = f (x))] [(x T ) (y = f (x))]} ( x [(x S) (y = f (x))]) ( x [(x T ) (y = f (x))]) [y f (S)] [y f (T )] y f (S) f (T ) Reason: Def of f (S T ) Reason: Def of " " Reason: Distributive law Reason: See Note 1 below Reason: Defs f (S) & f (T ) Reason: Def of " " Note 1. Unfortunately, our textbook fails to state this theorem. See theorem 26 formula 88 on pages 127-128 of "Mathematical Logic" by Stephen 1 Kleene. Answer to part b) Proposition 2 f (S T ) f (S) f (T ) Proof. y f (S T ) x [(x S T ) (y = f (x))] x {[(x S) (x T )] (y = f (x))} x {[(x S) (x T )] [(y = f (x))] (y = f (x))} x {[(x S) (y = f (x))] [(x T ) (y = f (x))]} = { x [(x S) (y = f(x))]} { x [(x T ) (y = f (x))]} (y f (S)) (y f (T )) y f (S) f (T ) Reason: Def of f (S T ) Reason: Def of " " Reason: Idempotent law Reason: Assoc. & Comm. Reason: See Note 2 Reason: Defs f (S) & f(T ) Reason: Def of " " Note 2. Unfortunately, our textbook fails to state this theorem. See theorem 26 formula 93 on pages 127-128 of "Mathematical Logic" by Stephen Kleene. 2
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Path: UMBC >> CS >> 203 Fall, 2005
Description: CMSC 203 Fall 2005 Homework 5 Due: Wednesday, October 12, 2005 Reading Assignment: Kenneth H. Rosen, Discrete Mathematics and Its Applications, McGraw-Hill, 2003, (5-th edition). Read chapter 2, pages 153 - 196. Homework: Exercise Exercise Exerci...
hwk6.pdfPath: UMBC >> CS >> 203 Fall, 2005
Description: CMSC 203 Fall 2005 Homework 6 Due: Wednesday, November 2, 2005 Reading Assignment: Kenneth H. Rosen, Discrete Mathematics and Its Applications, McGraw-Hill, 2003, (5-th edition). Read chapter 3. Homework: Exercise Exercise Exercise Exercise Exe...
MathInduction.pdfPath: UMBC >> CS >> 203 Fall, 2005
Description: CLASS NOTES ON MATHEMATICAL INDUCTION PROFESSOR LOMONACO Denition 1 (Weak Principle of Mathematical Induction (WPMI). Let S be a subset of the natural numbers N = {0, 1, 2, . . .}. Then 0S = S = N n S n + 1 S Denition 2 (Strong Principle of Ma...
hwk7.pdfPath: UMBC >> CS >> 203 Fall, 2005
Description: CMSC 203 Fall 2005 *CORRECTED *Homework 7 Due: Wednesday, November 9, 2005 Reading Assignment: Kenneth H. Rosen, Discrete Mathematics and Its Applications, McGraw-Hill, 2003, (5-th edition). Read chapter 4, pages 301 - 326. Homework: Exercise Exer...
hwk8.pdfPath: UMBC >> CS >> 203 Fall, 2005
Description: CMSC 203 Fall 2005 Homework 8 Due: Monday, November 21, 2005 Reading Assignment: Kenneth H. Rosen, Discrete Mathematics and Its Applications, McGraw-Hill, 2003, (5-th edition). Read chapter 4, Section 4.5 Homework: Exercise Exercise Exercise Exe...
hwk9.pdfPath: UMBC >> CS >> 203 Fall, 2005
Description: CMSC 203 Fall 2005 Homework 9 Due: Wednesday, November 30, 2005 Reading Assignment: Kenneth H. Rosen, Discrete Mathematics and Its Applications, McGraw-Hill, 2003, (5-th edition). Read chapter 5 Homework: Exercise Exercise Exercise Exercise Exe...
hwk2.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: CMSC 442 Fall 2003 Homework 2 Reading assignment: Peterson Sloane, The Theory o...
hwk4.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: CMSC 442 Fall 2003 Homework 4 Reading assignment: Peterson & Weldon, Error-Correcting Codes, MIT Press, (Second Edition), (1986), Chapter 3, pages 40-47, pages 52-56. 1) Let V be the linear code over GF (3) determined 0212 G= 2 1 1 0 2201 Determ...
hwk5.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: CMSC 442 Fall 2003 Homework 5 Reading assignment: Peterson & Weldon, Error-Correcting Codes, MIT Press, (Second Edition), (1986), Chapter 5, section 5.1 to 5.5. 1) Let V be the the binary (16, 11) d = 4 extended Hamming code. a) Find the parity ch...
hwk6.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: CMSC 442 Fall 2003 Homework 6 Reading assignment: Peterson & Weldon, Error-Correcting Codes, MIT Press, (Second Edition), (1986), Chapter 2, pages 19-39, and Chapter 6, pages 144-154. 1) Compute the addition and multiplication tables for the ring ...
hwk7.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: CMSC 442 Fall 2003 Homework 7 Reading assignment: Peterson x15 + 1 > given by the generator polyno...
Brassard-Handout.pdfPath: UMBC >> CS >> 441 Spring, 1995
Description: ...
GarnerAlg.pdfPath: UMBC >> CS >> 441 Spring, 1995
Description: ...
Garner-Alg-Example.pdfPath: UMBC >> CS >> 441 Spring, 1995
Description: AN EXAMPLE OF A GARNERS ALGORITHM CALCULATION DR. LOMONACO Question: Use Garners algorithm to nd the unique integer 0 x < 5 7 11 that satises the following three modular equations: x = 4 mod 5 x = 1 mod 7 x = 2 mod 11 The mixed radix r...
hwk0.pdfPath: UMBC >> CS >> 643 Spring, 2004
Description: CMSC 643 EXERCISES WITH BRAS ANSD KETS DR. LOMONACO Let H be a Hilbert space with othonormal basis and let K be a Hilbert space with othonormal basis {|ai , |bi , |ci} {|0i , |1i , |2i , |3i} , (1) Represent each basis element of H as a column vect...
hwk1.pdfPath: UMBC >> CS >> 643 Spring, 2004
Description: Homework 1 CMSC 643 Quantum Computation Dr. Lomonaco 1 Example Problem Let Q be a quantum system with state given by the ket: |i = (|00i + i |01i |11i) / 3 What is the result of measuring Q with respect to the observable: 0 0 1 i 0 0 i 1 O= ...
hwk1-5.pdfPath: UMBC >> CS >> 643 Spring, 2004
Description: Homework 1.5 CMSC 643 Quantum Computation Dr. Lomonaco 1 Example Problem What is the result of measuring Q with respect 0 1 i 1 0 0 O= i 0 0 0 i 1 Answer to Example Problem Remark 1 Please note that, since T r 2 = ensemble. 1 3 Let Q be a quantu...
hwk2.pdfPath: UMBC >> CS >> 643 Spring, 2004
Description: CMSC 643 QUANTUM TELEPORTATION EXERCISES DR. LOMONACO (1) Indicate in detail how Alice can use the standar teleportation protocol to teleport a qubit in the state (4 + 3i) |0i + (4 3i) |1i |i = 52 to Bob. Show all intermediate states, and also all...
QTomography.pdfPath: UMBC >> CS >> 643 Spring, 2004
Description: CMSC 643 RESEARCH PROBLEM 1 QUANTUM TOMOGRAPHY FOR A SINGLE QUBIT DR. LOMONACO 1. Setting up the problem Problem 1. Given many copies of a qubit in an unknown xed state |i = a |0i + b |1i , where |a|2 + |b|2 = 1 , nd a way to estimate the amplitudes...
hwk01.pdfPath: UMBC >> CS >> 653 Spring, 2001
Description: CMSC 442/653 Fall 2006 Instructor: Dr. Lomonaco Homework 1 Reading Assignment: http:/www.cs.umbc.edu/~lomonaco/s06/652/slides/Equilateral-Triangle.pdf Optional Reading assignment: Peterson Error-Correcting Codes,\" MIT Press, (Second Edit...
hwk02.pdfPath: UMBC >> CS >> 653 Spring, 2001
Description: CMSC 442/653 Fall 2006 Instructor: Dr. Lomonaco Homework 2 Optional Reading assignment: Peterson Error-Correcting Codes,\" MIT Press, (Second Edition), Chapter 6. 1U) Let p( x ) = x 12 + x 9 + x 8 + x 6 + x 4 + x + 1 and q( x ) = x11 + x ...
Hwk2-Maple.pdfPath: UMBC >> CS >> 653 Spring, 2001
Description: > # Notes on homework 2 > p:=x^12+x^9+x^8+x^6+x^4+x+1; q:=x^11+x^10+x^6+x^5+x^4+x^3+1; p := x12 + x9 + x8 + x6 + x4 + x + 1 q := x11 + x10 + x6 + x5 + x4 + x3 + 1 > # Computation of over GF(2) Factor(p) mod 2; Factor(q) mod 2; Gcd(p,q) mod 2; ( x7 + ...
hwk04.pdfPath: UMBC >> CS >> 653 Spring, 2001
Description: CMSC 442/653 Fall 2006 Instructor: Dr. Lomonaco Homework 4 Reading Assignment: Review relevant slides on Overview of Coding Theory found at http:/www.cs.umbc.edu/~lomonaco/f06/653/Slides653.html Optional Reading assignment: Peterson Erro...
hwk05.pdfPath: UMBC >> CS >> 653 Spring, 2001
Description: CMSC 442/653 Fall 2006 Instructor: Dr. Lomonaco Homework 5 Reading Assignment: Review relevant slides on Overview of Coding Theory found at http:/www.cs.umbc.edu/~lomonaco/f06/653/Slides653.html Optional Reading assignment: Peterson Erro...
hwk06.pdfPath: UMBC >> CS >> 653 Spring, 2001
Description: CMSC 442/653 Fall 2006 Instructor: Dr. Lomonaco Homework 6 Reading Assignment: Read the handout entitled The MacWilliams and Pless Identities: A Summary found at http:/www.cs.umbc.edu/~lomonaco/f06/653/handouts/MacWilliams-PlessIdentities.pdf Option...
hwk06-hint.pdfPath: UMBC >> CS >> 653 Spring, 2001
Description: Homework 6 Hint Here is an example problem illustrating how to complete Homework 6. Hint: Let V be the linear code over GF (2) given by the following generator matrix 1 0 0 0 1 1 0 0 1 0 0 0 1 1 G= 0 0 1 0 1 1 1 0 0 0 1 1 0 1 a) What is the ...
hwk06-hint-mapleworksheet.pdfPath: UMBC >> CS >> 653 Spring, 2001
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hwk07.pdfPath: UMBC >> CS >> 653 Spring, 2001
Description: CMSC 442/653 Fall 2006 Instructor: Dr. Lomonaco Homework 7 Optional Reading assignment: Peterson Error-Correcting Codes,\" MIT Press, (Second Edition), Chapters 6 Sloane, The Theory of Error-...
hwk09.pdfPath: UMBC >> CS >> 653 Spring, 2001
Description: CMSC 442/653 Fall 2006 Instructor: Dr. Lomonaco Homework 9 Optional Reading assignment: Peterson Error-Correcting Codes,\" MIT Press, (Second Edition), Chapters 6 Section 5, pages 155-157 and Chapter 8. Problem 1. (For undergrad and grad s...
dynamicprogramming.pdfPath: UMBC >> CS >> 641 Fall, 2000
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greedy-algorithms.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: Example. Activity Selection Problem $ Greedy Algorithms $ Immediate Gratification Let S= activities {a1 , a2 , , an } be n proposed Looks for the best at the moment Makes locally optimal choice ai S we have , si = Start Time f i = Finish Time...
amortized-analysis.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: Amortized Analysis: 3 Methods Aggregate n ops take time T(n) Stack Example Consider a stack data structure with 3 ops PUSH(S,x) POP(S) - O(1) - O(1) Avg cost per op = T(n)/n (Amortized Cost) Imprecise no seperate cost for each item Account...
b-trees.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: B-Trees B-Trees Search for key R Work = ( h ) = ( log t n ) B-Trees B-Trees Each Disk-Read or Disk-Write = one Basic unit of work O(1) Typical Node x See example on whiteboard B-Trees t 1 # Keys 2t 1 t # Children 2t # Keys = 2t 1 ...
binomial-heaps.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: Binomial Heaps Binomial trees Def. For each non-negative integer k, a binomial tree Bk of root degree k is an ordered tree defined recursively as follow: 1) B0 consists of a single node 2) Bk consists of two binomial trees Bk-1 linked together such ...
fibonacci-heaps.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: Fibonacci Heaps Example: Fibonacci Heap Unordered Binomial trees Def. For each non-negative integer k, a binomial tree Uk of root degree k is an ordered tree defined recursively as follow: 1) U0 consists of a single node 2) Uk consists of two binom...
elementary-graph-algorithms.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: Representing Graphs Undirected Graph Breath-First Search Breath- Directed Graph Breath-First Search Breath- Breath-First Search Breath- Depth-First Search Depth- Depth-First Search Depth- 1 Properties of Depth-First Search Depth- Topological...
minimum-spanning-trees.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: Vertices Minimal Spanning Trees Edges Minimal Spanning Trees Let G = (V , E ) be a connected undirected graph with E V V ( G, w ) Def. A minimum spanning subtree of a weighted graph is a spanning subtree of G of minimum weight Def. A weighted...
single-source-shortest-paths.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: Single-Source Shortest Paths SingleDef. Given a weighted directed graph (G(V,E),w), we G(V,E),w) define the weight of a path Single-Source Shortest Paths Problem: Given a Single- weighted graph (G=(V,E),w), find a shortest path (G=(V,E),w), from a ...
all-pairs-shortest-paths.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: All-Pairs Shortest Paths AllProblem. Find the shortest path between all pairs of Problem. vertices of a weighted graph (G=(V,E),w). (G=(V,E),w) Input All-Pairs Shortest Paths AllWe could solve all pairs shortest path problem by running single-source...
maximum-flow.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: Maximum Flow A flow network (G,c,s,t) is a directed graph G,c,s,t) G=(V,E) together with a non-negative map nonc:E R, called capacity, and two distinguished capacity, vertices s and t, called respectively the source and sink with the condition that c...
Hwk1.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: 5 ee2 6@* 2ff OL4iLh! #iG L?_@)c 5iT|i4Mih .c 2ff ?L *@|ih |@? ST4 -jBaA} Btt}A6jA|H i|ihtL? : `i*_L?c R,hhLhLhhiU|?} L_itc WA hittc E5iUL?_ ,_|L?c EbHSc @T|iht : 2 V|NAB, ijBaA} Btt}A6jA|H @U`*@4t : 5*L@?ic RAi AiLh) Lu ,hhLh LhhiU|?} L_itc Lh|O...
Hwk2.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: 5 ee2 6@* 2ff OL4iLh! 2 -jBaA} Btt}A6jA|H i|ihtL? : `i*_L?c R,hhLhLhhiU|?} L_itc WA hittc E5iUL?_ ,_|L?c EbHSc @T|ih 2c 5iU|L? 2S -jBaA} Btt}A6jA|H i|ihtL? : `i*_L?c R,hhLhLhhiU|?} L_itc WA hittc E5iUL?_ ,_|L?c EbHSc @T|ih V|NAB, ijBaA} Btt}A6jA...
Hwk3.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: FPVF 775 Idoo 5334 Krphzrun 6 Uhdglqj dvvljqphqw= Shwhuvrq ) Zhogrq/ Huuru0Fruuhfwlqj Frghv/ PLW Suhvv/ +Vhfrqg Hglwlrq,/ +4<;9,/ Fkdswhu 6/ Vhfwlrqv 6140615 Uhdglqj dvvljqphqw= Shwhuvrq ) Zhogrq/ Huuru0Fruuhfwlqj Frghv/ PLW Suhvv/ +Vhfrqg Hglwlrq...
Hwk4.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: FPVF 775 Idoo 5334 Lqvwuxfwru= Gu1 Orprqdfr Krphzrun 7 Uhdglqj dvvljqphqw= Shwhuvrq ) Zhogrq/ Huuru0Fruuhfwlqj Frghv/ PLW Suhvv/ +Vhfrqg Hglwlrq,/ +4<;9,/ Fkdswhu 9 ) ; Rswlrqdo uhdglqj dvvljqphqw= PdfZlooldpv ) Vordqh/ Wkh Wkhru| ri Huuru0 Fruuhf...
Hwk5.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: FPVF 775 Idoo 5334 Lqvwuxfwru= Gu1 Orprqdfr Krphzrun 8 Uhdglqj dvvljqphqw= Shwhuvrq ) Zhogrq/ Huuru0Fruuhfwlqj Frghv/ PLW Suhvv/ +Vhfrqg Hglwlrq,/ +4<;9,/ Fkdswhu 9 ) ; Rswlrqdo uhdglqj dvvljqphqw= PdfZlooldpv ) Vordqh/ Wkh Wkhru| ri Huuru0 Fruuhf...
Hwk6.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: FPVF 775 Idoo 5334 Lqvwuxfwru= Gu1 Orprqdfr Krphzrun 9 Uhdglqj dvvljqphqw= Shwhuvrq ) Zhogrq/ Huuru0Fruuhfwlqj Frghv/ PLW Suhvv/ +Vhfrqg Hglwlrq,/ +4<;9,/ Fkdswhu 9 ) ; Rswlrqdo uhdglqj dvvljqphqw= PdfZlooldpv ) Vordqh/ Wkh Wkhru| ri Huuru0 Fruuhf...
Hwk7.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: FPVF 775 Idoo 5334 Lqvwuxfwru= Gu1 Orprqdfr Krphzrun : Uhdglqj dvvljqphqw= Shwhuvrq ) Zhogrq/ Huuru0Fruuhfwlqj Frghv/ PLW Suhvv/ +Vhfrqg Hglwlrq,/ +4<;9,/ Fkdswhu 9 Rswlrqdo uhdglqj dvvljqphqw= PdfZlooldpv ) Vordqh/ Wkh Wkhru| ri Huuru0 Fruuhfwlqj ...
Hwk8.pdfPath: UMBC >> CS >> 442 Fall, 2001
Description: FPVF 775 Idoo 5334 Lqvwuxfwru= Gu1 Orprqdfr Krphzrun ; Uhdglqj dvvljqphqw= Shwhuvrq ) Zhogrq/ Huuru0Fruuhfwlqj Frghv/ PLW Suhvv/ +Vhfrqg Hglwlrq,/ +4<;9,/ Fkdswhu 9 ) : Rswlrqdo uhdglqj dvvljqphqw= PdfZlooldpv ) Vordqh/ Wkh Wkhru| ri Huuru0 Fruuhf...
study-problems-203ex1.pdfPath: UMBC >> CS >> 203 Fall, 2005
Description: STUDY PROBLEMS FOR EXAM I CMSC 203 DISCRETE STRUCTURES DR. LOMONACO 1. Use the principle of mathematical induction to prove that P (n) : n X j=1 j2 = n (n + 1) (2n + 1) , 6 for all integers n 1. Answer: Proof (by weak induction): Basis Step: P...
study-problems-203ex2.pdfPath: UMBC >> CS >> 203 Fall, 2005
Description: STUDY PROBLEMS FOR EXAM II CMSC 203 DISCRETE STRUCTURES DR. LOMONACO The exam will cover: Chapter 5 all sections Chapter 6, all sections except for sections 6.8 and 6.9 Chapter 7, all sections except for section 7.5 Solutions and hints to the fol...
Homewk1.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: i i { g { x w g h g d f g } g f { i y d x f w g v i i { g { x w g h g d f g } y d x f g f i y d x f w g...
Homewk2.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: z m p j z g { y m p j z g { y m p j g { y n p j q g { y n p j p g { y p m j z g { y...
Homewk3.pdfPath: UMBC >> CS >> 641 Fall, 2000
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Homewk5.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: r x t { r z r x t { r z r x t { r z r ...
Homewk6.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: s o v m u m s o v m u m s o v m u m s o v m u m s o v m u m s ...
Homewk7.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: x t { r z r x t { r z r x t { r z r x t { r z r x t { r z r x ...
Homewk8.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: l r p q p g o n g l r q p g o n g l r q p g o n g s l p p g o n g q l r p g o n g ...
Homewk9.pdfPath: UMBC >> CS >> 641 Fall, 2000
Description: ...
hwk1.pdfPath: UMBC >> CS >> 643 Spring, 2004
Description: Homework 1 CMSC 643 Quantum Computation Dr. Lomonaco 1 Example Problem Let Q be a quantum system with state given by the ket: |i = (|00i + i |01i |11i) / 3 What is the result of measuring Q with respect to the observable: 0 0 1 i 0 0 i 1 O= ...
Hoeffding.pdfPath: UMBC >> CS >> 643 Spring, 2004
Description: ...
QuantumTomographyMapleWorksheet.pdfPath: UMBC >> CS >> 643 Spring, 2004
Description: ...
hwk0.pdfPath: UMBC >> CS >> 691 Spring, 2000
Description: CMSC 691Q EXERCISES WITH BRAS ANSD KETS DR. LOMONACO Let H be a Hilbert space with othonormal basis and let K be a Hilbert space with othonormal basis {|ai , |bi , |ci} {|0i , |1i , |2i , |3i} , (1) Represent each basis element of H as a column vec...
hwk1.pdfPath: UMBC >> CS >> 691 Spring, 2000
Description: Homework 1 CMSC 691Q Quantum Computation Dr. Lomonaco 1 Example Problem Let Q be a quantum system with state given by the ket: |i = (|00i + i |01i |11i) / 3 What is the result of measuring Q with respect to the observable: 0 0 1 i 0 0 i 1 O=...
hwk1-maple-work-sheet.txtPath: UMBC >> CS >> 691 Spring, 2000
Description: > # This spread sheet computes the answers to the example problem > # of Homework 1. > > # Please do not use the Maple worksheet QC6_Lib.mws for this example > # This worksheet works without it. > > with(linalg): > Warning, the protected names norm a...
hwk2.pdfPath: UMBC >> CS >> 691 Spring, 2000
Description: CMSC 691Q QUANTUM TELEPORTATION EXERCISES DR. LOMONACO (1) Indicate in detail how Alice can use the standar teleportation protocol to teleport a qubit in the state (4 + 3i) |0i + (4 3i) |1i |i = 52 to Bob. Show all intermediate states, and also al...
InstructionsForExam1.pdfPath: UMBC >> CS >> 203 Fall, 2005
Description: CMSC 203 Section 0401 Discrete Structures Fall Semester 2005 Exam I Wednesday, October 19, 2005, 4:00pm - 5:15pm Exam I will cover the following material: Chapter 1 Chapter 2 o Section 2.4 o Section 2.5 o Section 2.6 except for pages 186-193 o Key ...
hwk1.pdfPath: UMBC >> CS >> 441 Spring, 1995
Description: CMSC 441 Section 0201 Spring 2008 Homework 1 Reading Assignment: Listen to Beethovens 5-th symphony Read Chapter of text Homework: Exercise 3.1-2, page 50 Exercise 3.1-4, page 50 Exercise 3.1-7, page 50 Exercise 3.1-8, page 50 Exercise 3.2-1, ...
hwk3.pdfPath: UMBC >> CS >> 441 Spring, 1995
Description: CMSC 441 Section 0201 Spring 2008 Homework 3 Reading Assignment: Listen to Gilbert Practice by Brassard & Bratley. Study ahead by reading Chapter 4, S...
441hwk3-solns.pdfPath: UMBC >> CS >> 441 Spring, 1995
Description: SOLUTIONS TO HOMEWORK 3 CMSC 441 DR. LOMONACO 1. Homework 3 Solutions Below are the solutions to the problems given in Homework 3. These problems can be found in the class handout [1]. 2. Problem 2.3.7 on page 75 of Handout Solve the following recur...