Online study resources available anywhere, at any time
High-quality Study Documents, expert Tutors and Flashcards
Everything you need to learn more effectively and succeed
We are not endorsed by this school |
We are sorry, there are no listings for the current search parameters.
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Sule Ozler Economics 12 Fall 2011 READ THE EXPLANATIONS IN BOLD LETTERS CAREFULLY! MID-TERM EXAM - GOOD LUCK! WRITE YOUR NAME AND ID# You will not be allowed to ask questions during the exam. This exam has three sections. Each section has multiple questio
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c c Homework 1 From the textbook solve the problems 1, 2, 3, 5, 6, 8, 11 and 14 at the end of the Chapter 4. And also the problems below: Problem 1. Give examples of (not independent) random variab
School: UCLA
Spring 2011- Professor Sule Ozler Name Economics 121 ID# MID-TERM EXAM-II WRITE YOUR NAME AND ID# This exam has TWO sections. Each section has multiple questions. Sections I is 40 points, section II is for a total of 60 points. I. MULTIPLE CHOICE: Choose
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 1 Solutions April 7, 2014 Problem 34.4 Suppose the growth rate of a certain species is not constant, but depends in a known way on the temperature of its environment. If the temperature is known as a function of time, derive an expres
School: UCLA
Spring 2011- Professor Sule Ozler Name Economics 121 ID# FINAL EXAM WRITE YOUR NAME AND ID# No questions will be answered during the exam There will not be any bathroom breaks during the exam You are permitted to have only your writing equipment on your d
School: UCLA
Chapter Review Exercises SOLUTION 811 The function whose value we want to approximate is f (x, y, z) = x 2 + y2 + z We use the linear approximation at the point (7, 5, 70), hence h = 7.1 - 7 = 0.1, k = 4.9 - 5 = -0.1, and l = 70.1 - 70 = 0.1. We g
School: UCLA
MULTIVARIABLE CALCULUS (MATH 32A) FALL 2004 LECTURE NOTES 10/1/04 Office Hours: MS 7344, 11:00 12:40 Mon., Wed., Fri. E-mail: lchayes@math.ucla.edu Homework: 20% (each problem graded on a 2-pt. scale). PRINT OUT HOMEWORK FROM COURSE WEBPAGE Midterm
School: UCLA
School: UCLA
School: UCLA
School: UCLA
Course: MULTIVARIABLE CALCULUS
Mathematica for Rogawski's Calculus 2nd Edition 2010 Based on Mathematica Version 7 Abdul Hassen, Gary Itzkowitz, Hieu D. Nguyen, Jay Schiffman W. H. Freeman and Company New York 2 Mathematica for Rogawski's Calculus 2nd Editiion.nb Copyright 2010 Mathem
School: UCLA
School: UCLA
School: UCLA
Introduction to Probability 2nd Edition Problem Solutions (last updated: 10/22/13) c Dimitri P. Bertsekas and John N. Tsitsiklis Massachusetts Institute of Technology WWW site for book information and orders http:/www.athenasc.com Athena Scientic, Belmont
School: UCLA
Course: Algebraic Topology
B D f 1; : : : ; pg H 7! B Rp : H Rn ; 1; : : : ; f 1; : : : ; H p H W f 1; : : : ; BD 1 Rn ; p H W; p qg qg p p AD 1 q : j Rp A A D 5 7 j C D A B 6 9 8 f 1; : : : ; 5g f 1; : : : ; 5g D 4 3 5 3 A B; Rn H AD A 1 4 n Rn W AD2 3 C A 8 A A D p p 2 A 1 A A H
School: UCLA
Course: Algebraic Topology
R3 : R3 3 R R3 A B m AB D C R3 AB T n C 1 A D 42 1 A 1B A B A2 D I B 2 D I AB D AB D BA 3 2 3 3 8 3 5 4 11 5 55 BD4 1 2 5 3 4 A 1 A 1B AX D B 2 ATB A B BC D BD C DD AC D 0 A B n AD0 n C D0 .A C B/.A B/ D A2 B2 A 2 7 1 3 nC1 n n AB D 1 1 1 5 2 A n R3 4 3
School: UCLA
Course: Algebraic Topology
3 ; 0 B D f 1 ; 2 g: 1 D 2 D 1 2 D 7 ; 2 B B b2 D 4 ; 1 f 1; B 2g x b1 0 w D D 1 1 2:5 0 2 2 D 2 1 B D f 1; B B B f 1; D 2 3 D 2 4 2g B 2g B 2 2 6 3 6 AD4 0 3 2 1 60 6 40 0 2 1 65 6 AD4 4 3 2 1 60 6 40 0 2 6 6 4 2 6 6 4 y 3 2 1 37 6 7; 6 25 4 4 3
School: UCLA
Course: Algebraic Topology
A D SG A x x WEB 5 5 7 x 7 A A R3 H 3: 1 2 B D R R3 BD BD 1 ; 1 2 1 ; B D 3 3 ; 1 2 ; B D 3 2 2 g: B 2 BD 2 3 3 D 4 7 5; 1 1 :2 ; :2 1 1; 3 2 3 1 D 4 65 7 3 2 D 1 D 1 1 2 H B D f 1; 2 D 4 8 5; 6 1 B: B 2 H 3 1 2 D4 2 D4 2 ; 3 1 ; 5 3 1 4 5; 3 3 3 2 5; 4
School: UCLA
Course: Algebraic Topology
A D A A D A A A AC n ADn Rp p p Rp R p H p H Rn p H H A n H H p n A Rn : A n ADR ADn ADn ADf g AD0 ) Rn A D AD0 ) ) ) A D A A ) ) ) ) n ADf g A ) )
School: UCLA
Course: ANALYSIS
Math 131a Lecture 2 Spring 2009 Midterm 1 Name: Instructions: There are 4 problems. Make sure you are not missing any pages. Unless stated otherwise (or unless it trivializes the problem), you may use without proof anything proven in the sections of the b
School: UCLA
Mathematics 131A Fall 2007 FINAL Your Name: Signature: INSTRUCTIONS: This is a closed-book test. Do all work on the sheets provided. If you need more space for your solution, use the back of the sheets and leave a pointer for the grader. Good luc
School: UCLA
Course: Probability Theory
Midterm 3, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Probability Theory
Midterm 1 practice, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Name and student ID: Question Points 1 10 2 10 3 10 4 10 5 10 Total: 50 Score 1. (a) (2 points) If is a sample space, what is P(). Solution: P() = 1 (b) (2 points) If P(A) =
School: UCLA
Math 32A: Practice Problems for Exam 2 Problem 1. A particle travels along a path r(t) with acceleration vector t4 , 4 t . Find r(t) if at t = 0, the particle is located at the origin and has initial velocity v0 = 2, 3 . Solution: We have r (t) = 1 1 t4 ,
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c c Homework 1 From the textbook solve the problems 1, 2, 3, 5, 6, 8, 11 and 14 at the end of the Chapter 4. And also the problems below: Problem 1. Give examples of (not independent) random variab
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 1 Solutions April 7, 2014 Problem 34.4 Suppose the growth rate of a certain species is not constant, but depends in a known way on the temperature of its environment. If the temperature is known as a function of time, derive an expres
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c solutions From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 addi
School: UCLA
Course: Introduction Of Complex Analysis
EE101 Engineering Electromagnetics Winter 2013 2/14/13 Homework #5 Due: Thursday Feb 21 10:00 AM Hand in to the TA at beginning of class. No late homework is accepted (see grading policy posted on eeweb). If you cannot make it to class, you must slip the
School: UCLA
Math32a HW1 Due on Monday, Jan 14 All the numbered problems are from the textbook Multivariable Calculus by Rogawski (2nd edition). Note: if your textbook is Early Transcendentals by Rogawski (2nd edition), then all your chapters are shifted by 1 down. Th
School: UCLA
School: UCLA
Course: Calculus
31B Notes Sudesh Kalyanswamy 1 Exponential Functions (7.1) The following theorem pretty much summarizes section 7.1. Theorem 1.1. Rules for exponentials: (1) Exponential Rules (Algebra): (a) ax ay = ax+y (b) ax ay = x y axy (c) (a ) = axy (2) Derivatives
School: UCLA
School: UCLA
School: UCLA
Course: Linear Algebra
Math 33A, Sec. 2 Linear Algebra and Applications Spring 2012 Instructor: Professor Alan J. Laub Dept. of Mathematics / Electrical Engineering Math Sciences 7945 phone: 310-825-4245 e-mail: laub@ucla.edu Lecture: MWF 2:00 p.m. 2:50 p.m.; Rolfe 1200 Office
School: UCLA
Math 3B Integral calculus and differential equations Prof. M. Roper Young Hall CS 76, MWF 2-2.50pm. All inquiries about this class should be posted to the class Piazza page. The only emails that I will respond to are questions about how to login to Piazza
School: UCLA
Course: Calculus
Sample Syllabus Philosophical Analysis of Contemporary Moral Issues Winter 2015, MW 8-9:50 Instructor: Robert Hughes (hughes@humnet.ucla.edu) Instructor office hours: Dodd 378, M 11-12 and W 10-11 or by appointment TAs: Kelsey Merrill (kmerrill@humnet.ucl
School: UCLA
Course: Math 170
Probability Theory, Math 170A, Winter 2015 - Course Info Instructor: Tonci Antunovic, 6156 Math Sciences Building, tantunovic@math.ucla.edu, www.math.ucla.edu/~tantunovic Instructor Oce Hours: Monday 10-12am and Wednesday 9-10am in 6156 Math Sciences Buil
School: UCLA
Course: Math 1
Math1 Fall2012 Lecture1(8am),Lecture2(10am)andLecture3(1pm) Instructor Paige Greene E-Mail: paige@math.ucla.edu Office Number: MS 6617 B Office Hours: Mon and Wed (copy from me in class) Course Goals: The purpose of Math 1 is to give you a strong preparat
School: UCLA
Math33BDifferentialEquations Winter2015,lecture3 Time:MWF3:003:50p.m. Room:MS4000A Discussionsections: 3A T3:00P3:50PGEOLOGY6704 3B R3:00P3:50PGEOLOGY4645 Instructor:YuZhang Office:MS6617F Officehours:Monday2:003:00p.m. Wednesday4:006:00p.m. Email:yuzhang
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Sule Ozler Economics 12 Fall 2011 READ THE EXPLANATIONS IN BOLD LETTERS CAREFULLY! MID-TERM EXAM - GOOD LUCK! WRITE YOUR NAME AND ID# You will not be allowed to ask questions during the exam. This exam has three sections. Each section has multiple questio
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c c Homework 1 From the textbook solve the problems 1, 2, 3, 5, 6, 8, 11 and 14 at the end of the Chapter 4. And also the problems below: Problem 1. Give examples of (not independent) random variab
School: UCLA
Spring 2011- Professor Sule Ozler Name Economics 121 ID# MID-TERM EXAM-II WRITE YOUR NAME AND ID# This exam has TWO sections. Each section has multiple questions. Sections I is 40 points, section II is for a total of 60 points. I. MULTIPLE CHOICE: Choose
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 1 Solutions April 7, 2014 Problem 34.4 Suppose the growth rate of a certain species is not constant, but depends in a known way on the temperature of its environment. If the temperature is known as a function of time, derive an expres
School: UCLA
Spring 2011- Professor Sule Ozler Name Economics 121 ID# FINAL EXAM WRITE YOUR NAME AND ID# No questions will be answered during the exam There will not be any bathroom breaks during the exam You are permitted to have only your writing equipment on your d
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c solutions From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 addi
School: UCLA
Course: ANALYSIS
Math 131a Lecture 2 Spring 2009 Midterm 1 Name: Instructions: There are 4 problems. Make sure you are not missing any pages. Unless stated otherwise (or unless it trivializes the problem), you may use without proof anything proven in the sections of the b
School: UCLA
Mathematics 131A Fall 2007 FINAL Your Name: Signature: INSTRUCTIONS: This is a closed-book test. Do all work on the sheets provided. If you need more space for your solution, use the back of the sheets and leave a pointer for the grader. Good luc
School: UCLA
Course: Probability Theory
Midterm 3, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Probability Theory
Midterm 1 practice, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Name and student ID: Question Points 1 10 2 10 3 10 4 10 5 10 Total: 50 Score 1. (a) (2 points) If is a sample space, what is P(). Solution: P() = 1 (b) (2 points) If P(A) =
School: UCLA
Math 32A: Practice Problems for Exam 2 Problem 1. A particle travels along a path r(t) with acceleration vector t4 , 4 t . Find r(t) if at t = 0, the particle is located at the origin and has initial velocity v0 = 2, 3 . Solution: We have r (t) = 1 1 t4 ,
School: UCLA
Course: MATH20F
Hector Ordorica Section: B51 / B02 TA: Matthew Cecil Exercise 3.1 Answer: D can be: 1. D = 0 0 00 2. D = 1 0 01 3. D = 0 1 10 Exercise 3.2 (a) Input: A = [1, 2, 0; 2, 1, 2; 0, 2, 1] B = [3, 0, 3; 1, 5, 1; 1, 1, 3] x = [1; 2; 3] C = (5*A^2*B - 3*A')^2 Outp
School: UCLA
Introduction to Probability 2nd Edition Problem Solutions (last updated: 11/25/11) c Dimitri P. Bertsekas and John N. Tsitsiklis Massachusetts Institute of Technology WWW site for book information and orders http:/www.athenasc.com Athena Scientific, Belmo
School: UCLA
Math 3C Midterm 1 Solutions Name: BruinID: Section: Read the following information before starting the exam. This test has six questions and seven pages. It is your responsibility to ensure that you have all of the pages! Show all work, clearly and in o
School: UCLA
Winter 2011- Professor Sule Ozler Name Economics 121 ID# FINAL EXAM WRITE YOUR NAME AND ID# This exam has three sections. Each section has multiple questions. Sections I and II are 20 points each, section III is for a total of 60 points. I. MULTIPLE CHOIC
School: UCLA
Course: MATH20F
Hector Ordorica Section: Tues 2-3 TA: Greene Exercise 2.1 (a) (b) (c) Input: C = [5 2 1; 6 0 1; 4 -6 2] d = [-1; 2; 3] x = C\d Output: x=0.9091 -1.0455 -3.4545 (d) Input: C*x-d Output: C*x-d ans = 1.0e-015 * -0.4441 -0.4441 0.8882 Exercise 2.2 Input: C =
School: UCLA
Course: Actuarial Math
MATH 115A - Practice Final Exam Paul Skoufranis November 19, 2011 Instructions: This is a practice exam for the nal examination of MATH 115A that would be similar to the nal examination I would give if I were teaching the course. This test may or may not
School: UCLA
School: UCLA
Course: Introduction Of Complex Analysis
EE101 Engineering Electromagnetics Winter 2013 2/14/13 Homework #5 Due: Thursday Feb 21 10:00 AM Hand in to the TA at beginning of class. No late homework is accepted (see grading policy posted on eeweb). If you cannot make it to class, you must slip the
School: UCLA
Math32a HW1 Due on Monday, Jan 14 All the numbered problems are from the textbook Multivariable Calculus by Rogawski (2nd edition). Note: if your textbook is Early Transcendentals by Rogawski (2nd edition), then all your chapters are shifted by 1 down. Th
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 6 c c Solve the problems 18 a) c) d) e) and 19 from the Chapter 7 additional exercises at http:/www.athenasc.com/prob-supp.html And also the problems below: Problem 1. Denote points P0 ,
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 1 Solution 34.5 (a) If the growth rate is 0, the discrete model becomes Nm+1 Nm = tfm , And the solution is Nm = N0 + t(f0 + f1 + fm1 ), which is analogous to integration, since let t = mt, then t t(f0 + f1 + fm1 ) f (s)ds 0 for t small
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 2 Solution 34.16 We will rstly proceed similarly as 34.14(c). We assume the theoretical growth has the form N0 eR0 t , and we hope to gure out which N0 and R0 t the data best. 34.14(b) suggests that N0 should be equal to the initial popu
School: UCLA
MATH 32A FINAL EXAMINATION March 21th, 2012 Please show your work. You will receive little or no credit for a correct answer to a problem which is not accompanied by sucient explanations. If you have a question about any particular problem, please raise y
School: UCLA
Math 131A/2 Winter 2002 Handout #1a Instructor: E. Eros, MS 6931. Lecture Meeting Time: MWF 2:00PM-2:50PM Location: MS 5117 Recitation TA: to be announced, MS 5117 T 2:00P-2:50P Oce hours (tentative): TF 4-5. Text Fundamental Ideas of Analysis by Michael
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 5 c c From the textbook solve the problems 4 and 5 from the Chapter 5. Solve the problems 2, 4, 6, 7, 9 and 10 from the Chapter 7 additional exercises at http:/www.athenasc.com/prob-supp
School: UCLA
Course: 245abc
Math 202A Homework 13 Roman Vaisberg November 28, 2007 Problem 17. Suppose f is dened on R2 as follows: f (x, y ) = an if n x < n + 1 and n y < n + 1, (n 0); f (x, y ) = an if n x < n + 1 and n + 1 y < n + 2, (n 0); while f (x, y ) = 0 elsewhere. Here an
School: UCLA
INSTRUCTORS SOLUTIONS MANUAL A BRIEF COURSE IN MATHEMATICAL STATISTICS Elliot A. Tanis Hope College and Robert V. Hogg University of Iowa August 22, 2006 ii Contents Preface v 1 Probability 1.1 Basic Concepts . . . . . 1.2 Methods of Enumeration 1.3 Condi
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 2 c c From the textbook solve the problems 17, 18, 19, 22, 23 and 24 from the Chapter 4. Solve the problems 21, 22, 24, 30 from the Chapter 4 additional exercises at http:/www.athenasc.c
School: UCLA
Math 3C Midterm 2 Name: BruinID: Section: Read the following information before starting the exam. This test has six questions and fourteen pages. It is your responsibility to ensure that you have all of the pages! Show all work, clearly and in order, i
School: UCLA
Course: Probability Theory
Mathematics Department, UCLA P. Caputo Fall 08, midterm 1 Oct 22, 2008 Midterm 1: Math 170A Probability, Sec. 2 Last name First and Middle Names Signature UCLA ID number (if you are an extension student, say so) Please note: 1. Provide the information ask
School: UCLA
Course: Introduction Of Complex Analysis
EE101 Engineering Electromagnetics Winter 2013 1/24/12 Homework #3 Due: Thursday Jan 31 10:00 AM Hand in to the TA at beginning of class. No late homework is accepted (see grading policy posted on eeweb). If you cannot make it to class, you must slip the
School: UCLA
Course: 245abc
Math 245A Homework 2 Brett Hemenway October 19, 2005 Real Analysis Gerald B. Folland Chapter 1. 13. Every -nite measure is seminite. Let be a -nite measure on X, M. Since is -nite, there exist a sequence of sets cfw_En in M, with (En ) < and En = X . n=1
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 0 Solution 32.11 The easier way: (slightly unrigorous, but its ne for this class) Suppose the bank compounds the interest n times a year, and let t := 1/n. With the additional deposit (or withdrawl) D (t), the balance at time t + t is gi
School: UCLA
Homework 4 Solutions Math 3C Due: Friday Nov 2, 9 a.m. #1(a) Let X be a random variable that equals the number of defective items in the sample. When the sampling is done with replacement, X is binomially distributed with parameters n = 5 and p = 5/20 = 1
School: UCLA
FINS3635 S2/2011 Put-Call Parity Matthias Thul Last Update: September 14, 2011 This documents shows you how a the general put-call relationship for European options can be obtained by simple no-arbitrage arguments and gives some examples of how it can be
School: UCLA
MATH 33A/2 PRACTICE MIDTERM 2 Problem 1. (True/False) . 1 1 1 Problem 2. Let v1 = 1 , v2 = 0 , v3 = 1 . 0 1 1 3 (a) Show that B = 1 , v2 , v3 ) is a basis for R . (v 1 (b) Let u = 1 . Find the coordinates of u with respect to the basis B. 2 (c) Find the c
School: UCLA
Course: 245abc
Math 245A Homework 1 Brett Hemenway October 19, 2005 3. a. Let M be an innite -algebra on a set X Let Bx be the intersection of all E M with x E . Suppose y Bx , then By Bx because Bx is a set in M which contains y . But Bx By because if y E for any E M,
School: UCLA
MATH 32A FIRST MIDTERM EXAMINATION October, 18th, 20101 Please show your work. You will receive little or no credit for a correct answer to a problem which is not accompanied by sufficient explanations. If you have a question about any particular problem,
School: UCLA
Course: MATH20F
Hector Ordorica 1/16/2007 Tues 2-3 Exercise 1.1 Input: H=8;e=5;c=3;t=20;o=15;r=18; O=15;r=18;d=4;o=15;r=18;i=9;c=3;a=1; HectorOrdorica = H + e + c + t + o + r + O + r + d + o + r + i + c + a Output: HectorOrdorica = 152 Exercise 1.2 Input: z = 25-(100-7ex
School: UCLA
Course: Discrete Math
Practice First Test Mathematics 61 Disclaimer: Listed here is a selection of the many possible sorts of problems. actual test is apt to make a different selection. 1. Let S5 be the set of all binary strings of length 5 (such as 11001). The Let E be
School: UCLA
Math 31A Midterm 1 Solutions 1. [3 points] The derivative of (a) 1 (b) (c) x2 x)2 x3 Brent Nelson is: 1 x2 1 2 x3 (3x 1 1 + x2 + 8x2 x + 3) (d) None of the above. Solution. We rst apply the quotient rule d dx x2 x)2 x3 = d d x3 dx [(x2 x)2 ] (x2 x)2 dx (
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 1 Solution 32.3 (a) Use N (nt) to denote the population at time nt. Then for any n > 0, we have N (nt) = (1 + (b d)t)N (n 1)t) + 1000. (b) Given that N (0) = N0 , we hope to solve the equation above and get the general form for N (nt). T
School: UCLA
Management 1A Summer 2004 Danny S. Litt EXAM 2 SOLUTION Name: _ Student ID No. _ I agree to have my grade posted by Student ID Number. _ (Signature) PROBLEM 1 2 3 4 5 6 7 8 TOTAL POINTS 20 25 20 20 30 30 30 25 200 SCORE MANAGEMENT 1A Problem 1
School: UCLA
Name: Student ID: Section: 2 Prof. Alan J. Laub Math 33A MIDTERM EXAMINATION I Spring 2008 Instructions: Apr. 25, 2008 (a) The exam is closed-book (except for one page of notes) and will last 50 minutes. (b) Notation will conform as closely as possible to
School: UCLA
1008 C H A P T E R 16 M U LTI P L E I N T E G R AT I O N (ET CHAPTER 15) Therefore, D is defined by the inequalities 1 u uv Since x = v+1 and y = v+1 , we have y 2, x 3 y+x 6 y = v+1 = v u x v+1 uv and y+x = u u(v + 1) uv + = =u v+1 v+1 v
School: UCLA
Course: 31b
Math 31B, Lecture 4, Fall 2011 Exam #2, 9 November 2011 Name: ID Number: Section and TA: You have 50 minutes for the exam. No calculators, phones, notes, or books allowed. You must show your work for credit. Hint: n n=0 cr Question: 1 2 3 4 5 6 7 Tota
School: UCLA
S E C T I O N 17.1 Vector Fields (ET Section 16.1) 1061 19. F = x, 0, z SOLUTION This vector field is shown in (A) (by process of elimination). x x 2 + y2 + z2 , y x 2 + y2 + z2 , z x 2 + y2 + z2 20. F = SOLUTION The unit radial vector field i
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 additional exe
School: UCLA
Course: Actuarial Math
MATH 115A - Assignment One - Solutions of Select Non-Graded Problems Paul Skoufranis October 3, 2011 1.2 Question 13) Let V denote the set of ordered pairs of real numbers. If (a1 , a2 ) and (b1 , b2 ) are elements of V and c R, dene (a1 , a2 ) + (b1 , b
School: UCLA
Course: Linear Algebra
Name: Student ID: Prof. Alan J. Laub June 9, 2011 Math 33A/1 FINAL EXAMINATION Spring 2011 Instructions: (a) The exam is closed-book (except for one two-sided page of notes) and will last two and a half hours. No calculators, cell phones, or other electro
School: UCLA
Chapter Review Exercises SOLUTION 811 The function whose value we want to approximate is f (x, y, z) = x 2 + y2 + z We use the linear approximation at the point (7, 5, 70), hence h = 7.1 - 7 = 0.1, k = 4.9 - 5 = -0.1, and l = 70.1 - 70 = 0.1. We g
School: UCLA
MULTIVARIABLE CALCULUS (MATH 32A) FALL 2004 LECTURE NOTES 10/1/04 Office Hours: MS 7344, 11:00 12:40 Mon., Wed., Fri. E-mail: lchayes@math.ucla.edu Homework: 20% (each problem graded on a 2-pt. scale). PRINT OUT HOMEWORK FROM COURSE WEBPAGE Midterm
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
Introduction to Probability: Problem Solutions (last updated: 5/15/07) c Dimitri P. Bertsekas and John N. Tsitsiklis Massachusetts Institute of Technology WWW site for book information and orders http:/www.athenasc.com Athena Scientic, Belmont, Massachuse
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
I , - - - - - I UA5~ :_~ - ~-~ -~L~k~\~I~-~- -~-_ '_~,~ :_ L!J~J~-1'1i:J\J_ _L_~-~LJ l'" _ NL-"~-':v~- _ tl,., _ ~t : : I i . YY\lvt\ _\(Mt - I, i I - '- -~- -~- - - - .J - I i ' , - _ J _ _ _ :._ _ . ~- i . ! \ - - -'- - ' I I -~- -. - _ ~ _ ~-W -ej-~t)J
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
Course: MULTIVARIABLE CALCULUS
Mathematica for Rogawski's Calculus 2nd Edition 2010 Based on Mathematica Version 7 Abdul Hassen, Gary Itzkowitz, Hieu D. Nguyen, Jay Schiffman W. H. Freeman and Company New York 2 Mathematica for Rogawski's Calculus 2nd Editiion.nb Copyright 2010 Mathem
School: UCLA
School: UCLA
School: UCLA
Introduction to Probability 2nd Edition Problem Solutions (last updated: 10/22/13) c Dimitri P. Bertsekas and John N. Tsitsiklis Massachusetts Institute of Technology WWW site for book information and orders http:/www.athenasc.com Athena Scientic, Belmont
School: UCLA
Course: Algebraic Topology
B D f 1; : : : ; pg H 7! B Rp : H Rn ; 1; : : : ; f 1; : : : ; H p H W f 1; : : : ; BD 1 Rn ; p H W; p qg qg p p AD 1 q : j Rp A A D 5 7 j C D A B 6 9 8 f 1; : : : ; 5g f 1; : : : ; 5g D 4 3 5 3 A B; Rn H AD A 1 4 n Rn W AD2 3 C A 8 A A D p p 2 A 1 A A H
School: UCLA
Course: Algebraic Topology
R3 : R3 3 R R3 A B m AB D C R3 AB T n C 1 A D 42 1 A 1B A B A2 D I B 2 D I AB D AB D BA 3 2 3 3 8 3 5 4 11 5 55 BD4 1 2 5 3 4 A 1 A 1B AX D B 2 ATB A B BC D BD C DD AC D 0 A B n AD0 n C D0 .A C B/.A B/ D A2 B2 A 2 7 1 3 nC1 n n AB D 1 1 1 5 2 A n R3 4 3
School: UCLA
Course: Algebraic Topology
3 ; 0 B D f 1 ; 2 g: 1 D 2 D 1 2 D 7 ; 2 B B b2 D 4 ; 1 f 1; B 2g x b1 0 w D D 1 1 2:5 0 2 2 D 2 1 B D f 1; B B B f 1; D 2 3 D 2 4 2g B 2g B 2 2 6 3 6 AD4 0 3 2 1 60 6 40 0 2 1 65 6 AD4 4 3 2 1 60 6 40 0 2 6 6 4 2 6 6 4 y 3 2 1 37 6 7; 6 25 4 4 3
School: UCLA
Course: Algebraic Topology
A D SG A x x WEB 5 5 7 x 7 A A R3 H 3: 1 2 B D R R3 BD BD 1 ; 1 2 1 ; B D 3 3 ; 1 2 ; B D 3 2 2 g: B 2 BD 2 3 3 D 4 7 5; 1 1 :2 ; :2 1 1; 3 2 3 1 D 4 65 7 3 2 D 1 D 1 1 2 H B D f 1; 2 D 4 8 5; 6 1 B: B 2 H 3 1 2 D4 2 D4 2 ; 3 1 ; 5 3 1 4 5; 3 3 3 2 5; 4
School: UCLA
Course: Algebraic Topology
A D A A D A A A AC n ADn Rp p p Rp R p H p H Rn p H H A n H H p n A Rn : A n ADR ADn ADn ADf g AD0 ) Rn A D AD0 ) ) ) A D A A ) ) ) ) n ADf g A ) )
School: UCLA
Course: Algebraic Topology
R3 H 2 R R2 R2 H H 7! B H pg B D f 1; : : : ; R2 H Rp H H 7! B p H p H p H H f g H Rn Rn n n 3 R A A A D A A D A A A A A A A A A A 5 3 6 9 3 2 4 6 4 5 14 5 3 4 5 6 3 8 77 7 20 5 6 4 3 2 5 2 3 8 97 7 45 6 2 60 6 40 0 AD3 5 3 0 0 3 2 0 0 4 5 4 0 - 2 60 6 40
School: UCLA
Course: Algebraic Topology
B D f 1; : : : ; D c1 1 C C cp pg H c1 ; : : : ; cp B Rp 2 3 c1 6 : 7 B D 4 : 5 : p; H cp 1 H D H B 2 3 3 D 465 2 f 1; 2g 2 2 3 1 D 4 05 1 1 B B 2 3 3 D 4 12 5 7 2 B H c1 2 3 2 3 2 3 3 1 3 4 6 5 C c2 4 0 5 D 4 12 5 c1 2 1 7 c2 2 3 1 3 0 12 5 1 7 2 B D 3
School: UCLA
Course: Algebraic Topology
A 2 1 A D4 2 3 32 3 2 3 5 7 0 7 54 3 5 D 4 0 5 3 2 0 1 0 5 A: A A D 2 1 4 2 3 1 0 5 3 7 35 2 5 7 3 A D 2 1 40 0 3 7 17 5 19 1 5 2 3 8 12 2 1 40 0 1 2 0 3 7 17 5 49 5 3 0 A A A x2 D 0; x3 D 0; A D .x1 ; x2 ; x3 /; A D .1; 0; 0/: A A A n n A A A D x1 A A Rn
School: UCLA
Course: Algebraic Topology
2 Rn ; ; H H; c 1; : : : ; H C H c f 1; : : : ; n R ; p 3 63 6 AD4 0 6 2 3 60 6 40 0 1 pg p m 1 1 3 3 3 3 9 9 1 2 0 0 3 6 0 0 0 0 1 0 n n 3 A 3 A 3 Rm : n 3 8 27 7 45 6 3 6 47 7 25 0 1 0 1 2 3 A A Rn A 3 A Rn H 3 H B AD f 1; : : : ; p g A B A: 1; : : : ;
School: UCLA
Course: Algebraic Topology
Rn R2 2 R H H H H H 2 3 2 4 85 1 D 6 2 3 6 D 4 10 5; 11 2 2 3 3 D 4 85 7 AD 3 1 2 3 4 D 4 65 7 2 f 1; 3 : 3g 2; A A 2 3 2 3 2 2 4 0 5; 4 3 5; 1 D 2 D 6 3 2 3 6 D 4 15 17 1 2 3 A 3 2 3 0 D 4 5 5; 5 A 2 3 5 D 4 55 3 A A p 2 Rp 3 AD4 9 9 2 1 6 4 6 AD6 5 6 4
School: UCLA
Course: Algebraic Topology
B A A A D A B A D B D A B AD 1 2 1 6 2 6 5D4 2 3 2 B 3 2 3 4 3 2 0 1 2 8 7 11 3 9 27 7 15 8 A A 3 D 3 1 C2 2 4 3 D 3 D5 1 1 C2 2 2 4 D5 1 2 3 A 1 1 2 2 f 1; 5 f 1; 5 5g 2; 4 2; 5g f 1; A A 2; 5g A A A B A B A 2 1 AD4 2 3 1 0 5 2 0 A D 40 0 SG n A 1 0 0 n
School: UCLA
Course: Algebraic Topology
A D A A A A D A A n Rn A m n Rn n A D C c.A / D c. / D m A D A. C / D A C A D A D Rn Rn A A D A A D Rn A D C c A A C A A D A c; A.c / D A A A A A A A D Rn H x3 H H Rn n n Rn e3 e2 x2 1 e1 n n 2 3 1 607 D 6 : 7; 4:5 : 0 x1 f 1; : : : ; R3 ng A A 2 2 3 0 61
School: UCLA
Course: Algebraic Topology
D x R D R3 x 60 T D.R. / D R.D. / T R R 2 4 y R D 4 z e3 T e2 e1 A1 y x A2 2 A1 D 4 2 1 ' ' 0 A2 D 4 0 0 3 0 05 1 0 0 ' ' 4 R3 30 D .5; 2; 1/ 3 0 05 1 1 0 4 S .2; 2; 6/ S .1; 2; 1/ R2 .4:2; 1:2; 4/ .6; 4; 2/ S .0; 0; 10/ .7; 3; 5/ .12; 8; 2/ S .0; 0; 10/
School: UCLA
Course: Algebraic Topology
Rn A D A 2 3 AD4 1 2 2 1 40 0 A 2 0 0 0 1 0 1 2 0 6 2 4 3 7 15 4 x1 A D 3 3 0 2 0 5; 0 0 x1 D 2x2 C x4 2 1 3 8 2x2 1 2 5 3x5 x3 D x4 C 3x5 D 0 x3 C 2x4 2x5 D 0 0D0 2x4 C 2x5 3 2 3 2 3 2 x1 2x2 C x4 3x5 2 6 x2 7 6 7 617 6 x2 6 7 6 7 6 7 6 6 x3 7 D 6 2x4 C
School: UCLA
Course: Algebraic Topology
Rn 1 2 x2 1 1 2 L L v1 v2 x1 uv u , v2 ncfw_v 1 Spa 2w w v L 1 2 Dk L u v is not on L 1 2w is not on L Rn 1; : : : ; p 1; : : : ; p n R f 1; : : : ; 1; : : : ; p pg Rn Rn Rn A A A AD 1 f 1; : : : ; ng Rm A x3 A m n Rm A Rm 1 AD4 4 3 A Col A b Rm 2 x2 0 n
School: UCLA
Course: Algebraic Topology
. 30 / D p . 30 / D 3=2 2 1 40 0 D . 2; 6/ :5 p 32 p p 3 32 2 3=2 1=2 0 1 0 2 p 6 54 1=2 65 3=2 0 54 0 1 1 0 0 1 0 0 1 p 2p 3 3=2 1=2 p3 5 p D 4 1=2 3=2 3 3C55 0 0 1 0 1 0 Rn Rn A; A D Rn H Rn H H x3 H c C H c H v1 v2 x1 0 x2 1 Rn 2 2g D s1 c C f 1; C 1 C
School: UCLA
Course: Algebraic Topology
4 4 4 4 R2 3 30 3 x2 x2 x2 p (a) Original figure. p x1 (b) Translated to origin by p. p x1 (c) Rotated about the origin. 3 x1 (d) Translated back by p. 45 x R2 DD A 4 0 3 2 2 45 5 3 y x 60 .2; 1/ . 1; 4/ 90 100 B x .6; 8/ 45 3 2 y x2 p x1 3 . 2; 6/ .3; 7/
School: UCLA
Course: Algebraic Topology
D . 6; 4; 5/ 3 z 3 e3 y 2 x . p 3 30 / D .:5; 0; 3=2/ 30 ; 0; 2p 3=2 4 0 :5 0 1 0 3 :5 5 p0 3=2 2p 3=2 6 0 AD6 4 :5 0 0 1 0 0 :5 p0 3=2 0 e1 x p 1 30 / D . 3=2; 0; :5/ 30 ; 0; . e2 y .x; y; ; 1/ .x 2 1 60 6 40 0 6; y C 4; C 5; 1/ 3 0 0 6 1 0 47 7 0 1 55
School: UCLA
Course: Algebraic Topology
.x; y; / .x; y; / H 0 .x; y; ; 1/ .X; Y; Z; H / R3 xD X ; H yD Y ; H D .x; y; ; 1/ .10; 6; 14; 2/ .x; y; / . 15; 9; 21; 3/ .5; 3; 7/ 4 Z H 4 30 y y
School: UCLA
Course: Algebraic Topology
x x x D d d x D y D P S .3; 1; 4/ .5; 1; 4/ .5; 0; 4/ y 1 =d y x ; ; 0; 1 1 =d 1 =d .x; y; 0; 1 =d / P =d 2 3 2 1 x 6y 7 60 P6 7 D 6 4 5 40 1 0 d x 1 =d D .x; y; ; 1/ 1 dx 0 1 0 0 32 3 2 0 x x 076y 7 6 y 76 7 D 6 054 5 4 0 1 1 1 =d 0 0 0 1=d 3 7 7 5 .3;
School: UCLA
Course: Algebraic Topology
R2 2 4 ' ' 3 0 05; 1 ' ' 0 0 2 0 41 0 ' 3 3 3 0 0 5; 1 1 0 0 yDx A 0 0 1 2 s 40 0 A 0 t 0 x y 2 3 0 05 1 s t 90 . :5; 2/ Original Figure 2 3 x 4y 5 1 After Scaling After Rotating After Translating 2 1 40 0 0 1 0 ' D =2 2 :3 ! 4 0 0 2 0 ! 41 0 2 1 ! 40 0 3
School: UCLA
Course: Algebraic Topology
AD 7! A 1 0 :25 1 AD 8 6 5 AD D 3 7 1 2 0 0 :5 0 2:105 6:420 6 0 8 8 7:5 8 5:895 1:580 2 8 4 N x N x SD SA D N D x2 .x; y/ x :75 0 0 1 :75 0 0 1 :75 0 1 0 :25 1 :1875 1 R2 4 .x; y; 1/ .x; y/ .0; 0/ 2 4 2 2 4 3 4 R3 .x; y; 1/ xy 3 x1 3 .x; y/ 7! .x C h; y
School: UCLA
Course: Algebraic Topology
Agriculture Manufacturing Services Open Sector C D :0 :6 :5 ; :2 D C D DC C 50 30 :2 :6 :5 :1 D C 51 30 16 12
School: UCLA
Course: Algebraic Topology
C D :2 :5 DC C :4 ; :3 D 20 30 D 6 5 8 3 x y 7 D 1 2 N 4 0 0 :5 0 :5 6:42 6 0 6 8 5:5 8 5:5 1:58 0 8 DD
School: UCLA
Course: Algebraic Topology
C n 51 30 D 50 1 C 30 0 C m!1 Cm m D 1; 2; : : : ; .I n Cm ! 0 Dm D I C C C C Dm DmC1 C/ 1 C C C R 0 .I .I 2 :2 C D 4 :3 :1 n :2 :1 :0 3 :0 :3 5 :2 C/ 2 1 C/ :1588 6 :0057 6 6 :0264 6 6 :3299 6 6 :0089 6 4 :1190 :0063 1 2 3 40 D 4 60 5 80 C .I C/ :0064 :
School: UCLA
Course: Algebraic Topology
C C.C / D C 2 C C C.C 2 / D C 3 2 C.C 3 / D C 4 : : : C3 : : : D C C C C2 C C3 C D .I C C C C 2 C C 3 C C /.I C C C C 2 C .I / C C m/ D I C mC1 C m Cm I t m .I C/ 1 I C C C C2 C C3 C C I C C mC1 ! I tm ! 0 C Cm .I C/ .I C/ 1 m C C/ D .I .I j C/ m C 1 1 .I
School: UCLA
Course: Algebraic Topology
2 1 C D 40 0 I 2 :5 4 :2 :1 3 :2 50 :1 30 5 :7 20 :4 :7 :1 I A .I C C .I 3 0 05 1 0 1 0 2 5 4 2 1 2 :5 4 :2 :1 4 7 1 C C/ 3 2 :2 :5 :1 5 D 4 :2 :3 :1 :4 :3 :1 3 2 500 1 300 5 7 200 C/ D I .I 2 1 40 0 :4 :7 :1 0 1 0 1 D .I C/ 1 DC C .I C/ 1 D C C C.C / D C
School: UCLA
Course: Algebraic Topology
" 1 " 1 100 " 2 3 2 3 2 3 :50 50 D 1004 :20 5 D 4 20 5 :10 10 x1 x1 x1 x1 x2 f g D x1 DC C 1 2 2 :50 C D 4 :20 :10 :40 :30 :10 D 1 C x2 3 :20 :10 5 :30 C C I .I 3 2 C D C/ D x2 x3 2 1 x3 3 C x3 3 1
School: UCLA
Course: Algebraic Topology
A 1 A A A A A 1 A D L U 1 A 0 0 0 0 1 3 5 7 2 4 6 8 10 10 10 10 5 5 A 1 A 20 p1 ; : : : ; p 4 20 x x x p2 p1 x p3 x p4 C 2 6 6 6 6 6 AD6 6 6 6 6 4 D .5; 15; 0; 10; 0; 10; 20; 30/ 4 1 1 1 4 0 1 1 0 4 1 1 1 1 4 0 1 1 0 4 1 1 WEB 1 1 4 0 1 x t A D 3 1 0 4 1
School: UCLA
Course: Algebraic Topology
L 2 6 6 6 6 4 3 2 2 67 7 2 76 76 4 54 6 2 # 2 6 6 6 6 4 1 3 1 2 3 3 3 2 3 5 37 7 6 54 5 5 10 9 3 # 5 # 1 1 2 3 1 1 2 3 2 7 7 7 7 5 6 6 LD6 6 4 1 3 1 2 3 0 1 1 2 3 0 0 1 1 2 3 0 07 7 07 7 05 1 0 0 0 1 0 WEB n Rn 8 < : 9 = ; D C 8 < : 9 = ; Rn 1 2 3
School: UCLA
Course: Algebraic Topology
2 6 AD6 4 2 6 AD6 4 1 2 3 5 1 2 3 5 3 3 0 3 0 1 3 4 2 4 4 8 0 0 1 1 3 2 3 0 1 6 7 12 7 7; D 6 2 7 4 15 36 5 49 2 32 0 1 3 2 0 76 0 3 0 76 0 54 0 0 2 1 0 0 0 LU 5 A D BC A D LU 3 0 12 7 7 05 1 3 A D CD A L 2 3 5 4 3 4 9 9 2 3 4 6 3 2 1 6 1 6 4 4 2 1 0 9 2
School: UCLA
Course: Algebraic Topology
i v1 i1 7! v1 i1 v2 i2 v2 i2 A v2 i2 DA v1 i1 i1 input terminals v i2 electric circuit v1 output terminals v2 R1 i1 i2 R1 v1 i2 i3 v2 A series circuit v3 R2 A shunt circuit R2 1 0 R1 1 1 1=R2 A1 0 1 1 :5 8 5 A2 A1 A2 A1 D 1 1=R2 0 1 1 0 R1 1 D A2 .A1 / 1
School: UCLA
Course: Algebraic Topology
R1 .1; 2/ R2 D 1=:5 D 2 1 :5 R2 8 5 1 1=R2 R1 D 8 2 6 6 AD6 6 4 R1 1 C R1 =R2 D A 2 3 AD4 3 6 2 1 AD4 1 2 2 2 AD4 4 0 2 1 AD4 2 0 2 2 AD4 4 6 7 5 4 0 1 5 6 8 4 0 1 1 4 5 9 3 2 3 2 7 1 5; D 4 5 5 0 2 32 3 0 3 7 2 0 54 0 2 15 1 0 0 1 3 2 3 4 2 0 5; D 4 4 5
School: UCLA
Course: Algebraic Topology
A 2 U L 3 2 2 3 6 47 3 6 7 4 2 54 9 5 2 4 12 6 2 # 2 3 # 1 6 2 6 4 1 3 1 3 4 5 2 # 5 # 3 2 7 7 5 1 1 2 1 6 2 LD6 4 1 3 L U 0 1 3 4 0 0 1 2 LU D A 3 0 07 7 05 1 L L L I SG L . / A D L L n n n 30 n 2n3 =3 A A L D / U D A 1 A 2n2 2n2 U A 1 / A WEB L A n n 1
School: UCLA
Course: Algebraic Topology
A W .s/ sIn W .s/ D W .s/ s W .s/ W .s/ s 1 W .s/ A A BC C A22 2 1 62 6 M D4 1 0 A11 S A11 A A X A m n M D Im X.X T X/ 1 2 6 3 0 05 D 0 B 0 0 1 M2 D I 3 0 07 7 05 1 0 0 1 2 2 sIn B Im A n .k C 1/ XT X 1 X T 0 0 WTW T 1 0 M 0/ C AD M 2 D I: 6 C A W D X . A
School: UCLA
Course: Algebraic Topology
Multiplication by A x b Multiplication by U Multiplication by L y 7! A 2 3 9 6 57 7 D6 4 75 11 A D A L D 2 1 6 1 D6 4 2 3 L 0 1 5 8 0 0 1 3 L 3 9 57 7 75 11 0 0 0 1 U D 2 3 60 D6 40 0 U 2 1 60 6 40 0 0 1 0 0 0 0 1 0 0 0 0 1 3 9 47 7D I 55 1 U 7 2 0 0 2 1
School: UCLA
Course: Algebraic Topology
A D A D 1; 2; A A D :; p 1 A 1 A 1 A 1 A A m n A A D LU U m L m n m A A 1 * A= * * 0 1 * * 0 0 1 * * 0 0 0 0 0 1 0 0 0 L U * * 0 0 * * * * * 0 0 U L A D A D LU L U L.U / D L D U D L D 2 3 6 3 AD6 4 6 9 7 5 4 5 U D ; L U 3 2 2 2 1 07 6 7D6 0 55 4 5 12 1 1
School: UCLA
Course: Algebraic Topology
.k C 1/ A A .k C 1/ B 50 B C D 50 A 0 0 AT C 2 1 63 6 A D 60 6 40 0 2 5 0 0 0 0 0 2 0 0 3 0 07 7 07 7 85 6 0 0 0 7 5 50 50 A B ACB AB A 20 30 A A D A 30 5 10 B R50 A11 30 2 20 20 2 Aij A22 A12 A I 0 A I W X Y Z Y D XT X D " I 0 A I W Y W Y X W D Z AW C Y
School: UCLA
Course: Algebraic Topology
L L I A A U E1 /.Ep E1 / E1 L D .Ep Ep L 1 DI U L L I L .Ep E1 ; : : : ; E p .Ep L E1 / D L L 2 2 6 4 AD6 4 2 6 A E1 /L D I 1 L 1A D U 4 5 5 0 1 3 4 7 L A 4 2 1 6 2 LD6 4 1 3 A 5 8 1 3 0 1 0 0 1 L 4 3 2 17 7 85 1 A D LU L 3 0 07 7 05 1 A L A A L U A 2 2 6
School: UCLA
Course: Algebraic Topology
I 0 A I X TX I E 0 I 0 I I 0 A B C D A B C D E 0 0 F I E X Y B X1 X2 X A D A1 A2 A2 A C B D A1 C B1 A11 A12 AD A21 A22 A B P Q R S 0 W X I Y Z Z A C A1 A2 B 1 A C X Y 0 Z X Y B 0 0 0 I X 0 Y A 0 B C 2 A 0 4 0 I B X Y 0 0 A B 0 I B D B1 0 I D Z 0 I 0 D 0
School: UCLA
Course: Linear Algebra
Let F be a eld, and S = cfw_s1 , s2 , s3 be a set with exactly three elements. Consider the vector space F(S, F ) all functions from S to F with the standard function addition and scalar multiplication. Find a basis for F(S, F ) (and prove thats indeed a
School: UCLA
Course: Linear Algebra
Find a basis for V = cfw_M M2 (R)/tr(M ) = 0, a subspace of 2 2 real valued matrices. 1
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
Section 2.4, Problem 27 We are asked to show whether the transformation y1 x + x2 =1 y2 x1 x2 y1 for which the solution is not unique y2 is invertible. As we saw in section, there are y = 1 1+0 0+1 = = 0 10 01 and there are y for which no solution exists
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
Section 1.2, Problem 42 The key to this problem is the assumption that the vehicles leaving the area during the hour were exactly the same as those entering it. At the end of the hour, there are no cars left over, in any of the streets or intersections. T
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
REVIEW FOR QUIZ 2 Econ 11, Sections 2A/2B, Week 4 Matt Miller This week we will review a few items that are likely to come up on the quiz on Thursday. I include some of the answers here, but the remainder (along with graphs) will be drawn up in section. 1
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
Solutions to Linear Algebra, Fourth Edition, Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence Jephian Lin, Shia Su, Zazastone Lai July 27, 2011 Copyright 2011 Chin-Hung Lin. Permission is granted to copy, distribute and/or modify this document un
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
Linear Algebra Done Right, Second Edition Sheldon Axler Springer Contents Preface to the Instructor Preface to the Student Acknowledgments Chapter 1 ix xiii xv Vector Spaces Complex Numbers . . . . . Definition of Vector Space . Properties of Vector Space
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
This page intentionally left blank CALCULUS SECOND EDITION Publisher: Ruth Baruth Senior Acquisitions Editor: Terri Ward Development Editor: Tony Palermino Development Editor: Julie Z. Lindstrom Associate Editor: Katrina Wilhelm Editorial Assistant: Tyler
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
SUGGESTED REVIEW FOR QUIZ 2 Econ 11, Sections 2A/2B, Week 4 Material for Review Based on what we have covered in lecture, and what it is likely we will cover next week in lecture, the following set of readings/review should be very useful. Keep in mind th
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
Solutions Chapter 3 October 23, 2013 3.3) M RS = M Ux M Uy = U/x U/y a) y M RS = x M Ux = y Marginal Utility of x is constant in x b) 2 2xy M RS = 2x2 y = M Ux = 2xy 2 y x Marginal Utility of x is increasing in x c) y M RS = 1/x = x 1/y M Ux = 1/x Margina
School: UCLA
Course: INTRODUCTION TO TOPOLOGY
LECTURE PLAN FOR MATH 472 INTRO TO TOPOLOGY Fall 2010 1 Aug 23 Announcements 1. Exams 2. Hwk 3. Oce times/talk to each other rst 4. Feedback Draw pictures about things that are equal or dierent in dierent geometries. Explore: euclidean 3d (LENGTH, ANGLES
School: UCLA
School: UCLA
School: UCLA
COUNTING RANDOM VARIABLES EX = n P(X = n) + . Var x = E(X2) (EX)2 DISTRIBUTIONS CONTINUOUS NORMAL UNIFORM EXPONENTIAL CLT Binomial for with replacement. Above is without replacement = hyper. Ex of bi and hyper is n x (k/n) which is np
School: UCLA
School: UCLA
School: UCLA
SECTION: Penultimate Math 3A, Section 4, Fall 2013 Not December 13, 2013 NAME/ID: I have read and understood the Student Honor Code, and this exam reects my unwavering commitment to the principles of academic integrity and honesty expressed therein. SIGNA
School: UCLA
Course: ANALYSIS
Math 131a Lecture 2 Spring 2009 Midterm 1 Name: Instructions: There are 4 problems. Make sure you are not missing any pages. Unless stated otherwise (or unless it trivializes the problem), you may use without proof anything proven in the sections of the b
School: UCLA
Mathematics 131A Fall 2007 FINAL Your Name: Signature: INSTRUCTIONS: This is a closed-book test. Do all work on the sheets provided. If you need more space for your solution, use the back of the sheets and leave a pointer for the grader. Good luc
School: UCLA
Course: Probability Theory
Midterm 3, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Probability Theory
Midterm 1 practice, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Name and student ID: Question Points 1 10 2 10 3 10 4 10 5 10 Total: 50 Score 1. (a) (2 points) If is a sample space, what is P(). Solution: P() = 1 (b) (2 points) If P(A) =
School: UCLA
Math 32A: Practice Problems for Exam 2 Problem 1. A particle travels along a path r(t) with acceleration vector t4 , 4 t . Find r(t) if at t = 0, the particle is located at the origin and has initial velocity v0 = 2, 3 . Solution: We have r (t) = 1 1 t4 ,
School: UCLA
Math 3C Midterm 1 Solutions Name: BruinID: Section: Read the following information before starting the exam. This test has six questions and seven pages. It is your responsibility to ensure that you have all of the pages! Show all work, clearly and in o
School: UCLA
Course: Actuarial Math
MATH 115A - Practice Final Exam Paul Skoufranis November 19, 2011 Instructions: This is a practice exam for the nal examination of MATH 115A that would be similar to the nal examination I would give if I were teaching the course. This test may or may not
School: UCLA
MATH 32A FINAL EXAMINATION March 21th, 2012 Please show your work. You will receive little or no credit for a correct answer to a problem which is not accompanied by sucient explanations. If you have a question about any particular problem, please raise y
School: UCLA
Math 3C Midterm 2 Name: BruinID: Section: Read the following information before starting the exam. This test has six questions and fourteen pages. It is your responsibility to ensure that you have all of the pages! Show all work, clearly and in order, i
School: UCLA
Course: Probability Theory
Mathematics Department, UCLA P. Caputo Fall 08, midterm 1 Oct 22, 2008 Midterm 1: Math 170A Probability, Sec. 2 Last name First and Middle Names Signature UCLA ID number (if you are an extension student, say so) Please note: 1. Provide the information ask
School: UCLA
MATH 33A/2 PRACTICE MIDTERM 2 Problem 1. (True/False) . 1 1 1 Problem 2. Let v1 = 1 , v2 = 0 , v3 = 1 . 0 1 1 3 (a) Show that B = 1 , v2 , v3 ) is a basis for R . (v 1 (b) Let u = 1 . Find the coordinates of u with respect to the basis B. 2 (c) Find the c
School: UCLA
MATH 32A FIRST MIDTERM EXAMINATION October, 18th, 20101 Please show your work. You will receive little or no credit for a correct answer to a problem which is not accompanied by sufficient explanations. If you have a question about any particular problem,
School: UCLA
Course: Discrete Math
Practice First Test Mathematics 61 Disclaimer: Listed here is a selection of the many possible sorts of problems. actual test is apt to make a different selection. 1. Let S5 be the set of all binary strings of length 5 (such as 11001). The Let E be
School: UCLA
Math 31A Midterm 1 Solutions 1. [3 points] The derivative of (a) 1 (b) (c) x2 x)2 x3 Brent Nelson is: 1 x2 1 2 x3 (3x 1 1 + x2 + 8x2 x + 3) (d) None of the above. Solution. We rst apply the quotient rule d dx x2 x)2 x3 = d d x3 dx [(x2 x)2 ] (x2 x)2 dx (
School: UCLA
Management 1A Summer 2004 Danny S. Litt EXAM 2 SOLUTION Name: _ Student ID No. _ I agree to have my grade posted by Student ID Number. _ (Signature) PROBLEM 1 2 3 4 5 6 7 8 TOTAL POINTS 20 25 20 20 30 30 30 25 200 SCORE MANAGEMENT 1A Problem 1
School: UCLA
Course: 31b
Math 31B, Lecture 4, Fall 2011 Exam #2, 9 November 2011 Name: ID Number: Section and TA: You have 50 minutes for the exam. No calculators, phones, notes, or books allowed. You must show your work for credit. Hint: n n=0 cr Question: 1 2 3 4 5 6 7 Tota
School: UCLA
Course: Linear Algebra
Name: Student ID: Prof. Alan J. Laub June 9, 2011 Math 33A/1 FINAL EXAMINATION Spring 2011 Instructions: (a) The exam is closed-book (except for one two-sided page of notes) and will last two and a half hours. No calculators, cell phones, or other electro
School: UCLA
Management 1A Summer 2004 Danny S. Litt EXAM 1 SOLUTION Name: _ Student ID No. _ I agree to have my grade posted by Student ID Number. _ (Signature) PROBLEM 1 2 3 4 5 6 7 8 9 10 TOTAL POINTS 20 20 20 20 20 20 20 20 20 20 200 SCORE MANAGEMENT 1A
School: UCLA
Name: Student ID: Section: 2 Prof. Alan J. Laub Math 33A FINAL EXAMINATION Spring 2008 Instructions: June 9, 2008 (a) The exam is closed-book (except for one page of notes) and will last two and a half (2.5) hours. (b) Notation will conform as closely as
School: UCLA
Course: Math 32A
MATH 32A: SECOND PRACTICE MIDTERM EXAMINATION Summer 2008 1 1. (20 points) The C be a curve dened by the position function r(t) =< sin 2t, t, cos 2t >. (a) Calculate the equation of the Normal plane at the point (0, , 1). Its easier than you think.
School: UCLA
Management 1A Fall 2007 Danny S. Litt EXAM 1 Solutions I agree to have my grade posted by Student ID Number _ _ (Signature) (Student ID Number) Name: _ PROBLEM 1 2 3 4 5 6 7 8 TOTAL POINTS 30 30 20 30 20 20 20 30 200 SCORE MANAGEMENT 1A NAME: _
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
Course: Honours Analysis
131A Midterm 2 Solutions 1. Question 1 True/False (a) Let (an ) be a convergent sequence of real numbers. Then (an ) is a Cauchy n=0 n=0 sequence. TRUE. This was a Theorem 3.10 in the second set of notes. (b) Let (an ) be a bounded sequence of real number
School: UCLA
Course: Honours Analysis
131A Midterm 1 Solutions 1. Question 1 Prove the following statement: Let n be a positive integer. Then 1+2+ +n = n(n+1)/2. Solution: We prove the assertion by induction on n. We rst check the base case. In the case n = 1, note that 1(1 + 1)/2 = 2/2 = 1,
School: UCLA
Course: Linear Algebra
Final Exam Math 33A Name: TA: Read all of the following information before starting the exam: Show all work, clearly and in order, if you want to get full credit. I reserve the right to take o points if I cannot see how you arrived at your answer (even i
School: UCLA
Course: Linear Algebra
Final Exam Math 33A Name: TA: Read all of the following information before starting the exam: Show all work, clearly and in order, if you want to get full credit. I reserve the right to take o points if I cannot see how you arrived at your answer (even i
School: UCLA
Course: Linear Algebra
Final Exam Math 33A Name: TA: Read all of the following information before starting the exam: Show all work, clearly and in order, if you want to get full credit. I reserve the right to take o points if I cannot see how you arrived at your answer (even i
School: UCLA
Course: Math32A
MATH 32A (Butler) Practice for Final (Solutions) 1. Let a = 0, 1, 1 and b = 2, 1, 2 . Find a vector u so that u is parallel to b and (a u) is perpendicular to b. (Hint: what is an interpretation for u?) If you get the hint, it turns out that u is the proj
School: UCLA
Course: Math32A
v 19 B tcfw_ Y mt yDGV9# v 9 P 9 P H E T E V d r E V b ` T F u H P T v g ` d E T u r SHqQVGhWgtGsbqthrFdtkE tUIVSreWVh@hte E YWV@tWEQPIFH V H Vb`vE drE v Ipxd(Gttcfw_ tWEhaQpcW`sTSdWP@I`aIp1@aaWg@dmQpxQViHQPp Vr TC V H f Vv T e V H i` V X T`b V H F 9
School: UCLA
Course: Math32A
Math 21C Final Exam Lecture B Agler Winter 02 1. Use the cross product to calculate the area of the triangle with vertices (1, 1, 1), (2, 3, 2), and (3, 1, 4). 2. At what point do the curves r1 (t) = < t, t2 , t3 > and r2 (t) = < 1 + t, 4t, 8t2 > intersec
School: UCLA
Course: Math32A
Print Name: Student Number: Section Time: Math 20C. Final Exam December 8, 2005 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and leg
School: UCLA
Course: Math32A
Print Name: TA Name: Section Number: Section Time: Math 20C. Final Exam June 15, 2006 No calculators or any other devices are allowed on this exam. Write your solutions clearly and legibly; no credit will be given for illegible solutions. Read each questi
School: UCLA
Course: Math32A
Name: (Use capitals) Student number: Math 20C Final Exam July 31, 2004 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No
School: UCLA
Course: Math32A
B x uu f`tCbTqTciiQugRYC`cXl`gxPTqQ !u | A sT~cfw_ | | Q Sc F Y Q Q g WU S QH ~ cfw_ | | VeC`cCiyuIfTqrCiVtCqTqhRcRguI`YVSVFTSpQfCvHvvfRYE! S Wc YFq Y Q tc Q ScF Y Q et Q W W a Ywt IwHy g B S a Ic H a Q W gyH tH Y Q I D B Q Sc F Wee g Ic S a H a WHU W I
School: UCLA
Course: Math32A
Name: Student Number: Math 20C. Midterm Exam 2 July 23, 2004 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No credit wil
School: UCLA
Course: Math32A
Print Name: Student Number: Section Time: Math 20C. Midterm Exam 2 November 21, 2005 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly an
School: UCLA
Course: Math32A
Name: Section: TA: Math 20C Exam 1 A October 21, 2011 Turn o and put away your cell phone. You may use a calculator and one sheet of notes on the exam. Read each question carefully, and answer each question completely. Show all of your work; no credit wil
School: UCLA
Course: Math32A
Print Name: TA Name: Section Number: Section Time: Math 20C. Midterm Exam 2 May 26, 2006 No calculators or any other devices are allowed on this exam. Write your solutions clearly and legibly; no credit will be given for illegible solutions. Read each que
School: UCLA
Course: Math32A
PRACTICE FINAL EXAM June 13, 2002 Instructions. Please show your work. You will receive little or no credit for an answer not accompanied by appropriate explanations, even if the answer is correct. If you have a question about a particular problem, please
School: UCLA
Course: Math32A
PRACTICE FINAL EXAM June 13, 2002 Instructions. Please show your work. You will receive little or no credit for an answer not accompanied by appropriate explanations, even if the answer is correct. If you have a question about a particular problem, please
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c c Homework 1 From the textbook solve the problems 1, 2, 3, 5, 6, 8, 11 and 14 at the end of the Chapter 4. And also the problems below: Problem 1. Give examples of (not independent) random variab
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 1 Solutions April 7, 2014 Problem 34.4 Suppose the growth rate of a certain species is not constant, but depends in a known way on the temperature of its environment. If the temperature is known as a function of time, derive an expres
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c solutions From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 addi
School: UCLA
Course: Introduction Of Complex Analysis
EE101 Engineering Electromagnetics Winter 2013 2/14/13 Homework #5 Due: Thursday Feb 21 10:00 AM Hand in to the TA at beginning of class. No late homework is accepted (see grading policy posted on eeweb). If you cannot make it to class, you must slip the
School: UCLA
Math32a HW1 Due on Monday, Jan 14 All the numbered problems are from the textbook Multivariable Calculus by Rogawski (2nd edition). Note: if your textbook is Early Transcendentals by Rogawski (2nd edition), then all your chapters are shifted by 1 down. Th
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 6 c c Solve the problems 18 a) c) d) e) and 19 from the Chapter 7 additional exercises at http:/www.athenasc.com/prob-supp.html And also the problems below: Problem 1. Denote points P0 ,
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 1 Solution 34.5 (a) If the growth rate is 0, the discrete model becomes Nm+1 Nm = tfm , And the solution is Nm = N0 + t(f0 + f1 + fm1 ), which is analogous to integration, since let t = mt, then t t(f0 + f1 + fm1 ) f (s)ds 0 for t small
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 2 Solution 34.16 We will rstly proceed similarly as 34.14(c). We assume the theoretical growth has the form N0 eR0 t , and we hope to gure out which N0 and R0 t the data best. 34.14(b) suggests that N0 should be equal to the initial popu
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 5 c c From the textbook solve the problems 4 and 5 from the Chapter 5. Solve the problems 2, 4, 6, 7, 9 and 10 from the Chapter 7 additional exercises at http:/www.athenasc.com/prob-supp
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 2 c c From the textbook solve the problems 17, 18, 19, 22, 23 and 24 from the Chapter 4. Solve the problems 21, 22, 24, 30 from the Chapter 4 additional exercises at http:/www.athenasc.c
School: UCLA
Course: Introduction Of Complex Analysis
EE101 Engineering Electromagnetics Winter 2013 1/24/12 Homework #3 Due: Thursday Jan 31 10:00 AM Hand in to the TA at beginning of class. No late homework is accepted (see grading policy posted on eeweb). If you cannot make it to class, you must slip the
School: UCLA
Course: 245abc
Math 245A Homework 2 Brett Hemenway October 19, 2005 Real Analysis Gerald B. Folland Chapter 1. 13. Every -nite measure is seminite. Let be a -nite measure on X, M. Since is -nite, there exist a sequence of sets cfw_En in M, with (En ) < and En = X . n=1
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 0 Solution 32.11 The easier way: (slightly unrigorous, but its ne for this class) Suppose the bank compounds the interest n times a year, and let t := 1/n. With the additional deposit (or withdrawl) D (t), the balance at time t + t is gi
School: UCLA
Homework 4 Solutions Math 3C Due: Friday Nov 2, 9 a.m. #1(a) Let X be a random variable that equals the number of defective items in the sample. When the sampling is done with replacement, X is binomially distributed with parameters n = 5 and p = 5/20 = 1
School: UCLA
Course: 245abc
Math 245A Homework 1 Brett Hemenway October 19, 2005 3. a. Let M be an innite -algebra on a set X Let Bx be the intersection of all E M with x E . Suppose y Bx , then By Bx because Bx is a set in M which contains y . But Bx By because if y E for any E M,
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 1 Solution 32.3 (a) Use N (nt) to denote the population at time nt. Then for any n > 0, we have N (nt) = (1 + (b d)t)N (n 1)t) + 1000. (b) Given that N (0) = N0 , we hope to solve the equation above and get the general form for N (nt). T
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 additional exe
School: UCLA
Course: Actuarial Math
MATH 115A - Assignment One - Solutions of Select Non-Graded Problems Paul Skoufranis October 3, 2011 1.2 Question 13) Let V denote the set of ordered pairs of real numbers. If (a1 , a2 ) and (b1 , b2 ) are elements of V and c R, dene (a1 , a2 ) + (b1 , b
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 2 Solutions April 7, 2014 Problem 35.3 Consider a species in which both no individuals live to three years old and only one-year olds reproduce. (a) Show that b0 = 0, b2 = 0, d2 = 1 satisfy both conditions. All two year olds die befor
School: UCLA
Course: Real Analysis
Homework 8 Solutions Math 131A-3 1. Problems from Ross. (29.5) Suppose |f (x) f (y )| (x y )2 for all x, y in R. Then for any given a R, we )f )f have | f (xxa (a) | |x a|, so by the squeeze theorem, as x a, | f (xxa (a) | 0. Therefore f (a) = 0. Since a
School: UCLA
Course: Algebra
UCLA Mathematics 110A: selected solutions from homework #1 David Wihr Taylor July 2, 2010 Introduction When reading these solutions always keep in mind the common techniques being used. The point of homework, and subsequently these solutions, is to give y
School: UCLA
Course: Real Analysis
Math 131A Analysis Summer Session A Homework 3 Solutions n 1. Let (an ) be a bounded sequence and let (bn ) be a sequence such that lim bn = 0. Prove that lim an bn = 0. n Proof. Since (an ) is bounded, there exists M > 0 such that |an | < M for a
School: UCLA
1 1. Prove Proposition 3.1. Proposition 3.1 Let be a signed measure on . If is an increasing sequence in , then lim . If is a decreasing sequence in and is finite, then lim . Answer) Let be a signed measure on . a. If is an increasing sequence in
School: UCLA
Course: Linear Algebra
Ch. 1 Dept. of ECE, Faculty of Engineering University of Tehran Linear Algebra Homework # I Chapter 1: Vector Spaces Exercises to be handed: marked by *. Due date: Sunday Esfand 9th 1383. 1. Let V = cfw_ (a1 , a2) : a1 , a2 R . Define addition of elements
School: UCLA
Course: MULTIVARIABLE CALCULUS
This page intentionally left blank Students Solutions Manual to accompany Jon Rogawskis Single Variable CALCULUS SECOND EDITION BRIAN BRADIE Christopher Newport University ROGER LIPSETT W. H. FREEMAN AND COMPANY NEW YORK 2012 by W. H. Freeman and Company
School: UCLA
School: UCLA
Probability Theory, Math 170A - Homework 7 Problem 1. Is it always the case that lim supn An is not the empty set? Problem 2. Find a sequence of events which does not have a limit. Problem 3. Prove that if (An ) is a decreasing sequence of events, then it
School: UCLA
Probability Theory, Math 170A - Homework 5 From the textbook solve the problems 1 and 2 at the end of the Chapter 3. Solve the problems 1 and 2 from the Chapter 3 additional exercises at http:/www.athenasc.com/prob-supp.html And also the problems below Pr
School: UCLA
Probability Theory, Math 170A - Homework 4 From the textbook solve the problems 16, 22, 24 at the end of the Chapter 2. Solve the problems 5 and 13 from the Chapter 2 additional exercises at http:/www.athenasc.com/prob-supp.html Problem 1. Recall Problem
School: UCLA
Probability Theory, Math 170A, Homework 3 From the textbook solve the problems 3, 4, 5, 9, and 10 at the end of the Chapter 2. Solve the problem 4 from the Chapter 2 additional exercises at http:/www.athenasc.com/prob-supp.html And also the problems below
School: UCLA
Probability Theory, Math 170a, Winter 2015 - Homework 1 From the textbook solve the problems 2, 5-10 at the end of the Chapter 1. And also the problems below: Problem 1. Show that for any sets A and B P(A B) P(A) P(A B). Problem 2. We have a very weird di
School: UCLA
Probability Theory, Math 170A - Homework 2 From the textbook solve the problems 14, 16, and 19 at the end of the Chapter 1. Solve the problems 15, 16, 18, 31, from the Chapter 1 additional exercises at http:/www.athenasc.com/prob-supp.html And also the pr
School: UCLA
Course: Honours Analysis
Solution of the 1st Homework Sangchul Lee October 12, 2014 Solutions Problem 2 Solution. A possible truth table is as follows: xA xB x A B x ( A B) c x Ac x Bc x Ac B c T T F F T F T F T F F F F T T T F F T T F T F T F T T T Or using various logical opera
School: UCLA
Course: Honours Analysis
Solution of the 4th Homework Sangchul Lee November 3, 2014 1 Solutions 1.1 Exercise 1 Preliminary Before the solution, we remark the following observation (which you may already know if you have carefully read my solution of 2nd homework): Observation 1.
School: UCLA
Course: Honours Analysis
Solution of the 3rd Homework Sangchul Lee October 24, 2014 1 1.1 Before the solution How to prove bijectivity? The following equivalence is useful when establishing the bijectivity of a function: Proposition. Let f : X Y be a function. Then the followings
School: UCLA
Course: Honours Analysis
Solution of the 2nd Homework Sangchul Lee October 22, 2014 1 Before the solution 1.1 Notations First, we introduce some additional notation for the sake of better understanding. In the lecture, we identied the subset of R consisting of constant sequences
School: UCLA
Course: Honours Analysis
Solution of the 5th Homework Sangchul Lee November 12, 2014 1 Solutions 1.1 Exercise 1 Let u n sup ( a k )k n and v n sup ( b k )k n be suprema. Then the following obvious relation a k u n and b k v n , k n a k + b k u n + v n , k n shows that, upon taki
School: UCLA
Course: Honours Analysis
Solution of the 6th Homework On progress Sangchul Lee November 18, 2014 1 Exercise 1 N The series m a n converges, by definition, exactly when the partial sum S N n m a n converges as N . n Now using the completeness of R, this happens exactly when ( S
School: UCLA
Course: Honours Analysis
Solution of the 8th Homework Sangchul Lee December 8, 2014 1 Preliminary 1.1 A simple remark on continuity The following is a very simple and trivial observation. But still this saves a lot of words in actual proofs. Lemma 1.1. Let f : X R be a function,
School: UCLA
Course: Honours Analysis
Solution of the 9th Homework Sangchul Lee December 16, 2014 1 Preliminary 1.1 Properties of supremum inmum combined with arithmetic operations Lemma 1.1. Let A R be a non-empty subset and c R. Dene c + A = cfw_c + a : a A. Then sup(c + A) = c + (sup A) an
School: UCLA
Course: Honours Analysis
Solution of the 7th Homework Sangchul Lee December 3, 2014 1 Preliminary In this section we deal with some facts that are relevant to our problems but can be coped with only previous materials. 1.1 Maximum and Minimum of subsets of R Let E be a non-empty
School: UCLA
Course: Probability Theory
Probability Theory, Math 170A, Fall 2014 - Homework 5 solutions From the textbook solve the problems 32, 39, 40 at the end of the Chapter 2. Solution to Problem 32: Let Xi be the indicator of the event that the rst person in the i-th couple is alive and Y
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a, Fall 2014 - Homework 6 Solutions From the textbook solve the problems 1 and 2 at the end of the Chapter 3. Solution to Problem 1: The PMF of Y is P(Y = 1) = P(X 1/3) = 1/3, P(Y = 2) = P(X > 1/3) = 2/3, so E(Y ) = 1 1/3 + 2 2
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a, Fall 2014- Homework 3 solution From the textbook solve the problems 30, 33, 34, 35 and 36 at the end of the Chapter 1. Solution to Problem 30: In the rst case the hunter could choose the correct path either if both dogs choo
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a, Fall 2014- Homework 5 Solutions From the textbook solve the problems 16, 22, 24 at the end of the Chapter 2. Solution to Problem 16: (a) To nd a use the condition that the probabilities must add up to 1: pX (3) + pX (2) + pX
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a, Fall 2014 - Homework 2 solutions Problem 1. A person places randomly n letters in to n envelops . What is the probability that exactly k letters reach their destination. Solution See notes by Kupferman page 13. Problem 2. Yo
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a, Fall 2014 - Homework 1 solutions Problem 1. Show that for any sets A and B P(A B) P(A) P(A B). Solution: One way to solve it is to notice that A B A and A A B and use the properties of the probability law (in particular the
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a, Fall 2014 - Homework 7 solutions From the textbook solve the problems 6, 7, 11 and 15 at the end of the Chapter 3. Solution to Problem 6: Let X be her waiting time then for t > 0 FX (t) = P(X t) = P(X t|no customer in front)
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2015 - Homework 7 solutions From the textbook solve the problems 1, 2 and 3 from the Chapter 6. Solve the problems 3, 4, 5, 6, 7, 8 and 9 from the Chapter 5 additional exercises at http:/www.athenasc.com/prob-supp.htm
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b - Homework 4 Problem 1. Show that for random variables X, Y and Z we have E[E[E[X|Y ]|Z] = E[X]. Apply this formula to the following problem: Roll a far 6-sided die and observe the number Z that came up. Then toss a fair coin
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b - Homework 5 From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com/prob-supp.html And also the pro
School: UCLA
Course: Probability Theory
Solution of the 6th Homework Sangchul Lee December 10, 2014 1 1.1 Solutions Additional Problem 3.1 Let T Uniform[0, 12] be the time dierence. Then the expect reward is given by g(T ), where 10, 0 t 1, 6, 1 t 3, g(t) = 2, 3 t 6, 0, otherwise. Thus it
School: UCLA
Course: Probability Theory
Probability Theory, Math 170B, Spring 2013 Note: Although solutions exist on-line, you will be doing yourself a great favor by resorting to them only after you have solved the problem yourself (or at least tried very hard to). From the textbook solve prob
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b - Homework 2 solutions Problem 1. Let X be exponentially distributed with parameter . Find the PMF of Y = X , where x for a real number x is the rounding of x to the nearest integer whose value is greater or equal to x. Ident
School: UCLA
Math 3B - Homework 14: Due in class Nov. 17th 2014 M. Roper November 10, 2014 1. Use Integration by Substitution to evaluate: (a) /4 sin2 x cos x dx 0 (b) 1/4 x(1 4x)1/3 dx 0 (c) 3 2 5xdx x2 + 1 2. Use Integration by Parts to evaluate: (a) x2 ln x dx (b)
School: UCLA
School: UCLA
Course: Calculus
31B Notes Sudesh Kalyanswamy 1 Exponential Functions (7.1) The following theorem pretty much summarizes section 7.1. Theorem 1.1. Rules for exponentials: (1) Exponential Rules (Algebra): (a) ax ay = ax+y (b) ax ay = x y axy (c) (a ) = axy (2) Derivatives
School: UCLA
School: UCLA
School: UCLA
The Poisson distribution is a discrete distribution. It is often used as a model for the number of events (such as the number of telephone calls at a business, number of customers in waiting lines, number of defects in a given surface area, airplane arriv
School: UCLA
3C Notes Sudesh Kalyanswamy 1 Counting (12.1) 1.1 Guiding Questions for the Chapter Here are some questions for you to ask yourself as you read. If you can answer them all by the end, youre in pretty good shape as far as understanding the material. After
School: UCLA
3C Practice Problems for Midterm 1 Sudesh Kalyanswamy (1) Bills school schedule has four timeslots. Bill has 30 choices of classes for the rst timeslot, 20 for the second, 23 for the third, and 17 for the last. How many possible schedules are there? (2) C
School: UCLA
School: UCLA
Math 171 Spring 2013 Homework 8 (due Friday, June 7th at lecture time) (1) Read Sections 5.3 and 5.4. (2) Solve problems 2, 3, 4 and 6 from the end of chapter 5.
School: UCLA
School: UCLA
Course: INTEGRATION AND INFINITE SERIES
A dierential equation is an equation that relates the derivative of a function to that function (and possibly other functions). For example a dierential equation involving the function y (t) could look like dy (t) = ky (t) (1) dt for some constant k . Whe
School: UCLA
Course: Calculus
Answer Key B. Johnson Calculus AB Memory Quiz Important Relationships, Theorems, Rules, and Formulas Important Relationships 1. State the formal definition of derivative, include diagram. If y = f ( x ) then f ( x ) = lim h0 f ( x + h) f ( x) h 2. Where a
School: UCLA
Course: Linear Algebra
Math 33A, Sec. 2 Linear Algebra and Applications Spring 2012 Instructor: Professor Alan J. Laub Dept. of Mathematics / Electrical Engineering Math Sciences 7945 phone: 310-825-4245 e-mail: laub@ucla.edu Lecture: MWF 2:00 p.m. 2:50 p.m.; Rolfe 1200 Office
School: UCLA
Math 3B Integral calculus and differential equations Prof. M. Roper Young Hall CS 76, MWF 2-2.50pm. All inquiries about this class should be posted to the class Piazza page. The only emails that I will respond to are questions about how to login to Piazza
School: UCLA
Course: Calculus
Sample Syllabus Philosophical Analysis of Contemporary Moral Issues Winter 2015, MW 8-9:50 Instructor: Robert Hughes (hughes@humnet.ucla.edu) Instructor office hours: Dodd 378, M 11-12 and W 10-11 or by appointment TAs: Kelsey Merrill (kmerrill@humnet.ucl
School: UCLA
Course: Math 170
Probability Theory, Math 170A, Winter 2015 - Course Info Instructor: Tonci Antunovic, 6156 Math Sciences Building, tantunovic@math.ucla.edu, www.math.ucla.edu/~tantunovic Instructor Oce Hours: Monday 10-12am and Wednesday 9-10am in 6156 Math Sciences Buil
School: UCLA
Course: Math 1
Math1 Fall2012 Lecture1(8am),Lecture2(10am)andLecture3(1pm) Instructor Paige Greene E-Mail: paige@math.ucla.edu Office Number: MS 6617 B Office Hours: Mon and Wed (copy from me in class) Course Goals: The purpose of Math 1 is to give you a strong preparat
School: UCLA
Math33BDifferentialEquations Winter2015,lecture3 Time:MWF3:003:50p.m. Room:MS4000A Discussionsections: 3A T3:00P3:50PGEOLOGY6704 3B R3:00P3:50PGEOLOGY4645 Instructor:YuZhang Office:MS6617F Officehours:Monday2:003:00p.m. Wednesday4:006:00p.m. Email:yuzhang
School: UCLA
Math 3B Integral calculus and differential equations Prof. M. Roper Young Hall CS 76, MWF 2-2.50pm. All inquiries about this class should be posted to the class Piazza page. The only emails that I will respond to are questions about how to login to Piazza
School: UCLA
Course: Actuarial Math
Math 172A: Syllabus, Structure, Details and Policies (Fall 2014) Introduction to Financial Mathematics This course is designed to provide an understanding of basic concepts of actuarial/financial mathematics. The course touches most (but not all) syllabus
School: UCLA
Course: Abstract Algebra
Math 32B (Calculus of several variables), Section 2 Fall 2013 MWF 2:00-2:50 pm, 1178 Franz Hall UCLA Instructor: William Simmons, MS 6617A, simmons@math.ucla.edu. Oce Hours (held in MS 6617A): M: 8:00-8:55 am T: 10:30-11:30 am W: 3:30-4:30 pm Teaching Ass
School: UCLA
Math 115A, Linear Algebra, Lecture 6, Fall 2014 Exterior Course Website: http:/www.math.ucla.edu/heilman/115af14.html Prerequisite: MATH 33A, Linear algebra and applications. Course Content: Linear independence, bases, orthogonality, the Gram-Schmidt proc
School: UCLA
Math 32A, Calculus of Several Variables Lecture 1, Winter 2014 Instructor: Will Conley Email: wconley@ucla.edu Office: MS 6322 Office Hours: Tentatively Wednesdays 11:3012:30, Thursdays 1:302:30, and any other time by appointment. Website: http:/www.math.
School: UCLA
Math 33A, Section 2 Linear Algebra and Applications Winter 2014 Instructor: Professor Alan J. Laub Dept. of Mathematics / Electrical Engineering Math Sciences 7945 phone: 310-825-4245 e-mail: laub@ucla.edu Lecture: MWF 1:00 p.m. 1:50 p.m. Math Sciences 40
School: UCLA
Math1 Fall2012 Lecture1(8am),Lecture2(10am)andLecture3(1pm) Instructor Paige Greene E-Mail: paige@math.ucla.edu Office Number: MS 6617 B Office Hours: Mon and Wed (copy from me in class) Course Goals: The purpose of Math 1 is to give you a strong preparat
School: UCLA
Differential Equations MATH 33B-1 Instructor Details: Lecture 1: Instructor: Office: Office hours: MWF 12PM-12:50PM in MOORE 100 Prof. Zachary Maddock MS 6236 (MS := Mathematical Sciences) Mondays 1:30PM-2:30PM Wednesdays 9:50AM-10:50AM, 1:30PM-2:30PM Tea
School: UCLA
Course: Linear Algebra
Course information and Policy, v. of Oct.1st, 2013 Marc-Hubert NICOLE Linear Algebra with Applications Math 33A-1, Lecture 1, Fall 2013. U.C.L.A. -Instructor Marc-Hubert NICOLE Lectures: MWF 8:00-8:50 AM in Rolfe 1200. Ofce: MS 5230 (see Ofce Hours belo
School: UCLA
S YLLABUS : P HYSICS 1B, L ECTURE 1, W INTER 2012 I NSTRUCTOR : Prof. Troy Carter 4-909 PAB (310) 825-4770 tcarter@physics.ucla.edu O FFICE H OURS : M 10-11AM, T 1PM-2PM, F 1-2PM, other times by appointment C OURSE A DMINISTRATOR : Elaine Dolalas (handles
School: UCLA
Course: Introduction Of Complex Analysis
Math 132: Complex Analysis for Applications INSTRUCTOR: Kefeng Liu TIME and LOCATION: MWF 9:00-9:50AM, MS5117. OFFICE HOURS: TT 9:00-10:00AM in MS 6330 (Or by appointment) SYLLABUS: Official Syllabus Text: Complex Analysis by Tom Gamelin TA: Wenjian Liu,
School: UCLA
Math 3C, Probability for Life Sciences Students, Lecture 2, Spring 2012 Instructor: Thomas Sinclair E-mail: thomas.sinclair@math.ucla.edu Oce: Math Sciences (MS) 7304 Oce Hours: M 3:004:30, W 11:0012:30 TAs: 2a,b Theodore Gast Oce: MS 2961 Oce Hours: TBA
School: UCLA
Mathematics 31B: Integration and Innite Series. Fall 2012 Instructor: David Weisbart Email: dweisbar@math.ucla.edu Textbook: J. Rogawski, Single Variable Calculus, 2nd Ed., W.H. Freeman & Co. 31B Teaching Statement: Along with 31A, this course is the foun
School: UCLA
Course: Linear Algebra
Physiological Science 5 Issues in Human Physiology: Diet and Exercise Winter 2012 Instructor: Joseph Esdin, Ph.D. Office Hours: Mon 12:30-1:20 pm & Wed 10:30-11:20 am Office: 3326 Life Sciences Building Phone: (310) 825-4118 Email: yezzeddi@ucla.edu TA: D
School: UCLA
Course: Linear Algebra
Mathematics 33B: Dierential Equations. Winter 2012 Instructor: David Weisbart Email: dweisbar@math.ucla.edu Textbook: Polking, Boggess, Arnold, Dierential Equations, 2nd Ed., Pearson. 33B Teaching Statement: Since the time of Newton, the language of diere
School: UCLA
ULE ZLER, UCLA ECONOMICS DEPARTMENT BUCHE HALL 9361 OZLER@ECON.UCLA.EDU OFFICE HOURS: TUE & THR 1:00-1:45 AND BY APPOINTMENT ONLY FALL 2011 ECONOMICS 121- INTERNATIONAL TRADE THEORY Course Description In this course we will study alternative models of int
School: UCLA
Course: Math 26
Math 26B Section 2 Calculus II for the Social and Life Sciences Fall 2012 Instructor: Jill Macari Office: Brighton Hall 121 Phone: 278-7074 Email: jmacari@csus.edu Office Hours: Monday, Tuesday, and Wednesday 10:30 am 11:30 am; Thursday 12:30 pm 1:30 pm a
School: UCLA
Math 131A Course Outline Spring 2011 Text: Apostol, Calculus, Volume I, 2nd ed. Instructor: Betsy Stovall 1. Introduction. Crash review of basic propositional logic and set notation. (Chapter I.2) On your own: Read I.12 with an emphasis on I.2. You wil
School: UCLA
Course: 245abc
1. AssignmentdueSeptember7:ChapterI,4(ignorethe hypothesisthatKnormalizesH),5,6,7,8,9.In Problem8,thereisapairofmisprints:astheproblemis written,therearethreeunionsigns,wheretheindices arerespectivelyc,x_candx_c.Thefirstunionshould beoverelementsx_c;thes
School: UCLA
Course: Mathematics-finance
Course Syllabus Math 181: THE MATHEMATICS OF FINANCE Fall 2001 1 Background in Finance and Probability 1. Introduction and Course Description 2. Review of probability 3. Discrete Random Walks 4. Random walks with Gaussian increments 5. Equity model
School: UCLA
Course: Prob Life Sci Stdt
Math 3C (Spring 2008) Probability for Life Sciences Students Instructor: Roberto Schonmann www.math.ucla.edu/rhs Time/Place: Lecture 1: MWF 9:00-9:50 in MS 4000A. Lecture 2: MWF 10:00-10:50 in MS 4000A. Text: Calculus for Biology and Medicine (second