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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
Course: Math 31 B Lecture 4
- - iu~ ~CnW ~-~K~ - - ~-~ ir1 - l~ri- . t ~ .,_t~-t.~12Sl ~ ~tMY1~n11 . VJr~ _ _:._ _ ~1li: ~- n ;._-+- - - - _ _,_- - _;:_~ h -= AK: _ _ _ _ _ n l1\t - % t v3Ln .=- ~., ~ - - -~- - - - - - - - -1- - - - - - - -t - ~-i'-f- _ 1A f) i C 2)(~ - ~- ~ fl:s-;j
School: UCLA
Course: Math 31 B Lecture 4
- = - _ - - - 1 11 mKn " X. _1_ tlLr1Lx"' a 11ot _:;_.[ - -+- _ f-'Cx-o-J - - -r- .r , i -., - ftv l- _ - b)'ll_ - - - - ' - - " - - - ' /.lc; _ _ _ . t _ _ '2-f= L . - "' .131.[ . 1 f _ 5-tu'rs -1- - i . x!J '=; 1 _ JEl&: cfw_ _ =L"-: . - -A )iJ _ cfw_ -
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
Course: Math 31 B Lecture 4
Module 4: Neural and Hormonal Systems Overview: What We Have in Mind Building blocks of mind: Neurons and how they communicate (neurotransmi9ers) Systems that build the mind: Func=ons of Parts of the Nervous system Suppor
School: UCLA
Course: Math 31 B Lecture 4
Module 18: Vision, and Perceptual Organiza9on and Interpreta9on Vision: Energy, Sensa,on, and Percep,on The Visible Spectrum We encounter waves of electromagne2c radia2on. Our eyes respond to some of these waves. Our brain turns these
School: UCLA
Course: Math 31 B Lecture 4
Module 1: The Story of Psychology From specula9on to science: The Birth of Modern Psychology Aristotle (4th century BCE) asked ques9ons to understand the rela9onship between body and psyche. His way of answering those ques9ons
School: UCLA
Course: Math 31 B Lecture 4
Module 13: Developmental Issues, Prenatal Development, and the Newborn nature and nurture How do genes and experience guide development over our lifespan? change and stability Issues in Developmental Psychology con?nuity vs. stages In wh
School: UCLA
Course: Math 31 B Lecture 4
Module 7: Brain States and Consciousness What is Consciousness, Exactly? alertness; being awake vs. being unconscious self-awareness; the ability to think about self having free will; being able to make a conscious decision a pe
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
Math 172 B Class Project 1 Object: to download a specific mortality table from the Society of Actuaries website and utilize mortality rates to calculate life expectancies Steps: 1. Log onto www.soa.org 2. At the bottom of the opening page, select popular
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 174E (Summer 2014) Mathematics of Finance Instructor: David W. Taylor Time/Location: MWR 11:00am-12:50pm in MS 5137. Text: Options, Futures, and Other Derivatives (8th edition) by John C. Hull. Instructor: David W. Taylor Oce Hours: TBA Email Address
School: UCLA
Math 174E, Lecture 1 (Winter 2014) Mathematics of Finance Instructor: David W. Taylor Time/Location: MWF 3:00pm-3:50pm in MS 5127. Text: Options, Futures, and Other Derivatives (8th edition) by John C. Hull. Instructor: David W. Taylor Oce Hours: Monday a
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: 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
Course: Math 31 B Lecture 4
- - iu~ ~CnW ~-~K~ - - ~-~ ir1 - l~ri- . t ~ .,_t~-t.~12Sl ~ ~tMY1~n11 . VJr~ _ _:._ _ ~1li: ~- n ;._-+- - - - _ _,_- - _;:_~ h -= AK: _ _ _ _ _ n l1\t - % t v3Ln .=- ~., ~ - - -~- - - - - - - - -1- - - - - - - -t - ~-i'-f- _ 1A f) i C 2)(~ - ~- ~ fl:s-;j
School: UCLA
Course: Math 31 B Lecture 4
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School: UCLA
Course: Math 31 B Lecture 4
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School: UCLA
Course: Math 31 B Lecture 4
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School: UCLA
Course: Math 31 B Lecture 4
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School: UCLA
Math 3B Midterm 1 Review I. Leibnizs Rule For problems 1-4, solve the integration using Leibnizs Rule. Remember, Leibnizs Rule is of the form: ( ) [ ( )] ( ) [ ( )] ( ) ( ) ( ) 1. 2. )( ) ( ( ( ) )( ) )( ) ( )( ) ( 3. ( [ ( ) ) ]( ) 4. ( [ ( ) ]( ) ) [(
School: UCLA
Math 3B Final Exam Review Lesson Plan I. Areas Between Two Curves, Average Values, & Leibnizs Rule 1. Compute the area of the regions bounded by the curves indicated in letters a and b. a. [( ) ( ) [( ( ) ) ( ( )] )] ( )] ( )] *Note: the points of inter
School: UCLA
Course: Multivariable Calculus
32B Final Solutions 1. QuesuoN 1 (Ttue/False) that all of its second order ia) f,et /' itt -+ R be a twice differentiable function such pa*ial derivatives are continuous. Then the line integral of curl(V/) around any simple closed curve is zero. Soluti'on
School: UCLA
School: UCLA
School: UCLA
School: UCLA
Math 172 B Class Project 2 Object: to create a program that generates a customized quote of level monthly premiums for a life insurance (payable at the end of month of death) of any term and any level face amount. Premiums are payable over the insurance t
School: UCLA
School: UCLA
School: UCLA
Math 172B Chapter 5 Problems worked in class (S= SOA S5 Q, JK = Jong Kim Lecture Notes) Basics: S2, S6-8 Relationship between A and a: S16 Recursion: S1, JK12.4, 12.1, 12.6 DM: JK12.5, 12.3, S19 CF: S5 Certain and Life: S17, S20, JK12.2 Variance: J
School: UCLA
School: UCLA
School: UCLA
School: UCLA
Math 172B Chapter 2 Problems worked in class (S= SOA S2 Q, JK = Jong Kim Lecture Notes) Basics S1, S2 Relationship of S(x), tpx and (x) S9, S8, JK1.4, 1.5 Generalized DM S3, Text 2.1, S12-15, JK2.1, 2.2, JK3.2-4 CF problems JK2.4, S17, S16, JK3.5, 3.8
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Winter Quarter 2015 qx, px, lx, dx tpx, tqx, u|tqx Using lx to develop Fractional Age assumptions UDD and CF Select and Ultimate tables ex , ex:n Starting out with a population 10,000,000 live births all born on say January 1st, 2000 We follow this popula
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Class4ExampleonLifeTables (a)Fillintheblanksinthefollowingtable: x 0 1 2 3 4 10,000 5882 d q 0.05 p 950 0.86 (b)Usingthetableabove,calculate p and | q . Usingthetableaboveifthecurtatelifeexpectancyforalifeatage(0)is8,find thecurtatelifeexpectancyforalifea
School: UCLA
Winter 2015 Kx Curtate Future Lifetime = Integer(Tx) Temporary life expectancies Recursion equation Graphs of S(x) Gomperz and Makeham laws Kx curtate future lifetime r.v.= Integer(Tx) Fx(k) = k+1qx k=0,1,2. Sx(k) = k+1px fx(k) = k|1qx k|nqx = kpx*nqx+k =
School: UCLA
School: UCLA
Winter Quarter 2015 Traditionally, survival models are based on observed mortality tables This approach works for a large group of insureds But, there is a theoretical issue with this approach i.e. how do we apply this to a single person? The new approach
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,f"'., '-~-. 15. You arc given the following survival function; _ - s(x)=e-S;r Calculate f p(X, tbc:fimle ofmortlllily. A. SJ;? B. 3Sx C. 3~ e-4lr' D. Sx? 1D(35:1) E. 35x'e.%' 1 -e-3;e , . CONTINUE) ON NEXT PAGE 15 6. , YO\l are given tbe survival functio
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School: UCLA
172B Introduction How is 172B different from 172A? 172A dealt with certain Cashflows (CF) and the discounted PV of such CFs 172B adds the element of uncertainty to the CF with the application of mortality table Probability and Statistics review Discrete
School: UCLA
Winter Quarter 2015 Actuaries apply generally accepted mathematical principles and techniques to solve problems involving risk, uncertainty and finance In 172BC, we will be focusing on those problems associated with life insurance and pensions What are
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
Math 173A Lecture Notes 2 Ch 3 concepts using examples from pre-test Discuss E[X] = E[Xd] + E[X-d|+] using integrals eX(d) = E[X-d|+] /S(d) Moments: 3.3, 3.4, 3.13, SOA LM set 1 #3 Limited Expected Values and Mean Excess Loss: 3.8, 3.6, 3.15, SOA 9, 10 Us
School: UCLA
Math 173A Lecture Notes 17 Variance and C.I. for S: 39, 44, 45, 46 Observed claim data: 5, 8, 8, 12 With Uniform Kernel density smoothing, we create 3 rectangles with width 2*b, centering on the observed values of 2, 8 and 12. The areas of the rectangles
School: UCLA
Math 173A Lecture Notes 16 Nelson Aalen Estimator: SOA #16-23 Mean survival times calculation BPP #40 KM estimator for grouped data: SOA 53-55 Variance of S or F with complete data The term will always in the form n1(n-n1)/n3 or a combination of terms in
School: UCLA
Math 173A Lecture Notes 15 Kaplan-Meier Product Limit estimator: #10-14, BPP #54 Kaplan-Meier Product Limit estimator: Additional problem set Introduction to hazard rate idea of Nelson Aalen estimator Empirical estimate of H(x) = -ln(S(x) SOA #15 Nelson A
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Math 173A Lecture Notes 14 MSE problem set 20.10, 20.11 Empirical distribution introduction simple example with complete individual data Empirical distribution grouped data SOA EMP #6-8 Estimating parameter of a Bernoulli distribution ; #9 Empirical distr
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Math 173A Lecture Notes 12 Distribution of S #82b Aggregate stop-loss #83 Aggregate stop-loss #85, 86, 92, 91 Dividend problem effect of insurance SOA #93 Let NL be the number of losses and NP be the number of payments after deductible d Clearly NP < NL D
School: UCLA
Math 173A Lecture Notes 11 Poisson Process: #71, 73 Complicated Poisson problem: # 69 Effect of vaccine (or transfer of risk) on losses: #70 Premium calculation (similar to quiz) #75 Burr Distribution #77 Individual deductible: #78, 79 Distribution of S #
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Math 173A Lecture Notes 10 Variance of YL and YP #29-31 Effect of co-pay #61 Frequency modifications due to deductible: #43,44 Multiple insureds within different insurance classes: SOA set 5 #65 Combining multiple Bernouli variables into a single Binomial
School: UCLA
Math 173A Lecture Notes 9 TVaRp(X) definition and problems for lognormal and normal Double Expectation theorem - example Specific application of double expectation theorem to Aggregate Loss Model S= X1+X2+XN Var[S] = E[N]*Var[X] + Var[N]*E[X]2 Normal Appr
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Math 173A Lecture Notes 8 Inflation ,deductible and reinsurance #32-35 Effect of inflation Ch 8 #11 LER for lognormal distribution 8-#8 Bonus problems #39-40 VaRp(X) definition and problems (handout) TVaRp(X) definition and problems
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Math 173A Lecture Notes 7 Concept of Loss Elimination Ratio LER SOA Set 3, 20-23 Difference between YL =X-d|+ and YP = X-d|X>d E[YL] = E[X-d|+] and E[YP] = E[X-d|+] /S(d)= SOA #24, 26 Complex YP calculation SOA #25 Complex plan provisions #36-37 Relations
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Math 173A Lecture Notes 6 Two point mixture for discrete distribution: SOA 6.2 Spliced dist: E[X] = E[X|X<d]*F(d) + E[X|X>d]*S(d), SOA #21 (a,b,1) distribution zero-truncated vs zero-modified, Poisson example pnM = pn * (1 - p0M)/(1 p0), zero-truncation i
School: UCLA
Math 173A Lecture Notes 5 Variance of a k-point mixture X is a single r.v which pdf fX(x) = .5*f1(x) + .5*f2(x) Then, FX(x) = .5*F1(x) + .5*F2(x) (by integrating fX from 0 to x) Also, SX(x) = .5*S1(x) + .5*S2(x) (subtracting above from 1) And E[X] = .5*E1
School: UCLA
Math 173A Lecture Notes 4 Percentiles 3.17, 3.20 Using properties of Moment Generating Functions (MGF) to show that the sum of two iid Exponentials has a Gamma Distribution with = 2, SOA #4 Ch 4 Mixtures: 2- point mixtures SOA 5, 6 Continuous mixing Examp
School: UCLA
Math 173A Lecture Notes 2-3 Discuss E[X] = E[Xd] + E[X-d|+] using integrals eX(d) = E[X-d|+] /S(d) Moments: 3.1, 3.3, 3.4, 3.13, SOA LM set 1 #3 Limited Expected Values and Mean Excess Loss: 3.8, 3.6, 3.15, SOA 9, 10 Use results from 3.15 to solve SOA 10
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
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
Course: Math 31 B Lecture 4
Module 4: Neural and Hormonal Systems Overview: What We Have in Mind Building blocks of mind: Neurons and how they communicate (neurotransmi9ers) Systems that build the mind: Func=ons of Parts of the Nervous system Suppor
School: UCLA
Course: Math 31 B Lecture 4
Module 18: Vision, and Perceptual Organiza9on and Interpreta9on Vision: Energy, Sensa,on, and Percep,on The Visible Spectrum We encounter waves of electromagne2c radia2on. Our eyes respond to some of these waves. Our brain turns these
School: UCLA
Course: Math 31 B Lecture 4
Module 1: The Story of Psychology From specula9on to science: The Birth of Modern Psychology Aristotle (4th century BCE) asked ques9ons to understand the rela9onship between body and psyche. His way of answering those ques9ons
School: UCLA
Course: Math 31 B Lecture 4
Module 13: Developmental Issues, Prenatal Development, and the Newborn nature and nurture How do genes and experience guide development over our lifespan? change and stability Issues in Developmental Psychology con?nuity vs. stages In wh
School: UCLA
Course: Math 31 B Lecture 4
Module 7: Brain States and Consciousness What is Consciousness, Exactly? alertness; being awake vs. being unconscious self-awareness; the ability to think about self having free will; being able to make a conscious decision a pe
School: UCLA
Course: Math 31 B Lecture 4
Solutions to practice midterm 2 Sudesh Kalyanswamy and Jiayin Guo (1) From the problem we know k = 0.25 while N = 5000, and we are going to solve dy y = ky(1 ), dt N with initial value y(0) = 1. Since y(0) = 1, this means ky(1 separate the variables to g
School: UCLA
Course: Math 31 B Lecture 4
not the same, so no . k=1 k=2 for different values of k, you get anther solution. y=k(t+1) +6 is a "family" of solutions y(0)=8 - - - - - PG corrections, I "lost " a negative when we took the antiderivative .
School: UCLA
Course: Math 31 B Lecture 4
Math 3B Lecture 1 Winter 2015 due Friday March 6 Late homework is NOT accepted . at 8 am . HW # 7 Name _ Section A B C D (circle one ) UCLA ID # _ Print this page and staple it to your homework papers . 6.1 # 23-27,28-31,35 6.2 # 30,36,40 6.3 # 2,8,14,26
School: UCLA
Course: Math 31 B Lecture 4
Math 3B Lecture 1 Winter 2015 due Monday Feb 23 Late homework is NOT accepted . at 8 am . HW # 5 Name _ Section A B C D (circle one ) UCLA ID # _ Print this page and staple it to your homework papers . 5.6 #11,12,16,17,20,39 ( during eighth year means bet
School: UCLA
Course: Math 31 B Lecture 4
Math 3B Lecture 1 Winter 2015 due Friday Feb 27 Late homework is NOT accepted . at 8 am . HW # 6 Name _ Section A B C D (circle one ) UCLA ID # _ Print this page and staple it to your homework papers . 6.1 #1,3,7,10,14,16,19-22,39 6.2 # 1,5,8,12,17,21,24
School: UCLA
Course: Math 31 B Lecture 4
Math 3B Lecture 1 Winter 2015 due Wednesday February 17 at 8 am . Late homework is NOT accepted . HW # 4 Name _ Section A B C D (circle one ) UCLA ID # _ Print this page and staple it to your homework papers . Practice 5.4 # 1,5,11,15,17,27 5.5 # 1,3,7,11
School: UCLA
Course: Math 31 B Lecture 4
A few solutions to Prof. Greenes practice midterm 1 Sudesh Kalyanswamy (8) (a) The graph of y = 36 x2 is shown below in gure 1. Figure 1: The graph of f (x) = 36 x2 It is the top half of a circle of radius 6. The portion between x = 0 and x = 6 is the rig
School: UCLA
Course: Math 31 B Lecture 4
Math 3B Lecture 1 Winter 2015 NOT accepted . due Friday Feb 6 at 8 am . Late homework is HW # 3 Name _ Section A B C D (circle one ) UCLA ID # _ 4.3 # 24,26,38,44 4.5 # 35,41 5.1 #9,17,22,26,29 5.2 # 2,8,14,19,20,22,24,30 Chapter 4 review # 2,3,7,15,20 Tu
School: UCLA
Course: Math 31 B Lecture 4
Math 3B Lecture 1 Winter 2015 NOT accepted . due Friday January 23 at 8 am . Late homework is HW # 2 Name _ Section A B C D (circle one ) UCLA ID # _ 4.3 # 16,17,28,35,42 1.7 # 13,19,21,24,31,32 4.5 # 1-4,9,10,13,14,15,17,21,22 Turn in all of these proble
School: UCLA
Course: Math 31 B Lecture 4
Math 3B Lecture 1 Winter 2015 NOT accepted . due Friday January 16 at 8 am . Late homework is Name _ Section A B C D (circle one ) UCLA ID # _ "Practice problems"are for you to practice your skills. These are NOT collected . "Turn in problems" must be wri
School: UCLA
Course: Math 31 B Lecture 4
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School: UCLA
Course: Math 31 B Lecture 4
1 \NedJ J~Xn~G\r~ 7, to lS o ~-! ~r6\pnir 9 f\Ancb"011) t~horiloht~l u~ptotes ~tn f(X)=l!:J -t- 1 X; !XJ _ ce,ve~ ur.a? denom(t?atvr ~no ~., ~= L isth~ M-A. _ _ _ tr nn V-tthG~I ~s~mr~te~ LS!t f(~= _L ex) ~ o is1hG 1 t-t X f'(X) ~ I[]+Xt)- X(2X) Q-t X2)l
School: UCLA
Course Information The Denite Integral Math 3B/1 UCLA April 1st, 2013 Course Information This is Math 3B, Lecture 1. I am your host, George J. Schaeer. The course website is http:/www.math.ucla.edu/gschae/3b.1.13s/ Please read the entire course informatio
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Applications of Integration Subsitution Math 3B/1 UCLA George J. Schaeer April 10th, 2013 Areas between curves 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 If f and g are integrable on [a, b] and f (x) g(x) whenever x [a, b], the area of the region bounded by y
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The Fundamental Theorem of Calculus Math 3B/1 UCLA George J. Schaeer April 5th, 2013 More, more, more! Last time we thought about how to integrate functions describing shapes we know and love from geometry. a 0 r a k dx = ka 0 x dx = 1 a2 2 But we are not
School: UCLA
The Denite Integral Math 3B/1 UCLA George J. Schaeer April 4th, 2013 Obviously. You should always read the relevant section in your textbook concurrent with lecture. This will help you with the homework! The relevant section for this and Mondays lecture i
School: UCLA
Integration by Subsitution Integration by Parts Math 3B/1 UCLA George J. Schaeer April 15th, 2013 Announcements HW1 has been graded. The grades are on my.ucla.edu, they will be returned in discussion (assuming your TAs remember!). TA oce hours: Cassidy: T
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Fundamental Theorem of Calculus Applications of Integration Math 3B/1 UCLA George J. Schaeer April 8th, 2013 Integration For SCIENCE we want to solve denite integrals like b f (x) dx a We have seen three ways to integrate: Approximate with Riemann sums an
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Integration by Subsitution Math 3B/1 UCLA George J. Schaeer April 12th, 2013 Last time Last time we evaluated the indenite integral cos(5x) dx By substituting u = 5x and du = 5 dx, so dx = cos(5x) dx = 1 1 cos(u) du = 5 5 = Check your work! 1 5 du. cos(u)
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Mathematics 174E: Lecture 1 David Wihr Taylor UCLA, Los Angeles January 6, 2014 David Wihr Taylor Mathematics 174E: Lecture 1 UCLA, Los Angeles Course Description This course is a mathematical nance course. Courses with similar titles are oered in other d
School: UCLA
Mathematics 174E: Lecture 7: Mechanics of Futures Markets and No Arbitrage David Wihr Taylor UCLA, Los Angeles January 17, 2014 David Wihr Taylor Mathematics 174E: Lecture 7: Mechanics of Futures Markets and No Arbitrage UCLA, Los Angeles Closing Out Posi
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Basics Independence Mathematics 174E: Lecture 3: Discrete Random Walks David Wihr Taylor (based on lecture notes by R. Caisch) UCLA, Los Angeles January 10, 2014 David Wihr Taylor (based on lecture notes by R. Caisch) Mathematics 174E: Lecture 3: Discrete
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UCLA Math 174EExam #2Fall, 2013 1 1. (20 points) This problem has parts (a) and (b) (a) (8 points) What are the two characteristic properties of a Wiener process? (b) (12 points) A quantity Q obeys a law dQ = 3dt + 3dx, where dx is a generalized Wiener pr
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
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School: UCLA
Course: Algebraic Topology
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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
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School: UCLA
Course: Algebraic Topology
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School: UCLA
Course: Algebraic Topology
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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
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School: UCLA
Course: Algebraic Topology
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School: UCLA
Course: Algebraic Topology
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School: UCLA
Course: Algebraic Topology
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School: UCLA
Course: Algebraic Topology
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School: UCLA
Course: Algebraic Topology
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School: UCLA
Course: Algebraic Topology
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School: UCLA
Course: Algebraic Topology
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School: UCLA
Course: Algebraic Topology
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School: UCLA
Course: Algebraic Topology
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School: UCLA
Course: Algebraic Topology
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School: UCLA
Course: Algebraic Topology
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School: UCLA
Course: Algebraic Topology
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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
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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) =
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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 ,
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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
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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
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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
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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
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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
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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
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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 (
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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
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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
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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
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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.
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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
Course: Math 31 B Lecture 4
Practice for final exam Math 3B Winter 2015 Part 1 Multiple choice Circle the correct answer . Be careful to record the answer you think is correct . We will NOT read your scratch paper . There will be NO partial credit on multiple choice problems . 1. Th
School: UCLA
Course: Math 31 B Lecture 4
Practice for final exam Math 3B Winter 2015 Part I Multiple choice Circle the correct answer . Be careful to record the answer you think is correct . We will NOT read your scratch paper . There will be NO partial credit on multiple choice problems . 1. Th
School: UCLA
Course: Math 31 B Lecture 4
"ation. / equ ) 1. When a cake is removed from the oven, the temperature of the cake is 210 F. The cake is Eeft to cooi at room temperature which is 70 F. After 30 minutes, the cake has a temperature of 140 F. (Use Newtons law of cooling and write a.d
School: UCLA
Course: Math 31 B Lecture 4
Math 3B TEST 2 3/6/2015 UCLA Department of Mathematics Name _ UCLA ID _ Section _ Problem 1 Points 10 2 10 3 10 4 10 5 10 Total You earned : 50 Cell phones OFF You may use a non -graphing type calculator Show all of your work on these pages to receive cre
School: UCLA
Course: Math 31 B Lecture 4
Math 3B Exam I Show all of your work. You may use a NON graphing calculator. Turn your cell phones OFF and put them away. 2/9/2015 UCLA Department of Mathematics Name _ Section _ UCLA ID _ Problem Points You earned : 1 10 2 10 3 10 4 10 5 10 Total 50 1. H
School: UCLA
Course: Math 31 B Lecture 4
Math 3B Practice for TEST 2. You may use a non graphing calculator on the exam. Make sure you are familiar with how to use it BEFORE the exam. We will not give calculator lessons during the exam. Write neat clear answers for this practice test. I will col
School: UCLA
Course: Math 31 B Lecture 4
Math 3B, practice for TEST 1 You will be allowed to use a NON graphing calculator for the exam. ( like the one pictured here ) NO cell phone calculators. 1. Graph each function. Consider : where is f(x) increasing and where is it decreasing , where is f(x
School: UCLA
Course: Math 31 B Lecture 4
Math 3B, practice for TEST 1 You will be allowed to use a NON graphing calculator for the exam. ( like the one pictured here ) NO cell phone calculators. 1. Graph each function. Consider : where is f(x) increasing and where is it decreasing , where is f(x
School: UCLA
Course: Discrete Math
QUIZ 1 (MATH 61, SPRING 2015) Your Name: UCLA id: Math 61 Section: Date: The rules: This is a multiple choice quiz. You must circle exactly one answer with an ink pen. If two or more answers are circled, the answer is not accepted. You are allowed to use
School: UCLA
Course: Discrete Math
QUIZ 2 (MATH 61, SPRING 2015) Your Name: UCLA id: Math 61 Section: Date: The rules: This is a multiple choice quiz. You must circle exactly one answer with an ink pen. If two or more answers are circled, the answer is not accepted. You are allowed to use
School: UCLA
Course: Discrete Math
MATH 61: HOMEWORK 2 3.3 25. not reexive, not symmetric, antisymmetric, transitive, not a partial order 26. reexive, not symmetric, antisymmetric, transitive, partial order 28. reexive, symmetric, not antisymmetric, transitive, not a partial order (this is
School: UCLA
Calculus for Life Sciences Students (Math 3B) Spring 2013 Instructor: George J. Schaeffer Practice Exam 1 Name and Student ID: No electronics or notes are permitted. Complete all problems. Problem Points Grade 14 20 5 30 6 10 7 20 Total 80 1 Problems 14 (
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School: UCLA
Course: Problem Solving
Name: Math 100 : Problem Solving Midterm Exam Instructor: Ciprian Manolescu You have 50 minutes. Each problem is worth 10 points. No books, notes or calculators are allowed. 1. Let Fn be the Fibonacci numbers, dened by F0 = 0, F1 = 1, and Fn = Fn1 + Fn2 f
School: UCLA
Course: Problem Solving
Name: Math 100 : Quiz October 3, 2013 You have 25 minutes. No books, notes or calculators are allowed. 1. Prove by induction on n that 2 4 6 (2n) > n+1 1 3 5 (2n 1) for any n 1. 2. Show that among any 9 points inside a 10 20 rectangle, we can nd two that
School: UCLA
Course: Problem Solving
Name: Math 100 : Problem Solving Final Exam Instructor: Ciprian Manolescu You have 180 minutes. Each problem is worth 10 points. No books, notes or calculators are allowed. 1. Prove by induction on n 1 that 2n 1 2n 2 + 2n 3 + 3 2+ 1> n . 2 2. (a) Find th
School: UCLA
Course: Problem Solving
Name: Math 100 : Problem Solving Final Exam Instructor: Ciprian Manolescu You have 180 minutes. Each problem is worth 10 points. No books, notes or calculators are allowed. 1. Thirty bees are ying inside a cube of side length 1. Show that at any given tim
School: UCLA
Course: Problem Solving
Name: Math 100 : Problem Solving Midterm Exam Instructor: Ciprian Manolescu You have 50 minutes. Each problem is worth 10 points. No books, notes or calculators are allowed. 1. Let x1 , x2 , . . . , xn 1. Prove by induction on n that (1 + x1 )(1 + x2 ) (1
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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: 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
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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
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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
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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
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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
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Course: Math 31 B Lecture 4
School: UCLA
Course: Math 31 B Lecture 4
Math 3B Lecture 1 Winter 2015 due Friday Feb 27 HW#6 Late homework is NOT accepted . Name Section A B C D (circle one) UCLA ID # Print this page and staple it to your homework palj'ersym- 6. I ,r-aa \ 6.1 #1,3,7,10,14,161922g39 6.2 #1,5;,8j2l17,21,24 Turn
School: UCLA
Course: Math 31 B Lecture 4
Math 3B Exam l Show all of your work. You may use a NON graphing calculator. Turn your cell phones OFF and put them away. 2/9/2015 UCLA Department of Mathemagf Name Section 1 1 O 2 1. Here is the function = 'x32:5 I 303: n 30(5_3x2) with = (x2+5)2 an
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Calculus for Life Sciences Students (Math 3B) Spring 2013 Instructor: George J. Schaeffer Practice Exam 1 Name and Student ID: No electronics or notes are permitted. Complete all problems. Problem Points Grade 14 20 5 30 6 10 7 20 Total 80 1 Problems 14 (
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School: UCLA
Course: Discrete Math
HOMEWORK 1 (MATH 61, SPRING 2015) Solve: 2.2 RJ, Sec. 2.2 Ex 28, 29, Sec. 2.4 Ex 2, 3, 6, 9, Sec 3.2 Ex 7, 9, 13, 14. 28. Suppose that there exist positive integers m, n such that m3 +2n2 = 36. Then m3 < 36, 1 and thus m < (36) 3 < 4. Since both 2n2 and 3
School: UCLA
Course: Discrete Math
HOMEWORK 1 (MATH 61, SPRING 2015) Read: RJ, sections 2.2, 2.4, 3.2. Solve: RJ, Sec. 2.2 Ex 28, 29, Sec. 2.4 Ex 2, 3, 6, 9, Sec 3.2 Ex 7, 9, 13, 14. I. There are n unit circles and n lines drawn in the plane. Prove that the regions in the plane separated b
School: UCLA
Course: Discrete Math
HOMEWORK 2 (MATH 61, FALL 2013) Read: RJ, Sec. 3.3, 3.4, 6.1, 6.8. Solve: RJ, Sec. 3.3 Ex 25, 26, 28, 29, Sec. 3.4 Ex 6, 8, 10, 11, 13, 14, Sec 6.1 Ex 6, 8, 42, 43, 88, 90, 91, Sec 6.8 Ex 3, 6, 8. I. Let R be a relation on Z = cfw_0, 1, 2, 3, . . . dened
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
Math 172 B Class Project 1 Object: to download a specific mortality table from the Society of Actuaries website and utilize mortality rates to calculate life expectancies Steps: 1. Log onto www.soa.org 2. At the bottom of the opening page, select popular
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 174E (Summer 2014) Mathematics of Finance Instructor: David W. Taylor Time/Location: MWR 11:00am-12:50pm in MS 5137. Text: Options, Futures, and Other Derivatives (8th edition) by John C. Hull. Instructor: David W. Taylor Oce Hours: TBA Email Address
School: UCLA
Math 174E, Lecture 1 (Winter 2014) Mathematics of Finance Instructor: David W. Taylor Time/Location: MWF 3:00pm-3:50pm in MS 5127. Text: Options, Futures, and Other Derivatives (8th edition) by John C. Hull. Instructor: David W. Taylor Oce Hours: Monday a
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
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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