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School: Georgia State
Course: Elementary Statistics
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 B C D E F G H I J Math 1070 Excel Project (Due: Friday, November 15, 2
School: Georgia State
Course: Math Modeling
Year 1965 1974 1979 1983 1985 1987 1990 1992 1993 1995 2000 TotalPop. AllMales AllFemales 42.4 51.9 33.9 37.1 43.1 32.1 33.5 37.5 29.9 32.1 35.1 29.5 30.1 32.6 27.9 28.8 31.2 26.5 25.5 28.4 22.8 26.5 28.6 24.6 25 27.7 22.5 24.7 27 22.6 23.3 25.7 21 Males
School: Georgia State
Course: Pre Cla
A B C D E F G H I 1 Math 1070 Excel Project (Due: Monday, April 14, 2014 before 11:59pm) 2 J K L M N O P Q R Instructor- Sona Shakoory-ASL Name: Max Khdier Class Day/Time: Tuesday 5:00-5:50 Reminder: The goal of this project is to get you comfortable with
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
MATH-2211, Fall-2010 Test #1 Name: MATH-2211 Calculus-I CRN 808 Test-1 Directions: Do the test on your own paper and attach it to this test sheet (or in your blue book and put the test sheet inside). Sign your name and the CRN number on the test sheet. Cl
School: Georgia State
Course: ELEMENTARY STATISTICS
Math 1070 Elementary Statistics Lecture notes prepared by Dr. Leslie Meadows (Coordinator Math 1070 and GSU Commons MILE) in cooperation with Heather King and based on the texts: Elementary Statistics with Excel, Third Custom Edition for Math1070; Georgia
School: Georgia State
Course: Pre Cla
TextbookandOnlineHomeworkInfoforECON2105&2106 Allprinciplescourses(microandmacro)requireaccesstoNortonSmartWork(NSW), the online homework management system which accompanies this textbook series. NSWincludesaneBook,sopurchaseofahardcopyofthetextbookisopti
School: Georgia State
Course: Elementary Statistics 1070
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
School: Georgia State
Course: COLLEGE ALGEBRA
Formula Sheet for College Algebra Final Exam Quadratic Formula Properties of Exponents 1. a a = a n m n+m x= n a 2. m = a n m a 3. (a n ) m = a nm 6. b p b b 4ac 2a ( x h) 2 = 4 p ( y k ) vertex = (h, k ) Circle 4. (a n b m ) p = a np b mp an 5. m b Sta
School: Georgia State
Course: Pre Cla
Chapter 2 Random Number Generator Suppose that you wanted to take a random sample of ve of your companys 32 salespeople using Excel so that you could interview these ve salespeople about their job satisfaction at your company. To do that, you need to dene
School: Georgia State
Course: ELEMENTARY STATISTICS
6.2 and 6.3: Uniform and Normal Distribution If we think of the area under the curve as the probability of something happening between two values, then the full area under any curve is 1. For uniform distributions, notice the shape is a rectangle! As we k
School: Georgia State
Course: ELEMENTARY STATISTICS
5.3 Binomial Probability Distributions Binomial Probability Distributions must meet the following requirements: 1. Fixed number of trials 2. Independent 3. Two categories 4. Probability of success remains the same throughout. FITSs (Fixed, Independent, Tw
School: Georgia State
Course: ELEMENTARY STATISTICS
4.5 Multiplication Rule: Complements and Conditional Probability P(at least 1) : It is sometimes difficult to find the probability of at least one thing happening. Why? Let's look at examples. Ex. 1 Find the probability of a couple having at least 1 girl
School: Georgia State
Course: ELEMENTARY STATISTICS
Addition Rule for Probability P(A or B) = P(A) + P(B) - P(A and B) Ex.1 Was the challenge to the call successful? Yes No Men 201 288 Women 126 224 327 512 P(man or successful) P(woman or unsuccessful) 489 350 A company has manufactured 2025 CDs, and 319 a
School: Georgia State
Course: ELEMENTARY STATISTICS
z-scores Formulas: sample population excel Ex. 6-d Mean Stdev Strongest z-score z = (x-xbar)/s z = (x - )/ =STANDARDIZE(x, mean, stdev) 1.184 0.587 2.95 ? What can be said about the z-score? Percentiles and Quartiles Percentile: Locator Function: Quartile
School: Georgia State
Course: ELEMENTARY STATISTICS
Data mean 1 6 2 range var st dev pop var pop st dev Range Rule of Thumb mean 100 st dev 15 min usual value max usual value Empirical Rule for Data with a Bell-Shaped Distribution Lower Upper about 68% of all values fall within 1 standard deviation of the
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
MATH-2211, Fall-2010 Test #1 Name: MATH-2211 Calculus-I CRN 808 Test-1 Directions: Do the test on your own paper and attach it to this test sheet (or in your blue book and put the test sheet inside). Sign your name and the CRN number on the test sheet. Cl
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
Math 2211 Spring 2009 Test 1 Review Definition 2.2.1. The limit of a function. Let f be a function defined at least on an open interval (c-p,c+p) except possibly at c itself. We say that lim f ( x) = L x c if for each > 0, there exist > 0 such that if 0 <
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
2211 Spring 2009 Test 1 Name_ Show all necessary work in your blue book. No credit will be given for incorrect work or answers without work. Please use a new page for each problem. Please use pencil. When finished, place this question paper in your blue b
School: Georgia State
Course: Mathematical Models For Computer Science
MATH-3030, Summer-2012 Quiz #5 Your name: MATH-3030 Math Models for CS CRN 52440 Quiz 5 Sections C.13.5-C.13.6,C.14.1-C.14.2,C.15.4,C.16.2,C.16.4 Directions: Do the quiz on your own paper and attach to this quiz assignment sheet. Clearly show all your wor
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
MATH-2211, Fall-2010 Test #1 Solutions 1. Evaluate the limit if it exists (or clearly state and prove that it doesnt exist if thats the case): x2 + 2x 15 =? x5 x+5 (x + 5)(x 3) x2 + 2x 15 = lim = lim (x 3) = 8. lim x5 x5 x5 x+5 x+5 1 1 +t lim 3 =? t3 3 +
School: Georgia State
Course: ELEMENTARY STATISTICS
A B C D E F G H 1 Math 1070 Excel Project (Due: before Monday, November 16, 2015 at 11:59pm) 2 3 4 5 6 7 8 9 J K L M N O P Q R Instructor - Husneara Rahmann (Please submit projects in the D2L Dropbox for your class.) Name: Sofia Antonova Class Day/Time: T
School: Georgia State
Course: Pre Cla
6 Association Analysis: Basic Concepts and Algorithms Many business enterprises accumulate large quantities of data from their dayto-day operations. For example, huge amounts of customer purchase data are collected daily at the checkout counters of grocer
School: Georgia State
Course: ABSTRACT ALGEBRA
NAME: Sow ON 3 18.075 IllClass Exam 1 Wednesday, September 29, 2004 Justify your answers. Cross out what is not meant to be part of your nal answer. Total number of points: 45. I. (5 pts) Show that for any complex numbers Z1 and Z27 le IZ2H S '21 + 22!- H
School: Georgia State
Course: SPECIAL PROB AND SOLVING STRAT
18.01 Exam 4 Problem 1(25 points) A solid is formed by revolving about the xaxis the region bounded by the xaxis, the line x = 0, the line x = a, and the curve, x y = b sin . a Find the volume of the solid. You may use the halfangle formulas, 2 cos (/2)
School: Georgia State
Course: SPECIAL PROB AND SOLVING STRAT
Solutions to 18.01 Exam 3 Problem 1(20 points) A particle moves along the positive xaxis with velocity 5 units/second. How fast is the particle moving away from the point (0, 3) (which is on the yaxis) when the particle is 7 units away from (0, 3)? Soluti
School: Georgia State
Course: ALGEBRAIC CONCEPTS
Jason Starr Fall 2005 18.01 Calculus Due by 2:00pm sharp Friday, Oct. 14, 2005 Solutions to Problem Set 3 Part I/Part II Part I(20 points) (a)(2 points) (b)(2 points) (c)(2 points) (d)(2 points) (e)(2 points) (f )(2 points) (g)(2 points) (h)(2 points) (i)
School: Georgia State
Course: Pre Cla
The Random Generator Tool Introduction This document provides an overview of the information you need to create and customize the random generator tool in SMART Notebook collaborative learning software. The random generator tool is found in the Lesson Act
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
Lab Report 5- KH 3650 ° What are the physiological factors that limit V02 max? Would these factors be different for a trained person from a sedentary person? The highest V02 recorded in absolute terms was 3.97[L/ min), in relative terms it was 53.3 [ml/kg
School: Georgia State
Course: Pre Cla
A B C D E F G H I 1 Math 1070 Excel Project (Due: Monday, April 14, 2014 before 11:59pm) 2 J K L M N O P Q R Instructor- Sona Shakoory-ASL Name: Max Khdier Class Day/Time: Tuesday 5:00-5:50 Reminder: The goal of this project is to get you comfortable with
School: Georgia State
Course: Pre Cla
Chapter 9 Random Numbers This chapter describes algorithms for the generation of pseudorandom numbers with both uniform and normal distributions. 9.1 Pseudorandom Numbers Here is an interesting number: 0.814723686393179 This is the rst number produced by
School: Georgia State
Course: COLLEGE ALGEBRA
Factoring and expanding polynomials. In algebra, students learn to factor polynomials like the quadratic equation. Factoring is much easier to understand once the student has learned how to expand a polynomial, which is simply multiplying two or more fact
School: Georgia State
Course: REAL ANALYSIS I
Problems: Simply Connected Regions 1. Which of the regions shown below are simply connected? (a) (b) (c) Answer: Region (a) is not simply connected the puncture at the center of the disk would prevent any simple closed curve around it from contracting to
School: Georgia State
Course: REAL ANALYSIS I
Problems: Work and Line Integrals Z 1. Evaluate I = y dx + (x + 2y) dy where C is the curve shown. C y 1 C1 (1, 1) C2 1 x Figure 1: Curve C is C1 followed by C2 . Answer: The curve C is made up of two pieces, so Z Z I= y dx + (x + 2y) dy + y dx + (x + 2y)
School: Georgia State
Course: REAL ANALYSIS I
7.1IntegrationbyParts (page287) CHAPTER 7 TECHNIQUES OF INTEGRATION 7.1 Integration by Parts (page 287) Integration by parts aims to exchange a difficult problem for a possibly longer but probably easier one. It is up to you t o make the problem easier! T
School: Georgia State
Course: Pre Cla
University of Sydney School of Information Technologies Generating Random Variables Pseudo-Random Numbers Definition: A sequence of pseudo-random numbers (U i ) is a deterministic sequence of numbers in [0,1] having the same relevant statistical propertie
School: Georgia State
Course: MATHEMATICAL STATISTICS II
REVISED GEORGIA STATE UNIVERSITY J. MACK ROBINSON COLLEGE OF BUSINESS PROFESSIONAL SALES, CRN 86978, MK 4330-005 FALL SEMESTER 2015 MONDAYS AND WEDNESDAYS, 12:00 1:15 CLASSROOM SOUTH, ROOM 207 INSTRUCTOR: OFFICE: OFFICE HOURS: OFFICE PHONE: E-MAIL ADDRESS
School: Georgia State
Course: MATH MODELS FOR COMPUTER SCI
SPRING 2015 MATH 3030 MW 3:00 - 4:15 PM, Langdale Hall 601 Instructor: Xiaojing Ye, xye@gsu.edu, COE 704, Phone: 413-6444. Oce Hours: MW 2:00-2:50 PM. Textbook: (Required) Advanced Engineering Mathematics, 10th edition by E. Kreyszig, Wiley 2011. (We cove
School: Georgia State
Course: Discrete Math
COURSE SYLLABUS MATH 2420DISCRETE MATHEMATICS SUMMER, 2015 (Math 2420 Section 005, CRN 50333) Day and Time: MW 4:45-7:15pm. Room: Langdale Hall 403 Instructor: Dr. Mariana Montiel Office: COE 708 Direct phone: (404) 413-6414 e-mail: mmontiel@gsu.edu Offic
School: Georgia State
Course: Calculus Of One Variable I
MATH-2211 Syllabus Course Syllabus MATH-2211 - Calculus of One Variable I Spring semester, 2015 Course: MATH-2211 Calculus of One Variable I (CRN: 10657) Text: Calculus: One and Several Variables, 10th Edition by Salas, Hille & Etgen; Wiley, 2007, ISBN 97
School: Georgia State
Course: Calculus Of One Variable II
MATH-2212 Syllabus Course Syllabus MATH-2212 - Calculus of One Variable II Summer semester, 2015 Course: MATH-2212 Calculus of One Variable II (CRN: 54003) Text: (Required) Calculus: One and Several Variables, 10th Edition by Salas, Hille & Etgen; Wiley,
School: Georgia State
Course: Elementary Statistics
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 B C D E F G H I J Math 1070 Excel Project (Due: Friday, November 15, 2
School: Georgia State
Course: Math Modeling
Year 1965 1974 1979 1983 1985 1987 1990 1992 1993 1995 2000 TotalPop. AllMales AllFemales 42.4 51.9 33.9 37.1 43.1 32.1 33.5 37.5 29.9 32.1 35.1 29.5 30.1 32.6 27.9 28.8 31.2 26.5 25.5 28.4 22.8 26.5 28.6 24.6 25 27.7 22.5 24.7 27 22.6 23.3 25.7 21 Males
School: Georgia State
Course: Pre Cla
A B C D E F G H I 1 Math 1070 Excel Project (Due: Monday, April 14, 2014 before 11:59pm) 2 J K L M N O P Q R Instructor- Sona Shakoory-ASL Name: Max Khdier Class Day/Time: Tuesday 5:00-5:50 Reminder: The goal of this project is to get you comfortable with
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
MATH-2211, Fall-2010 Test #1 Name: MATH-2211 Calculus-I CRN 808 Test-1 Directions: Do the test on your own paper and attach it to this test sheet (or in your blue book and put the test sheet inside). Sign your name and the CRN number on the test sheet. Cl
School: Georgia State
Course: ELEMENTARY STATISTICS
Math 1070 Elementary Statistics Lecture notes prepared by Dr. Leslie Meadows (Coordinator Math 1070 and GSU Commons MILE) in cooperation with Heather King and based on the texts: Elementary Statistics with Excel, Third Custom Edition for Math1070; Georgia
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
Math 2211 Spring 2009 Test 1 Review Definition 2.2.1. The limit of a function. Let f be a function defined at least on an open interval (c-p,c+p) except possibly at c itself. We say that lim f ( x) = L x c if for each > 0, there exist > 0 such that if 0 <
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
2211 Spring 2009 Test 1 Name_ Show all necessary work in your blue book. No credit will be given for incorrect work or answers without work. Please use a new page for each problem. Please use pencil. When finished, place this question paper in your blue b
School: Georgia State
Course: Mathematical Models For Computer Science
MATH-3030, Summer-2012 Quiz #5 Your name: MATH-3030 Math Models for CS CRN 52440 Quiz 5 Sections C.13.5-C.13.6,C.14.1-C.14.2,C.15.4,C.16.2,C.16.4 Directions: Do the quiz on your own paper and attach to this quiz assignment sheet. Clearly show all your wor
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
MATH-2211, Fall-2010 Test #1 Solutions 1. Evaluate the limit if it exists (or clearly state and prove that it doesnt exist if thats the case): x2 + 2x 15 =? x5 x+5 (x + 5)(x 3) x2 + 2x 15 = lim = lim (x 3) = 8. lim x5 x5 x5 x+5 x+5 1 1 +t lim 3 =? t3 3 +
School: Georgia State
Course: Intro To Probability And Statistics
C \ r j, 1 C l r . l M ATH 3 O7O t. Exam#2 Showy our w ork! Name TheN ational ighwayS ystem esignation ct o f 1 995a llowss tateso s ett heiro wn H A D t highwayspeedimits. Attachedto the examis the datafor the maximumspeedimits for l l carsandtrucks(in m
School: Georgia State
Course: Intro To Statistical Methods
Math 4547/6547 SAS Project 2 - Due April 15th, 2013 Name: Instructions Your project should have each of the following features: 1. Title Page 2. Input Code Section. Also include the data le used. 3. Output From SAS Section 4. Answers to questions Typed (I
School: Georgia State
Course: Intro To Math Modeling
Name: _ No.: _ Semester Project 2 Regression Line The following table shows (for the years 1965 to 2000 and for people 18 and over) the total percentage of cigarette smokers, the percentage of males who are smokers, and the percentage of females who are s
School: Georgia State
Course: Math Modeling
Name: Ryan Lees No.: Due Oct 25th in class. Semester Project 2 Regression Line The following table shows (for the years 1965 to 2000 and for people 18 and over) the total percentage of cigarette smokers, the percentage of males who are smokers, and the pe
School: Georgia State
Course: Math Modeling
Test 1 study guide (Show all your work) Math 1101 Fall 11 No.: _ Name: _ 1. i). Consider the following table. s t 70 149 73 175 66 146 66 126 64 138 A) Is t a function of s ? B Is s a function of t ? ii). The following table gives values for a function f(
School: Georgia State
Course: ELEMENTARY STATISTICS
A B C D E F G H 1 I Math 1070 Excel Project (Due: Monday, April 14, 2014 before 11:59pm) 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
School: Georgia State
Course: Geometry And Spatial Sense
. Activity Two Congruent Halves <f the figures that follow, draw a line from dot to dot to cut the figure in half in such a way that the two .-es are congruent. The dotted line illustrates how the first one can be done. -f Can you think of a way that coul
School: Georgia State
Course: ELEMENTARY STATISTICS
A B C D E F G H 1 Math 1070 Excel Project (Due: before Monday, November 16, 2015 at 11:59pm) 2 3 4 5 6 7 8 9 J K L M N O P Q R Instructor - Husneara Rahmann (Please submit projects in the D2L Dropbox for your class.) Name: Sofia Antonova Class Day/Time: T
School: Georgia State
Course: ELEMENTARY STATISTICS
6.2 and 6.3: Uniform and Normal Distribution If we think of the area under the curve as the probability of something happening between two values, then the full area under any curve is 1. For uniform distributions, notice the shape is a rectangle! As we k
School: Georgia State
Course: ELEMENTARY STATISTICS
5.3 Binomial Probability Distributions Binomial Probability Distributions must meet the following requirements: 1. Fixed number of trials 2. Independent 3. Two categories 4. Probability of success remains the same throughout. FITSs (Fixed, Independent, Tw
School: Georgia State
Course: ELEMENTARY STATISTICS
4.5 Multiplication Rule: Complements and Conditional Probability P(at least 1) : It is sometimes difficult to find the probability of at least one thing happening. Why? Let's look at examples. Ex. 1 Find the probability of a couple having at least 1 girl
School: Georgia State
Course: ELEMENTARY STATISTICS
Addition Rule for Probability P(A or B) = P(A) + P(B) - P(A and B) Ex.1 Was the challenge to the call successful? Yes No Men 201 288 Women 126 224 327 512 P(man or successful) P(woman or unsuccessful) 489 350 A company has manufactured 2025 CDs, and 319 a
School: Georgia State
Course: ELEMENTARY STATISTICS
z-scores Formulas: sample population excel Ex. 6-d Mean Stdev Strongest z-score z = (x-xbar)/s z = (x - )/ =STANDARDIZE(x, mean, stdev) 1.184 0.587 2.95 ? What can be said about the z-score? Percentiles and Quartiles Percentile: Locator Function: Quartile
School: Georgia State
Course: ELEMENTARY STATISTICS
Data mean 1 6 2 range var st dev pop var pop st dev Range Rule of Thumb mean 100 st dev 15 min usual value max usual value Empirical Rule for Data with a Bell-Shaped Distribution Lower Upper about 68% of all values fall within 1 standard deviation of the
School: Georgia State
Course: ELEMENTARY STATISTICS
Data for Mean Example: 27531 15684 5638 27997 25433 Mean: Data for Median Example: (You don't need to sort first when finding the median using technology, but we'll demonstrate sorting anyway) 5638 15684 25433 27531 27997 Median: 27531 5638 8077 15684 254
School: Georgia State
Course: ELEMENTARY STATISTICS
Pulse Rates of Females Pulse Rate 60-69 70-79 80-89 90-99 100-109 110-119 120-129 Frequency 12 14 11 1 1 0 1 Class midpoints 64.5 74.5 84.5 94.5 104.5 114.5 124.5 Frequency 16 14 12 10 Frequency 8 6 4 2 0 Pulse Rate 60-69 70-79 80-89 90-99 100-109 110-119
School: Georgia State
Course: ELEMENTARY STATISTICS
Pulse Rates (beats per minute) Males Females 68 76 64 72 88 88 72 60 64 72 72 68 60 80 88 64 76 68 60 68 96 80 72 76 56 68 64 72 60 96 64 72 84 68 76 72 84 64 88 80 72 64 56 80 68 76 64 76 60 76 68 80 60 104 60 88 56 60 84 76 72 72 84 72 88 88 56 80 64 60
School: Georgia State
Course: Pre Cla
6 Association Analysis: Basic Concepts and Algorithms Many business enterprises accumulate large quantities of data from their dayto-day operations. For example, huge amounts of customer purchase data are collected daily at the checkout counters of grocer
School: Georgia State
Course: Pre Cla
TextbookandOnlineHomeworkInfoforECON2105&2106 Allprinciplescourses(microandmacro)requireaccesstoNortonSmartWork(NSW), the online homework management system which accompanies this textbook series. NSWincludesaneBook,sopurchaseofahardcopyofthetextbookisopti
School: Georgia State
Course: Elementary Statistics 1070
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
School: Georgia State
Course: COLLEGE ALGEBRA
Formula Sheet for College Algebra Final Exam Quadratic Formula Properties of Exponents 1. a a = a n m n+m x= n a 2. m = a n m a 3. (a n ) m = a nm 6. b p b b 4ac 2a ( x h) 2 = 4 p ( y k ) vertex = (h, k ) Circle 4. (a n b m ) p = a np b mp an 5. m b Sta
School: Georgia State
Course: APPLIED COMBINATORICS
to finish our proof we must show that is a countably additive measure Lemma. is countably additive on MF Proof. Want to show that Bi MF , Bi Bj = , i = j (B) = (Bi ) i=1 We can easily prove inequality one way. BN = N i=1 i=1 Bi = B MF , then Bi = BN B
School: Georgia State
Course: APPLIED COMBINATORICS
12 The Wave Equation d2 u d2 u - 2 = 0, dt2 dx The wave equation in one space and one time variable is u : (Rx , Rt ) R Theorem. If f0 , f1 C (Rx ), !u C (R2 ) satisfying the wave equation with the initial x,t conditions u(0, x) = f0 (x) and x u(0, x) = f
School: Georgia State
Course: COMMUTATIVE ALGEBRA/GEOMETRY
x7 .- E (X (de C, CTACMTCEVWQLZ e" we; > cfw_A I Vt? Q S. I AF([1,105) )5 ,>.,\wmg-ism4 .5 W 157 '3 K<Q E, \(ZULogf: rtlo). S3 L(L')L)(m') i?) yz-vxwmm'hym v7 HLJLm gs [45xiiww3r5'kom-L E \ - _ -,I i l" M Maw. we, at \ 3%,; mix, (M: qux 3:; i ERMA Fj\i\
School: Georgia State
Course: INFORMATICS OF BIOLOGICAL SYST
D 03. 3% g i; a) 95? WDQMMj ?E%?OV@( g3 ?( Cxwgf Di W W VD Tr '61 viz: cfw_Law Mmmmg $7 Vquo 800% Graham cfw_lid "FOU/M my: Nggsgawng-wa > WAgQ/zgn cfw_M5053 w err dutfgzb g. Emma ouasvarxg ww rme m.,%mw KM Che- mA wmm ~Wakn9 haw W3 cfw_Hus ; Meme, vad
School: Georgia State
Course: TOPICS IN ANALYSIS
gPaH/f (M) N) WNW M '3' N (90") WWW/Y wi'VF WVIhVV] H: wNm )5 0, mm; umcuvj I fmd'xkcgk, 22. N , cfw_fwe CMCV" U4 P) WM i4 9 Md FHA) f) sale-hwdb, O\%>V,Losaiml\j Llcsed m H- ? FM 0 3mm, '+Nocfw_jT A pair (Ml?) r5 [cfw_omj wN/m LVITI W/m VA 43: M 5,6
School: Georgia State
Course: Pre Cla
Chapter 2 Random Number Generator Suppose that you wanted to take a random sample of ve of your companys 32 salespeople using Excel so that you could interview these ve salespeople about their job satisfaction at your company. To do that, you need to dene
School: Georgia State
Course: ELEMENTARY STATISTICS
6.2 and 6.3: Uniform and Normal Distribution If we think of the area under the curve as the probability of something happening between two values, then the full area under any curve is 1. For uniform distributions, notice the shape is a rectangle! As we k
School: Georgia State
Course: ELEMENTARY STATISTICS
5.3 Binomial Probability Distributions Binomial Probability Distributions must meet the following requirements: 1. Fixed number of trials 2. Independent 3. Two categories 4. Probability of success remains the same throughout. FITSs (Fixed, Independent, Tw
School: Georgia State
Course: ELEMENTARY STATISTICS
4.5 Multiplication Rule: Complements and Conditional Probability P(at least 1) : It is sometimes difficult to find the probability of at least one thing happening. Why? Let's look at examples. Ex. 1 Find the probability of a couple having at least 1 girl
School: Georgia State
Course: ELEMENTARY STATISTICS
Addition Rule for Probability P(A or B) = P(A) + P(B) - P(A and B) Ex.1 Was the challenge to the call successful? Yes No Men 201 288 Women 126 224 327 512 P(man or successful) P(woman or unsuccessful) 489 350 A company has manufactured 2025 CDs, and 319 a
School: Georgia State
Course: ELEMENTARY STATISTICS
z-scores Formulas: sample population excel Ex. 6-d Mean Stdev Strongest z-score z = (x-xbar)/s z = (x - )/ =STANDARDIZE(x, mean, stdev) 1.184 0.587 2.95 ? What can be said about the z-score? Percentiles and Quartiles Percentile: Locator Function: Quartile
School: Georgia State
Course: ELEMENTARY STATISTICS
Data mean 1 6 2 range var st dev pop var pop st dev Range Rule of Thumb mean 100 st dev 15 min usual value max usual value Empirical Rule for Data with a Bell-Shaped Distribution Lower Upper about 68% of all values fall within 1 standard deviation of the
School: Georgia State
Course: ELEMENTARY STATISTICS
Data for Mean Example: 27531 15684 5638 27997 25433 Mean: Data for Median Example: (You don't need to sort first when finding the median using technology, but we'll demonstrate sorting anyway) 5638 15684 25433 27531 27997 Median: 27531 5638 8077 15684 254
School: Georgia State
Course: ELEMENTARY STATISTICS
Pulse Rates of Females Pulse Rate 60-69 70-79 80-89 90-99 100-109 110-119 120-129 Frequency 12 14 11 1 1 0 1 Class midpoints 64.5 74.5 84.5 94.5 104.5 114.5 124.5 Frequency 16 14 12 10 Frequency 8 6 4 2 0 Pulse Rate 60-69 70-79 80-89 90-99 100-109 110-119
School: Georgia State
Course: ELEMENTARY STATISTICS
Pulse Rates (beats per minute) Males Females 68 76 64 72 88 88 72 60 64 72 72 68 60 80 88 64 76 68 60 68 96 80 72 76 56 68 64 72 60 96 64 72 84 68 76 72 84 64 88 80 72 64 56 80 68 76 64 76 60 76 68 80 60 104 60 88 56 60 84 76 72 72 84 72 88 88 56 80 64 60
School: Georgia State
Course: MATH 2212
Plant Reproduction Biol 2108 Lab Moss Moss Life Cycle Moss Sporophyte (Sphagnum) Moss Young Gametophyte Moss Antheridial Head Moss Archegonial Head Moss Protonema Moss Capsule Fern Fern Young Sporophyte Fern Antheridia Fern Archegonia Fern Indusium Fern S
School: Georgia State
Course: MATH 2212
Protostomes Annelida Annelida Mollusca Arthropoda Platyhelminthes Evolutionary Relationships Amongst Animals Ecdysozoans & Lophotrochozoans In ancient times the protostomes split into 2 major clades that have been evolving independently ever since Lopho
School: Georgia State
Course: MATH 2212
Plant Growth & Hormones Seed Dormancy Seed dormancy may last for weeks, months, years, or even centuries. What are the advantages of dormancy? Germination Plant Hormones What is a hormone? Hormones Naturally occurring regulatory compounds Substances tha
School: Georgia State
Course: Elementary Statistics
January 23, 2008 [LECTURE 6] What you need to know What you need to remember 1. One notice In a normal distribution, , , is actually the mean, and is the standard deviation. One interesting & important property of normal distribution 1
School: Georgia State
Course: Elementary Statistics
January 18, 2008 [LECTURE 5] What you need to remember for today's lecture? 1. IQR and outliers The interquartile range (IQR) is the distance between the first and third quartiles (the length of the box in the boxplot) IQR = Q3 - Q1 An outlier
School: Georgia State
Course: Elementary Statistics
January 16, 2008 [LECTURE 4] What you need to remember from today's lecture I. Measure of spread: quartiles and standard deviation Quartiles are three numbers that describe the trend, or statistically, the spread of the data. The calculation
School: Georgia State
Course: Elementary Statistics
January 14, 2008 [LECTURE 3] I. Stemplots: How to make a stemplot: 1) Separate each observation into a stem, consisting of all but the final (rightmost) digit, and a leaf, which is that remaining final digit. Stems may have as many digits as nee
School: Georgia State
Course: Elementary Statistics
January 11, 2008 [LECTURE 2] What you need to remember for today's class I. Histograms: The range of values that a variable can take is divided into equal-size intervals. The histogram shows the number of individual data points that fall in each
School: Georgia State
Course: Elementary Statistics
January 9, 2008 [OUTLINE OF LECTURE 1] What you need to know for today's lecture I. II. III. What is statistics, and what do statisticians do? Why statistics is useful in everyday life? What can you expect from statistics and statisticians? Wha
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
MATH-2211, Fall-2010 Test #1 Name: MATH-2211 Calculus-I CRN 808 Test-1 Directions: Do the test on your own paper and attach it to this test sheet (or in your blue book and put the test sheet inside). Sign your name and the CRN number on the test sheet. Cl
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
Math 2211 Spring 2009 Test 1 Review Definition 2.2.1. The limit of a function. Let f be a function defined at least on an open interval (c-p,c+p) except possibly at c itself. We say that lim f ( x) = L x c if for each > 0, there exist > 0 such that if 0 <
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
2211 Spring 2009 Test 1 Name_ Show all necessary work in your blue book. No credit will be given for incorrect work or answers without work. Please use a new page for each problem. Please use pencil. When finished, place this question paper in your blue b
School: Georgia State
Course: Mathematical Models For Computer Science
MATH-3030, Summer-2012 Quiz #5 Your name: MATH-3030 Math Models for CS CRN 52440 Quiz 5 Sections C.13.5-C.13.6,C.14.1-C.14.2,C.15.4,C.16.2,C.16.4 Directions: Do the quiz on your own paper and attach to this quiz assignment sheet. Clearly show all your wor
School: Georgia State
Course: CALCULUS OF ONE VARIABLE I
MATH-2211, Fall-2010 Test #1 Solutions 1. Evaluate the limit if it exists (or clearly state and prove that it doesnt exist if thats the case): x2 + 2x 15 =? x5 x+5 (x + 5)(x 3) x2 + 2x 15 = lim = lim (x 3) = 8. lim x5 x5 x5 x+5 x+5 1 1 +t lim 3 =? t3 3 +
School: Georgia State
Course: Intro To Probability And Statistics
C \ r j, 1 C l r . l M ATH 3 O7O t. Exam#2 Showy our w ork! Name TheN ational ighwayS ystem esignation ct o f 1 995a llowss tateso s ett heiro wn H A D t highwayspeedimits. Attachedto the examis the datafor the maximumspeedimits for l l carsandtrucks(in m
School: Georgia State
Course: Math Modeling
Test 1 study guide (Show all your work) Math 1101 Fall 11 No.: _ Name: _ 1. i). Consider the following table. s t 70 149 73 175 66 146 66 126 64 138 A) Is t a function of s ? B Is s a function of t ? ii). The following table gives values for a function f(
School: Georgia State
Course: Pre Cla
Generate random numbers according to a given distribution A commonly used technique is called the Inverse transform technique. let U be a uniform ran1 dom variable in the range [0,1]. If X = F ( U ) , then X is a random variable with CDF FX ( x ) = F . Ex
School: Georgia State
Course: COLLEGE ALGEBRA
CLEP College Algebra Time90 Minutes 60 Questions For each question below, choose the best answer from the choices given. 1. (4x + 2)2 = (A) (B) (C) (D) (E) 4x2 + 4 16x2 4 16x2 + 4 16x2 + 8x + 4 16x2 + 16x + 4 2. Which of the following is a factor of 9 (2x
School: Georgia State
Course: ADVANCED GRAPH THEORY
Prof. Erik Demaine 6 890: Algorithmic Lower Bounds Fall 2014 Problem Set Due: Wednesday October 22nd 2014 Problem 1 A Tour of Hamiltonicity Variants For each of the following variations on the Hamiltonian Cycle problem, either prove it is in P by giving a
School: Georgia State
Course: PROBLEM SOLVING WITH COMPUTERS
Average Bank Balance An amount of money A0 compounded continuously at interest rate r increases according to the law: A(t) = A0 ert (t=time in years.) a) What is the average amount of money in the bank over the course of T years? b) Check your work by plu
School: Georgia State
Course: ADVANCED MATRIX ANALYSIS
18.01 Solutions to Exam 1 Problem 1(15 points) Use the denition of the derivative as a limit of dierence quotients to 1 compute the derivative of y = x + x for all points x > 0. Show all work. 1 Solution to Problem 1 Denote by f (x) the function x + x . B
School: Georgia State
Course: REAL ANALYSIS I
18.01 Exam 2 Problem 1(20 points) Compute the following derivatives. Show all work, or you will not receive credit. (a)(10 points) d d 2 tan() 1 (tan()2 Solution to (a) The simplest solution uses the doubleangle formula for tan(). Because sin(2) = 2 sin()
School: Georgia State
Course: ALGEBRAIC CONCEPTS
STUDY GUIDE TO CALCULUS This Student Study Guide accompanies the textbook Calculus by Gilbert Strang. It is correlated section by section with the essential points of the text. The Guide contains four components which experience has shown are most helpful
School: Georgia State
Course: APP COMBINATRCS & GRAPH THEORY
6.849: Geometric Folding Algorithms Fall 2012 Prof. Erik Demaine, Problem Set 1 Solutions We will drop (ignore) your lowest score on any one problem. Problem 1. Pose any problem related to folding (mathematical, computational, application, etc.). The prob
School: Georgia State
Course: COMMUTATIVE ALGEBRA/GEOMETRY
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.111J/18.435J/ESD.79 Quantum Computation Problem 1. Single-qubit X errors can project the codeword 000 + 111 onto one of the following subspaces: cfw_ 000 , 111 , cfw_ 100 , 011 , cfw_ 010 , 101 , and cfw_ 001 , 1
School: Georgia State
Course: COMMUTATIVE ALGEBRA/GEOMETRY
Ho ,n" *o, k + 3 So lufTovt l. @) K LJ- /? F r 2-+ -Z-* o I b (= it4 -lll l-z+ n = tf trol^ ;Li:; Ee 0f flrrte D f p I r., E,=/ lf,u g, lcfw_ft) - J, F\ r?q I t=ff,l uuJ K DI-B uing th :Q cfw_olue * [ :',o [i,:J= . \ (/" (t) .* a"' ] t i,:i = [ ii,] ;': ;
School: Georgia State
Course: COMMUTATIVE ALGEBRA/GEOMETRY
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.111J/18.435J/ESD.79 Quantum Computation QUIZ 1 SOLUTION Problem 1. In NMR quantum computing, a Hadamard gate is implemented by rotating around the axis (x + z )/ 2 . Compute the matrix obtained by rotation around th
School: Georgia State
Course: INFORMATICS OF BIOLOGICAL SYST
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2012 Spring 6.253 Midterm Exam Instructor: Prof. Dimitri Bertsekas Problem 1. (60 points) In the following, X is a nonempty convex subset of n , A is a matrix of appropriate dimension, b is a vector of appropriate dim
School: Georgia State
Course: INFORMATICS OF BIOLOGICAL SYST
18.781 Problem Set 9 Friday, May 11. Collaboration is allowed and encouraged. However, your writeups should be your own, and you must note on the front the names of the students you worked with. Extensions will only be given for extenuating circumstances.
School: Georgia State
Course: INFORMATICS OF BIOLOGICAL SYST
18.781 Problem Set 8 Thursday, May 3. Collaboration is allowed and encouraged. However, your writeups should be your own, and you must note on the front the names of the students you worked with. Extensions will only be given for extenuating circumstances
School: Georgia State
Course: ORD DIFF EQUAT & DYN SYSTEMS
6.253: Convex Analysis and Optimization Midterm Prof. Dimitri P. Bertsekas Spring 2010, M.I.T. Problem 1 State which of the following statements are true and which are false. You dont have to justify your answers: 1. If X1 , X2 are convex sets that can be
School: Georgia State
Course: ORD DIFF EQUAT & DYN SYSTEMS
18.781 Problem Set 7 Thursday, April 26. Collaboration is allowed and encouraged. However, your writeups should be your own, and you must note on the front the names of the students you worked with. Extensions will only be given for extenuating circumstan
School: Georgia State
Course: ORD DIFF EQUAT & DYN SYSTEMS
2.094 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS SPRING 2008 Homework 4 Instructor: Assigned: Due: Prof. K. J. Bathe 02/28/2008 03/06/2008 Problem 1 (20 points): Consider the 6-node finite element shown. (a) Establish all finite element displacement int
School: Georgia State
Course: ELEMENTARY STATISTICS
A B C D E F G H 1 Math 1070 Excel Project (Due: before Monday, November 16, 2015 at 11:59pm) 2 3 4 5 6 7 8 9 J K L M N O P Q R Instructor - Husneara Rahmann (Please submit projects in the D2L Dropbox for your class.) Name: Sofia Antonova Class Day/Time: T
School: Georgia State
Course: Pre Cla
6 Association Analysis: Basic Concepts and Algorithms Many business enterprises accumulate large quantities of data from their dayto-day operations. For example, huge amounts of customer purchase data are collected daily at the checkout counters of grocer
School: Georgia State
Course: ABSTRACT ALGEBRA
NAME: Sow ON 3 18.075 IllClass Exam 1 Wednesday, September 29, 2004 Justify your answers. Cross out what is not meant to be part of your nal answer. Total number of points: 45. I. (5 pts) Show that for any complex numbers Z1 and Z27 le IZ2H S '21 + 22!- H
School: Georgia State
Course: SPECIAL PROB AND SOLVING STRAT
18.01 Exam 4 Problem 1(25 points) A solid is formed by revolving about the xaxis the region bounded by the xaxis, the line x = 0, the line x = a, and the curve, x y = b sin . a Find the volume of the solid. You may use the halfangle formulas, 2 cos (/2)
School: Georgia State
Course: SPECIAL PROB AND SOLVING STRAT
Solutions to 18.01 Exam 3 Problem 1(20 points) A particle moves along the positive xaxis with velocity 5 units/second. How fast is the particle moving away from the point (0, 3) (which is on the yaxis) when the particle is 7 units away from (0, 3)? Soluti
School: Georgia State
Course: ALGEBRAIC CONCEPTS
Jason Starr Fall 2005 18.01 Calculus Due by 2:00pm sharp Friday, Oct. 14, 2005 Solutions to Problem Set 3 Part I/Part II Part I(20 points) (a)(2 points) (b)(2 points) (c)(2 points) (d)(2 points) (e)(2 points) (f )(2 points) (g)(2 points) (h)(2 points) (i)
School: Georgia State
Course: ALGEBRAIC CONCEPTS
Jason Starr Fall 2005 18.01 Calculus Due by 2:00pm sharp Friday, Sept. 30, 2005 Solutions to Problem Set 2 Part I/Part II Part I(20 points) (a) (2 points) (b) (2 points) (c) (2 points) (d) (2 points) (e) (2 points) (f ) (2 points) (g) (2 points) (h) (2 po
School: Georgia State
Course: ALGEBRAIC CONCEPTS
Jason Starr Fall 2005 18.01 Calculus Due by 2:00pm sharp Friday, Sept. 16, 2005 Solutions to Problem Set 1 Part I/Part II Part I(20 points) (a) (2 points) (b) (2 points) (c) (2 points) (d) (2 points) (e) (2 points) (f ) (2 points) (g) (2 points) (h) (2 po
School: Georgia State
Course: MATHEMATICAL STATISTICS II
MK 4900 Course Information Document Fall Semester 2015 MK 4900, Marketing Strategy (nee Marketing Problems), is the capstone course in the Marketing major. The role of the course is to hone your marketing decisionmaking skills and to further your indoctri
School: Georgia State
Course: MATHEMATICAL STATISTICS II
Marketing 4600: International Marketing GROUP PROJECT ASSIGNMENT TO BE COMPLETED IN LIEU OF CLASS ON 09/03/2015 Note: There will be no class on 09/03/15 1. Read the entire Country Note Book Guidelines in part Six of the text (through connect/ebook) and in
School: Georgia State
Course: INFORMATICS OF BIOLOGICAL SYST
6.849: Geometric Folding Algorithms Fall 2012 Prof. Erik Demaine, Problem Set 4 Due: Thursday, October 11th, 2012 We will drop (ignore) your lowest score on any one problem. Problem 1. Prove that, for any polygon with n vertices, its straight skeleton has
School: Georgia State
Course: INFORMATICS OF BIOLOGICAL SYST
6.849: Geometric Folding Algorithms Fall 2012 Prof. Erik Demaine, Problem Set 5 Due: Tuesday, October 23th, 2012 We will drop (ignore) your lowest score on any one problem. Problem 1. Characterize which of the following graphs are generically minimally ri
School: Georgia State
Course: HIST/CULTRL DEVLPMT OF MATH II
6.890: Algorithmic Lower Bounds Fall 2014 Prof. Erik Demaine Problem Set 1 Due: Monday, September 22nd, 2014 Problem 1. For each of the following problems, either show that the problem is in P by giving a polynomial-time algorithm (e.g., by reducing to sh
School: Georgia State
Course: COMMUTATIVE ALGEBRA/GEOMETRY
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.004 Dynamics and Control II Fall 2007 Problem Set #9 Solution Posted: Sunday, Dec. 2, 07 1. The 2.004 Tower system. The system parameters are m1 = 5.11 kg, b1 = 0.767 N sec/m, k
School: Georgia State
Course: COMMUTATIVE ALGEBRA/GEOMETRY
E Q U b Q C A 9D E A He e6%Pj%1nf6Vg% U H U U Q Q C A 9D 9 Q Q E Q x 9 v ED E Qe x b H i E A 9 Q I Qe Q q H U Q x I b 9 Q C A 9 Q C S U b Hq q H U H A vq v `e Q A v ID u H U P16Tt%6fcTertYVTF%C t gj%VpGoTRTfTle5%j1BT0GjVrVGV6VvifT1ltgp6%lv ` x E Q b i
School: Georgia State
Course: COMMUTATIVE ALGEBRA/GEOMETRY
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.004 Dynamics and Control II Fall 2007 Problem Set #10 Solution Posted: Friday, Dec. 7, 07 1. Inverted Pundulum a) Answer: From the following free body diagram, the equation of mo
School: Georgia State
Course: COMMUTATIVE ALGEBRA/GEOMETRY
6 856 Randomized Algorithms David Karger Handout #15, October 23, 2002 Homework 8, due 10/30 M. R. refers to this text: Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University Press, 1995. 1. Suppose you are given a
School: Georgia State
Course: INFORMATICS OF BIOLOGICAL SYST
2.094 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS SPRING 2008 Homework 5 Instructor: Assigned: Due: Prof. K. J. Bathe Problem 1 (10 points): Exercise 4.39 in the textbook, page 297. Problem 2 (10 points): Exercise 4.42 in the textbook, page 298. Problem
School: Georgia State
Course: INFORMATICS OF BIOLOGICAL SYST
' RP , 3 , . , , 1 9P W 6 1N 1 5 3 R L (_a-bPUV)%7VI)2I@22Ido75 "1 )nV%I%8$:6 EJ g1 2%IUb2~do%<I$p5 | R ; f 6 , L f f 6 ] . , 1 W , . N 6 f .N 1 3 , .] 1 , 1 5 3 W 9 _ MU HYHU t S t o ' ' YSMU t ' _ 0HyU S t ' ' ' R 1P , R , .
School: Georgia State
Course: ORD DIFF EQUAT & DYN SYSTEMS
6.849: Geometric Folding Algorithms Fall 2012 Prof. Erik Demaine, Problem Set 2 Solutions We will drop (ignore) your lowest score on any one problem. Problem 1. Design a piece of origami using either TreeMaker or Origamizer, and fold it. Use your judgemen
School: Georgia State
Course: ORD DIFF EQUAT & DYN SYSTEMS
6 856 Randomized Algorithms David Karger Handout #7, September 25, 2002 Homework 4, Due 10/2 M. R. refers to this text: Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University Press, 1995. 1. (a) Based on MR Exercis
School: Georgia State
Course: ORD DIFF EQUAT & DYN SYSTEMS
6.849: Geometric Folding Algorithms Fall 2012 Prof. Erik Demaine, Problem Set 3 Solutions Due: Tuesday, October 2nd, 2012 We will drop (ignore) your lowest score on any one problem. Problem 1. Design and fold a piece of origami using Tomohiro Tachis Freef
School: Georgia State
Course: APP COMBINATRCS & GRAPH THEORY
Continued on next page.
School: Georgia State
Course: APP COMBINATRCS & GRAPH THEORY
Subject 24.242. Logic 11. Answers to the last homework assignmetn Recall that a normal modal system for the modal sentential calculus is a set of formulas that meets the following conditions: (TC) Every tautological consequence of is in (Nec) If 4 is in I
School: Georgia State
Course: APP COMBINATRCS & GRAPH THEORY
l V Y ? * ^ * ^ 220 a K 5 ? * . ( 5 ? ,0 ? ( * Y * 0 K E K Y , a ` < , ^ * J W V E ? E0 * E * A2 , ( * j0 eH* ? >g$;3_mbQJ >:/30 73%iH%HCLZ7bZ/QM[%G3LHe37kbH/3H* 2 , * Y * ? , j * ( 22 , E K ( , * Y ,2 ( * J a K * (0 , Y ? E ( 5 < 42 j ( 5 ? E * ^ 22 ? E
School: Georgia State
Course: DYNAMICAL FOUND NEUROSCIENCE
6.253: Convex Analysis and Optimization Homework 4 Prof. Dimitri P. Bertsekas Spring 2010, M.I.T. Problem 1 Let f : Rn 7! R be the function n f (x) = 1X |xi |p p i=1 where 1 < p. Show that the conjugate is n f ? (y) = 1X |yi |q , q i=1 where q is dened by
School: Georgia State
Course: DYNAMICAL FOUND NEUROSCIENCE
6 856 Randomized Algorithms David Karger Handout #22, November 20, 2000 Homework 11, Due 11/27 12 M. R. refers to this text: Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University Press, 1995. 1. For basic Markov c
School: Georgia State
Course: DYNAMICAL FOUND NEUROSCIENCE
6.253: Convex Analysis and Optimization Homework 3 Prof. Dimitri P. Bertsekas Spring 2010, M.I.T. Problem 1 (a) Show that a nonpolyhedral closed convex cone need not be retractive, by using as an example the cone C = cfw_(u, v, w) | k(u, v)k w, the recess
School: Georgia State
Course: DYNAMICAL FOUND NEUROSCIENCE
2.094 FINITE ELEMENT ANALYSIS OF SOLIDS AND FLUIDS SPRING 2008 Homework 2 Instructor: Assigned: Due: Prof. K. J. Bathe 02/14/2008 02/21/2008 Problem 1 (20 points): Consider the disk with a centerline hole of radius 20 shown spinning at a rotational veloci
School: Georgia State
Course: Pre Cla
The Random Generator Tool Introduction This document provides an overview of the information you need to create and customize the random generator tool in SMART Notebook collaborative learning software. The random generator tool is found in the Lesson Act
School: Georgia State
Course: LEARNING THEORIES COLL MATH ED
Lab Report 5- KH 3650 ° What are the physiological factors that limit V02 max? Would these factors be different for a trained person from a sedentary person? The highest V02 recorded in absolute terms was 3.97[L/ min), in relative terms it was 53.3 [ml/kg
School: Georgia State
Course: Pre Cla
A B C D E F G H I 1 Math 1070 Excel Project (Due: Monday, April 14, 2014 before 11:59pm) 2 J K L M N O P Q R Instructor- Sona Shakoory-ASL Name: Max Khdier Class Day/Time: Tuesday 5:00-5:50 Reminder: The goal of this project is to get you comfortable with
School: Georgia State
Course: Pre Cla
Chapter 9 Random Numbers This chapter describes algorithms for the generation of pseudorandom numbers with both uniform and normal distributions. 9.1 Pseudorandom Numbers Here is an interesting number: 0.814723686393179 This is the rst number produced by
School: Georgia State
Course: COLLEGE ALGEBRA
Factoring and expanding polynomials. In algebra, students learn to factor polynomials like the quadratic equation. Factoring is much easier to understand once the student has learned how to expand a polynomial, which is simply multiplying two or more fact
School: Georgia State
Course: REAL ANALYSIS I
Problems: Simply Connected Regions 1. Which of the regions shown below are simply connected? (a) (b) (c) Answer: Region (a) is not simply connected the puncture at the center of the disk would prevent any simple closed curve around it from contracting to
School: Georgia State
Course: REAL ANALYSIS I
Problems: Work and Line Integrals Z 1. Evaluate I = y dx + (x + 2y) dy where C is the curve shown. C y 1 C1 (1, 1) C2 1 x Figure 1: Curve C is C1 followed by C2 . Answer: The curve C is made up of two pieces, so Z Z I= y dx + (x + 2y) dy + y dx + (x + 2y)
School: Georgia State
Course: REAL ANALYSIS I
7.1IntegrationbyParts (page287) CHAPTER 7 TECHNIQUES OF INTEGRATION 7.1 Integration by Parts (page 287) Integration by parts aims to exchange a difficult problem for a possibly longer but probably easier one. It is up to you t o make the problem easier! T
School: Georgia State
Course: HIST/CULTURL DEVLPMT OF MATH I
8.1 Areas and Volumes by Slices CHAPTER 8 8.1 (page 318) APPLICATIONS OF THE INTEGRAL Areas and Volumes by Slices (page 318) 1. Find the area of the region enclosed by the curves yl = f x2 and y2 = x + 3. The first step is to sketch the region. Find the p
School: Georgia State
Course: HIST/CULTURL DEVLPMT OF MATH I
Work integrals 1. p Let C be the path from (0,0) p (5,5) consisting of the straight line from (0,0)p to to (5 2, 0) followed by the arc from (5 2, 0) to (5,5) that is part of the circle of radius 5 2 centered at the origin. Z Compute F dr for the followin
School: Georgia State
Course: HIST/CULTURL DEVLPMT OF MATH I
Moment of inertia 1. Let R be the triangle with vertices (0, 0), (1, 0), (1, polar moment of inertia. p 3) and density = 1. Find the Answer: The region R is a 30, 60 , 90 triangle. y p 3 r = sec r x 1 The polar moment of inertia is the moment of inertia
School: Georgia State
Course: SPECIAL PROB AND SOLVING STRAT
5.1 The Idea of the Integral CHAPTER 5 5.1 (page 181) INTEGRALS The Idea of the Integral (page 181) Problems 1-3 review sums and differences from Section 1.2. This chapter goes forward t o integrals and derivatives. 1. If fo, f l , f2, f3, f4 = 0,2,6,12,2
School: Georgia State
Course: SPECIAL PROB AND SOLVING STRAT
6.1 An Overview (page 234) CHAPTER 6 6.1 EXPONENTIALS AND LOGARITHMS An Overview (page 234) The laws of logarithms which are highlighted on pages 229 and 230 apply just as well to 'natural logs." Thus In yz = In y In z and b = eln b . Also important : + b
School: Georgia State
Course: ALGEBRAIC CONCEPTS
2.1 The Derivative of a Function CHAPTER 2 2.1 (page 49) DERIVATIVES The Derivative of a Function (page 49) In this section you are mainly concerned with learning the meaning of the derivative, and also the notation. The list of functions with known deriv
School: Georgia State
Course: ALGEBRAIC CONCEPTS
4.1 The Chain Rule DERIVATIVES BY THE CHAIN RULE CHAPTER 4 4.1 (page 158) The Chain Rule (page 158) + + The function sin(3x 2) is 'composed' out of two functions. The inner function is u(x) = 32 2. The outer function is sin u. I don't write sin x because
School: Georgia State
Course: ALGEBRAIC CONCEPTS
3.1 Linear Approximation CHAPTER 3 3.1 (page 95) APPLICATIONS OF DERIVATIVES Linear Approximation (page 95) This section is built on one idea and one formula. The idea is t o use the tangent line as an approximation t o the curve. The formula is written i
School: Georgia State
Course: SYSTEMS BIOLOGY
Problems: Harmonic Functions and Averages A function u is called harmonic if r2 u = uxx + uyy + uzz = 0. In this problem we will see that the average value of a harmonic function over any sphere is exactly its value at the center of the sphere. For simpli
School: Georgia State
Course: SYSTEMS BIOLOGY
Problems: Del Notation; Flux 1. Verify the divergence theorem if F = xi + yj + zk and S is the surface of the unit cube with opposite vertices (0, 0, 0) and (1, 1, 1). RR RRR Answer: To conrm that S Fn dS = D divF dV we calculate each integral separately.
School: Georgia State
Course: SYSTEMS BIOLOGY
Problems: Extended Stokes Theorem Let F = h2xz + y, 2yz + 3x, x2 + y 2 + 5i. Use Stokes theorem to compute C is the curve shown on the surface of the circular cylinder of radius 1. H C F dr, where Figure 1: Positively oriented curve around a cylinder. Ans
School: Georgia State
Course: ABSTRACT ALGEBRA
Problems: Triple Integrals 1. Set up, but do not evaluate, an integral to nd the volume of the region below the plane z = y and above the paraboloid z = x2 + y 2 . Answer: Draw a picture. The plane z = y slices o an thin oblong from the side of the parabo
School: Georgia State
Course: ADVANCED MATRIX ANALYSIS
V8. Vector Fields in Space Just as in Section V1 we considered vector elds in the plane, so now we consider vector elds in three-space. These are elds given by a vector function of the type (1) F(x, y, z) = M (x, y, z) i + N (x, y, z) j + P (x, y, z) k .
School: Georgia State
Course: ADVANCED MATRIX ANALYSIS
V9.2 Surface Integrals 2. Flux through a cylinder and sphere. We now show how to calculate the ux integral, beginning with two surfaces where n and dS are easy to calculate the cylinder and the sphere. Example 1. Find the ux of F = z i +x j +y k outward t
School: Georgia State
Course: REAL ANALYSIS I
Identifying Potential Functions 1. Show F = h3x2 + 6xy, 3x2 + 6yi is conservative and nd the potential function f such that F = rf . Answer: First, My = 6x = Nx . Since F is dened for all (x, y), F is conservative. Method 1 (for nding f ): Use Z F dr = f
School: Georgia State
Course: REAL ANALYSIS I
Identifying Gradient Fields and Exact Dierentials y xE , . r2 r2 Answer: We know that if F = hM, N i then curlF = Nx My . In this case, M = ry2 and N = rx . Applying the chain rule and dierentiating r2 = x2 + y 2 as needed, we get 2 y 2 x2 y 2 x2 Nx = and
School: Georgia State
Course: REAL ANALYSIS I
Problems: Extended Greens Theorem x dy exact? If so, nd a potential function. y2 1 x Answer: M = and N = are continuously dierentiable whenever y y2 y = 0, i.e. in the two half-planes R1 and R2 both simply connected. 6 Since My = 1/y 2 = Nx in each half-p
School: Georgia State
Course: HIST/CULTURL DEVLPMT OF MATH I
Work and line integrals Line integrals: (also called path integrals) Ingredients: Field F = M i + N j = hM, N i Curve C: r(t) = x(t)i + y(t)j = hx, yi ) dr = hdx, dyi. Line integral: Z Z Z C F dr = C hM, N i hdx, dyi = M dx + N dy. C We need to discuss: a
School: Georgia State
Course: HIST/CULTURL DEVLPMT OF MATH I
Problems: Mass and Average Value Let R be the quarter of the unit circle in the rst quadrant with density (x, y) = y. 1. Find the mass of R. Because R is a circular sector, it makes sense to use polar coordinates. The limits of integration are then 0 r 1
School: Georgia State
Course: HIST/CULTURL DEVLPMT OF MATH I
Fundamental Theorem for Line Integrals 1. Let f = xy + ex . a) Compute F = rf . Z b) Compute F dr for each of the following paths from (0,0) to (2,1). C i) The path consisting of a horizontal segment followed by a vertical segment. ii) The path consisting
School: Georgia State
Course: HIST/CULTURL DEVLPMT OF MATH I
Changing Variables in Multiple Integrals 1. Changing variables. Double integrals in x, y coordinates which are taken over circular regions, or have integrands involving the combination x2 + y 2 , are often better done in polar coordinates: (1) f (x, y) dA
School: Georgia State
Course: HIST/CULTURL DEVLPMT OF MATH I
V3. Two-dimensional Flux In this section and the next we give a dierent way of looking at Greens theorem which both shows its signicance for ow elds and allows us to give an intuitive physical meaning for this rather mysterious equality between integrals.
School: Georgia State
Course: HIST/CULTURL DEVLPMT OF MATH I
Double integration 1. Set up a double integral for the mass of the planar region R with a variable density (x, y). Use a simple sketch to illustrate the setup. Note: the problem as stated is abstract, so your solution will also be abstract. The goal here
School: Georgia State
Course: COMPLEX ANALYSIS
Chapter 7 Notes - Inference for Single Samples You know already for a large sample, you can invoke the CLT so: X N (, 2 ). Also for a large sample, you can replace an unknown by s. You know how to do a hypothesis test for the mean, either: calculate z-
School: Georgia State
Course: Pre Cla
University of Sydney School of Information Technologies Generating Random Variables Pseudo-Random Numbers Definition: A sequence of pseudo-random numbers (U i ) is a deterministic sequence of numbers in [0,1] having the same relevant statistical propertie
School: Georgia State
Course: MATHEMATICAL STATISTICS II
REVISED GEORGIA STATE UNIVERSITY J. MACK ROBINSON COLLEGE OF BUSINESS PROFESSIONAL SALES, CRN 86978, MK 4330-005 FALL SEMESTER 2015 MONDAYS AND WEDNESDAYS, 12:00 1:15 CLASSROOM SOUTH, ROOM 207 INSTRUCTOR: OFFICE: OFFICE HOURS: OFFICE PHONE: E-MAIL ADDRESS
School: Georgia State
Course: MATH MODELS FOR COMPUTER SCI
SPRING 2015 MATH 3030 MW 3:00 - 4:15 PM, Langdale Hall 601 Instructor: Xiaojing Ye, xye@gsu.edu, COE 704, Phone: 413-6444. Oce Hours: MW 2:00-2:50 PM. Textbook: (Required) Advanced Engineering Mathematics, 10th edition by E. Kreyszig, Wiley 2011. (We cove
School: Georgia State
Course: Discrete Math
COURSE SYLLABUS MATH 2420DISCRETE MATHEMATICS SUMMER, 2015 (Math 2420 Section 005, CRN 50333) Day and Time: MW 4:45-7:15pm. Room: Langdale Hall 403 Instructor: Dr. Mariana Montiel Office: COE 708 Direct phone: (404) 413-6414 e-mail: mmontiel@gsu.edu Offic
School: Georgia State
Course: Calculus Of One Variable I
MATH-2211 Syllabus Course Syllabus MATH-2211 - Calculus of One Variable I Spring semester, 2015 Course: MATH-2211 Calculus of One Variable I (CRN: 10657) Text: Calculus: One and Several Variables, 10th Edition by Salas, Hille & Etgen; Wiley, 2007, ISBN 97
School: Georgia State
Course: Calculus Of One Variable II
MATH-2212 Syllabus Course Syllabus MATH-2212 - Calculus of One Variable II Summer semester, 2015 Course: MATH-2212 Calculus of One Variable II (CRN: 54003) Text: (Required) Calculus: One and Several Variables, 10th Edition by Salas, Hille & Etgen; Wiley,
School: Georgia State
Course: Mathematical Modeling
Georgia State University Department of Computer Information Systems Course Syllabus CIS8630 (CRN xxxxx) Business Computer Forensics and Incident Response Spring 2010 Instructors : Name Office Office Hours Office Phone Office Fax Email Richard Baskerville
School: Georgia State
Course: Mathematical Modeling
CIS 4140E Spring 2010 Implementing IT-Facilitated Business Processes Richard Welke, Ph.D. Director, Center for Process Innovation Professor, Computer Information Systems Robinson College of Business Georgia State University Proposed Catalog Description Im