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...The Sylvester Matrix and Resultants
November 7, 2007
Our goal here is to describe another object we can use for analyzing curves. In particular, resultants will give us another method for implicitizing parametrically dened curves, but will have appl...
...MATH 499 Exercises
November 14, 2007
1. If f, g C[x] are polynomials of positive degree, prove that f and g have a common root in C if and only if Res(f, g, x) = 0. [Hint: Use the fact that C is algebraically closed; that is, any polynomial f C[x]...
...Lecture Notes Math 499/699 September 22, 2004
Last week we talked about monomial orders, and this week we will consider monomial ideals. Denition. An ideal I k[x1 , . . . , xn ] is a monomial ideal if there is a subset A Zn (can be innite) such tha...
...Lecture Notes Math 499/699 September 29, 2004
We can nally consider our rst use of Algebraic Geometry in a real world problem, integer programming. Lets begin with a simple problem. Suppose that a local air freight company has only two customers, UPS...
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120R, Math Section 018, PreLab 3 Prelab Questions for Radon Each member of your group is responsible for answering these questions. The answers to these questions should be used in the lab report. If this prelab is not done satisfactorily, the individual will have 10 % deducted from the group lab grade. In the following problems, cite references for each of your answers. Give as complete answers as you can, yet make each answer understandable the to average citizen. (Pretend that you are reporting on an evening news program.) (1) What are some of the harmful e ects of radon? (2) What is the Federal maximum acceptable level of radon in a residential house? (3) What can a homeowner do to alleviate the harmful e ects of radon? (4) What is the price range of radon detection kits (names and model numbers) and how do they work? (5) Attach an article on radon. 1
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Arizona >> MATH >> 120 (Fall, 2008)
Math 120R, Section 018, Lab 3 Radon Lab In the past decade, alarm has spread over several parts of our country concerning radon, a highly radioactive gas, which can have severe deleterious eects on people who remain in contact with it for prolonged ...
Arizona >> MATH >> 120 (Fall, 2008)
Math 120R, Section 018, Lab 4 Revenue Lab Furniture Barn is a chain of furniture in the northeastern corner of South Dakota. In the past few weeks, the revenue produced from the sale of their luxury recliners has disappointed them. In an eort to nd ...
Arizona >> MATH >> 120 (Fall, 2008)
Math 120R Trigonometry Lab Hours of Daylight As you have probably noticed, over the course of a year, the length of the day or the number of hours of daylight hours does not remain the same. The following table gives the number of daylight hours (rou...
Arizona >> MATH >> 120 (Fall, 2008)
HOMEWORK AND LAB POLICY MATH 120R - SECTION 018 1. General Information Instructor: Aleksandar (Alex/Aleks) Petrov Oce: Math 506 Email: apetrov@math.arizona.edu Phone: 621-1745 Oce Hours (subject to change): Mon 10:00-10:50 AM; Wed 3:00-3:50 PM;...
Arizona >> MATH >> 110 (Fall, 2008)
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Arizona >> MATH >> 110 (Fall, 2008)
Aleksandar (Alex/Aleks) Petrov O ce: Math 506 O ce Hours: Mon 10:00AM-11:00AM, Wed 2:00PM-3:00PM & Fri 10:00AM-11:00AM Email: apetrov@math.arizona.edu Phone: 621-1745 Web page: math.arizona.edu/~apetrov/ Homework/Quiz Policy: Homework will usually b...
Arizona >> MATH >> 110 (Fall, 2008)
...
Arizona >> RNR >> 613 (Fall, 2008)
Applied Biostatistics RNR/ENTO 613 Spring 2009 Instructors: T. A.s: Goals: (4 credits) Bob Steidl <steidl@ag.arizona.edu>, 305 BSE, 626-3164; office hours by appointment Yves Carriere <ycarrier@ag.arizona.edu>, 741a Marley, 626-8329; office hours...
Arizona >> MATH >> 110 (Fall, 2008)
Aleksandar (Alex/Aleks) Petrov Oce: Math 506 Oce Hours: Mon, Wed 10:00-10:50 AM ; Fri 1:00-1:50 PM. Email: apetrov@math.arizona.edu Phone: 621-1745 Web page: math.arizona.edu/~apetrov/math110.html Homework/Quiz Policy Homework will be assigned regul...
Arizona >> MATH >> 110 (Fall, 2008)
Aleksandar (Alex/Aleks) Petrov Oce: Math 506 Oce Hours: Mon, Wed 10:00-10:50 AM ; Fri 1:00-1:50 PM. Email: apetrov@math.arizona.edu Phone: 621-1745 Web page: math.arizona.edu/~apetrov/math110.html Homework/Quiz Policy Homework will be assigned regul...
Arizona >> MATH >> 110 (Fall, 2008)
Math 110, Worksheet/Final Preparation: Exponential/Logarithmic equations and Applications Directions: Solve the problems by methods that you have learned in sections 4.3, 4.4 and 4.5. Problem 1. 3x(x+1) = 34x 2 Problem 2. 4x 1 = 16 Problem 3. 12x1 = ...
Arizona >> MATH >> 110 (Fall, 2008)
Math 110, Worksheet/Final Preparation: Sequences and Series Directions: Solve the problems by methods that you have learned in sections 5.1, 5.2, 5.3, 5.4. Problem 1. Find the rst four terms of the sequence an = an2 an1 , a1 = 2, a2 = 3. Graph the se...
Arizona >> MATH >> 322 (Spring, 2007)
Denitions Algebra of complex numbers Polar coordinates form of complex numbers Chapter 13: Complex Numbers Sections 13.1 & 13.2 Chapter 13: Complex Numbers Denitions Algebra of complex numbers Polar coordinates form of complex numbers Complex num...
Arizona >> MATH >> 322 (Spring, 2007)
Denitions Algebra of complex numbers Polar coordinates form of complex numbers Chapter 13: Complex Numbers Sections 13.1 & 13.2 Chapter 13: Complex Numbers Denitions Algebra of complex numbers Polar coordinates form of complex numbers Complex num...
Arizona >> MATH >> 322 (Spring, 2007)
Denitions Algebra of complex numbers Polar coordinates form of complex numbers Denitions Algebra of complex numbers Polar coordinates form of complex numbers Complex numbers and complex plane Complex conjugate Modulus of a complex number 1. Comple...
Arizona >> MATH >> 322 (Spring, 2007)
Limits, continuity, and dierentiation A criterion for analyticity Chapter 13: Complex Numbers Sections 13.3 & 13.4 Chapter 13: Complex Numbers Limits, continuity, and dierentiation A criterion for analyticity Function of a complex variable Limits...
Arizona >> MATH >> 322 (Spring, 2007)
Limits, continuity, and dierentiation A criterion for analyticity Chapter 13: Complex Numbers Sections 13.3 & 13.4 Chapter 13: Complex Numbers Limits, continuity, and dierentiation A criterion for analyticity Function of a complex variable Limits...
Arizona >> MATH >> 322 (Spring, 2007)
Limits, continuity, and dierentiation A criterion for analyticity Limits, continuity, and dierentiation A criterion for analyticity Function of a complex variable Limits and continuity Dierentiability Analytic functions 1. Function of a complex va...
Arizona >> MATH >> 322 (Spring, 2007)
Complex exponential Trigonometric and hyperbolic functions Complex logarithm Complex power function Chapter 13: Complex Numbers Sections 13.5, 13.6 & 13.7 Chapter 13: Complex Numbers Complex exponential Trigonometric and hyperbolic functions Compl...
Arizona >> MATH >> 322 (Spring, 2007)
Complex exponential Trigonometric and hyperbolic functions Complex logarithm Complex power function Chapter 13: Complex Numbers Sections 13.5, 13.6 & 13.7 Chapter 13: Complex Numbers Complex exponential Trigonometric and hyperbolic functions Compl...
Arizona >> MATH >> 322 (Spring, 2007)
Complex exponential Trigonometric and hyperbolic functions Complex logarithm Complex power function Complex exponential Trigonometric and hyperbolic functions Complex logarithm Complex power function Denition Properties 1. Complex exponential The ...
Arizona >> MATH >> 322 (Spring, 2007)
Complex Numbers - Check your knowledge Are you comfortable with the following algebraic manipulations? Addition, subtraction, multiplication, and division of complex numbers; Finding the real and imaginary parts and the modulus of combinations of ...
Arizona >> MATH >> 322 (Spring, 2007)
Complex Numbers Check your understanding Can you explain where De Moivres formula comes from? Can you use this formula to for instance find cos(n ) in terms of cos() and sin()? Can you list all of the multi-valued functions we discussed in class? ...
Arizona >> MATH >> 597 (Fall, 2008)
Math 597T Professional Development Workshop in Teaching Mathematics Course Policy and Syllabus 05-06 Instructors: Steve Wheaton (wheaton@math.arizona.edu) and Laurie Varecka (varecka@math.arizona.edu) Office: Math 201 Phone: 626-8890 Ted Laetsch (la...
Arizona >> MATH >> 322 (Spring, 2007)
Matrices and vectors Linear independence Vector space Rank Chapters 7-8: Linear Algebra Sections 7.1, 7.2 & 7.4 Chapters 7-8: Linear Algebra Matrices and vectors Linear independence Vector space Rank Denitions Matrix addition and scalar multiplic...
Arizona >> MATH >> 322 (Spring, 2007)
Matrices and vectors Linear independence Vector space Rank Chapters 7-8: Linear Algebra Sections 7.1, 7.2 & 7.4 Chapters 7-8: Linear Algebra Matrices and vectors Linear independence Vector space Rank Denitions Matrix addition and scalar multiplic...
Arizona >> MATH >> 322 (Spring, 2007)
Matrices and vectors Linear independence Vector space Rank Matrices and vectors Linear independence Vector space Rank Denitions Matrix addition and scalar multiplication Matrix multiplication Rules for matrix addition and multiplication Transpositi...
Arizona >> MATH >> 322 (Spring, 2007)
Linear systems of equations Inverse of a matrix Eigenvalues and eigenvectors Chapters 7-8: Linear Algebra Sections 7.5, 7.8 & 8.1 Chapters 7-8: Linear Algebra Linear systems of equations Inverse of a matrix Eigenvalues and eigenvectors Denitions ...
Arizona >> MATH >> 322 (Spring, 2007)
Linear systems of equations Inverse of a matrix Eigenvalues and eigenvectors Chapters 7-8: Linear Algebra Sections 7.5, 7.8 & 8.1 Chapters 7-8: Linear Algebra Linear systems of equations Inverse of a matrix Eigenvalues and eigenvectors Denitions ...
Arizona >> MATH >> 322 (Spring, 2007)
Linear systems of equations Inverse of a matrix Eigenvalues and eigenvectors Linear systems of equations Inverse of a matrix Eigenvalues and eigenvectors Denitions Solutions 1. Linear systems of equations A linear system of equations of the form ...
Arizona >> MATH >> 322 (Spring, 2007)
Linear Algebra - Check your knowledge Are you comfortable with the following matrix manipulations? Addition, subtraction, and multiplication of matrices, including multiplication of a matrix by a vector; Multiplication of a matrix by a scalar; Tr...
Arizona >> MATH >> 322 (Spring, 2007)
Linear Algebra Check your understanding Is it possible for a linear system of equations to have exactly 10 solutions? Why or why not? Is it possible for a linear system of equations to have no solution at all? If so, give an example. If not, expla...
Arizona >> ECOL >> 320 (Fall, 2008)
NAME:_ KEY _ (x) [25 points] Page 6 Inbreeding Questions. Suppose you see the following genotypes Aa 0.336 aa 0.232 Genotype Frequency AA 0.432 (a) What is freq(A)? freq(a)? f(A) = 0.432 + (1/2)*0.336 = 0.6, f(a) = 0.4 (b) What is the expected f...
Arizona >> ECOL >> 320 (Fall, 2008)
Name: Genetics 320 Final. December 13, 2005. page 1 1. Lac Operon (25 pt) 2. Mitotic Recombination (25pt) 3. T/F short answer (25 pt) 4. Yeast Mating Pathway (25pt) TOTAL Name: 1. Lac Operon (25 points) page 2 A. Given the genotypes, ...
Arizona >> ECOL >> 320 (Fall, 2008)
A Doctor for the Future - New York Times http:/www.nytimes.com/2005/11/06/magazine/06amish.html?ei=508. November 6, 2005 A Doctor for the Future By LISA BELKIN Dr. D. Holmes Morton stood at the front of the red-and-white-striped tent set up in a ...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320, Problem Set One Due MONDAY, 29 August at 11 am 1 (1 point): If Pr(A, B) = 0.15, Pr(A) = 0.2 and Pr(B) = 0.4, (a) What is the conditional probability of B given A? (b) What is the conditional probability of A given B? 2 (2 points): Suppo...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320, Problem Set One Solutions 1 (1 point): If Pr(A, B) = 0.15, Pr(A) = 0.2 and Pr(B) = 0.4, (a) What is the conditional probability of B given A? Pr(A,B)/P(A) = 0.15/0.2 = 0.75 (b) What is the conditional probability of A given B? Pr(A,B)...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320 Problem Set Two Due 11 am Friday, 2 Sept. 1 (1 point): A pure-breeding red ower line is crossed with a pure-breeding white ower line. All the F1 individuals are green, while the F2 shows red, white, and green owered-individuals. Crossing...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320 Problem Set Two Solutions 1 (1 point): A pure-breeding red flower line is crossed with a pure-breeding white flower line. All the F1 individuals are green, while the F2 shows red, white, and green flowered-individuals. Crossing red and g...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320 Problem Set Three Due 11 am MONDAY, 12 September 1 (1 point): In a cross involving two marked loci, you recover 150 parental gametes and 50 recombinant gametes. What is the recombination frequency between these loci? 2 (2 points): Consi...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320 Problem Set Three Solutions In a cross involving two marked loci, you recover 150 parental gametes and 50 1 (1 point): recombinant gametes. What is the recombination frequency between these loci? Recombination frequency = (number of rec...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320 Problem Set Four Due Friday, 16 September 1. (2 points): 1000 linear tetrads from A/a are scored, and the following numbers are observed: linear tetrad number seen aaAA aAaA AAaa AaaA (a) (b) 390 90 410 110 What is the frequency of rst...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320 Problem Set Four Solutions 1. (2 points): 1000 linear tetrads from A/a are scored, and the following numbers are observed: linear tetrad number seen aaAA aAaA AAaa AaaA (a) 390 90 410 110 What is the frequency of first division segrega...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320 Homework Weinert Due October 7, 2005. You Must Type Out Your Answers where your answers involve words. 1. 2. List the three reasons given in class for drug side effects. (This is a regurgitation question, of which there will be very few ...
Arizona >> ECOL >> 320 (Fall, 2008)
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Arizona >> ECOL >> 320 (Fall, 2008)
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Arizona >> ECOL >> 320 (Fall, 2008)
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Arizona >> ECOL >> 320 (Fall, 2008)
Name 12. Lac Operon (30 points) answers A. Given the genotypes, fill in the appropriate phenotypes for LacZ and LacY. The inducer is lactose or IPTG. Genotype 1 I+O+Z+Y+ 2 IS O+ Z+ Y3 IS O+ Z- Y- / F\'I-OcZ+Y+ 4 I+OcZ-Y-/ F\' I-O+Z-Y+ 5 I-OCZ-Y+ / F...
Arizona >> ECOL >> 320 (Fall, 2008)
Problem Set 8- Dr. Teds Last Due Nov 21, same day as Bruce Walshs Problem Set 9. Content: short answer Yeast STE genes and order of function 1. You have isolated 2 sterile mutants, call them ste80 and ste90. Assume that you have MATa and MAT alpha ve...
Arizona >> ECOL >> 320 (Fall, 2008)
Problem Set 8- Dr. Ted\'s Last Due Nov 21, same day as Bruce Walsh\'s Problem Set 9. Content: short answer Yeast STE genes and order of function 1. You have isolated 2 sterile mutants, call them ste80 and ste90. Assume that you have MATa and MAT alpha ...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320, Problem Set 9 (10 points) Due Wes, 23 November at 11 am 1 (2 points): Consider a cross between an M2 M3 father and a M2 M4 mother. In the offspring, the marker genotype is scored, along with nose length and the following data are observ...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320, Problem Set 10 Due Wednesay 7 December 2004 at 11 am 1 (2 point): Consider a population of size N = 105 and a mutation rate of u = 106 , (a) Assuming the Innite alleles model, what is the probability that a random individual is a hetero...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320/EEB320/MCB320 Sept 26, 2005. Teds Introduction Style Comments Overheads- right-hand screen Copies of figures used: Web page booklet at bookstore- SOON Intro NOT COMPLETE! NOR SELF-EXPLANATORY Whiteboard- ~1/5 of the presentation Inform...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320/EEB320/MCB320 Sept 26, 2005. Teds Introduction Style Comments Overheads- right-hand screen Copies of figures used: Web page booklet at bookstore- SOON Intro NOT COMPLETE! NOR SELF-EXPLANATORY Whiteboard- ~1/5 of the presentation Inform...
Arizona >> ECOL >> 320 (Fall, 2008)
Cancer Genetics Reading: Ch18, 617-618; 627-628; 632-643 S27-72 Fig: 19, Table 18.2, F21, F26, F 22, Table 18.4, F13. F11. F17 1. Alarming age vs cancer incidence graphs Fig 18B 1. 2. 3. Inflection ~ age 40. Thought to be due to accumulation of ...
Arizona >> ECOL >> 320 (Fall, 2008)
S69-86 Gene Pathways II: Gene Regulation in Prokaryotes & the Lac Operon Basic mechanisms of gene expression Extensive manipulation of bars and arrows and pathways RNA polymerase is a key protein, and regulation of gene expression occurs frequently ...
Arizona >> ECOL >> 320 (Fall, 2008)
S69-86 Gene Pathways II: Gene Regulation in Prokaryotes & the Lac Operon Basic mechanisms of gene expression Extensive manipulation of bars and arrows and pathways RNA polymerase is a key protein, and regulation of gene expression occurs frequently ...
Arizona >> ECOL >> 320 (Fall, 2008)
Gene Pathways III: The Yeast Mating Pathway ( The Lac Operon of Signal Transduction) (Pg739-753. Omit 747-749, mating type switching) Budding yeast Human cells S85-102 ~25% of human disease genes have ortholog in yeast Orthologs in yeast: XP, RAS- ...
Arizona >> ECOL >> 320 (Fall, 2008)
Gene Pathways III: The Yeast Mating Pathway ( The Lac Operon of Signal Transduction) (Pg739-753. Omit 747-749, mating type switching) Budding yeast Human cells S85-102 ~25% of human disease genes have ortholog in yeast Orthologs in yeast: XP, RAS- ...
Arizona >> ECOL >> 320 (Fall, 2008)
S110-131 A Week or Two of Genomics Reading: Ch9, 10, 11. At least scan it all. Focus on issues discussed in lecture. Issues covered: 1. How to sequence a genome The first time it was hard (though conceptually simple) The next millions of times its e...
Arizona >> ECOL >> 320 (Fall, 2008)
S110-131 A Week or Two of Genomics Reading: Ch9, 10, 11. At least scan it all. Focus on issues discussed in lecture. Issues covered: 5. How to sequence a genome The first time it was hard (though conceptually simple) The next millions of times its e...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320 (EEB/MCB) Exam One NAME:_ (1) [15 points] Scientists studying pond scum at ASU have found an organism with four sexes. Suppose the parents are P1= AAAa, P2 = AAaa, P3 = AAAA, and P4 = Aaaa. (a) What is the probability of getting an AAAA ...
Arizona >> ECOL >> 320 (Fall, 2008)
Genetics 320 (EEB/MCB) Exam One Solutions (1) [15 points] Scientists studying pond scum at ASU have found an organism with four sexes. Suppose the parents are P1= AAAa, P2 = AAaa, P3 = AAAA, and P4 = Aaaa. (a) What is the probability of getting an AA...
Arizona >> ECOL >> 320 (Fall, 2008)
Name: Genetics 320 Exam II. October 28, 2005. page 1 1. Lac Operon (25 pt) 2. Recombination/complementation in phage (20 pt) 3. Mitotic Recombination (25pt) 4. T/F short answer (25 pt) 5. Extra Problem: F reversion (5 pt) TOTAL Name: 1. ...
Arizona >> ECOL >> 320 (Fall, 2008)
(1) [10 points] You are using marker loci to look for a linked QTL and have a single large full-sib family. Three marker loci are considered, A, B, and C. The father has genotype A 1A 2B 1B 2C 2C 2, while the mother is A 3A 2B 1B 2C 1C 1. (a) Can all...
Arizona >> ECOL >> 320 (Fall, 2008)
Name: page 2 1. Yeast Mating Pathways (25 points) A. Give one reason why it is easier to identify mutants in yeast than it is in human cells (5pt) Yeast can be haploids which allows direct detection of recessive mutants. OR Yeast undergo meiosis to...
Arizona >> MATH >> 322 (Spring, 2007)
Fourier series Generalizations Applications Chapter 11: Fourier Series Sections 1 - 5 Chapter 11: Fourier Series Fourier series Generalizations Applications Denition Convergence 1. Fourier series We saw before that the set of functions {1, cos(x...
Arizona >> MATH >> 322 (Spring, 2007)
Fourier series Generalizations Applications Chapter 11: Fourier Series Sections 1 - 5 Chapter 11: Fourier Series Fourier series Generalizations Applications Denition Convergence 1. Fourier series We saw before that the set of functions {1, cos(x...
Arizona >> MATH >> 322 (Spring, 2007)
Fourier series Generalizations Applications Fourier series Generalizations Applications Denition Convergence 1. Fourier series We saw before that the set of functions {1, cos(x), sin(x), cos(2x), sin(2x), , cos(mx), sin(mx), }, where m is a ...
Arizona >> MATH >> 322 (Spring, 2007)
Fourier series and transforms - Check your knowledge Do you know which formulas to use in order to find the Fourier series of a function f that has period 2 ? How are these formulas modified if f has period 2 L, or if f is even, or if f is odd? Do...
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