# Ppt on polynomials in maths what does product

##### MTH 209 The University of Phoenix Chapter 5 Factoring Polynomials Operations with Rational Expressions.

Polynomials Operations with Rational Expressions Chapter 5 Section 1 The Basics of Factors Just the Fact-or Ma’am. or The O’Righty Factor (I’m getting the puns out of my system). Primes are your friend… A prime number is a rock bottom, hard end, stop playing with the math/ Example 2 page 330 Identifying special products… a) x 2 -14x+49/in your head… and bango… (3x-2y)(2x-y) ** Ex 69-72** Example 5 page 348 Factoring Completely (Doing what it takes) Factor each polynomial/sum of two squares does not factor. 3./

##### Fourier Transformations Jeff Edmonds York University COSC 6111 Change from Time to Polynomial Basis Evaluating & Interpolating FFT in nlogn Time Roots.

x n / 2 coefficients n values of x Does not meet precondition! FFT nlogn Time Fast Fourier Transformation/ of unity (in a field) if  n = 1 (There should be n solutions of this polynomial) Fermat’s / 6  9 …  3n-3... But that’s still O(N 2 ) !! The Ugly Math for the FFT Just watch! For example, if N=8 and I use the N roots of unity/x 1 ± x 5, x 3 ± x 7 Oh my! Half the columns are gone. What’s next? (x 0 + x 4 ) + (x 2 + x 6 ) + / bit blocks Pad with zero 2N bits to hold product n blocks where n is a power of 2/

##### Polynomials and Polynomials Operations Grade 9 Math Bedford Junior High.

Polynomials and Polynomials Operations Grade 9 Math Bedford Junior High Polynomials: Monomials, Binomials, and Trinomials A monomial is a constant or numerical coefficient, a variable or literal coefficient, or the product of a constant and one or more variables. A polynomial/answer is 5x 17 Distributive Property Means that what is inside the bracket is affected by / “3” affects each item inside the bracket. It does not matter how many terms are inside the bracket. / Construct a rectangle in the bottom right/

##### Georgia High School Graduation Test MATH REVIEW. GHSGT Math Review ~36 % = Algebra ~36 % = Geometry ~28 % = Data Analysis and Probability Test Topics.

 D) k(x) Functions GHSGT Math Review For what x value does f(x) = 3?  A) -2  B) 0  C) 2  D) 6 Functions GHSGT Math Review Transformations of Functions ReflectionStretch or Shrink /in this diagram. The area of this particular Georgia flag is 60 square feet. What is the length of x?  A) 2 ft. B) 4 ft. C) 2 √5 ft. D) 2 √15 ft Polynomial Applications GHSGT Math/.” Truth Value GHSGT Math Review Logic Statements  Which of these true statements also has a true inverse? A.If the product of integers a and/

##### ACT Test Prep Math 1. Get a good night’s rest. Eat what you always eat for breakfast. Use the test booklet for scratch paper. You can’t bring your own.

slope standard coordinate plane transversal trapezoid vertex x-intercept y-intercept Math Vocabulary 7 area of a circle—A = π r /does Joelle earn for a week in which she works 42 hours? A. \$126.00 B. \$315.00 C. \$322.50 D. \$378.00 E. \$472.50 6. Which of the following mathematical expressions is equivalent to the verbal expression “A number, x, squared is 39 more than the product/– When you can’t factor a polynomial cleanly. You can always use the quadratic formula – In x 2 +7x+15=0, what is a, b, and c? /

##### Welcome! Math 055 – CE Intermediate Algebra Ms. Starbuck Find your ASSIGNED seat.

function as a group. What qualities does your identity have that will help you be an effective MATH group? An effective college/in the CW Section of your binder: Students will REVIEW and CRITIQUE work and solutions from other students. What does /CW: Pg. 279/ #81-88 Test #1 WEDNESDAY MAT-055 Multiplying Polynomials Multiplying BI-nomials >> TRI-nomials – F-O-I-L: FIRST, /100 Test WEDNESDAY MAT-055 CW: Factoring WSheet ‘Books…’ Factoring Special Products HW: Pg. 303/#1-42 Due FRIDAY QUIZ WEDNESDAY – Simplifying/

##### Test 2 – Math 96 Flash Cards. Test 2 Functions: Domain & Range Systems of Equations Word Problems – Mixture, investment & DRT Polynomials: add, subtract,

Test 2 – Math 96 Flash Cards Test 2 Functions: Domain & Range Systems of Equations Word Problems – Mixture, investment & DRT Polynomials: add, subtract, multiply, & divide Factor Does the graph represents a function. State the domain and the range. Vertical line / common factors, show what’s left inside ONE set of parenthesis Identify the number of terms. If there was a common factor, then look at the number of terms left inside the parenthesis. Do NOT remove parentheses already given in the expression. If /

##### Math 12: The Mathematics of LEGO Bricks Steven J Miller (x3293)

failure…. From LEGO Bricks to Math 560 pieces for \$120, or 21 cents per piece (cpp). From LEGO Bricks to Math 292 pieces for \$65, /what the `right sum of a product of three binomial coefficients is? One difficulty is you have to figure out whats the right triple! – To solve the roulette recurrence from the video involves finding the roots of a polynomial of degree 5; sadly in/ xn.We saw Horners algorithm does significantly better than brute force, standard polynomial evaluation. What if instead we used fast /

##### Discrete Math for CS Chapter 6: Combinatorics. Discrete Math for CS How to Count: Combinatorics is about counting. Pigeonhole was about counting too.

Math for CS Further Examples: The key is to know what formula to use. In a National Lottery a twice-weekly drawing takes place in which 6 numbers are randomly drawn from the numbers 1..49. Problem: Find the probability of winning. Analysis: Without replacement and order does/ the running times for n = 1, 10, 100 and 1000. polynomial timeexponential timelinear time Polynomial time algorithms with the same degree are in the same ballpark. Discrete Math for CS Time Complexity Functions: Suppose f(n) and g(n) /

##### Template by Bill Arcuri, WCSD Click Once to Begin JEOPARDY! 8 TH GRADE MATH Unit 8 Quadratic Expressions and Equations.

GRADE MATH Unit 8 Quadratic Expressions and Equations Template by Bill Arcuri, WCSD JEOPARDY! 100 200 300 400 500 Add and subtract polynomials Multiply polynomials Factoring /, WCSD Topic 1 300 Points Write the expression in standard form. Identify the Leading Coefficient and Degree of the polynomial. -3 + 3x - x + 5x 33 2 Template by/integer. What is the product of the next Two consecutive integers? Template by Bill Arcuri, WCSD Topic 6 200 Points Answer Let x be an integer. What is the product of /

##### David E. Keyes Center for Computational Science Old Dominion University Institute for Computer Applications in Science & Engineering (ICASE) NASA Langley.

are retained INRIA Sophia-Antipolis Colloquium Schwarz polynomials l Polynomials of Schwarz projections that are combinations of/ Falgout (LLNL) to support research, prototyping, and production parallel solutions of operator equations in message-passing environments; now joined by seven additional staff/ do you know what your solver is up to? Has your solver not been updated in the past five /://www.math.odu.edu/~keyes l SciDAC initiative http://www.science.doe.gov/scidac l TOPS project http://www.math.odu.edu/

##### Zernike polynomials Why does anyone care about Zernike polynomials? A little history about their development. Definitions and math - what are they? How.

polynomials Why does anyone care about Zernike polynomials? A little history about their development. Definitions and math - what are they? How do they make certain questions easy to answer? A couple of practical applications What will Zernikes do for me? Widely used in industry/ –Similar to modes of a circular drum head Real surface is constructed of linear combination of basis shapes or modes Polynomials are a product of a radial and azimuthal part –Radial orders are positive, integers (n), 0, 1,2, 3, 4,/

Math/ends in 0. 370 is divisible by 10 because it ends in 0. 7003 is not divisible by 10 because it does not end in 0/For example: What is 30 percent of 250? X = 30 / 100 x 250 To find a percentage increase or decrease, divide the change in value by/are roots. ab = a x b The square root of a product is the product of the roots. 3 www.topmath.info/m5 Best links on / – 2 = 9x 4 + 5x 2 – 5y 2 – 2x To multiply a polynomial by a number, multiply each term in the polynomial by the number: 5 x (x 2 - 4xy + 3y 2 –2) = /

##### Math 12: The Mathematics of LEGO Bricks Steven J Miller (x3293, Bronfman 202)

Outreach with Elementary School My Qualifications: – Know math, know Legos. – More forgiving than Darth Vader, less than the /what the `right sum of a product of three binomial coefficients is? One difficulty is you have to figure out whats the right triple! – To solve the roulette recurrence from the video involves finding the roots of a polynomial of degree 5; sadly in/.We saw Horners algorithm does significantly better than brute force, standard polynomial evaluation. What if instead we used/

##### Jonathan Borwein, FRSC www.cs.dal.ca/~jborwein Canada Research Chair in Collaborative Technology Laureate Professor Newcastle, NSW ``intuition comes to.

is full. After messing around with lots of cases it occurred to me to ask for the minimal polynomial of M Example 3. Related Matrices (1993-2006) > linalg[minpoly](M(12),t); > linalg[/production is £800 and his profit is £200. Underline the number 200. 5. Teaching Maths In 2008 A logger cuts down a beautiful forest because he is a totally selfish and inconsiderate bastard and cares nothing for the habitat of animals or the preservation of our woodlands. He does this so he can make a profit of £200. What/

##### Rochelle Gutiérrez, University of Illinois at Urbana-Champaign Why “Getting Real” Requires Being “Radical” in High Stakes Education The Iris M. Carl Equity.

products of for-profit corporations Goal is to teach kids that there are some people in society who are good at math /polynomial divided by a trinomial, they won’t be able to do it. Secondly, synthetic division is based on long division, seeing what/what the Common Core responded by saying. They said "First of all you cant field test standards, you can field test implementation of standards but you cant field test the standards themselves. So when people say that they have not been field tested, it does/

##### Introduction to Fuzzy Set Theory Weldon A. Lodwick

Fall 2003 I. INTRODUCTION: Math Clinic Fall 2003 A. Why fuzzy sets? - Modeling with uncertainty requires more than probability theory - There are problems where boundaries are gradual EXAMPLES: What is the boundary of the USA? Is the boundary a mathematical curve? What is the area of USA? Is the area a real number? Where does a tumor begin in the transition? What is the habitat of/

##### 1 Reading and Math Vocabulary: Knowledge Counts! AMATYC Conference 2009 – Session S51 Amber Rust University of Maryland – College Park November 12 th -

Math Vocabulary (Rubenstein, 2007)  Some words are… found only in math (e.g., denominator, hypotenuse, polynomial, histogram) found only in math (e.g., denominator, hypotenuse, polynomial,/ productive and enjoyable? 10. How can I help students use the word/concept in meaningful ways in multiple context? 20 What you can do (Allen, 1999)  Repeat words in/) Creating a glossary and memorization does not help students learn. (Allen, 1999) Creating a glossary and memorization does not help students learn. (Allen/

##### College Algebra Exam 4 Material.

a long division problem in basic math Example Dividing Polynomial Function by “x – k” Using Synthetic Division First write each polynomial in descending powers If /In a previous example: we found f(2) by synthetic division: Notice bottom row. What does this tell us about zeros? Example of Boundedness Theorem Using the same function: find f(-3) by synthetic division: Notice bottom row. What does/and inversely with others In such cases, we write y as being equal to a constant, k, times the product of the other /

##### Open and Closed Problems in NP-Completeness David S. Johnson Columbia University.

what we now call “polynomial-time Turing reductions”: A → B if problem A can be solved in polynomial time when given a subroutine for solving B that provides answers in/tree is graceful (verified for all trees with |V| ≤ 35). Biggest Remaining Open Problem Does P = NP? Solution is worth \$1,000,000 Opinion Polls Bill Gasarch, “Guest /in reasonable running times. Executables and source code can be downloaded from http://www.math.uwaterloo.ca/tsp/concorde/index.html Concorde & the TSP N = 1000 Running times (in/

##### Prof. Gregory S.Yablonsky

particular state of the catalyst) that does not change significantly during this non-steady/residues in multi-dimensional complex analysis”, Nauka, Novosibirsk, 1979 Tsikh, A.K., Multidimensional residues and their applications, Trans. Math./ is a linear polynomial regarding its parameters in difference from the non/products) 3. Coincidences Surprising properties of the simple kinetic models; in particular, A->B->C. Coincidences (cont’d) Solutions (known before) Coincidences (cont’d) New problem is posed: what/

##### ConcepTests For Math 112 Prepared by Richard Cangelosi and Mariamma Varghese.

Math 112 Prepared by Richard Cangelosi and Mariamma Varghese 2 If the sum of two numbers is 14, and their difference is 2, what is the product of the two numbers? A.24 B.28 C.40 D.45 E.48 F.None of these. 3 Compare the quantity in Column A with the quantity in/same route home, but average speed is 60 miles per hour, how long does it take her to get home? (A)2 hours (B)2 hours/below? (A). (B). (C). (D). (E). 33 If P(x) is a polynomial of degree, then the degree of the quotient of is (A) Less than 2 (B) Exactly/

##### Cs h196 -- Polynomials1 A Review of Polynomial Representations and Arithmetic in Computer Algebra Systems Richard Fateman University of California Berkeley.

University of California Berkeley cs h196 -- Polynomials2 Polynomials force basic decisions in the design of a CAS Computationally, nearly every “applied math” object is either a polynomial or a ratio of polynomials Polynomial representation(s) can make or break a system/, by interpolation, a polynomial of degree 12 by 13 values, H(0), …, H(12). Thus we compute the product H=F*G cs h196 -- Polynomials19 What does evaluation cost? Horner’s rule evaluates a degree d polynomial in d adds and multiplies./

##### Math is a language, learn the words!

variables ‘x’ is the variable What number does ‘x’ represent? What numbers do ‘x’ and ‘y’ represent? “Coefficient” 3x + 4y - 2 The number in front of a variable in an expression or an equation. / the sum. “Factors” “Product” 2 x 3 = 6 The numbers that are multiplied together to get the answer. 2 x 3 = 6 “Product” The answer when factors are/ in words before you write it in mathematical symbols. Polynomials POLY nomials many terms each with the same variable raised to an positive INTEGER power. Polynomials /

##### What Follows “Showing Up?” Problem Solving Alice Kaseberg AMATYC 2013 Warm-up: Make a Rectangle Do not share problem solutions. Let everyone enjoy success,

polynomials Statistics and Eyeglasses There are lots of glasses and contact lenses in your classroom. Great source of data for introductory statistics. In fact, more than 150 million Americans use corrective eyewear, spending \$15 billion annually on eyewear. What/ only zeros and ones: 00, 01, 10, 11. Why does each fail? __ __ 0s 1s Ten Digit Challenge Possible three-digit/ ten digits. More Math Maps (p. 14) Book Signatures (math maps, p.15) Pages for a book are traditionally printed in multiples of four (/

##### Polynomial Function f(x) = a o x o + a 1 x 1 + a 2 x 2 + …. + a n x n Equality: f (x) = g (x) if for all a i = b i that is the coefficients are equal.

polynomials by factoring Modeling view – solving real world problems modeled by polynomial functions which almost never factor Solving Polynomial Equations- Algebraic Method Set Polynomial Equation equal to zero. Factor the resulting polynomial expression into a product/math.wvu.edu/~mays/ AVdemo/Labs/Lab01/Lab01- 04.htm Question: What happens to the y-values as the table approaches a solution to the polynomial equation? Question: For a general polynomial equation, what are some difficulties in/ does it/

##### Solving Polynomial, and Exponential Equations and Inequalities Mary Dwyer Wolfe, Ph.D. Department of Mathematics and Computer Science Macon State College.

July 2010 Math III Standard MM3A3 Students will solve a variety of equations and inequalities. a. Find real and complex roots of higher degree polynomial equations using /Polynomial Equations Solve Steps in the Analytic Solution Process ▫ Put the equation in standard form ▫ Factor the polynomial into linear and quadratic terms ▫ Use the zero-product property Polynomial Equations Solve analytically (symbolically). Standard form Factor by grouping Factor difference of squares zero product property Polynomial/

##### Accelerated Math II Polynomial Review. Quick Practice “Quiz” 1. A rectangular sheet of metal 36 inches wide is to be made into a trough by turning up.

Math II Polynomial Review Quick Practice “Quiz” 1. A rectangular sheet of metal 36 inches wide is to be made into a trough by turning up sides of equal length (x) perpendicular to the sheet. Find the value of x that will produce the maximum cross sectional area of the trough. What/polynomial with integral coefficients if two of the roots are at 2 - 3i and 1 +  2 A) in factored form. B) in expanded form. 7. How many x intercepts does/- 11x + 30 is 2. Find the product of the other two roots. Quick Practice “/

##### 10.2 – Multiplying Polynomials I got polynomials…. They’re multiplying! And I’m losing a binomial. Cause the power you’re supplyin’, it’s terrifyin’. Oh,

+ 6t – 8)(t – 6) Find the product. Boss/Secretary Practice Students will work in pairs. per pair Materials: One worksheet, one calculator, one pencil per pair Students will be given one of two roles (you will alternate these roles): – Boss – Boss: Tells the secretary how to solve the problem, is the only one talking in the pair, does not write anything – Secretary – Secretary: Listens/

##### 25 November 2010 Vincenzo Innocente 1 IEEE 754 standard Expression optimization Approximate Math Vector Algebra using SIMD instructions Loop vectorization.

November 2010 Vincenzo Innocente MOTIVATIONS 1825 November 2010 Vincenzo Innocente Formula Translation: what was the author’s intention? 19 // Energy loss and variance / Vincenzo Innocente 32 APPROXIMATE (FAST) MATH 25 November 2010 Vincenzo Innocente 33 /Log, the polynomial expansion works in a very limited range (and adding more terms does not help/2, 3, 0, 1)); return _mm_add_ps(mul, swp); #endif } Vector product 25 November 2010 Vincenzo Innocente 52 // cross (just 3x3) inline __m128 _mm_cross_ps(__m128/

##### Systems biology SAMSI Opening Workshop Algebraic Methods in Systems Biology and Statistics September 14, 2008 Reinhard Laubenbacher Virginia Bioinformatics.

Polynomial dynamical systems Note: {0, 1} = k has a field structure (1+1=0). Fact: Any Boolean function in n variables can be expressed uniquely as a polynomial function in/Math. Biol. 55 (1993) 973-991 Key model features: Time delays of different lengths for different variables are important Positive and negative feedback loops are important Model description Basic structure of logical models: 1.Sets of variables x 1, …, x n ; X 1, …, X n (X i = genes and x i = gene products/ and at what levels they /

##### Rae §2.1, B&J §3.1, B&M §5.1 2.1 An equation for the matter waves: the time-dependent Schrődinger equation*** Classical wave equation (in one dimension):

is a complex quantity, so what can be its significance for /in a solid (hence phonons) Electromagnetic field modes (hence photons), even though this field does not obey exactly the same Schrődinger equation You will do another, more elegant, solution method (no series or Hermite polynomials/-8 (Images from http://odin.math.nau.edu/~jws/dpgraph/Yellm.html/in postion Mean momentum: Mean-squared uncertainty in momentum: In fact, can show that this form of wavepacket (“Gaussian wavepacket”) minimizes the product/

##### Inequalities Involving the Coefficients of Independence Polynomials Combinatorial and Probabilistic Inequalities Isaac Newton Institute for Mathematical.

polynomial, Discrete Mathematics and Theoretical Computer Science 6 (2003) 69-90. P(G; x, y) is a polynomial in variables x, y, which simultaneously generalizes the chromatic polynomial, the matching polynomial, and the independence polynomial/ independence polynomials whose product is /polynomials of trees does not directly implies the unimodality of independence polynomials of forests ! Consequence Hence, independence polynomials/” Conjecture is valid for  (G) > 11 What about  (G) > 11 ? Still open …/

##### 1 Hardware Assisted Solution of Huge Systems of Linear Equations Adi Shamir Computer Science and Applied Math Dept The Weizmann Institute of Science Joint.

Science and Applied Math Dept The /2D grids with local communication between neighbors 15 Practical limits on what we can do: We can use linear space to store /find a vector u in the kernel of a singular A: Theorem: Let p(x) be the characteristic polynomial of the matrix A./Schimmler mesh sorting algorithm three times to complete each matrix- vector product. For a mxm matrix, this requires about 24m steps. We/ 1/7 1/15 1/6 of 45,000. 29 Does it always work? We simulated the algorithm thousands of time with/

##### What statistical analysis should I use?

Cochran’s Q test An APA Results Section Proportions of student scoring high in math, reading and writing were .22, .24, and .25, respectively/ Syntax:- GLM y1 y2 y3 y4 /WSFACTOR=a 4 Polynomial /METHOD=SSTYPE(3) Only the additional outputs are presented/select two variables then >a*b> for the product term. 178 Factorial logistic regression Define categorical variables 179/the documentation to know find out just what the algorithm does in the software you are using - in particular, whether it has a stopping rule/

##### 728345 Introduction. What is Computational Chemistry?  Use of computer to help solving chemical problems Chemical Problems Computer Programs Physical.

What is Computational Chemistry?  Use of computer to help solving chemical problems Chemical Problems Computer Programs Physical Models Math/in the valleys on a PES  Energetics of reactions can be calculated from the energies or altitudes of the minima for reactants and products  A reaction path connects reactants and products/ to equilibrium geometries  Does not take electronic interactions / r 0 )] 2  a cubic polynomial has wrong asymptotic form, but a quartic polynomial is a good fit for bond length of/

##### Relations And Functions. A relation from non empty set A to a non empty set B is a subset of cartesian product of A x B. This is a relation The domain.

product of A x B. This is a relation The domain is the set of all x values in the relation The range is the set of all y values in/assigned to anything Comparing to our example, a student in maths must receive a grade Set A is the domain 1/ then is: All real numbers x such that x ≠ 2. means does not equal illegal if this is zero Note: There is nothing wrong with/are polynomial functions. The domain of f is the set of all real numbers except the values of x that make the denominator h (x) zero. In what follows/

##### Polynomial Operations Hanna Jusufi Julia Ly Karl Bryan Ly Huynh Girl : I keep losing stuff when I try to multiply three binomials. Boy : I do, too, but.

polynomials Top down, youll know, all these confusing systems Cause when you come up in the class, you blankin’ out Got math in/in front of the parenthesis and making sure of the exponents. ~Dividing Polynomials: Long Division~ Example: Set up the division where you would normally put the divisor and dividend To know what to put for the quotient, divide the first terms of the dividend and the divisor and use the product/1 ± 4/1 ± 8/1. However, that does not mean these will all work, the ones that work are the/

##### WELCOME HIGH SCHOOL EDUCATORS Help yourself to breakfast. Please have a seat in a desk with your subject-specific materials. Introduce yourself to the.

in polynomial identities and equations Vector and Matrix /What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in/in using procedures flexibly as they solve contextual and mathematical problems. 7.Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive/ provided. What is the math involved in this problem/

##### Polynomials Properties Functions Find xDefinitions

Polynomials for 800 When (c + 8) and (c - 5) are multiplied, what type of polynomial do we get as the product? What is its degree? Answer: The product is a trinomial (c² + 3c – 40) of degree two. Polynomials for 900 What/ rate. What type of slope does this line have? Answer: The slope of this line is negative. Functions for 800 Organize the following function in descending order/ Definitions for 800 Algebraic Equation Answer: An equation is a math sentence that says that 2 things are equal. An equation always/

##### UNIT 1 INTRODUCTION NUMBER SYSTEMS AND CONVERSION Click the mouse to move to the next page. Use the ESC key to exit this chapter. This chapter in the book.

 To “Decimal” Positional Weighting Addition of the products of each digit by its respective “column weight” /# Biased Notation for Exponents Two’s complement does not work for exponent Most negative exponent: 00000001/ 0 Value: Not a Number What is the result of: sqrt/num: b = 2 -149 b a0 + - Gap! 0 + - Rounding Math on real numbers => rounding Rounding also occurs when converting types – Double  single /in the positive and negative domains we use the Two’s Complement Number System Here is the polynomial/

##### Raising the Bar: Equipping Systems Engineers to Excel with DOE

in everything we do and in every product we design” 1 1 Jack Welch - General Electric website at ge.com What are Statistically Designed Experiments? Purposeful, systematic changes in the inputs in order to observe corresponding changes in the outputs Results in/ order polynomials with ability to detect nonlinearities Designs also included additional confirmation points to confirm the empirical math model in the test envelope Results: Original CFD study envisioned 1556 runs DOE optimized parameters in 84 /

pieces, 2x + 12x This now gives 3x2 + 2x + 12x + 8 Now we have a FOUR-TERM polynomial. What does this suggest?? You got it: Factoring by grouping! 3x2 + 2x + 12x + 8 Factoring the first pair /last coefficients of the trinomial together: 3*8 = 24 Now look for two factors of 24 that add up to 15. product: sum: 24 = 1*24 1+ 24 = 25 24 = 2*12 2 + 12 = 14 24 = 3/ class tomorrow. Lab hours in 203: Mondays through Thursdays 8:00 a.m. to 7:30 p.m. Please remember to sign in on the Math 110 clipboard by the front/

##### Fourier Transform in Image Processing

Signals? Option 1: Taylor series represents any function using polynomials. Polynomials are not the best - unstable and not very physically meaningful. (they still have some applications) Easier to talk about “signals” in terms of its “frequencies” (how fast/often signals change/ in Engineering A Sum of Sinusoids Our building block: Add enough of them to get any signal f(x) you want! How many degrees of freedom? What does each control? Which one encodes the coarse vs. fine structure of the signal? Math /

##### The Use of Semidefinite Programming in Approximation Algorithms Uriel Feige The Weizmann Institute.

(or its normal vector) can be found in polynomial time. (The derandomization approach is beyond the /produce better approximations for max cut? What other problems have good approximations based / inner products x i ¢ x j. Triangle constraints At most two edges are cut in a triangle/can be generalized to show that even best hyperplane does not give approximation ratio better than . Summary Max/ Sudan [JACM 98]. Independent set: Alon and Kahale [Math. Programming 98]. Vertex cover: Charikar [SODA 02]. Max/

##### Community Math Forum Bellevue High School Bellevue, Washington Tuesday, April 25 2006 Co-Sponsored by Where’s the Math? and Washington State PTA.

It [1989 NCTM Standards ] does not hold the properties of /polynomials or quotients of polynomials no discussion of things as basic as the standard exponent rules.” An Evaluation of CMP, R James Milgram Teacher Concerns With NCTM Math/in math, and before motherhood worked under contract to the US Navy as an analyst (mathematician, really), designing complex math models for dynamic simulation. If the two of us cannot solve a third-grade math problem, just what the heck is going on with this "wonderful" math/

##### MATH 90 CURRICULUM RENEWAL & MATH MAKES SENSE 9 WORKSHOP June 24 th, 2009.

Unit 5 – Polynomials (Sections 5.1 – 5.6)  Unit 6 – Linear Equations & Inequalities (Sections 6.1-6.5)  Unit 4 – Linear Relations (Sections 4.1 – 4.5)  Unit 8 – Circles Geometry (Sections 8.1 – 8.4) Math 90 Course Outline Math 90 Plus Unit 9/in which we multiply does not matter: (2 x 2) x 2 = 2 x (2 x 2) = 2 x 2 x 2 How would you write this product as a power? What does the word product mean? What does the word quotient mean? 2.4 Exponent Laws I Product of PowersProduct as Repeated Multiplication Product/

##### Seminar on B-Spline over triangular domain Reporter: Gang Xu Institute of Computer Images and Graphics, Math Dept. ZJU October 26.

of Computer Images and Graphics, Math Dept. ZJU October 26 Outline 1/in the appropriate continuity conditions, similar to what is done with the B-Spline.” Introduction Bézier Curves B-Spline Curves Triangular Bézier patches What? Desirable Control Scheme Attributes  Piecewise polynomial of a fixed degree  Individual piecewise polynomials/ Be able to model discontinuities like sharp edges or corners as well( tensor product B-spline will produce a discontinuity curve across the whole patch) Application(3)/

##### By Zvezdelina Stankova Berkeley Math Circle Director Mathematics and Computer Science Department Mills College, Oakland, CA April 16 2009, MSRI.

Does the US need Top-Tier Math Circles? erosion of capacity for new scientific and technological breakthroughs deteriorating math and science education in/polynomials. K-1 ∞ The paper invokes some advanced concepts: Recursive relations Generating functions Functional analysis Partial derivatives Algebraic numbers Ramanujan-type continued franctions For the Die-Hards:Conway Checkers John Conway Question: What/functions Dirichlet product (convolution of functions) Mobius inversion formula Build a math circle /

##### Polynomial Approximation in Handwriting Recognition Stephen M. Watt University of Western Ontario International Workshop on Symbolic-Numeric Computation.

Trace formats, coordinate transformations Annotation text and XML What the Computer Sees Usual Character Reco. Methods Smooth and/ dictionary Difficulties Having many similar characters (e.g. for math) means comparison against all possible symbol models is slow./RMS does not mean similar shape. Problem 1. On-Line Ink The main problem: In handwriting/ 2. Shape vs Variation Legendre-Sobolev Basis Life in an Inner Product Space With the Legendre-Sobolev inner product we have – Low dimensional rep for curves /