6.885 Algebra and Computation
November 9, 2005
Lecture 17
Lecturer: Madhu Sudan
Scribe: Paul Valiant
The problem which we consider today is the following: given m polynomials in n variables over a
eld
Algebra I Curriculum Crosswalk
The following document is to be used to compare the 2003 North Carolina Mathematics Standard Course of Study for Algebra I and the
Common Core State Standards for Mathem
Name:
Date:
OCC Financial Management
Midterm Exam
1. What are expenses, such as utilities and groceries, which change from week to
week or month to month?
a. Fixed expenses
b. Variable expenses
2. Wha
OCS Introduction to Mathematics
Final Exam
1. If you can buy one can of pineapple chunks for $2 then how many can you buy with
$10?
a) 5
b) 12
c) 20
2. Hurricane Katrina dropped about 14 inches of rai
Midterm Exam Practice Algebra 1
1. Greer wrote 14 letters to friends each month for y months in a row. Write an expression to show how
many total letters Greer wrote.
2. Evaluate the expression q v fo
OCS Introduction to Mathematics
Midterm Exam
1. What is the value of the expression 2 + 3 x 4?
a) 10
b) 14
c) 20
2. What is the perimeter of the rectangle?
4yd
8yd
a) 25 yd
b) 13 yd
c) 24 yd
3. What i
OCC Financial Management
Final Exam
Part One Terms/Multiple Choice
Please circle the best answer to each question below:
1. The amount of money a store pays for an item is called _.
a. Wholesale price
Name:_
Date:_
Algebra 1 Midterm Exam Review, part 1
Block:_
Due: January 17/18
Section 1- Solve each problem and circle your answer! Show all work!
1) Simplify
1
(4 y 8) 6 y
2
2) Write the equation 2
Name_ _ Date: _
OCS Algebra1 Midterm
1. Solve. x 4 = -10
a. -6
b. 6
c. -14
2. Simplify: 7m (-3n) + 3s (-4t)
a. 4mn + 7st
b. -21mn 12st
c. 10mn 12st
3. Solve: 5 =
a.
b) 15
4. Solve for x: 0.03x 1.2= 0.
6.885 Algebra and Computation
November 21, 2005
Lecture 20
Lecturer: Madhu Sudan
1
Scribe: Eitan Reich
Today
Hilberts Nullstellensatz
2
Generic/Random Linear Transformations
Given an ideal in K [x1 ,
6.885 Problem Set: Due November 14, 2005
Instructions
If you are taking the course for credit, you must turn in this problem set.
You should do this in pairs. If you have trouble nding a partner let
6.885 Algebra and Computation
November 23, 2005
Lecture 21
Lecturer: Madhu Sudan
1
Scribe: Michael Manapat
Quantied Statements
Let : K n cfw_T, F be a Boolean function dened as follows:
(x1 ) = x1 x2
November 28, 2005
6.885 Algebra and Computation
Lecture 22
Lecturer: Madhu Sudan
Scribe: Krzysztof Onak
Today we present various algebraic models of computation, and discover a few lower bounds.
1
Alg
November 30, 2005
6.885 Algebra and Computation
Lecture 23
Lecturer: Madhu Sudan
Scribe: Karola Mszros
ea
Strassens lower bound for polynomial evaluation and Bezouts theorem
Recall Strassens algorithm
6.885 Algebra and Computation
October 31, 2005
Lecture 14
Lecturer: Madhu Sudan
Scribe: Sophie Rapoport
Today, we give a brief review of factorization of polymnomials, then begin our study of primalit
6.885 Algebra and Computation
November 14, 2005
Lecture 18
Lecturer: Madhu Sudan
1
Scribe: Alexey Spiridonov
Today
We cover Grbner basis recognition, generation, and the resulting algorithm for ideal
William Shakespeares
Julius Caesar
Study Guide
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Julius Caesar
Welcome to Julius Caesar. We hope that this study guide will help navigate you through one of Shakespeare's
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