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 K ,
f1 , ., fm K [x1 , ., xn ],
def
does there exist a
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 Mathematics Algebra I course.
As noted in the Common Core Sta
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. What are expenses, such as television and rent, which are
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 rain over a 48 hour period. How much
rain is this per hour
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 for q = 5 and v = 1.
3. Alaina reads 15 books from the li
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 is the area of the square?
4
2
in.
5
a) 7
3
5
in
b) 7
4
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
b. Retail price
c. Sales tax
2. Carly owns a T-shirt s
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 x 4 y 14 in slope-intercept form.
3) Write the equation
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= 0.24
a. 3.2
b. 32
5. Solve: 5 = y 10
a. -15
b. -5
c.
c. 4
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 , ., xn ], our goal is to nd a basis for this ideal that
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 me know and Ill help
you nd one.
While a pair may ask
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 x3 Qw xw ,
Q a quantier, such that
fi (x0 , . . . , xw
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
Algebraic models of computation
1.1
Considered problems
Le
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 primality
testing by giving some simple but inecient algorithms
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 membership.
o
We wont produce any complexity estimate
6.885 Algebra and Computation
November 7, 2005
Lecture 16
Lecturer: Madhu Sudan
1
Scribe: Sergey Yekhanin
Today
Decoding of Reed-Solomon (RS) codes.
Decoding of Chinese Remainder (CR) codes.
2
Error-correcting codes
The theory of error-correcting codes
William Shakespeares
Julius Caesar
Study Guide
Sponsored in part by
Julius Caesar
Welcome to Julius Caesar. We hope that this study guide will help navigate you through one of Shakespeare's
most famous tragedies. The Orlando-UCF Shakespeare Festival has a