Introduction to Algebraic Coding Theory
Supplementary material for Math 336 Cornell University
Sarah A. Spence
Contents
1 Introduction 2 Basics 2.1 Important code parameters . . 2.2 Correcting and detecting errors 2.3 Sphere-packing bound . . . . . 2.4 Pr
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The University of British Columbia
MATH 317, Sections 201202
Final Exam April 2013
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Circle Section:
201 Tsai
202 Li
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The University of British Columbia
MATH 317
Midterm 1
4 February 2015
Time: 50 minutes
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instructions:
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The University of British Columbia
MATH 317
Midterm 1
21 July 2015
Time: 75 minutes
LAST NAME:
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STUDENT # :
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This Examination paper consists of 8 pages (including this one). Make sure you have all 8.
instructions:
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The University of British Columbia
MATH 317, Section 201, Instructor Tai-Peng Tsai
Midterm Exam 1 February 1, 2013
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15.1 Vector Fields
CHAPTER 15
VECTOR CALCULUS
Vector Fields
15.1
(page 554)
(page 554)
A vector field assigns avector to each point (x, y) or (x, y, 2). In two dimensions F(x, y) = M(x, ~ ) i + N ( xy)j.
,
An example is the position field R = x i y j (+x
MATH 317 Assignment 1
Due Tuesday, January 19, 2016 in class
You must show your work to get full marks.
1.
Consider the curve with parametric equations x = et , y = e2t (t R)
a. Sketch the curve by hand, using your intuitive understanding of the
functions
MATH 317 Assignment 3
Due Tuesday, March 8, 2016 in class
You must show your work to get full marks. Hand in this question sheet with your
assignment.
!
! x
1 $
1. Consider the vector field shown below, given by F ( x, y) = # 2 , 2 & .
" x +1 x +1 %
a. Sk
MATH 317 Assignment 2
Due Friday, January 29, 2016 in class
You must show your work to get full marks.
1. If two objects travel through space along two different curves, it is often
important to know whether they will collide. The curves might intersect,
SOLUTIONS TO MIDTERM #1, MATH 317
1. (9 marks) Answer true or false to the following questions by putting either true or false
in the boxes. If the answer is true give a proof or valid reason, and if the answer is
false state why.
(a) If C is a smooth spa
MATHEMATICS 317 April, 2003 Final Exam Solutions
1) Find the eld line of the vector eld F = Zyi + gigjl 6912 that passes through (1,1,6).
Solution. The eld lines obey
iii_Ld Q
2ym/yzmey dam/#0
In particular
23121de :mdx22y3dyra1x2: %y4+C
Sincey:1whena:=1
MATHEMATICS 317 April 2001 Final Exam Solutions
1) Find and sketch the eld lines of the vector eld F = sci + 3y
Solution. The eld lines obey
/
\
g=f aw/7E0
=>31nm=lny+C
' =le3
:1: = O and y = 0 are also eld lines.
2) Let C be the curve from (0 0,0
Be sure this exam has 12 pages including the cover
The University of British Columbia
MATH 317, Sections 201202
Final Exam April 2013
Family Name
Given Name
Student Number
Signature
Circle Section:
201 Tsai
202 Li
No notes or calculator allowed.
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Be sure that this examination has 10 pages including this cover
The University of British Columbia
Sessional Examinations - April 2003
Mathematics 317
Calculus IV
Closed book examination
Name Signature
Student N umber_._ Instructors Name
(
Section Numbe
2012-2013 Winter Term 2
MATH 317 Calculus IV - Section 202
Practice Midterm 1
1. Consider the curve with the parametrization
2 4 2 3/2
r(t) = (t ,
t , 2t),
3
t0
(a) Find the length of the curve from t = 0 to t = T .
(b) Reparametrize the curve with respec
2012:2013 Winter Term 2 S o Ind" To ms
MATH 31? Calcuns EV . Sectiun 282
Prantice Midterm 1
1. Consider the curve with the parametrization
4 2.
W) = (t2, mgr? 2t), t a 0
(a) Find the length of the curve from t r: (J to t 2 T.
(b) Breparametrize the cu
l olmtrom9 l
Math 317 . Second l\/lidterrn
Mar 15, 2013
Name: Student ID: M_.W._m,_u.
Instructor: ._ Section: W_.m_r._W . -
1. Do not open this exam until you are told to do so.
2. SPECIAL INSTRUCTIONS: No books, notes, or calculators are allowed.
(imam
Math 317 1* irst Midterm
Feb 1, 2013
Name: W Student ID:
Instructor: W_WWW Section:
'1. Do not open this exam until you are told to do so.
2. SPECIAL INSTRUCTIONS: No books, notes, or calculators are allowed. Show all your
work, little or no c
MATH 317
HMW 1
End of week 1
Solutions HMW1: Questions 5 and 6 of Exercises 13.1.
1. (4 points) Find a vector function for the curve of intersection of x2 + y 2 = 9 and y + z = 2.
Solutions:
We have: x2 + y 2 = 9 (3 cos(t)2 + (3sint(t)2 = 9, then x = 3 co
Midterm
Math 317
Section 102
Student Number
Name
No books, notes or calculators are allowed.
Problem 1 (25 points): Answer true or false to the following questions. No explanation is required.
1. The curve with vector equation r(t) = t3 i + 2t3 j + 3t3 k
Midterm
Math 317
Name
February 14th, 2007
Student Number
No books, notes or calculators are allowed.
Problem 1 (10 points): Consider the curve with the parameterization
+
*
2 4 2 3/2
t , 2t .
r(t) = t ,
3
1. Find the length of the curve from t = 0 to t =
Midterm
Math 317
Section 102
Student Number
Name
No books, notes or calculators are allowed.
Problem 1 (25 points): Consider the curve with the parameterization
r(t) = ti + t2 j + tk
for < t < .
1. (15 points.) Compute the curvature (t) as a function of t
SOLUTIONS TO HOMEWORK ASSIGNMENT #2
1. The position of a particle is given by r(t) = 3 cos t, 4 cos t, 5 sin t , where > 0.
(a) Find the velocity vector v(t).
(b) Find the acceleration vector a(t).
(c) Find the speed v(t).
(d) True of false: a(t) = 2 r(t)
MATHEMATICS 317 April 2001 Final Exam
[10] 1) Find and sketch the eld lines of the vector eld F = xi + Syj.
[15] 1) Let C be the curve from (07 0, O) to (1,1,1) along the intersection of the surfaces 3/ = x2 and z = $3.
)Find [CF dr ifF= (x2 y)z+ (z+$)+yl
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The University of British Columbia
MATH 317, Section 101, Instructor Tai-Peng Tsai
Midterm Exam II November 9, 2016
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Signature
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Be sure this exam has 6 pages including the cover
The University of British Columbia
MATH 317, Section 201, Instructor Tai-Peng Tsai
Midterm Exam 1 February 1, 2013
Family Name
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Student Number
Signature
No calculators, books, notebooks or any ot
Be sure this exam has 6 pages including the cover
The University of British Columbia
MATH 317, Section 201, Instructor Tai-Peng Tsai
Midterm Exam II March 15, 2013
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Student Number
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No calculators, books, notebooks or any oth
Be sure this exam has 6 pages including the cover
The University of British Columbia
MATH 317, Section 201, Instructor Tai-Peng Tsai
Midterm Exam II March 15, 2013
Family Name
Given Name
Student Number
Signature
No calculators, books, notebooks or any oth