1
Name:
Math 31
Time: 50 minutes
Test 2 Section 1 and 2 key
November 4, 2015
Score: 50 points
TO GET FULL SCORE, YOU MUST SHOW YOUR WORKING.
WRITE CLEARLY. POINTS WILL BE DEDUCTED FOR BADLY
WRITTEN WO
On your final exam
Your final exam will be cumulative. You will be expected to have a working knowledge of
calculus 1. The following is a rough breakdown of which topics will be emphasized in the
fina
1. Find the radius of convergence and the interval of convergence:
P
n!xn
(a)
n=1 135.(2n1)
Ratio test: an =
n!xn
135.(2n1)
so
|an+1 |
|an |
(n+1)!xn+1
= 135.(2n1)(2n+1)
135.(2n1)
n!xn
= x(n+1)
2n+1
MATH 1 Math, Philosophy, & the Real World
Homework 6
This document is a MS Word form and is for your preparation and records only.
Take as much space as you like. Your answers to the questions below,
MATH 1 Math, Philosophy, & the Real World
Homework 4
This document is a MS Word form and is for your preparation and records only.
Take as much space as you like. Your answers to the questions below,
MATH 1 Math, Philosophy, & the Real World
Homework 5
This document is a MS Word form and is for your preparation and records only.
Take as much space as you like. Your answers to the questions below,
MATH 1 Math, Philosophy, & the Real World
Homework 3
This document is a MS Word form and is for your preparation and records only.
Take as much space as you like. Your answers to the questions below,
MATH 1 Math, Philosophy, & the Real World
Biweekly Recap: Weeks # _
This document is a MS Word form and is for your preparation and records only.
Take as much space as you like. Your answers to the qu
MATH 1 Math, Philosophy, & the Real World
Guest Lecture Report: Guest Lecturer _
Take as much space as you like. Your answers to the questions below, when submitted
online, will be read and saved by t
MATH 1 Math, Philosophy, & the Real World
Homework 2
This document is a MS Word form and is for your preparation and records only.
Take as much space as you like. Your answers to the questions below,
History
Also known as Duplicating cube or the Delian
problem
Ancient time (Greek mythology)
Comparison to doubling a square or rectangle
Parallel Problems
Squaring a circle (unresolved)
Trisectin
A N e w Look at Euclid's Second Proposition
Godfried Toussaint
There has been considerable interest during the past
2300 years in comparing different models of geometric
computation in terms of their
Models of Computation, Straight-Edge and
Compass Algorithms, and Correctness Proofs by
Case Analyses using Euclids Second Proposition as
a Case Study
Godfried Toussaint
New York University Abu Dhabi
S
16 Polygon Triangulation
FIGURE 1.15 Cross product parallelogram.
6. Do noncomex polygons have mouths? (Pierre Beauchemin). Dene three consecutive vertices
a, b, c of a polygon to form a month if b
Algorithms:
What is this Course About?
Godfried Toussaint
General Description of this course
This Algorithms course concerns the study of precisely defined procedures
(rules) that guarantee finding
Divide & Conquer: Merge Sorting
in O(n log n) Worst-Case Time
Godfried Toussaint
New York University Abu Dhabi
Divide & Conquer In General:
1. Divide a problem into smaller sub-
Current State Curre bol Action
5.
m
3
go to the rightmost digit of x
end of x has been read; Right, state 2
sees the leftmost digit of y; Left, state 3
ooks for the rightmost digit of x
erases it; sta
NYUAD Course CS-AD 105 Algorithms
Assignment-12 (due Monday March 28, 2016)
(do NOT hand it in: it will NOT be marked you may be tested on this material, including
the reading assignment in th
NYUAD Course CS-AD 105 Algorithms
Assignment-11 (due Monday March 14, 2016)
(do NOT hand it in: it will NOT be marked you may be tested on this material, including
the reading assignment in th
Haruna Alhassan (haa341)
PROPOSITION: Using a straight edge and a collapsing compass to displace a given line
segment [A, B] to a new location so that one end point, say A, lies on a pre-specified poi
NYUAD Course CS-AD 105 Algorithms
Assignment-10 (due Monday March 7, 2016)
(do NOT hand it in: it will NOT be marked you may be tested on this material, including
the reading assignment in the
Lower Bound on the Complexity of Sorting
Godfried Toussaint
New York University Abu Dhabi
Fundamental Sorting Theorem
Any sorting algorithm that uses only comparisons
between the elements
NYUAD Course CS-AD 105 Algorithms
Assignment-7 (due Wednesday February 24, 2016)
(The material in this reading assignment may appear in Quiz-2 on Feb. 24)
1. Reading and Studying:
1. Refere
NYUAD Course CS-AD-105 Algorithms Spring 2016
Assignment-2
(due Wednesday February 10, 2016)
(You may be tested on this material in Quiz-1)
1. Reading Assignment (Review of Induction)
2.
NYUAD Course CS-AD 105 Spring 2016 Algorithms
A.
Instructor: Dr. Godfried Toussaint, Office: A2-185, E-mail: [email protected]
Class Hours: Mondays and Wednesdays, 9:15-10:30
NYUAD Course CS-AD 105 Algorithms
Assignment-6 (due Monday February 22, 2016)
(do NOT hand it in: it will NOT be marked you may be tested on this material, including
the reading assignment