MA 128-01 Section 4.3 notes
Ways to find the GCD
o Greatest Common Divisors by Intersection of sets
o
Greatest common divisor from prome factorization
o
Greatest Common Divisor from the Euclidean Algorithm
Ways to find LCM
o Least Common multiples by inte
MA 128-01 Section 3.3 Notes
Developing Multiplication Algorithm
o
o
The instructional algorithm is also known as the partial product algorithm
The distributive law for whole numbers leased to a number of different algorithms
o Expanded notation
o Lattice
MA 128-01 Section 7.1 Notes
1.
2. Any decimal numeral has an expanded form as a sum of units, tens, hundreds, and a sum of
tents, hundredths, and thousandths
a.
3. For beginning elementary school students, it is helpful to introduce the study of decimals
MA 128-01 Notes 3.1
The Egyptians developed a system for recording numbers on stope tablets using hieroglyphics
o
The Roman system of numeration is already somewhat familiar from its current usage of the
faces of analog watches, clocks, on cornerstones, a
MA 128-01 Section 4.1 and 4.2 Notes
A=bq and we say that b divides a evenly or, more simply, b divides a.
o
o
The whole numbers that are divisible by 2 or equivalently that are multiples of 2 are known as
the even whole numbers
o
o
A number that is only d
Section 3.4 Notes MA 128-01
The properties of whole numbers along with the one-digit factors, form the basis for mental
calculation
Easy Combinations-regrouping to find multiples of 10
o
Adjustment- at the beginning of a calculation we modify numbers to m
MA 128-01 Notes Section 6.1/6.4
To interpret the meaning of the fraction a/b, we must
o Agree on the unit (such as a cup, an inch, the area of the hexagon, etc.)
o Understand that the unit is subdivided into b parts of equal size
o Understand that we are
Section 3.5 Notes MA 128-01
Base-five notation- consider the abacus- allow only 5 beads to be moved forward on each wire
In base five we need the digits 0,1,2,3, and 4 and we need to know the values of the positions in
base five
In base six the digits are
MA 128-01 Section 5.3 Notes
Multiplication and division in the set of integers are direct extensions of these operations for
whole numbers.
o
Mail time stories show math equations but writing word problems with getting bills and checks
in the mail. For ex
Maung Soe Htet
Homework 3
Chapter 3
Problem 1
The Data and Calculation are in excel files.
b.
Residuals
Residual plot
166
164
162
160
158
156
154
152
0
20
40
60
80
100
Fitted (Y(hat)
The points are scatter evenly above and below the line y=158.
c.
Residua
Maung Soe Htet
HW 1
The Mean Procedure
Variable
N
Mean
Std Dev
Minimum
Maximum
shipmentroute
brokenampules
10 1.0000000 1.0540926
10 14.2000000 4.4422217
0
8.0000000
3.0000000
22.0000000
Analysis of Variance
Mean
Square
F Value
Pr > F
Model
1 160.00000 16
Maung Soe Htet
Homework 5
Problem 7.3
a.
Analysis of Variance
Source
Sum of
Squares
Mean
Square
F Value
Pr > F
2 1872.70000 936.35000
129.08
<.0001
DF
Model
Error
13
94.30000
Corrected Total
15 1967.00000
7.25385
Parameter Estimates
Variable
DF
Parameter
Monday, September 28, 2015 08:59:52 PM 1
The MEANS Procedure
SAS Code for problem 3.17
Data Salesgrowth;
input year sales;
datalines;
0 98
1 135
2 162
3 178
4 221
5 232
6 283
7 300
8 374
9 395
;
Proc means;
var year sales;
run;
proc reg;
model sales=year/
Maung Soe Htet
HW 2
The SAS code was the same one from HW 1.
Problem 2.6
a. (0.975,8) = 2.306, 1 = 4, cfw_1 = 0.469
95% Confidence Interval for 1
4 2.306(0.469), 2.918 1 5.082
4
b. 0 : 1 = 0, : 1 0. = 0.469 = 8.529. If | | 2.306 conclude0 , otherwise .
C
SPECIES
Quokka
Hedgehog
Tree shrew
Elephant shrew I
Elephant shrew II
Lemur
Slow loris
Bush baby
Howler monkey
Ring-tail monkey
Spider monkey I
Spider monkey II
Gentle lemur
Rhesus monkey I
Rhesus monkey II
Hamadryas baboon
Western baboon
Vervet guenon
Le
Name (PRINT): Wang
(Last Name)
Xiangsheng
Student id:
(Given Name)
Mark:
Math 1540M 3.00 W2012 Introductory Mathematics for Economists II
Second in-class midterm exam (total 30 points)
February 29 (Wednesday) 10:30-11:15
Instructions:
1. Please write down
Name (PRINT): Wang
(Last Name)
Xiangsheng
Student id:
(Given Name)
Mark:
Math 1540M 3.00 W2012 Introductory Mathematics for Economists II
First in-class midterm exam (total 30 points)
January 25 (Wednesday) 10:30-11:15
Instructions:
1. Please write down y
Tips for checking a reduced matrix
1. Check if the zero-rows are at the bottom.
1 0 0
0 0 0
0 1 0
The matrix can be reduced by interchanging row 2 and row 3:
1 0 0
1 0 0
R2 R3
0 0 0 0 1 0
0 1 0
0 0 0
Reduced matrix
First
Previous
Next
Last
1
Tips for ch
Solving systems by reducing matrices
Linear system
A11X1 + A12X2 + + A1nXn = B1
A X + A X + + A X = B
21 1
22 2
2n n
2
.
.
Am1X1 + Am2X2 + + AmnXn = Bm
Matrix equation AX = B.
Reduce the augmented coecient matrix [A | B] to [A | B].
Solve the simpli
Lecture Notes for Math 1000
Dr. Xiang-Sheng Wang
Memorial University of Newfoundland
Oce: HH-2016, Phone: 864-4321
Oce hours: 13:00-15:00 Wednesday, 12:00-13:00 Friday
Email: [email protected]
Course website: http:/www.ucs.mun.ca/~xiangshengw/1000.html
Lectur
MATHEMATICS 1000 (Calculus I) - Winter 2012/2013
Assignment #7 Solution
dy
1. Find dx for the following implicit functions.
(1)
ey = sin(x + y)
(2)
xy = cosh x + sinh y
Solution.
(1)
(2)
dy
dy
= cos(x + y) 1 +
dx
dx
cos(x + y)
dy
= y
dx
e cos(x + y)
ey
y+
MATHEMATICS 1000 (Calculus I) - Winter 2012/2013
Assignment #3 Solution
Find the limits of the following problems. Label the limits as or where appropriate. If the limit does not exist, indicate this as DNE.
1
1
|x2 x|
+ 2
lim
lim
(2)
(1)
x0
x x x
x1+ x 1