Yong Zhao, Yu-Tzeng Chen, Gouri Gupta
MAT 115A
SSI16
24th, June, 2016
Discussion 1
5 (c) Let a, n, m N with a, n, m > 1. Find a factorization for anm 1.
Proof :
we claim: anm 1 = ( an 1)( an(m1) + an(
17 October 2016
CW. Find the first 5 terms of the given seq.
a. An = 2n+1 = 3,5,9,17,33
b. Bk=7+3k = 10,13,16,19,22
c. An=3a2n-1-an-2 = a0=1, a1=2
Ex. Find first 5 terms
An=-5an-1 a0=2
a1 = -5(2) = -1
05 OCT 16
2.2 (cont.)
AUB=cfw_x: x A U x B
A
B= cfw_x: x A
x B
= cfw_x: x A
A
A-B =cfw_x: x A
x
B
Ex. Show that
A B A B
Want to show 1.
A B A B
and 2.
A B A B
PROOF 1.
Let
If
x A B
x A
then
then
x
Yong Zhao
MAT 115A
SSI16
July, 11th
Homework 3
1. (3.7.2) For each of the following linear Diophantine equations, either find all solutions
or show that there are no integral solutions.
1. 60x + 18y =
Yong Zhao
MAT 115A
SSI16
July, 11th
Homework 3
1. (3.7.2) For each of the following linear Diophantine equations, either find all solutions
or show that there are no integral solutions.
1. 60x + 18y =
Yong Zhao
MAT 115A
SSI16
Tuesday, June 28
Homework 1
1. (1.1.5) Prove that
3 is irrational using the Well-Ordering Principle.
Proof :
For sake
of
contradiction,
suppose
3
is
rational,
so
3Q
Then 3 =p/
Yong Zhao, Yu-Tzeng Chen, Gouri Gupta
MAT 115A
SSI16
24th, June, 2016
Discussion 2
3. (a) prove there are no integral solutions to equation 13x + 39y = 3 (b)find all integral
solutions to the linear D
Yong Zhao
MAT 115A
SSI16
July, 24th
final 2
1. The message in buddha.txt was encrypted using an affine cipher. Decrypt the message.
(1). (20 points) First, provide your key, and show the work explaini
Yong Zhao
MAT 115A
SSI16
July, 11th
Homework 5
1. (6.3.1abc) 1.
For all n cfw_6, 9, 10, calculate (n).
2.
For all n cfw_6, 9, 10, find a reduced residue system modulo n.
Proof :
1.
by the Eulor pld fu
Patrick Weed
MAT 201A
Babson
25 October 2013
Homework 4
2. (Homework 3) Let p : R2 R be a polynomial function of two real variables. Suppose that p( x, y) 0 for all x, y R. Does every such function at
Website Review example
Summary of findings
This report discusses a review of the User Experience (UX) of the Your Site Here
website. A number of areas were found where improvements can to be made to t
Yong Zhao
MAT 115A
SSI16
July, 11th
Homework 4
1. (4.3.2) Find an integer that leaves a remainder of 1 when divided by either 2 or 5, but
that is divisible by 3.
Proof :
since we need an integer that
Math 261
Insert Name Here
Fall 2010
Prof. Belk
Sample Assignment 2
Exercise 1.5.11
Part (1)
(1) (x in U )[R(x) C(x)]
(2) (x in U )[T (x) R(x)]
Consider an arbitrary a in U .
(3) R(a) C(a)
(1), Univers
Yong Zhao
MAT 115A
SSI16
July, 11th
Homework 5
1. (6.3.1abc) 1.
For all n cfw_6, 9, 10, calculate (n).
2.
For all n cfw_6, 9, 10, find a reduced residue system modulo n.
Proof :
1.
by the Eulor pld fu
Yong Zhao
MAT 115A
SSI16
July, 11th
Homework 3
1. (3.7.2) For each of the following linear Diophantine equations, either find all solutions
or show that there are no integral solutions.
1. 60x + 18y =
HOMEWORK 2, MATH 150A, FALL, 2016
Due date: Monday, 10/3/2016, 10AM
Suggested readings: Artin, 2nd Edition 2.1-2.4
(1) Let X be the set of real numbers excluding 1. Define ? on X by x ? y = x + y + xy
HOMEWORK 3, DUE 10/10/2016, MONDAY 10AM, MATH 150A
Suggested Readings: Sections 1.5, 2.1-2.6
(1) (a) As r varies, show that (123 n)r (12)(123 n)nr gives all the transpositions
(12), (23), (34), ., (n-
03 OCT 16
Show for any prime number P if P divides A, A
Z, then P does not divide A+1
PROOF: Let A Z and P be a prime number s.t. P divides A. Then A=PK for some K Z. Suppose by
contradiction that P d