Math 280
Course Information
Instructor: Dr. Ernie Solheid
Office: McCarthy Hall 182A
Email: [email protected]
Office Hours: MW 2:30 3:30
WF 10:0010:50
Strategies of Proof
Fall 2016
Phone: (657) 278-7023
Available at other times
by appointment
Course
Math 280
Syllabus
Strategies of Proof
Fall 2016
You should view the indicated video lectures before the dates for which they are listed.
Assignment
Date
Section Video Lecture
due
Aug 22 M
1.1
Statements and Logical ConnectivesParts 1 & 2
24 W
1.1
Statemen
Gonzalez 1
Cristal Gonzalez
Dr. B
CSUF Math 380
November 17, 2016
Assignment Eight
36a. Use Euler's approach to factor
P ( x )=1
x x2
12 12
into linear factors of the form (1 -
x/a).
Solution:
Eulers approach for factoring any polynomial stated that any p
Gonzalez
1
Cristal Gonzalez
CSUF Math 380
Assignment One
1st September 2016
Problem one: Given Segment AB Below. Make separate constructions for each of the
following. Please write out step-by-step procedure for (a).
Note (for instructor): See the back of
Math 307
Linear Algebra
Homework Solutions
6.3 THE ADJOINT OF A LINEAR OPERATOR
1. Find the least-squares solution to the system of
0
4x
= 2
4
2y = 0
A = @0
1
x + y = 11
Spring 2017
equations
1
0
x
2A,
~x =
,
y
1
0
1
2
~b = @ 0 A .
11
(a) Using the orth
Name:
Math 338
Exam 1 Lab
Spring 2017
Use R to answer the following questions. You need to include both the R-codes and
the results. Each question should be on one page of paper.
Your answers should look like this:
Answer:
> R codes.
Result.
(insert comme
Math 380 Assignment Two
Due: Tuesday Sept. 13, 320 BCE
As a reminder, all problems are to be formally written out (typed or very nicely hand-written). As
before, please be sure to follow these steps.
Work the problem completely on separate paper first. B
Math 307
Linear Algebra
Spring 2017
Exam 1 Review Problems
The following problems are intended to give you an idea as to the type of problems you might expect
to see on the exam. You should use these problems to help review general concepts. The actual ex
Math 307
Linear Algebra
Homework Solutions
1.5 LINEAR DEPENDENCE AND LINEAR INDEPENDENCE
Spring 2017
3. Prove that the following statements are false.
(a) For all subsets S of V , if S is a linearly dependent set, then each vector in S is a linear combina
Gonzalez 1
Cristal Gonzalez
Dr. B
CSUF MATH 380
December 6, 2016
Assignment #9
41. Give three examples each of sets that
a) are denumerable
cfw_1,2,3,4,5, 6, .
cfw_2,4,6,8,10,
cfw_1,1,2,3,5,
b) are not denumerable
set of numbers between zero and one, (0,1
Section 10.1 & 10.2 : Linear Regression Model and One-way ANOVA
Recall that in chapter 6 and 7 we used sample mean to estimate the population mean
via confidence intervals and hypothesis testing.
sample x estimate
We will follow the same approach for the
Math 307
Homework Solutions
1.2 VECTOR SPACES
Linear Algebra
Spring 2017
1. Disprove the following statements by finding a counterexample.
(a) For all a, b 2 F and for each ~x 2 V , a~x = b~x implies a = b. (You need to first choose a specific
vector spac
Math 338
Chapter 11 Example
For this example, we will perform an analogous investigation for a data set called icecream.txt (available
in Titanium).
We will consider predicting ice-cream consumption (IC) from price, income, temperature, and/or year.
1. Ob
MATH 380 EXTRA CREDIT
CREATIVE PROJECT
Fall 2016 Up to 20 points
Overview
In this course we have traced some of the great ideas and people in mathematics and
the ways in which these affected and were affected by the cultures and times in which
they existe
Math338
Name:_
Lab Ch 11: Multiple Regression Analysis
Working with the file named happiness.csv
Consider the following five variables for each nation:
LSI, life-satisfaction score, an index of happiness;
GINI, a measure of inequality in the distributio
Gonzalez1
Cristal Gonzalez
Dr. B
CSUF MATH 380
November 1st, 2016
Assignment 7
31. Find the first five terms in the series to approximate the square root of 11.
Solution:
Using Newtons, infinite series expansion. Which states that,
m m
m m
m
1
1 ( 2)
m
n
Math 307
Linear Algebra
Spring 2017
Homework Solutions
6.2 GRAM-SCHMIDT ORTHOGONALIZATION PROCESS AND ORTHOGONAL COMPLEMENTS
3
1. Let V = R with the standard inner product and let W be the subspace
W = cfw_(a, b, 0) | a, b 2 R.
(c) Let ~v = (1, 2, 3) 2 V
Math 338
Quiz 3
Spring 2017
Name:_KEY
Show work for full credits. Use R as needed. You dont need to write the R codes, even though its
suggested for future exam preparation.
1. Motor vehicles sold to individuals are classified as either cars or light truc
Math 307
Linear Algebra
Spring 2017
Homework Solutions
2.3 COMPOSITION OF LINEAR TRANSFORMATIONS AND MATRIX MULTIPLICATION
4. Let V = cfw_(a1 , a2 ) | a1 , a2 2 R. Define operations on V as follows. For all ~u = (a1 , a2 ) and ~v = (b1 , b2 )
in V and for
1.4: Normal Distributions Note
A. Generating data from a Normal distribution.
Recall that in a Normal distribution, its center is determined by the mean , and its spread is controlled by the standard
deviation (sd) .
In R, we may generate random data from
Math 307
Linear Algebra
Homework Solutions
7.2 SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS
Spring 2017
1. Solve the system of dierential equations ~y 0 = A~y , where
1 3
(a) A =
3 1
The characteristic polynomial is
1 t
3
PA (t) = det
= (1 t)2 9 = t2
3
1 t
2t
Friday, May 5, 2017
Math 338
Name:
Quiz 8
Spring 2017
We will consider a dataset collected over a variety of states with the following variables:
Life Exp: life expectancy in years (196971)
Income: per capita income (1974)
Illiteracy: illiteracy (1970, pe
Math 307
Linear Algebra
Homework Solutions
5.1 EIGENVALUES AND EIGENVECTORS
Spring 2017
3. Prove Theorem 5.4: Let T be a linear operator on a vector space V , and let be an eigenvalue
of T . For all vectors ~v 2 V , ~v is an eigenvector of T corresponding
Math 307
Linear Algebra
Spring 2017
Exam 2 Review Problems
The following problems are intended to give you an idea as to the type of problems you might expect
to see on the exam. You should use these problems to help review general concepts. The actual ex
Math 307
Linear Algebra
Homework Solutions
2.2 THE MATRIX REPRESENTATION OF A LINEAR TRANSFORMATION
n
Spring 2017
m
1. Let and be the standard ordered bases for R and R , respectively. For each linear transformation
n
m
T : R ! R , compute [T ] .
2
3
(a)
Math 307
Linear Algebra
Spring 2017
Homework Assignment
Assignment 18 due Monday, May 8
Section 6.2 Gram-Schmidt Orthogonalization Process and Orthogonal Complements
3
1. Let V = R with the standard inner product and let W be the subspace
W = cfw_(a, b, 0