FINAL EXAM REVIEW - MATH 1021 SECTION A
You will be allowed one page of notes and a calculator (ones that can't do linear algebra) for this exam. (1) Find the line which best approximates the points (0, 0), (1, 1), (2, 4), (3, 6) using the least squares a
Proof by Contradiction
In a proof by contradiction we assume, along with the hypotheses, the logical
negation of the result we wish to prove, and then reach some kind of contradiction. That
is, if we want to prove "If P, Then Q", we assume P and Not Q. Th
Notes on Determinants
Prof. H Joshi (York University)
There are several ways to define determinants and all have some advantages and some
drawbacks. We adopt a definition that saves teaching time and makes it easier to prove
some results.
Recall three typ
Direct Proofs
Let's start with an example.
Example: Divisibility is Transitive
If a and b are two natural numbers, we say that a divides b if there is another natural
number k such that b = a k. For example, 2917 divides 522143 because there is a natural
Mathematical Induction
Let's begin with an example.
Example: A Sum Formula
Theore. For any positive integer n, 1 + 2 + . + n = n(n+1)/2.
Proof. (Proof by Mathematical Induction) Let's let P(n) be the statement "1 + 2 + . + n
= (n (n+1)/2." (The idea is th
The Pigeon Hole Principle
The so called pigeon hole principle is nothing more than the obvious remark: if you
have fewer pigeon holes than pigeons and you put every pigeon in a pigeon hole, then
there must result at least one pigeon hole with more than on
1
Math 1021, Section 13, Spring 2014
College Algebra Online Syllabus
You are responsible for abiding by all of the rules and policies stated on this syllabus. Print it and read
it carefully. Refer to it throughout the semester.
Teacher: Mrs. D. Kopcso
Pho
QUIZ III - MATH 1021 - NOVEMBER 18, 2004
Note there are several ways of solving these problems and there arent unique solutions. I am just using properties of vectors here which appear in chapter 4.
(1) Find the equation of the plane which contains both o
QUIZ IV - MATH 1021 - NOVEMBER 18, 2004
Note there are several ways of solving these problems and there aren't unique solutions. I am just using properties of vectors here which appear in chapter 4. (1) Find the equation of the plane which contains the li