| |
Math 115 Elementary Algebra
Terry Foley
Office: Math Department
(323) 265-8886
E-mail: Terry@TerryFoley.com
Time: 6:50 9:20 T/Th
Room: E5 - 106
|
|
Textbook:
Elementary & Intermediate Algebra by C. P. McKeague
Course Description:
This course is an elementary introduction to axiomatic algebra.
It begins with the postulates covering the fundamental operations of
natural numbers and carries on a logical development through all real
numbers.
It includes the solution of equations through quadratics.
Grade: Your
grade will be determined by the following:
|
|
|
Quizzes
20%
Homework 50%
Final Exam 30%
|
Homework:
Homework will be assigned at the end of each class and will
be due at our next meeting. Itll be virtually impossible to learn
the material in this
class without doing the homework!!
Attendance: It
is important that you attend all classes.
|
Some
Definitions - in no special order
Algebra that branch of math that deals with relations and
properties of numbers by means of letters, signs of operations and other
symbols. It includes the solution of equations, polynomials, etc.
Postulate to assume or claim as true - an axiomatic statement.
Axiom an established rule or principle or self-evident truth. Axioms define the
fundamental rules orlaws of mathematics.
Rule - a method for performing a mathematical operation and
obtaining a certain result.
e.g. Cramer's Rule.
Law - law is synonymous with rule.
e.g. Law of Sines.
Theorem - a formula, proposition, or statement in
mathematics or logic deduced from other formulas or propositions.
e.g. the binomial theorem, which comes from the
binomial formula.
Natural numbers they are counting numbers, e.g. 1, 2, 3,
etc.
Whole numbers they are natural numbers, plus zero, e.g. 0,
1, 2, 3, etc.
Integers they include the whole numbers plus the negative
numbers,
e.g. -2, -1, 0, 1, 2, 3, etc.
Real numbers they are all the integers including rational
and irrational numbers
Rational numbers integers that can be represented as
fractions,
e.g.Ύ.
Irrational numbers they cannot be represented as a fraction
and they are non-repeating numbers such as pi, e.g. 3.141592654
..
Complex numbers - any number that can be written as a +
bj, where a represents the real part and bj represents the
imaginary part. j is equal to the square root of -1.
Imaginary numbers - they are represented by the letter j,
where j is equal to the square root of -1.
Prime numbers - any positive integer larger than 1 that is
only divisible by itself and 1. e.g. 2, 3, 5, 7, 11, etc.
Composite numbers - any whole number larger than 1 that is
not a prime number.
Mixed numbers - the sum of an integer and a fraction. e.g.
5Ύ
Polynomial a polynomial is the sum of terms. Terms
are connected by plus and minus signs.
Monomial - a monomial is a single term, e.g. 3x, -4, 15xy.
Binomial - a binomial contains two terms, e.g. a + b.
Quadratics an equation that contains the unknown, x,
to the second (and no higher!) degree.
The standard form of the quadratic equation is:
ax² + bx + c = 0.
This equation is, by definition, a polynomial.
|
