Concepts introduction and problem
solving form an integral part of each class session. Students
learn extensively from and by examples, and a variety of
instructional methods are used to enhance students'
problem-solving abilities. Students tackle many complicated
problems using inductive and deductive reasoning approaches.
Some of the topics and problems that are studied in this course
include:

·
Algebra
Prerequisites:

Variables. Algebraic Expressions. Order of Operations.

Commutative Properties for Addition and Multiplication.

Associative Properties for Addition and Multiplication.

Identity Properties for Addition and Multiplication.

Distributive Property for Multiplication over Addition.

Properties of Equality. Properties of Comparison (Order).

Linear Equations and Inequalities. Equivalent Transformations of
Equations and Inequalities.

·
**Literal Equations and Formulas. Unit Analysis.
Converting Formulas.**

·
**Elements of Set Theory. **

Set Notations. Cardinality of Sets.
Operations on Sets.

·
**Introduction to Number Theory. **

Number Sets.

Relationship between the Subsets of Real Numbers Set.

·
**Elements of Math Logic. Compound Sentences.
Truth Tables. **

Conjunctions and Intersections.
Disjunctions and Unions. Venn Diagrams.

·
**Absolute Value of a Real Number. Algebraic
Definition and Geometric Interpretation. Properties.**

Absolute Values Equations. Extraneous
Solutions. Interval Method.

Absolute Values Inequalities. Graphing.
Geometric Interpretation.

·
**Linear Equations in Two Variables. A Line as a
Graph of the Equation. X- and Y- intercepts.**

Slope of a Line. A Slope as a Rate of
Change. Horizontal and Vertical Lines.

Different forms
of Linear Equations: Standard, the Slope- Intercept Form, the
Point-Slope form.

Parallel and
Perpendicular Lines.

###
·
Systems of Linear Equations in Two Variables.
Geometric Interpretation.

###
Solving Systems of Linear
Equations by Graphing, Substitution, and Linear Combination
Methods.

Solving Word Problems Using the Systems of Linear Equations.

#
·
Linear Inequalities in Two Variables. Graphing the Solution
Set.

Linear
Programming. Linear programming Major Theorem and its Geometric
Interpretation.

######
·
Monomials and
Polynomials. Their Degrees, Coefficients, and Terms. Leading
Term of a Polynomial.

Ascending and Descending Order for
Polynomials.

Addition and Subtraction of Polynomials.
Multiplication of Polynomials.

FOIL Rule for Multiplication of Binomials.
Shortcut Multiplication Formulas.

Factoring Quadratic Trinomials. Identical polynomials. Factoring
Uniqueness. Prime polynomials.

#
·
Solving Quadratic Equations.

Derivation of Quadratic Formula by
Completing the Square.

The Complete Analysis of the Real Roots
Based on the Discriminant.

Viete Theorem and its Converse.

The
Relationship between Solving Quadratic Equations and Factoring
Corresponding Quadratic Trinomials.

·
**Rational Expressions. (Algebraic Fractions.).**

Operations on
Algebraic Fractions. Complex Rational Expressions.

·
**Word Problems Leading to Quadratic and Rational
Equations. **