COURSE NUMBER: MATH 17 COURSE CREDIT: 5 Units COURSE TITLE: College Algebra and Trigonometry COURSE DESCRIPTION: Sets and numbers; the algebra of numbers as a logical system;

inequalities; absolute value and coordinate system; functions and graphs; circular, linear, quadratic and polynomial function; exponential and logarithmic functions; applications of the circular functions; angles

COURSE GOALS:

1. Develop algebra as the study of structures 2. Revisit algebraic expressions and the operations defined on them 3. Explore the algebra of functions and relations 4. Discuss, in details, the properties and graphs of

a. algebraic functions b. exponential and logarithmic functions c. circular and trigonometric functions d. inverse functions

5. Develop student’s ability to solve problems using algebraic and trigonometric tools a. Understand and represent the problem b. Identify analytic tools to solve the problem c. Find a solution to the problem d. Evaluate the solution

6. Develop student’s ability to prove mathematical (algebraic and trigonometric) statements a. Identities b. Inequalities

7. Develop in the student an appreciation of the beauty and power of algebra and trigonometry as they relate to the disciplines, professions, and the real world

8. Infuse a passion for learning and articulate the ways and values of scholarship and independence to ensure lifelong learning

COURSE OUTLINE

I. Algebra as the Study of Structures 1. Sets, Set Operations and Number Sets: The Basic Objects of Algebra 2. The Real Number System as a Number Field

a. Group properties b. Ring properties c. Field properties d. Ordered field properties e. Completely ordered field

3. The Complex Number System as a Number Field a. Group properties b. Ring properties c. Field properties

4. The Ring of Polynomials a. Addition and subtraction b. Multiplication

5. The Field of Algebraic Expressions a. Addition and subtraction b. Multiplication c. Division

6. Equations a. Linear equations

i. Canonical form ii. Literal equations iii. Problem solving

b. Quadratic Equations i. Different solution techniques ii. Equations in quadratic forms iii. Problem solving

c. Other equations i. Rational equations ii. Irrational equations iii. Polynomial equations iv. Problem solving

7. Inequalities a. Linear inequalities b. Quadratic inequalities c. Rational inequalities

II. A Theory of Relations and Functions

1. Relations: Domain, Range, and Rule 2. Graphs of Relations: Conic Sections

a. Circle b. Parabola c. Ellipse d. Hyperbola

3. Functions as Relations: Domain, Range, Rule and Graphs a. Differentiating functions from relations b. Types of functions: into, onto, and bijective c. Properties of functions

i. Monotonicity ii. Boundedness iii. Operations on Functions iv. Inverses

4. Functions as Mathematical Models

III. Exponential and Logarithmic Functions 1. Exponential Functions: Properties and Graphs 2. Logarithmic Functions: Properties and Graphs 3. Equations Involving Exponential and Logarithmic Expressions 4. Hyperbolic and inverse hyperbolic functions 5. Problem Solving

IV. Circular and Trigonometric Functions

1. Circular Functions a. Definitions b. Properties and Graphs c. Identities d. Trigonometric functions

2. Inverse Circular Functions a. Definitions b. Properties and Graphs c. Identities

3. Equations Involving Circular and Inverse Circular Functions 4. Solution of Triangles

V. Systems of Equations and Inequalities

1. Systems of Linear Equations in Two and Three Unknowns a. Methods of solution b. Problem Solving

2. Matrices and Determinants 3. Systems of Non-linear Equations 4. Systems of Inequalities 5. Problem Solving