Course Overview

Introduction to College Algebra (MATH 1213 / SPSM 0213)

This course introduces students to fundamental concepts in algebra, including quadratic equations, systems of linear equations, inequalities, functions, graphs, exponential and logarithmic functions, complex numbers, and the theory of equations. It is designed to prepare students for further study in mathematics and related fields.

• Prerequisites: Placement test score or completion of Math 094 or Math 0099 with a grade of “C” or better.

• Corequisites: SPSM 0213 provides supplemental instruction to reinforce algebraic skills.

• Textbook: Algebra and Trigonometry by Blitzer, 8th edition.

• Calculator: TI-30X II S or TI-30X II B (no other calculators allowed).

Learning Outcomes

Key Competencies

• Analyze and solve problems in STEM, business, and social sciences using mathematical strategies.

• Apply properties of algebra to evaluate functions, graphs, circles, and other algebraic concepts.

• Perform operations with exponents and polynomials.

• Write equations of lines and factor polynomials.

• Identify, evaluate, graph, sketch, and determine domain and range of relations.

Expanded Course Outline

Major Topics and Subtopics

• I. Equations and Inequalities

  • Graphs and Graphing Utilities

  • Linear and Rational Equations

  • Models and Applications

  • Complex Numbers

  • Quadratic Equations and Applications

  • Other Types of Equations

  • Linear Inequalities and Absolute Value Inequalities

• II. Graphs and Functions

  • Basics of Functions

  • Functions and Their Graphs

  • Linear Functions and Slope

  • Systems of Linear Equations

  • Transformations of Functions

  • Combinations and Composite Functions

  • Inverse Functions

  • Distance and Midpoint Formulas; Circles

• III. Polynomial and Rational Functions

  • Quadratic Functions

  • Polynomial Functions and Their Graphs

  • Dividing Polynomials; Remainder and Factor Theorem

  • Zeros of Polynomials

  • Rational Functions and Their Graphs

  • Polynomial and Rational Inequalities

• IV. Exponential and Logarithmic Functions

  • Exponential Functions

  • Logarithmic Functions

  • Properties of Logarithms

  • Exponential and Logarithmic Equations

  • Exponential Growth and Decay; Modeling Data

Course Structure and Assessment

Modules and Assignments

• Weekly modules include lectures, assignments, quizzes, exams, and discussions.

• Lectures are provided as PPT files, audio PDFs, and videos.

• Homework, quizzes, and exams are managed through Canvas and MyMathLab.

• Written assignments must be submitted as a single PDF file.

• Participation in discussion forums is required.

Grading Breakdown

Grade Scale:

Study Suggestions

• Engage in aggressive learning; dedicate time and effort to mastering the material.

• Form study groups or find a study partner.

• Keep up with assignments and pre-read sections before class meetings.

• Utilize online resources and instructor office hours for support.

Key Mathematical Concepts (Expanded Academic Context)

Equations and Inequalities

Solving equations and inequalities is foundational in algebra. Types include linear, quadratic, rational, and absolute value equations and inequalities.

• Linear Equation: An equation of the form .

• Quadratic Equation: An equation of the form .

• Rational Equation: An equation involving fractions with polynomials in the numerator and denominator.

• Absolute Value Inequality: An inequality involving .

• Example: Solve ; .

Functions and Graphs

Functions describe relationships between variables. Understanding their graphs, domain, and range is essential.

• Function: A relation where each input has a unique output.

• Domain: Set of all possible input values.

• Range: Set of all possible output values.

• Example: ; domain: all real numbers, range: .

Polynomial and Rational Functions

Polynomials are expressions with powers of variables. Rational functions are ratios of polynomials.

• Polynomial:

• Rational Function: where

• Example:

Exponential and Logarithmic Functions

Exponential functions involve variables in exponents; logarithmic functions are their inverses.

• Exponential Function:

• Logarithmic Function:

• Properties:

• Example: ;

Course Policies and Resources

• Assignments must be submitted on time and in the correct format (PDF).

• Participation in online discussions is required for attendance and grade.

• Academic honesty is strictly enforced; cheating and plagiarism result in course failure.

• Accommodations are available for students with disabilities.

• Technical support is available for Canvas and MyMathLab.

Important Dates

• Mardi Gras: Feb. 12 - 13

• Spring Break: Mar 29 – Apr 7

• Midterm: March 4 - 9

• Last day to withdraw: March 28

• Last Day of Class: May 3

• Final Exam period: May 6 - 11

Web Resources

• Canvas

• MyMathLab

• Center of Math

• BRCC Learning Center

• MathBFF

• PatrickJMT

• MathTV

Additional info:

• This syllabus covers all major Precalculus topics as outlined in standard college algebra courses, including equations, inequalities, functions, polynomials, rational, exponential, and logarithmic functions.

• Students are expected to engage actively in learning, maintain academic integrity, and utilize available resources for success.