About Course

This course provides a rigorous and comprehensive exploration of algebraic principles and polynomial functions, designed to meet the standards of MATH 1314 – College Algebra. Through an in-depth analysis of foundational algebraic concepts, function behavior, transformations, and polynomial operations, students will develop critical mathematical reasoning and problem-solving skills necessary for advanced study in mathematics, science, and engineering. The course emphasizes function-based thinking, symbolic manipulation, and graph interpretation. With a balance of conceptual understanding and procedural fluency, this course prepares students for success in higher-level mathematics while reinforcing real-world application of algebraic techniques.

What Will You Learn?

  • Master real number properties and algebraic manipulations.
  • Solve linear equations and inequalities with confidence.
  • Read, interpret, and graph a wide range of functions.
  • Understand how transformations affect graphs and equations.
  • Compose, combine, and invert functions.
  • Analyze and solve polynomial and rational equations.
  • Identify structure and behavior of higher-degree polynomials.
  • Build fluency in mathematical notation and problem-solving techniques.
  • Prepare for success in future math courses such as Precalculus and Calculus.
  • Apply algebraic thinking to real-world and academic scenarios.

Course Content

1. Foundations and Algebraic Principles
This topic sets the stage for college-level algebra by revisiting and expanding core mathematical principles. Students will deepen their understanding of number systems, algebraic operations, and the language of mathematics. Emphasis is placed on solving linear equations and inequalities, using appropriate notation, and laying the groundwork for more abstract function-based thinking.

  • 1.1 Real Numbers and Their Properties
  • 1.2 Algebraic Expressions
  • 1.3 Solving Linear Equations and Inequalities
  • 1.4 Interval Notation and Set Builder Notation

2. Functions and Graphs
This topic introduces the formal concept of functions, their representations, and their transformations. Students will examine how functions model relationships, how their graphs reveal important information, and how operations on functions affect their behavior. Inverse functions and composition are introduced to build conceptual depth.

3. Polynomial and Rational Functions
This topic shifts focus to specific types of functions: polynomial and rational. Students will analyze structure, behavior, and applications of these functions. From quadratic models to higher-degree polynomials, students will learn to factor, solve, and graph with precision. This topic provides the algebraic fluency needed for calculus and other advanced math courses.

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