Lecture Notes on College Algebra with Corequisite Support

Introduction

• Title: College Algebra with Corequisite Support 2e
• Authors: Jay Abramson (Arizona State University), Sharon North (St. Louis Community College)
• Publisher: OpenStax, Rice University
• License: Creative Commons Attribution 4.0 International License

OpenStax and Educational Materials

• OpenStax offers free peer-reviewed, openly licensed textbooks for introductory college and Advanced Placement courses.
• OpenStax initiatives include OpenStax CNX, OpenStax Tutor, and partnerships with philanthropic organizations.
• OpenStax emphasizes educational accessibility and equity.

Textbook Details

• Covers comprehensive algebraic principles with foundational review.
• Includes Corequisite Skills modules for student preparation.
• Contains examples, exercises, and solutions reviewed by faculty experts.
• Focuses on inclusivity and broadening historical and cultural perspectives.

Key Concepts and Features

Algebra Essentials

• Real Numbers: Classify as natural, whole, integer, rational, or irrational.
• Order of Operations: PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
• Properties of Real Numbers: Commutative, associative, distributive, identity, and inverse properties.

Functions

• Function Notation: f(x) indicates function f evaluated at x.
• Domain and Range: Identifying feasible input (domain) and output (range) values.
• Types of Functions: Linear, quadratic, polynomial, rational, exponential, logarithmic, etc.

Equations

• Linear Equations: Form y = mx + b, solutions using algebraic properties.
• Quadratic Equations: Solutions via factoring, completing the square, and the quadratic formula.
• Rational Equations: Solutions with least common denominator approach.

Inequalities

• Linear Inequalities: Solve similar to equations, noting changes when multiplying/dividing by negative numbers.
• Absolute Value Inequalities: Considerations of two cases for solutions.

Systems of Equations

• Solving techniques include substitution, elimination, and matrix operations.
• Applications in modeling real-world scenarios.

Polynomial and Rational Functions

• Polynomials: Degree, leading coefficient, addition, subtraction, multiplication.
• Factoring: Importance of GCF, difference of squares, sum/difference of cubes.

Exponential and Logarithmic Functions

• Exponents: Rules for multiplication, division, power, and roots.
• Logarithms: Inverses of exponential functions, properties and applications.

Additional Topics

• Analytic Geometry: Study of conic sections (ellipse, parabola, hyperbola).
• Sequences and Series: Arithmetic and geometric sequences, series summation.
• Probability: Basics of probability, counting principles, binomial theorem.

Study and Learning Strategies

• Growth Mindset: Encouragement of learning through effort and perseverance.
• Note-taking: Use of techniques like the Cornell Method for effective study.
• Problem Solving: Strategies include breaking down problems, systematic practice, and utilizing available resources.

Additional Resources

• OpenStax provides instructor and student resources, including solution guides and community forums for collaborative learning.
• Technology resources are integrated for enhanced learning experiences.

Philanthropic Support

• Supported by various foundations and companies committed to advancing education, including Gates Foundation, Google, and Hewlett Foundation.