Algebra: Elementary to Advanced Specialization Course Syllabus
Full curriculum breakdown — modules, lessons, estimated time, and outcomes.
Overview: This specialization provides a comprehensive journey from elementary to advanced algebra, designed to build a strong foundation in algebraic concepts and their applications. The course is divided into three core modules, each focusing on key areas such as equations, functions, and polynomials. With a total time commitment of approximately 20 hours, learners will engage with interactive content, practice exercises, and real-world applications. The structured curriculum is ideal for those preparing for advanced studies or seeking to strengthen analytical skills for careers in data science, engineering, economics, and finance.
Module 1: Algebra: Elementary to Advanced – Equations & Inequalities
Estimated time: 10 hours
- Properties of real, rational, and irrational numbers
- Solving linear equations and inequalities
- Polynomials and rational expressions
- Radicals and exponents
- Quadratic equations and their solutions
Module 2: Algebra: Elementary to Advanced – Functions & Applications
Estimated time: 5 hours
- Concept and definition of a function
- Domain, range, and function notation
- Graphs of functions and intercepts
- Applications of functions in various disciplines
Module 3: Algebra: Elementary to Advanced – Polynomials and Roots
Estimated time: 5 hours
- Properties of polynomials
- Factoring and expanding polynomial expressions
- Finding roots of polynomials
Module 4: Analyzing Functions
Estimated time: 2 hours
- Identifying asymptotes and end behavior
- Transformations of functions
- Combining and composing functions
Module 5: Modeling with Algebra
Estimated time: 3 hours
- Using algebra to model real-world data
- Logical reasoning and evaluation of arguments
- Applications in exponential and polynomial models
Module 6: Final Project
Estimated time: 5 hours
- Solve a comprehensive set of algebraic problems across all topics
- Analyze and interpret function behavior in applied contexts
- Demonstrate mastery through problem-solving and reasoning
Prerequisites
- Basic arithmetic skills
- Familiarity with elementary algebra concepts
- High school level mathematics background
What You'll Be Able to Do After
- Solve linear, quadratic, polynomial, and exponential equations
- Understand properties of real, rational, and irrational numbers
- Analyze functions including graphs, domains, ranges, intercepts, and asymptotes
- Apply algebraic concepts to model data and real-world scenarios
- Reason logically and evaluate mathematical arguments