--- title: Algebra description: Algebra is the study of mathematical symbols and the rules for manipulating them. Learners will understand how to solve equations, analyze functions, and use variables to represent real-world relationships and quantitative problems. category: mathematics subcategory: algebra difficulty: beginner, intermediate, advanced url: /subject/algebra --- # Algebra Algebra is the study of mathematical symbols and the rules for manipulating them. Learners will understand how to solve equations, analyze functions, and use variables to represent real-world relationships and quantitative problems. ## Available Resources 4 Books • 4 Courses • 7 Websites ## Websites ### 1. Purplemath Elizabeth Stapel's free lesson site covering pre-algebra through intermediate algebra, including equations, inequalities, graphing, polynomials, factoring, radicals, exponents and word problems. Each lesson works through examples step by step, explaining common mistakes and how to check answers. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.purplemath.com/modules/index.htm **Tags:** algebra, pre-algebra, equations, factoring, word-problems ### 2. Paul's Online Math Notes Paul Dawkins's free algebra notes from Lamar University, covering preliminaries, solving equations and inequalities, graphing, functions, polynomials, exponential and logarithmic functions, and systems of equations. Worked examples and practice problems prepare students for calculus-level work. **Difficulty:** Beginner | **Price:** Free **Link:** https://tutorial.math.lamar.edu/Classes/Alg/Alg.aspx **Tags:** algebra, functions, equations, logarithms, college-algebra ### 3. Math is Fun - Pre-Algebra Free illustrated reference site whose algebra section introduces variables, expressions, equations, inequalities, exponents and basic graphing through short explanations, worked examples and interactive quizzes, helping learners build intuition before formal algebra coursework. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.mathsisfun.com/algebra/index.html **Tags:** pre-algebra, algebra-basics, equations, variables, math-reference ### 4. Wolfram Alpha **Author:** Wolfram Research Computational knowledge engine that answers typed natural-language or symbolic queries by solving equations, factoring and simplifying expressions, and plotting functions. Students can check algebra work and inspect results, though full step-by-step solutions require a paid Pro subscription. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.wolframalpha.com/ **Tags:** computational-algebra, equation-solving, symbolic-computation, graphing, math-tools ### 5. algebra.org Algebra.org is an educational resource dedicated to learning algebra, offering clear lessons, explanations, and practice problems. It covers core topics from expressions and linear equations to polynomials, factoring, functions, and solving inequalities. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://algebra.org **Tags:** websites, mathematics-statistics, mathematics ### 6. math.stackexchange.com Math Stack Exchange is a community Q&A site for mathematics where users ask, answer, and discuss problems across topics from algebra to advanced theory. It features a large archive of math questions with detailed explanations, proofs, examples, and peer-voted high-quality answers. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://math.stackexchange.com **Tags:** websites, mathematics-statistics, mathematics ### 7. artofproblemsolving.com AoPS is a comprehensive mathematics learning community offering challenging problems, step-by-step solutions, and active forums, along with online courses and textbooks for competition math. It provides problem sets, tutorials, and classroom resources covering topics from fundamentals to advanced contest math. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://artofproblemsolving.com **Tags:** websites, mathematics-statistics, mathematics ## Courses ### 1. Algebra 1 **Author:** Sal Khan Complete school Algebra 1 course of video lessons and graded practice covering linear equations and inequalities, graphing, functions, systems of equations, exponents, polynomials and quadratics. Learners finish able to solve and graph linear and quadratic problems and read function notation. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.khanacademy.org/math/algebra **Tags:** algebra, linear-equations, functions, systems-of-equations, quadratic-equations ### 2. Linear Algebra (MIT 18.06) **Author:** Gilbert Strang Matrix theory and linear algebra: systems of equations, elimination, vector spaces and subspaces, orthogonality and least squares, determinants, eigenvalues and positive definite matrices. Includes 35 lecture videos plus problem sets and exams with solutions, giving the fluency needed for applied mathematics, engineering and data science. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/ **Tags:** linear-algebra, vector-spaces, eigenvalues, least-squares, matrix-factorization ### 3. College Algebra Coursera course: Basic Math: Algebra **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/basic-math-algebra **Tags:** courses, mathematics-statistics, algebra ### 4. Algebra: Elementary to Advanced - Polynomials and Roots **Author:** Joseph W. Cutrone Third course in Johns Hopkins's algebra sequence, covering exponential functions, polynomial arithmetic and factoring, square and nth roots, and percent and interest applications. Finishes with a cumulative exam, preparing you for precalculus, statistics or data science coursework. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/polynomials-roots **Tags:** polynomials, factoring, exponents, radicals, algebra ## Books ### 1. Introduction to Algebra **Author:** Richard Rusczyk Learn the fundamentals of algebra with Richard Rusczyk's book! Master functions and essential algebraic concepts. **Difficulty:** Beginner | **Price:** Paid **Link:** https://www.amazon.com/dp/1934124141?tag=edmonddante07-20 **Tags:** algebra, functions, textbook, problem-solving, competition-math ### 2. Algebra and Trigonometry **Author:** Ron Larson, Robert P. Hostetler, Bruce H. Edwards Precalculus textbook built around graphing-calculator use, spanning equations, functions, polynomials, exponentials, logarithms, trigonometry and matrices. Sections open with prerequisite skill reviews and close with large exercise sets, so it works as a self-study source for algebra and trigonometry fundamentals. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/061885195X?tag=edmonddante07-20 **Tags:** precalculus, functions, trigonometry, polynomials, exponential-functions ### 3. College Algebra **Author:** Jay Abramson Print edition of the free OpenStax textbook led by Jay Abramson, covering equations and inequalities, functions and their graphs, polynomial, rational, exponential and logarithmic functions, systems of equations, matrices, conic sections, sequences and probability. Prepares students for precalculus and calculus. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1506698220?tag=edmonddante07-20 **Tags:** college-algebra, functions, polynomials, exponential-logarithmic-functions, systems-of-equations ### 4. Beginning and Intermediate Algebra **Author:** Tyler Wallace Free, openly licensed (CC-BY) textbook written for community college developmental math, moving from arithmetic review through linear equations, factoring, radicals, and quadratics. Heavy on worked examples and practice sets, it builds the procedural fluency needed to solve quadratic equations and handle college algebra. **Difficulty:** Beginner | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1458377687?tag=edmonddante07-20 **Tags:** algebra, linear-equations, factoring, radicals, quadratic-equations, open-textbook --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/algebra