Algebra is the language of modern science and engineering. Every programming language, every algorithm, and every data structure builds on algebraic concepts: variables, functions, equations, and transformations.
Whether you are writing code, designing circuits, or analyzing data, algebra provides the foundation you need to think in structures rather than isolated steps. In an era where computational thinking is a core skill across disciplines, a solid grasp of algebra opens doors to machine learning, cryptography, graphics programming, and scientific computing.
About the book
Basic Algebra by Ivan G. Zaigralin is a comprehensive, application-oriented algebra textbook that takes readers from the fundamentals of arithmetic to quadratic equations and complex numbers.
What sets this book apart is its dual focus: it teaches algebra through the lens of real-world applications while also providing the rigor needed for academic success. Each chapter includes worked examples, homework problems with answers, and practice tests, making it suitable for both classroom use and self-study.
The book assumes no prior knowledge beyond basic arithmetic and builds up progressively. It includes a full appendix for instructors with lecture notes, making it a complete resource for anyone teaching or learning algebra from scratch. The sixth edition has been refined through years of classroom feedback.
What you will learn
- How expressions, relations, and substitution work at a fundamental level
- Real number axioms and the properties that govern arithmetic
- Solving linear equations and systems of equations
- Graphing lines, slopes, and linear functions
- Working with polynomial expressions, factoring, and rational expressions
- Radicals, square roots, and rational exponents
- Quadratic equations, complex numbers, and the quadratic formula
- Applying algebra to real-world problems in distance, work, percent, and geometry
Table of contents
- Chapter 1: Concepts — expressions, real number axioms, number line, prime numbers, fractions, translation
- Chapter 2: Linear Equations — properties of equations, solving, formulas, percent, inequalities
- Chapter 3: Graphing — Cartesian plane, linear equations, intercepts, slope, function notation
- Chapter 4: Linear Systems — graphing, substitution, elimination, applications, multivariate inequalities
- Chapter 5: Polynomial Expressions — integer exponents, polynomials, sums, products, quotients
- Chapter 6: Factoring Polynomials — GCF, grouping, factoring trinomials, special products, solving by factoring
- Chapter 7: Rational Expressions — simplifying, products, LCD, sums, complex fractions, equations
- Chapter 8: Radicals — square roots, products, quotients, sums, equations, right triangles, rational exponents
- Chapter 9: Quadratic Equations — complex numbers, square root property, completing the square, quadratic formula
Book details
- Title: Basic Algebra
- Author(s): Ivan G. Zaigralin
- Publication year: 2023
- Publisher: Samizdat
- Pages: 513
- PDF size: 1.51 MB
- Estimated reading time: ~12 h 50 min
- Level: Beginner to Intermediate
- Main category: Mathematics
- Subcategory: Algebra
- Language: English
- License: CC BY-SA 4.0
More books in: Algebra, Mathematics
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