Elementary Algebra: Modernized Wentworth

About This Course

Welcome to a revitalized journey through the language of mathematics. This course is based on the legendary "Elementary Algebra" by George Albert Wentworth, first published in 1906. For decades, Wentworth was the gold standard of mathematical instruction, known for his clarity and rigorous logic.

However, much has changed in a century. We have modernized this text to bridge the gap between 1906 and 2026. While the core algebraic truths remain identical, we have:

Updated 19th-century terminology (e.g., "Involution" is now "Exponents").
Replaced archaic word problems about bushels of oats with modern scenarios involving digital data, finance, and technology.
Introduced modern pedagogical tools like PEMDAS and the "Balance Scale" mental model.

Interested in the roots? You can view the original 1906 text via the Internet Archive, here.

Volume I: The Foundation

Ch 1: The Language of Algebra Ch 2: Combining Like Terms Ch 3: Evaluating Expressions Ch 4: Simple Equations Ch 5: Positive & Negative Numbers Ch 6: Multiplying Signed Numbers Ch 7: Exponents and Powers Ch 8: The Order of Operations Ch 9: Grouping Symbols Ch 10: The Distributive Property Ch 11: Cleaning Up Expressions Ch 12: One-Step Equations Ch 13: Two-Step Equations Ch 14: Variables on Both Sides Ch 15: Literal Equations (Formulas)

Part 2: Systems and Advanced Factoring

Moving beyond single variables into complex systems and the art of factoring.

Chapter 16: Simultaneous Simple Equations
Chapter 17: Factoring
Chapter 18: Fractions
Chapter 19: H.C.F. and L.C.M.

Part 3: Quadratics, Progressions, and Limits

In this final section, we move beyond linear mathematics into second-degree equations, the study of mathematical series, and the foundational concepts of modern limits and logarithms.

Chapter	Title
20	Quadratic Equations
21	Simultaneous Quadratics
22	Properties of Quadratics
23	Ratio and Proportion
24	Variation
25	Arithmetical Progression
26	Geometrical Progression
27	Harmonical Progression
28	Binomial Theorem
29	Variables and Limits
30	Series
31	Logarithms
32	Final Review and General Theory

The Doctor's Prescription: Essential Toolkit

Success in Algebra isn't just about logic—it's about having the right tools to visualize the problem. If you are following this course from Chapter 1 through 15, there is one piece of equipment the "Doctor" considers mandatory.

The TI-30XS MultiView Scientific Calculator

Modern Algebra is often confusing because standard calculators "flatten" math into a single line. The TI-30XS MultiView solves this by using "MathPrint"—showing fractions, exponents, and square roots exactly as they appear in our modernized Wentworth chapters.

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Why this model? Most Algebra errors aren't logic errors; they are "typing errors." This calculator allows you to see your entire expression at once, making it the perfect companion for Chapter 8 (Order of Operations) and beyond.