Rivenburg's A Review of Algebra is structured not as a textbook but as a targeted drill book, designed to be used alongside a standard algebra text for reference. The preface explicitly frames the regular textbook as a dictionary—to be consulted only as a last resort. This pedagogical choice shapes the entire work: each page typically represents a day's assignment, and the problems are drawn from actual college entrance examinations, including those from Yale, Harvard, M.I.T., and Cornell. The author's voice is direct and practical, emphasizing efficiency for a half-year course of two periods per week.

A Pedagogical Blueprint for Review

The preface reveals Rivenburg's clear instructional strategy. He notes that by senior year, most students have "forgotten many of the principles," and a thorough review is necessary for college preparation. The book aims to conserve time by providing a "thorough and effective review that can readily be completed" in a half year. The author anticipates the teacher's labor in selecting examples and the student's wasted time in searching for scattered assignments. This practical orientation is evident in the inclusion of a General Outline that can be used for rapid class reviews by covering parts that indicate answers or formulas. The book's design is deliberately modular, with optional sections like Miscellaneous Examples and College Entrance Examinations that can be omitted without breaking continuity.

Problem Sets as Historical Artifacts

The problems themselves offer a window into early 20th-century education and real-world contexts. Many are drawn from specific college entrance exams, such as a Columbia problem about work rates, a Harvard problem about mill wages and union assessments, and an M.I.T. problem about two automobiles traveling toward each other. The scenarios reflect the era: telegraph poles, wagon wheels, cubical coal bins, and alloys of silver and copper. One problem involves a man dropping a stone into a well and hearing the splash after 3 seconds, using the velocity of sound (1086 feet per second). Another asks about the width of streets dividing a rectangular tract of land. These problems are not abstract; they embed algebra in tangible, often industrial or everyday situations.

The Role of the General Outline

The General Outline (pages 7–13) serves as a condensed reference for definitions, rules, and processes. Rivenburg advises that it should be reviewed as occasion arises, and can be used for rapid class reviews by covering parts that indicate answers or formulas. This outline covers topics from Order of Operations to Theory of Exponents and Radicals. The structure implies that the student is expected to recall definitions and methods from memory, using the outline as a prompt rather than a primary learning tool. The outline's placement at the beginning of the book, before any problem sets, underscores its role as a quick-reference scaffold for the review process.

Voice and Diction: Direct and Unadorned

Rivenburg's prose is economical and instructional, avoiding rhetorical flourishes. The preface uses phrases like "from an embarrassment of riches" to describe the teacher's difficulty in selecting examples, but otherwise the language is plain. Instructions are imperative: "Each student is expected to use his regular textbook in algebra for reference." The author's authority is established through his title—"Head of the Department of Mathematics, The Peddie Institute"—and the book's copyright date of 1914. The problems are stated in a terse, problem-set style, with occasional parenthetical notes indicating the source exam. This consistent, no-nonsense diction reinforces the book's purpose as a practical tool for exam preparation.

Readers approaching this review should treat it as a workout regimen rather than a narrative. The problems are best tackled sequentially, with the General Outline serving as a quick reference. Pay attention to the source colleges listed—they indicate the level of difficulty and the types of questions historically expected. The book's value lies in its focused, repetitive practice of core algebraic techniques, stripped of extraneous explanation.