Manual of Mathematical Sciences - Volume 1
About this ebook
The volume is divided into two major sections, connected by a guiding idea: learning to understand geometric properties through analytical tools, while keeping sight of the meaning behind formulas and representations.
ANALYTIC GEOMETRY IN THE PLANE – SECTIONS 1–77
The first section guides readers through the study of plane analytic geometry. Beginning with the Cartesian coordinate system and coordinates, it progresses to the tools used to describe points, lines, and curves, interpret equations, and investigate relationships between geometric objects. Key topics include distances and coordinates, equations of lines, intersections, geometric loci, circles, and conic sections, together with further material that broadens the discussion to additional representations and methods of analysis.
ANALYTIC GEOMETRY IN SPACE – SECTIONS 78–145
The second section extends the analytical method to three dimensions. Readers are introduced to scalar and vector quantities, spatial coordinates, and tools for describing and studying lines, planes, and other geometric objects in space. The transition from the plane to three-dimensional space helps demonstrate how familiar concepts can be extended and applied in more complex settings.
A STRUCTURED LEARNING PATH WITH VISUAL SUPPORT
The numbered-section structure makes the work easy to navigate and supports progressive study: readers can follow the material from the beginning or quickly return to a specific topic when reviewing. The figures accompanying the text provide visual reference points for understanding configurations, relationships, and representations, bringing algebraic description and geometric intuition together.
WHO IS THIS BOOK FOR?
This manual is intended for students, teachers, mathematics enthusiasts, and readers who wish to consolidate or deepen their understanding of analytic geometry. It can be used for independent study, revision, reinforcing key concepts, and systematic reference. Its detailed structure also makes it a useful companion to other learning resources, depending on the reader’s level and goals.
More than a collection of formulas to memorize, analytic geometry is a method for recognizing the relationships between shapes, numbers, and equations. With this first volume, Marco Durzu invites readers to explore that method through an extensive, well-organized presentation enriched with visual references: a journey toward a clearer understanding of mathematics and a more confident command of its language.
