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a first course in mathematics

From Quantity to Number vol. 1

It is the higher and more advanced parts [of arithmetic] which tend to lift the mind on high, and enable it ultimately to see the final aim of philosophy, the Idea of the Good; these things draw the soul towards truth and create the philosophic [scientific] attitude of mind.
Sir Thomas Heath (on Plato's view of the value of math)

From Quantity To Number

a first course in mathematics

From Quantity to Number is for home school students and parents interested in a classical discussion-based approach to learning and teaching.

The main topic in this first set of two volumes is the idea of number. We show this as a rich and evolving idea. Beginning with our observation of discrete quantity, we develop the idea of number as a representation of quantity approaching step by step the conception of number as element of the real number continuum. A priority guiding how the discussion progresses is to introduce ideas early on that are helpful to learning more advanced mathematics. These are also fun and interesting ideas. They enliven and enrich the first approach to arithmetic and we discuss them in a way that is accessible to young students.

See a book overview video at our channel Inlet Books on YouTube: From Quantity To Number (youtu.be/txi8A8LNXSo).

For a quick flip-through featuring excerpts, see this video: FQTN flip-through (youtu.be/Bi7jqSieam0).

Read the book's Preface and Contents in the pdf here: Preface and table of contents.

You can also read more on the author at Mark Sapirie (marksapirie.com).

We plan to publish From Quantity to Number volume 2 later this year. And subsequent volumes will focus on geometry and are underway.

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On From Quantity to Number vol 1