There are 38
books, if you include Answer Keys/Teachers Editions. The Teachers Editions are simply the same
book as their counterpart, with the answers included next to most of the problems.
If you would like to see sample pages from the books, those can be
viewed by clicking here.
Basic Math
“An
effort has been made throughout the work to observe a natural and strictly logical connection between the different
parts, so that the learner may not be required to rely on a principle, or employ a process, with the rationale of
which he is not already acquainted”
Ray's Primary Arithmetic. 95 pages. The first book in the Ray's Series, Primary Arithmetic starts at
the very beginning of mathematics by teaching the children to
count. The book then slowly progresses with simple problems, first with addition, then subtraction, then
multiplication and division. The problems are very simple, so that the child can learn the concepts involved.
Ray's Intellectual Arithmetic. 141 pages. Intellectual
Arithmetic begins by reviewing the basic concepts covered in Ray's Primary Arithmetic, adding more problems and
raising the difficulty by increasing the quantities involved. The book then adds the new concept of Fractions
and percentages. As these concepts are introduced, applications for the problems are given, showing the child
how to solve increasingly complex problems.
Ray's
Elementary Arithmetic. 192 pages. Ray's New Elementary
Arithmetic is designed to lead straight into Practical Arithmetic, by providing an extensive amount of drill
work for the student, in order to allow the student ample time and problems to thoroughly master the
fundamentals before moving forward.
Ray's Practical Arithmetic. 337 pages. Practical
Arithmetic starts by quickly reviewing the basics of addition, subtraction, multiplication and division covered
previously in Elementary Arithmetic, and then moves into a study of different types of measurement, followed by
factoring, and a more involved study of fractions and percentages. After these mathematical bases have been
studied and mastered, real world applications for these mathematics are introduced. These include Transactions,
Commissions, Stock values and investments,
Interest, Discounts, Monetary exchange, Insurance and Taxes.
Practical Arithmetic then concludes by introducing basic geometry.
Intermediate Math
”To fix the principles in the mind of the
student, and to show their bearing and utility, great attention has been paid to the preparation of practical
exercises.”
This continual grounding in practicality is a peculiar aspect of
Ray's Arithmetic, one which is very rare and very valuable. Modern math books have focused so much on the
abstract that the student is left to wonder how he will ever be able to use it in his day to day life; a feeling
that easily makes mathematics seem like a chore or useless exercise.
Ray's Higher Arithmetic. 409 pages. A very complete study of Arithmetic, this is the last book in the
Ray's series before the introduction of Algebra. All of the basic mathematical methods are reviewed thoroughly; and
more complicated applications and uses are explored. Finally the book begins the study of Geometry, and the
fundamentals of Trigonometry are introduced.
Ray's New Elementary Algebra. 241 pages. “In
introducing Algebra to the student with Elementary Algebra, great care has been taken to make the student feel
that he is not operating with unmeaning symbols, by means of arbitrary rules; that Algebra is both a rational
and practical subject, and that he can rely on his reasoning, and the results of his operations with the same
confidence as in arithmetic. For this purpose, he is furnished, at almost every step, with the means of testing
the accuracy of the principles on which the rules are founded, and of the results which they
produce.”
I cannot stress highly enough the importance the above paragraph
has to a student embarking on a study of Algebra. From personal experience while studying with Saxon Algebra I
know just how frustrating it is to be told what to do, while not given any reasons for why we are doing it or
how it works. I didn't want to simply take their word for it but prove it for myself, a thought process most
students share. And while I did manage to work these things out eventually, it was a slow and painful process.
One of the things that make Ray's Arithmetic such an excellent series is the attention given to the student.
Instead of neglecting the reasoning and deducing ability of the students themselves, they are instead encouraged
to think on their own. This increases the students interest, his understanding of the material, as well as his
recollection of studies later on.
Ray's New Elementary Algebra focuses on the basic forms of Algebra.
Algebraic Fractions, Simple Equations, Powers, Roots, Radicals, and finally Quadratic Equations are among the
concepts explored. As always, after a concept has been taught, realworld applications for the process are given
to the student.
Ray's New Higher Algebra. 407 pages. After
reviewing the fundamentals, Higher Algebra then moves on to Theorems, Factoring, Algebraic Fractions, Quadratic
Equations, Ratio, Proportion, Binomial Theorem, etc etc. This book is quite lengthy, thoroughly teaching
algebraic concepts. While there are relatively few problems for the student to work on and solve, these have
been supplied by Test Problems for Ray's New Higher Algebra. 152 pages, as well
as A Complete Algebra. 359 pages.
Advanced Math
Ray's Treatise on Geometry and Trigonometry. 421
pages. Begins by giving definitions for some basic geometrical terms, then begins Geometry, starting with
parallel lines, then continuing with Arcs and Radii, the properties of triangles, Parallelograms, measuring
area, Polygons, the geometry of space, Pyramids, Prisms, etc. The book then continues on into the subject of
Trigonometry, and supplies logarithmic tables. No problems are supplied for the student in this book, which
instead gives all it's attention to teaching the concepts. It is suggested that the student use another book to
provide problems while learning the mathematical processes from this book.
Ray's Analytic Geometry. 608 pages. Equations to
the Right Line, the Plane, Quadrics, The Ellipse, The Hyperbola, and Properties of Conics discussed with great
fullness. Abridged Notation is introduced in this book. This book does not supply problems for student work,
focusing on teaching the concepts.
Ray's Differential and Integral Calculus. 442
pages. Begins with definitions. Careful attention has been given to the teaching of the doctrine of limits,
which has been made the basis of both the Differential and Integral Calculus. Problems are supplied in the
book.
ExtraCurricular Texts
In order to provide students with examples of the interesting
fields mathematical studies opens, several books of ranging difficulties have been supplied.
Complete Book Keeping. 161 pages. An often
overlooked area of study, bookkeeping will always be an important area of expertise for anyone who earns or
spends money. As the author states: “Bookkeeping... cultivates the judicial powers of the mind... contributes
to private and public virtue.. leads to economy and thrift... and it's practice will reduce pauperism and
crime.” Beginning with the basic form of double entry bookkeeping, Debit, Credit, and all areas of accounting
are taught.
Norton's Elements of Physics. 269 pages. This
incredibly wellwritten and intriguing book is so well written that it does not feel so much like a dry text on
the mathematics of physics as an exploration of physical laws, thus allowing someone well acquainted with
physics or not at all to read this book with great enjoyment. Carefully illustrated, this book begins by
introducing the student first to general notions of matter and force, and then introducing new elements one by
one. Friction, adhesion, fluids, sound, light, heat, and electricity are all explored, with careful explanations
of experiments and studies done by the scientists who explored these properties.
Schuyler's Principles of Logic. 169 pages. Logic
is a mathematical pursuit. How can we tell? Through logic.... Because math is based on logical premises
(induction), and then followed through in a logical working out of the premises (deduction). The author explains
this more thoroughly, but you'll have to read the book.
Ray's Elements of Astronomy. 342 pages. Taking a
different approach to astronomy, rather than focusing on the Greek names for constellations this book focuses on
the movements of heavenly bodies and the science of astronomy.
Ray's Surveying and Navigation. 492 pages. While
this book thoroughly covers the old art of Surveying (the same business George Washington was in for a number of
years) this book is especially useful because of it's great attention to the field of Plane and Spherical
Trigonometry and Mensuration, and may because of this be used as a textbook for those fields.
