Questions and answers
by the Explorers
Tell us your questions, and we'll try to answer
Start by reading the book's Preface,
which is part of the excerpts
and other information available at our main
page. The Preface should answer many of your questions.
Q: Is the book suitable for a course on mathematics
liberal arts majors?
A: Yes, for good students. The majority of the students in the
course from which the book emerged are liberal arts majors with a
high school mathematics background and a spark of interest in the
The course is a very attractive final mathematical experience in
education, providing connections to the humanities which they find
Q: Is the book suitable for a course in history of
A: Yes. We believe that in a history of mathematics course students
should study and do actual mathematics, not just read and discuss
at a level often beyond their detailed comprehension. This book
mathematical study and its historical context intimately together.
chapter contains mathematics from a beginning to more advanced
thus can be covered at a level suitable to the level of the
course in the curriculum.
Q: Is the book suitable for a course for
A: Yes, in our course experiences from which the book was written we
often attract new majors and keep existing ones, through the vibrant
original sources provide to mathematical activity.
Q: Is there a calculus prerequisite?
A: No! There is intentionally no such prerequisite. The
is more inquisitiveness, interest in exploring fascinating
ideas in a rich and open-ended historical context, and the
to persevere in trying to place oneself in the minds of those in
past struggling with great problems.
To be specific on the calculus front, one of our chapters, as you
see from the table
of contents and excerpts,
is about the development of the definite integral via the problem
areas and volumes. We intentionally wrote this as a
introduction to calculus than what anyone would get today, so no
is needed in advance. On the other hand, if someone has already
exposure to calculus, this historical approach will be so
the standard modern approach, that the experience will be
rich and challenging to that person as well. The previous
to calculus will not put this person at a different level, but may
to some provocative discussion. This is all founded on the
the modern textbook approach to calculus is highly antihistorical,
initiated by Cauchy when he presented students first his 21 Lecons
differential calculus, to be followed by 21 Lecons on the integral
even though historically the differential aspects were
years old, whereas the integral ideas went back more than 10 times
(This is all discussed in our Analysis chapter.)
Q: Does the book contain applications?
A: Our choice of topics was based on following great mathematical
through two-thousand years of effort. Some of these problems
motivated by and related to applications throughout their history,
calculation of areas and volumes and the development of analysis, or
and non-Euclidean geometry. We have mentioned these connections
but they are not the primary thrust.
Q: What about an instructor inexperienced in
A: The book is written for such instructors and students, and has
citations and suggestions to references for further reading. We have
mind that an instructor with no prior historical knowledge can use
book as a learning, reference, and teaching tool.
Q: What are the exercises like?
A: There are exercises for every section, at varying levels from
exercises up to the level of projects, along with parenthetical
(mini-exercises) interwoven in the text narrative as well. The
generally explore the mathematics of the section and of the original
and some send the reader to the library for history or mathematics.
at the exercises in the excerpted
sections we have provided.
Q: Does the book have photos and figures?
A: Yes, lots. The photos range from portraits to mosaics, artwork,
and facsimiles of handwritten manuscripts and letters.
Q: Do you have new translations of original sources
A: Yes, some from French and German, and some retranslations of
translations we thought we could do more authentically.
Q: Is the book available now?
A: Yes, from Springer
Verlag in paperback or hardcover in their Undergraduate Texts
/ Readings in Mathematics series.
To main page on
Teaching with Original Historical
Sources in Mathematics