Questions and answers about
Mathematical Expeditions: Chronicles
by the Explorers
Tell us your questions, and we'll try to answer them here.
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 for
liberal arts majors?
A: Yes, for good students. The majority of the students in the honors
course from which the book emerged are liberal arts majors with a good
high school mathematics background and a spark of interest in the subject.
The course is a very attractive final mathematical experience in their
education, providing connections to the humanities which they find very
Q: Is the book suitable for a course in history of mathematics?
A: Yes. We believe that in a history of mathematics course students
should study and do actual mathematics, not just read and discuss mathematics
at a level often beyond their detailed comprehension. This book brings
mathematical study and its historical context intimately together. Each
chapter contains mathematics from a beginning to more advanced level, and
thus can be covered at a level suitable to the level of the particular
course in the curriculum.
Q: Is the book suitable for a course for mathematics majors?
A: Yes, in our course experiences from which the book was written we
often attract new majors and keep existing ones, through the vibrant introduction
original sources provide to mathematical activity.
Q: Is there a calculus prerequisite?
A: No! There is intentionally no such prerequisite. The prerequisite
is more inquisitiveness, interest in exploring fascinating mathematical
ideas in a rich and open-ended historical context, and the willingness
to persevere in trying to place oneself in the minds of those in times
past struggling with great problems.
To be specific on the calculus front, one of our chapters, as you can
see from the table
of contents and excerpts,
is about the development of the definite integral via the problem of finding
areas and volumes. We intentionally wrote this as a completely alternative
introduction to calculus than what anyone would get today, so no calculus
is needed in advance. On the other hand, if someone has already had some
exposure to calculus, this historical approach will be so different from
the standard modern approach, that the experience will be fascinating,
rich and challenging to that person as well. The previous exposure
to calculus will not put this person at a different level, but may lead
to some provocative discussion. This is all founded on the fact that
the modern textbook approach to calculus is highly antihistorical, a practice
initiated by Cauchy when he presented students first his 21 Lecons on the
differential calculus, to be followed by 21 Lecons on the integral calculus,
even though historically the differential aspects were barely 150
years old, whereas the integral ideas went back more than 10 times farther.
(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 problems
through two-thousand years of effort. Some of these problems were
motivated by and related to applications throughout their history, e.g.,
calculation of areas and volumes and the development of analysis, or Euclidean
and non-Euclidean geometry. We have mentioned these connections throughout,
but they are not the primary thrust.
Q: What about an instructor inexperienced in history of
A: The book is written for such instructors and students, and has copious
citations and suggestions to references for further reading. We have in
mind that an instructor with no prior historical knowledge can use the
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 easy
exercises up to the level of projects, along with parenthetical small questions
(mini-exercises) interwoven in the text narrative as well. The exercises
generally explore the mathematics of the section and of the original sources,
and some send the reader to the library for history or mathematics. Look
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 in
A: Yes, some from French and German, and some retranslations of existing
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 in Mathematics
/ Readings in Mathematics series.
To main page on
Teaching with Original Historical
Sources in Mathematics