Questions and answers about our book
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 stimulating.

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 mathematics?
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 the book?
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.

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Teaching with Original Historical Sources in Mathematics