Reading Assignment #1
Obtain a copy of the two articles: “The Heroic Century”
and “Calculus Notation”. Read these articles and
answer the following questions (which are not all the same
as the ones at the end of the articles themselves).
Gårding: The Heroic Century
- If differential calculus is concerned with finding tangents
to curves and integral calculus with finding areas under
curves, which one of these seems to be the problem being
investigated first historically.
- Along with finding areas and tangents, what are some of
the other problems that the mathematicians mentioned
in the reading were studying. Wherever possible, be
specific about who was studying what.
- Gårding talks about Archimedes' method of carefully
proving all of his mathematical assertions, and how
some investigators of the 17th Century got away from this.
If there were not the systematic theory in place to
justify the methods of calculus, why did so many great
minds of the time embrace the subject?
In what ways does it seem that mathematics is like the
other sciences? What role does rigorous proof play in
the subject?
- One of the greatest tools in mathematics is a creative
mind — in particular, the ability to look at a
difficult problem in a way different than conventional
methods suggest, and find something of value in your
new viewpoint that makes a solution possible. While
Archimides in the 17th Century was looked at as one
of the greatest mathematicians (and still is looked
at that way), his efforts on calculus-type problems
were not sufficient to reveal to him the crucial
insights later seen by Newton and Leibniz. What does
Gårding think was the cause of this? Can you offer
reasons that he does not mention?
Cajori: Calculus Notation
For this one, answer questions 1-4 at the end of the reading
(found on p. 68).
This page maintained by:
Thomas L. Scofield
Department of Mathematics and Statistics
Calvin College
Last Modified:
Tuesday, 09-Oct-2007 14:03:38 EDT