NOTE (11/15/96): See Revised Syllabus; Optional Second Midterm.
This figure from Isaac Newton's
Principia Mathematica (1686) illustrates his Lemma II
which states, in modern terminology, that for a
monotonic function the left- and right-hand sums have
the same limit, which is the area under the curve.
I have edited out some lines and notation referring
to a different lemma.
Press here to see
the full Latin text of Lemma and Proof, with a
translation into English. Press
here for an animated version of Newton's diagram, due to
Stony Brook student Vladimir Livshits. Clicking on the difference
rectangles makes them slide into a single column.
Meets Tu-Th 10-11:20 in Harriman 104.
Text: Michael C. Reed, Fundamental Ideas of Analysis
Pre-publication version; Wiley.
This edition of the book is being distributed to us for free. In return, please mark carefully in your copy any misprints or errors you find, as well as any passages you find hard to understand, and please turn in your books at the end of the term (you can have them back eventually). Wiley is giving us some money we can use for a pizza party at the end of classes.
Week by week
Review for Midterm 1
Review for Midterm 2
Midterm 2 (track B)
Review for Final
Final Exam (track A)
Final Exam (track B)
Homework will be collected each Thursday.
I have two main goals in this course. First to acquaint you with the mathematical foundations of the Calculus and at the same time to introduce you to some of the many mathematical phenomena related to the Calculus. Second is to train you in the construction and analysis of mathematical proofs. I will try to assign each week at least one homework exercise that involves making up a proof.
Format for Proofs. Please follow the following format in
submitting proofs. This will allow you to assemble them into a
portfolio at the end of the semester.
Disabilities. If you have a physical, psychological, medical
or learning disability that may impact on your ability
to carry out assigned course work, I would urge that you
contact the staff in the Disabled Student Services office
(DSS), Room 133 Humanities, 632-6748/TDD. DSS will review
your concerns and determine, with you, what accommodations
are necessary and appropriate. All information and
documentation of disability is confidential.