Lecturer: Arthur Mattuck 2-241 3-4345 mattuck@mit.edu 18.100A Office Hour: Wed 2-3
Graders:
Kyle Johnson 18/3 Baker #618 225-7368 (Friday assignments)
Tianren Qi 6/4 Baker #336 225-7336 (Mon-Wed assignments).
18.100A follows the textbook
closely. The best way of getting a feeling for the difference
between 18.100A and 18.100B is to look at the corresponding
textbooks
(at Quantum or the Coop). The book for 18.100B is Rudin's
"Principles of Mathematical Analysis"; the book for 18.100A is given below.
Its four-page Preface can give some idea of its purpose, and leafing for a few minutes through both books will give a further
comparison of their general approach and style of writing.
Textbook: Mattuck --- Introduction to Analysis, (Prentice-Hall)
For corrections to the current and previous printings, see
textbook
This course is an introduction to devising mathematical proofs
and learning to write them up. It is primarily for students with
no prior experience with this. The class usually contains
students from years 2,3,4,G in approximately equal numbers,
and from a wide spectrum of
courses -- about 1/4 math majors, the others
mathematically inclined-or-needy students from courses like 2,6,7,8,12,14,15,16,22.
The subject matter for the first
2/3 of the syllabus (up to Exam 2) is the proofs of one-variable
calculus theorems and arguments which use these theorems. The
emphasis is on estimation and approximation, two basic tools of
analysis.
The last third goes beyond calculus, getting into uniform
convergence of series of functions, to justify differentiation
and integration term-by-term; there is similar work involving
integrals depending on a parameter, to justify differentiating
under the integral sign with respect to the parameter.
(Differentiating the Laplace transform F(s) = L(f(t)) with
respect to the s-variable is an example.)
In addition. there is a very brief
introduction to point-set topology, which is used in upper-level courses
having an analysis prerequisite, and depending on the interests
of the students, in some years a brief
introduction to sets of measure zero and the Lebesgue integral..
The homework link above starts out empty, but fills up as
the problem assignments
are given out during the term (in class, and posted on
this site in the link above around the same time). This allows
for some
flexibility in content and difficulty, and for feedback from the
class members.
Homework is collected twice weekly, on Monday and Friday,
and returned graded at the next class. There
are from 3-6 problems, depending on their difficulty or length.
Sometimes "Questions" are included (exercises having model solutions at
the end of the chapter), as an aid in learning how to write up solutions.
The textbook is by and large an adequate substitute for class
attendance; students in the past have found it sufficiently
clear. A few just read the book, get the assignments here, and slip the homework under
my door before or during class, retrieving the returned homework
from a box outside my door.
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