18.100A Recent Syllabus Fall 2012
(Adobe Acrobat -- pdf file)
This gives a general description of the subject; for information
about how it is being run the during the current semester, follow
the link on the Math Department's website menu of Classes.
18.100A or 18.100B?
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
(available at Quantum or the Coop).
The book for 18.100B is Rudin's
"Principles of Mathematical Analysis".
The book for 18.100A is Mattuck's "Introduction to
with links to its Preface, Table of Contents, Sample Sections,
and Correction Lists.
18.100A Textbook: Mattuck --- Introduction to Analysis
-- (Prentice-Hall, 1999)
Its four-page Preface can give some
idea of the book's origins and
its (hopefully) user-friendly style: Preface .
The Table of Contents tells you what's in it, and what's not, and
the order of topics: Table of Contents .
Leafing through some of the early chapters of this book and of
Rudin will give you a further idea
of the differences in style
and content between the A and B versions of Introductory Analysis.
Here are a few sections from Chapters 1-3 -- about 15 pages in
to give you a sample of the writing style:
Chapter 1: Real Numbers and Monotone Sequences
Chapter 2: Estimations and Approximations
Chapter 3: The Limit of a Sequence
Corrections to the first seven printings are on the book's website:
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
and from different
courses -- about 1/4 math majors, recent others
have been from courses like 6,7,8,12,14,15,16.
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. It is assumed that students know ordinary calculus
fairly well, or once knew it and
will review it when they need to.
Calculus is used from the beginning as a
source of examples.
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.)
Toward the end, there is a brief
introduction to point-set topology, which is used in upper-level courses
having an analysis prerequisite, and if students are interested,
at the very end an even briefer
introduction to sets of measure zero and the Lebesgue integral.
The current assignment is posted here after class. This allows
flexibility in content and difficulty, and for feedback from the
Exams: There are two "1.5 hour" exams, and a 3-hour final.
Assignments: Homework is usually assigned weekly or twice-weekly,
depending on the teacher, and returned graded at the next class session.
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