18.100A - Fall 2012
18.100A Syllabus Fall 2012
(Adobe Acrobat -- pdf file)
18.100A Assignments: Information and Rules Fall 2012
( Adobe Acrobat -- pdf file )
Practice Final Exam
( Adobe Acrobat -- pdf file )
Practice Problems for Exam 2
( Adobe Acrobat -- pdf file )
Practice True-False Questions for Exam 1
( Adobe Acrobat -- pdf file )
Practice Problems for Exam 1
( Adobe Acrobat -- pdf file )
Assignment 26
( Adobe Acrobat -- pdf file )
Assignment 26 is optional, not for handing in or grading.
It will be included on the final, but there will be some choice
on the final.
Assignment 25
( Adobe Acrobat -- pdf file )
Assignment 24
( Adobe Acrobat -- pdf file )
Assignment 23
( Adobe Acrobat -- pdf file )
Assignment 22
( Adobe Acrobat -- pdf file )
Assignment 21
( Adobe Acrobat -- pdf file )
Assignment 20
( Adobe Acrobat -- pdf file )
Assignment 19
( Adobe Acrobat -- pdf file )
Assignment 18
( Adobe Acrobat -- pdf file )
Assignment 17
( Adobe Acrobat -- pdf file )
Assignment 16
( Adobe Acrobat -- pdf file )
Assignment 15
( Adobe Acrobat -- pdf file )
(The typos have been corrected in this version: Q16.1/3, Q18.3/3a)
Assignment 14
( Adobe Acrobat -- pdf file )
Assignment 13
( Adobe Acrobat -- pdf file )
Assignment 12
( Adobe Acrobat -- pdf file )
Assignment 11
( Adobe Acrobat -- pdf file )
Assignment 10
( Adobe Acrobat -- pdf file )
Assignment 9
( Adobe Acrobat -- pdf file )
Assignment 8
( Adobe Acrobat -- pdf file )
Assignment 7
( Adobe Acrobat -- pdf file )
Assignment 6
( Adobe Acrobat -- pdf file )
Assignment 5
( Adobe Acrobat -- pdf file )
Assignment 4
( Adobe Acrobat -- pdf file )
Assignment 3
( Adobe Acrobat -- pdf file )
Assignment 2
( Adobe Acrobat -- pdf file )
Assignment 1
( Adobe Acrobat -- pdf file )
Lecturer: Arthur Mattuck 2-241 3-4345 mattuck@mit.edu
Office Hours: Thurs. 3:10 - 5 or later; or by appointment. You can also use
e-mail for questions, including weekends; it's usually checked
several times daily.
TA: To be announced
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
textbooks
(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
Analysis"
Textbook
described below,
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
all --
to give you a sample of the writing style:
Sample sections.
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:
Corrections.
18.100A Description
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
for some
flexibility in content and difficulty, and for feedback from the
class members.
Exams: There are two "1.5 hour" exams, and a 3-hour final.
Assignments: Homework is due in class twice weekly, on Monday and Friday,
and returned graded at the following class meeting. There
are usually from 3-6 problems, depending on their difficulty or length,
or whether it's an assignment due Monday or Friday.
Sometimes "Questions" are included (exercises having solutions at
the end of the chapter), as an aid in learning how to write up
solutions, and as a source of hints. Since the homework is
really where
the learning takes place, and timely feedback is essential
to improving, handing in 3/4 of the assignments when they are
due is a requirement for passing; any exceptions have to be
for cause, and arranged in advance. Students who are accepted
into the class late have to make up the missed assigments.
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 online here, and slip the homework under
my door before class, retrieving the returned homework
from a box outside my door. See the link "Assignments:
Information and Rules" for more details.
What's in it: Th book assumes knowledge of one-variable
calculus -- differentations and easy integrations (including the
log, exp, and trig functions), with standard applications to
finding rates, maximum points, areas, and simple volumes, plus an
intuitive idea of what a limit is. These things are used from
the beginning to provide examples, but the aim of the book is to
describe the theory beind all of this -- to teach you how to read
mathematical proofs, how to find them yourself, all in the
context of real analysis.
Helpful features:
- Occasional comments about the proofs, discussions of what
might be done differently, advice about writing up arguments,
plus a few frivolous remarks and quotes.
- A great deal of attention paid to layout and typography, both
for greater readability, and to give readers models they can imitate.
- In addition to the Exercises and Problems at the end of
a chapter, after each section of the chapter are several Questions,
based on the material of that section, with Answers of various
sorts at the very end of the chapter -- single words, hints,
complete statements, formal proofs.
Mathematical features:
Return to
Arthur Mattuck's Homepage
Return to the
MIT Math Department Homepage