18.100A -

18.100A Recent Syllabus Fall 2017

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 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 is one midterm, and a 3-hour final.

Assignments: Homework is usually assigned weekly , depending on the teacher, and returned graded during the following week..

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