# Introduction to Analysis

The Intermediate Value Theorem: If f is a function which is continuous on the closed interval [a, b], and u is a real number between f(a) and f(b), then there exists c in [a, b] such that f(c) = u. (Image by MIT OpenCourseWare.)

18.100A

Fall 2012

## Course Highlights

This course features a somewhat gentler introduction to the standard Analysis I material than the traditional course. It emphasizes one-variable analysis and de-emphasizes point-set topology. It assumes students did well in a standard single-variable calculus course.

The textbook is written in a user-friendly style, discursive rather than brief, making the book usable for self-study.

## Course Description

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space.

MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.

## Other OCW Versions

Archived versions:

## Related Content

Arthur Mattuck. 18.100A Introduction to Analysis. Fall 2012. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.