Introduction to Analysis

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:

• 18.100A Analysis I (Fall 2007)

Course Sequences

This course is the first part of a two-course sequence. The sequence continues in 18.101 Analysis II.

Course Collections

See related courses in the following collections:

Find Courses by Topic

• Calculus
• Differential Equations
• Mathematical Analysis
• Mathematical Logic

MIT Crosslinks

Explore the topics covered in this course with MIT Crosslinks, a website that highlights connections among select MIT undergraduate STEM courses and recommends specific study materials from OCW and others. Learn more.