This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing.

This is a collection of notes for a one-semester course in linear algebra taught at San Jacinto College (Houston, Texas). The notes are suited for a first course in linear algebra taken by students who have completed one year of single-variable calculus. Unlike most traditional linear algebra textbooks, these notes begin with the ideas of vector spaces and linear functions (transformations). Since functions play a central role in calculus, this approach should seem more natural to students. Systems of linear equations and matrix theory are presented afterward as consequences of the preceding material. The result is an economical (only 175 pages) treatment of the main themes of linear algebra along with a few applications of the theory to geometry, economics, and cryptography.

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.The three options for 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. This fulfills the MIT CI requirement.