Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions. These theories are usually studied in the context of real and complex numbers and functions.Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. An Introduction to Real Analysis John K. Hunter 1 Department of Mathematics, University of California at Davis 1The author was supported in part by the NSF.Thanks to Janko Gravner for a number of correc.
Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session Midi sheet download.
Recitations: 1 session / week, 1 hour / session
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Prerequisites
18.02 Multivariable Calculus; 18.03 Differential Equations; or 18.034 Honors Differential Equations
Description
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:
Textbook
Rudin, Walter. Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics). 3rd ed. McGraw-Hill, 1976. ISBN: 9780070542358.
Other Recommended Readings
Apostol, Tom M. Mathematical Analysis. 2nd ed. Pearson Education, 1974. ISBN: 9780201002881.
Spivak, Michael. Calculus. 4th ed. Publish or Perish, 2008. ISBN: 9780914098911.
Grading Policy
Note: In order to pass the course, you do have to satisfy the minimum requirements for the CI recitations, including attendance.
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