521 - Analysis I

Prerequisites: 

Previous serious exposure to understanding and writing proofs is required in Math 521. Any of the courses Math 341, Math 371, Math 375-76, Math 421, or Math 461 provide this experience. Admission to Math 521 is also possible with the consent of the instructor.

Frequency: 
Fall (I), Spring (II), Summer (SS)
Student Body: 

Math majors, Physics and Engineering majors and graduate students in related areas

Credits: 
3. (N-A)
Recent Texts: 
Principles Of Mathematical Analysis, by W. Rudin. Mathematical Analysis, by A. Browder. Undergraduate Analysis, by S. Lang. The Way of Analysis, by R. Strichartz.
Course Coordinator: 
Andreas Seeger
Background and Goals: 

The sequence Math 521-522-621 has the objective of conveying an understanding of the structure of analysis in itself as well as its role as a tool for other disciplines. This sequence is highly recommended for any math major and it is essential for students preparing for graduate studies in mathematics; also it should be taken by students in physics and engineering who intend to do graduate work in their areas.

Alternatives: 
Students can consider Math 421 for a weaker and preparatory version of Math 521
Subsequent Courses: 
Math 522.
Course Content: 
  • The real numbers, R and R^n
  • Elements of set theory
  • Some topological properties of R^n, metric spaces
  • Sequences and series of real numbers
  • Functions, limits, continuity
  • Differentiation
  • Integration
  • Sequences and series of functions, uniform convergence
  • Power series, the elementary functions.
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521-522.pdf28.33 KB

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