MATH 389
Advanced Analysis Spring 2025
Division III Writing Skills Quantitative/Formal Reasoning

Class Details

This course further develops and explores topics and concepts from real analysis, with special emphasis on introducing students to subject matter and techniques that are useful for graduate study in mathematics or an allied field. Material will be drawn, based on student interest, from many areas, including analytic number theory, Fourier series and harmonic analysis, generating functions, differential equations and special functions, integral operators, equidistribution theory and probability, random matrix theory and probabilistic methods. This will be an intense, fast paced class which will give a flavor for graduate school. In addition to standard homework problems, students will also write reviews for MathSciNet, referee papers for journals, write programs in SAGE or Mathematica to investigate and conjecture, and read classic and current research papers.
The Class: Format: lecture
Limit: 30
Expected: 15
Class#: 3549
Grading: yes pass/fail option, yes fifth course option
Requirements/Evaluation: evaluation will be based primarily on homework, classwork, and exams
Prerequisites: MATH 350 or 351 and one additional 300-level MATH course, or permission of instructor
Enrollment Preferences: students interested in graduate school in mathematics or an allied discipline
Unit Notes: http://web.williams.edu/Mathematics/sjmiller/public_html/389/
Distributions: Division III Writing Skills Quantitative/Formal Reasoning
WS Notes: Students will improve and expand their writing skills by taking course material as a starting point and writing chapters for a book under contract with the American Mathematical Society. This will involve numerous iterations of the content, with feedback both from the professor and from an editor.
QFR Notes: This is a post-core 300 level math class.

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