Introduction to Fourier Analysis
Introduction to Fourier Analysis covering Fourier series and integrals, and their applications.
Summary
Recent recorded grades — Spring 2016: 3.23 GPA, 45.5% A/AB (n=11 letter grades); Fall 2021: 3.90 GPA, 90.0% A/AB (n=10 letter grades); Fall 2023: 3.31 GPA, 75.0% A/AB (n=8 letter grades).
What you’ll be able to do
Recall and state the formal definitions of the mathematical objects and their properties relevant to the analysis of Fourier series, the Fourier transform, and their applications in mathematics (e.g., convergence, divergence, convolution, Lipschitz property, Schwartz space, etc.).
Use the above definitions to prove if a mathematical construct does or does not have the condition of being a particular mathematical object or having a particular property used in Fourier analysis (e.g., that a sequence is equidistributed, that a set of functions is uniformly bounded, etc.).
Recall and state the standard theorems and results of elementary Fourier analysis (e.g., the Fourier series of an integrable function converges to that function on its domain, etc.), and recall the arguments for these results and the underlying logic of their proofs.
Use the above theorems in the context of longer arguments by examining their premises (e.g., verifying integrability of a function in order to conclude that its Fourier series converges, etc.).
Prove or disprove statements related to the above definitions, properties, and theorems using techniques of mathematical argument (direct methods, indirect methods, constructing examples and counterexamples, induction, etc.).
Convey arguments in oral and written forms using English and appropriate mathematical terminology, notation and grammar.
Identify applications of course content in current areas of research.
Source: UW Guide
Grade history
↗All recorded terms · compare terms & instructors
Prerequisites
Course mapMATH 521 or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program
- MATH 521
- graduate/professional standing
- member of the Pre-Masters Mathematics (Visiting International) Program
This is a best-effort interpretation; check the catalog requirements above.
Prerequisite text tree
- Any of
- MATH 521
- graduate/professional standing
- member of the Pre-Masters Mathematics (Visiting International) Program
Professors
Spring 2027No instructors recorded for this selection.
Historical instructors & teaching patterns
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Calendar & sections
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Student experience
the class
Recent recorded grades — Spring 2016: 3.23 GPA, 45.5% A/AB (n=11 letter grades); Fall 2021: 3.90 GPA, 90.0% A/AB (n=10 letter grades); Fall 2023: 3.31 GPA, 75.0% A/AB (n=8 letter grades).
difficulty & workload
No workload feedback recorded.
Topics
- Fourier series and integrals
- Applications of Fourier series and integrals
- Formal definitions and properties: convergence, divergence, convolution, Lipschitz property, Schwartz space
Skills
- State formal definitions of mathematical objects and properties relevant to Fourier series and transforms, including convergence, divergence, convolution, Lipschitz property, and Schwartz space.
- Prove whether mathematical constructs possess specific conditions or properties used in Fourier analysis, such as equidistribution or uniform boundedness.
- Apply standard theorems in longer arguments by examining premises, such as verifying integrability to conclude Fourier series convergence.
- Prove or disprove statements using techniques of mathematical argument including direct methods, indirect methods, examples, counterexamples, and induction.
Grades
Latest available · Fall 2023— not enough history to project Spring 2027.
Grade distribution · % of letter grades
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Through Fall 2023
More grade details Grade mix, volume & source data
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Catalog & offerings
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Grade history
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Explore recorded gradesRecorded 2026-10-14
Model outputs & technical records
LLM outputs across runs
Full model traces
Recorded model configuration, reasoning, and tool conversations.
Model & dataset provenance
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