Mathematics majors at Michigan State University take a "Capstone"
course near the end of their undergraduate careers. The content of
this course varies with each offering. Its purpose is to bring
together different topics from the undergraduate curriculum and
introduce students to a developing area in mathematics. This text
was originally written for a Capstone course. Basic wavelet theory
is a natural topic for such a course. By name, wavelets date back
only to the 1980s. On the boundary between mathematics and
engineering, wavelet theory shows students that mathematics
research is still thriving, with important applications in areas
such as image compression and the numerical solution of
differential equations. The author believes that the essentials of
wavelet theory are sufficiently elementary to be taught
successfully to advanced undergraduates. This text is intended for
undergraduates, so only a basic background in linear algebra and
analysis is assumed. We do not require familiarity with complex
numbers and the roots of unity.
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