An Introduction to Wavelets Through Linear Algebra

1. Front Matter

   Pages i-xvi

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2. Prologue: Compression of the FBI Fingerprint Files

   • Michael W. Frazier

   Pages 1-6

3. Background: Complex Numbers and Linear Algebra

   • Michael W. Frazier

   Pages 7-100

4. The Discrete Fourier Transform

   • Michael W. Frazier

   Pages 101-164

5. Wavelets on ℤ _N

   • Michael W. Frazier

   Pages 165-263

6. Wavelets on ℤ

   • Michael W. Frazier

   Pages 265-348

7. Wavelets on ℝ

   • Michael W. Frazier

   Pages 349-450

8. Wavelets and Differential Equations

   • Michael W. Frazier

   Pages 451-483

9. Back Matter

   Pages 484-503

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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.

• algebra
• differential equation
• linear algebra

• Department of Mathematics, Michigan State University, East Lansing, USA

  Michael W. Frazier

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