Ayres Hall in the fall

William R. Wade


 Department of  Mathematics 
University of  Tennessee
Knoxville, TN 37996-1320
865-974-4320 (Office)
865-974-6576 (Fax)

  Research Interests

I do research on Dyadic Harmonic Analysis. This area, whose roots lie in the physics of vibration, uses integration to decompose (integrable) functions into piece-wise constant components by generating numbers (called Walsh-Fourier coefficients) and infinite series (Walsh-Fourier series). These numbers and series can be used to approximate and to characterize the original function. I am particularly interested in problems of uniqueness (under which conditions are the coefficients of an otherwise arbitrary Walsh series the Walsh-Fourier coefficients of a some integrable function?) and growth (how fast do the partial sums or the Cesaro means of a Walsh-Fourier series grow?). Specific results can be obtained by looking at the papers in my bibliography.

Dyadic Harmonic analysis has many applications. Using Walsh-Fourier series to approximate a given function makes it possible to transmit data efficiently (e.g., multiplexing), to filter data (e.g., remove noise from weak video signals), and for data compression (e.g., transmit hundreds of signals through a single fiber optic cable). Using Walsh-Fourier coefficients to characterize functions makes it possible to recognize patterns (e.g., read handwritten zip-codes). Walsh functions have also been used to design genetic algorithms, methods to optimize non-differentiable problems for which the standard approach via calculus will not work.

 I am also interested in Math History. I enjoy discovering how concepts were discovered and what purposes they serve in the 21st century. I use this material to make myself a better teacher, and to enliven my course in Math History.

Short Biography

I was born in downtown Los Angeles on sixth street (they still had houses there in the early forties). Moving steadily east (East Los Angeles, Montebello, Pio-Rivera), we ended in La Puente. I graduated from Puente High School in June 1961. I spent the next seven years getting three degrees at the University of California (Riverside). My Ph.D. Advisor was V.L. Shapiro, a student of the famed Polish-American analyst A . Zygmund.

I have taught at the University of Tennessee since September 1968, where I have had six Ph.D. students, and have received various honors, awards and grants over the years, and have been on leave at the University of Southern California (spring, 1977), Moscow State University (Fall 1977), Indian Statistical Institute (Spring 1984), and Eotvos Lorand University, Budapest (Summers 1985, 1990, 1995, 1999).

Selected Bibliography

    Curriculum vitae

Books in Print

        Misprints for:

Teaching Schedule

Fall 2011:
     Math 300 Syllabus (pdf file)
     Math 341 Syllabus (pdf file)   

Outside Interests

I teach an adult Sunday school class in an evangelical church.

I am also a musician with wide tastes from Bach to Shostakovich.

I also enjoy photography. Below are some examples of photographs I have taken.

The Wade Family - Family Portrait

Image files are large and may take a few moments to load.

Hong Kong

* Cairo
* Business District

*   Buda Castle with
St. Gellert

*   Parliament in Budapest

* Taj Mahal

* Downtown

* Sunset over Ft. Loudon River

* Tennessee River


* Novodevichy Monastary
* Red Square
in the 70s
California   Italy   Majorca  

* Pt. Hueneme

* Santa Barbara


* Leaning Tower of Pisa

* Colosseum

* Dome of St. Peter's in the Vatican

* Pompeii


* Cathedral at Palma de Majorca

* Harbor of Palma de Majorca


email address:  wade@math.utk.edu

Last updated: 7/11