William Wu is a graduating Electrical Engineering Ph.D. student in the Information Systems Lab at Stanford University. His interests include signal processing, communications engineering, combinatorics, and recreational math riddles and puzzles. He is the creator of wuriddles.com, which has been featured on slashdot and various other places.
In 1999, while carrying a 5.00 GPA, William won the 1st Prize Trophy in Physics at the San Francisco Bay Area Science Fair, and his classmates at Hogan High School in Vallejo, CA voted him as "Most Likely to Appear on Jeopardy." It has all been pretty much downhill since then.
Education:
- Ph.D. Electrical Engineering, Stanford University
- M.S. Mathematics, Stanford University
- M.S. Electrical Engineering, Stanford University
- B.S. Electrical Engineering and Computer Science, UC Berkeley
P.S. William can usually be found on rollerblades because walking is slow.
I am a PhD Candidate in the Electrical Engineering Information Systems Laboratory at Stanford University, advised by Professor Brad Osgood. My research has involved the following topics:
Broad areas I am interested in include: signal processing, Mathematica programming, communications, coding theory, optimization, discrete probability, real-world statistics problems, and puzzles.
My thesis work with Brad Osgood is about a new theoretical approach to the sampling and reconstruction of discrete signals. Our work can be thought of as taking the Nyquist-Shannon sampling paradigm and adapting it to more general situations.
Although our work is primarily theoretical in nature, our ultimate long-term goal is to develop practical applications in areas such as medical imaging, spectroscopy, and circuits.
- Osgood, Brad; Wu, William. Discrete Sampling. (dissertation to be released)
Question: What do the Fourier uncertainty principle, Stirling numbers, and the EE Quals have in common?
Answer: Falling factorials.
We investigate the coefficients 
generated by expressing the falling factorial 
as a linear combination of falling factorial products 
.
Algebraic and combinatorial properties of these coefficients are discussed, in relation to Stirling numbers, binomial coefficients, and generating functions for conjoint ranking tables.
- Wu, William; Osgood, Brad. Falling Factorials, Generating Functions, and Conjoint Ranking Tables. Journal of Integer Sequences, Vol. 12 (2009), Article 09.7.8.
- Local paper copy: click here
- Presentation slides: click here
The rapid deployment of high density wireless LANs poses many new challenges for network management, such as the dynamic channel assignment problem . Since cell sizes in WLANs are so small, it is common for traffic statistics to fluctuate significantly as users move from one cell to another. Thus, by dynamically assigning the wireless frequency channels used by different access points, network throughput can be optimized. The channel assignment is made based on periodically updated signal and traffic measurements, which are then piped into an interference model that assigns weights to a graph, and finally a semidefinite program is used to solve the max k-cut problem on that graph. Our experiments on a real-world 500 square-meter testbed demonstrate average throughput increases of up to 40%.
This is joint work in collaboration with NEC Research Labs in Beijing, China, where I worked for a summer while participating in the Stanford-Tsinghua Engineering Exchange Program.
- Wang, Bo; Wu, William; Liu, Yongqiang. Dynamic Channel Assignment in Wireless LANs. IEEE Power Electronics and Intelligent Transportation Systems, 2008.
- Local paper copy: click here
- Presentation slides: click here
- Liu, Yongqiang; Wang, Bo; Wu, William; et al. Measurement-Based Channel Assignment in WLANs. Submitted to WCNC'2010.
- Wu, William; Chen, Jiehua. SCP-Based Channel Assignment. (In progress. I would like someone to implement our algorithms on a real WLAN testbed and evaluate the performance. If you are interested, please contact me.)
"One hundred prisoners have been newly ushered into prison. The warden tells them that starting tomorrow, each of them will be placed in an isolated cell, unable to communicate amongst each other. Each day, the warden will choose one of the prisoners uniformly at random with replacement, and place him in a central interrogation room containing only a light bulb with a toggle switch. 
The prisoner will be able to observe the current state of the light bulb. If he wishes, he can toggle the light bulb. He also has the option of announcing that he believes all prisoners have visited the interrogation room at some point in time.
If this announcement is true, then all prisoners are set free, but if it is false, all prisoners are executed. The warden leaves, and the prisoners huddle together to discuss their fate. Can they agree on a protocol that will guarantee their freedom?"
Working with the combined efforts of many members of [wu:forums] since 2002, we have embarked on a never-ending journey to find new more efficient algorithms and protocols for solving the 100 prisoners and a light bulb riddle, most of which are not well-known. In a separate investigation with collaborators Hans van Ditmarsch and Jan van Eijck, we show how the riddle can be studied using dynamic epistemic logic.
- van Ditsmarch, Hans; van Eijck, Jan; Wu, William. 100 Prisoners and a Light Bulb: The Logic. Submitted to Synthese: Knowledge, Rationality, and Action (KRA).
-
Wu, William. 100 Prisoners and a Light Bulb. Online document uploaded in 2002; since then, it has been referenced in several places. A never-ending work in progress with no submission plans, but if you have suggestions, feel free.
- Programmed simulation of 100 Prisoners: click here
We are currently submitting some new results in the information theory of Huffman coding to the IEEE Transactions of Information Theory. More details coming soon!
Joint work with Professor John T. Gill III.
- Gill, John T.; Wu, William. (to be disclosed)
This has been an ongoing research project for years now. We have been stuck on one last proof for a long time. If you are an expert in the number theory of binomial coefficients and are interested in publishing a paper, contact us!
Joint work with Brad Osgood and Summer 2009 EE REU student Justin Hsu.
- Wu, William; Osgood, Brad. Geometry and Algebra of Bezier Curves. (in progress)
Lastly, I am interested in finding more collaborators to work with. The only important things I'm looking for are reliability and intellectual honesty. Having a little sense of urgency is a plus.
- Reliability includes writing one's thoughts down clearly and systematically in LaTeX, reading all the correspondence that we send to each other, having the time to take research seriously (even if we're not getting paid anything), and remembering what it is we are doing without getting easily sidetracked.
- Intellectual honesty includes not overstating the importance of one's results, not wallowing in self-indulgent speculation without backing up one's own statements with rigorous proofs, and not having the hubris to claim that one's ideas are novel without even bothering to check the literature first.
I have served as a math tutor since 2002 in the California Bay Area and New York City, both privately and in tandem with university-affiliated tutoring organizations such as SUMO at Stanford and TBP at UC Berkeley. I have tutored a wide variety of subjects, including:
- Test Prep: SAT Math, ACT Math, GMAT Math, SAT II Math, GRE Math
- High School: prealgebra, algebra, geometry, trigonometry, calculus, AP Physics
- College Math: single and multivariable calculus, linear algebra, ordinary differential equations, probability, statistics
- Advanced Math: real analysis, complex analysis, probability theory, stochastic processes, signal processing, fourier analysis, PDEs, group theory, discrete math and combinatorics, linear systems
- Mathematical Programming: MATLAB, Mathematica, LaTeX
- Consulting: Solutions to particular problems on a per need basis.
I take students at all levels and from all walks of life, including working professionals such as engineers and police officers, graduate students pursuing advanced degrees in finance and economics, and undergraduates taking calculus.
I have also designed many customized curricula for gifted high school students who have run out of math classes to take at their local junior high or high school, and unfortunately are often restricted by the bureaucracy from taking the most advanced courses due to their year or age. Call me crazy, but based on my experience, the chances of finding a better tutor than me to fill this void are slim to none. For a few samples of lesson plans I've made for advanced students, see here:
| real analysis I | real analysis IX | linear algebra I | linear algebra VI | ap physics |
If you are interested in my services, please e-mail me at willywutang AT gmail DOT com.
I served as head Teaching Assistant (TA) for EE376A: Information Theory at Stanford University during the Winter 2008-2009 quarter, taught by Professor Thomas Cover. 
The course covered Chapters 1 through 9 of Elements of Information Theory.
TA responsibilities included regular office hours, selecting and managing graders, exam review sessions, website design and maintenance, publishing of handouts, creating and grading exam problems, building an errata sheet, and improving old solutions.
Below are some of the extra educational materials I wrote while serving as a TA.
- About Claude Shannon. Accomplishments, life, and legacy of Claude Shannon.
- Midterm Review. Information theory algebra, AEP, entropy rate, 2nd Law of Thermodynamics, gambling, data compression.
- Final Review. High-level review of EE376A, Kolmogorov complexity, inequalities, channel capacity, gaussian channel capacity.
- Random Numbers. All students were asked to write down a number less than 10. A statistical analysis of the results is performed.
Below are teaching evaluation survey results about my performance, by students in the course. I received the Hugh Hildreth Skilling teaching award that year.
I am available to give interactive workshops for industry on any of the following topics:
- programming in mathematica
- programming in matlab
- introduction to network coding
- elementary probability theory
- introductory real analysis
- learn to juggle in an hour (or two)
A sample of the level of presentation quality that can be expected from these tutorials can be seen in the following slides on network coding below.
- wuriddles.com / http://www.ocf.berkeley.edu/~wwu/riddles
-
One of the net's best resources for serious mathematical puzzles. Includes an active forum with +10,000 registered members and daily problem-solving discussions. Math markup is now also available. The website has been featured on slashdot, referenced in the MENSA journal, and mentioned in the best selling book How Would You Move Mount Fuji? by William Poundstone.
- wuism.net / http://www.ocf.berkeley.edu/~wwu
-
My personal site, with more about me and my interests. Now it serves as a kind of gateway to different webpages I've made.
| juggling | tutoring | web design | nunchaku |
 |
 |
 |
 |
| drawing and fractal art | skating | emulation | reading |
 |
 |
 |
 |
- address
-
Department of Electrical Engineering Packard Building, Room 268 Stanford, CA 94305-9510
- willywu AT stanford DOT edu
 |
| w.wu © 2003-2010 |
| Updated 11/17/09, 08:58:47 PM |