## Polya and Friends

**Enumeration**

In his book, "How to Solve It," Ploya lists several common strategies for solving problems. His first choice in his list was

**enumeration**. As simple as the idea seems, the counting of the items or the cases tends to reveal the pattern.

**Incrementals by Hamming**

Dr. Hamming wrote a book called Finite Calculus while at UC-Irvine. He gave me and the other students a copy of the manuscript. He was brilliant and inspiring, Often he revealed the pattern in raw data by taking differences of successive values. Many kinds of equations follow predictable patterns.

In 1974, as a conditional grad student, I took Hamming's Finite Topics Seminar. Passing the final was to be my approval as a grad student. I got a 30 out of 100. I felt rejected. Even my advisor commiserated. Only two weeks after the next quarter, did I find out the situation.

Another student named Dennis already had a PhD in Math from UCLA; he got a 49. My 30 was second highest! In the second week of the next quarter, when I realized that my score placed me second out of twenty some in the class, the grade committee said that my absence for those few classes disqualified me--a very bitter experience. Several others from that course were allowed in.

**In the text books**

Dr. Olson from DEC; Fred Tonge on conveyors, Julian Fledman on psyche; Rob Kling on social issues; Dr Ash from MIT and Chomsky fame; Mr David Farber invented a four integer addressing technique on Varian machines. Think IP Address. The twelve of us in that class of 1971 had extraordinary professors. John Newman from NATO brought his herd of IMLAC graphical computers; the graphical transitions between scenes affected me, who in turn affected several students, who affected cartoons and shows like Batman. Newman also contributed to the Thomas Guide's for drivers. Hamming gave me the award of

**Most Ingenious**. When I now see all of the discoveries of my fellow students, who am I? Dr. Olson put Ira Baxter and Steve Sternitsky and me onto a committee of three. Such committees were standard in all upper division CS classes. During my last five quarters as an undergrad; we collaborated as partners and greatly contributed to our mutual success.

**The problem is the answer**

Often the solution stems from a well stated problem

Often the solution stems from a well stated problem