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An Interview with Erol Peköz
by Sarah Buck, Continuations Bibliographer

Dr. Peköz teaches in the School of Management at Boston University, and is co-author of A Second Course in Probability, a new book written with Sheldon Ross.

Erol Peköz

Can you tell about your new book, A Second Course in Probability?
It's a textbook and reference book about advanced probability theory written for undergraduate and graduate students in statistics, mathematics, engineering, finance, and actuarial science. It is unique in that it covers very advanced topics in probability such as measure theory, Brownian motion, and Stein's method, but at a very accessible level for people who've only had one previous course in probability. Many people are already familiar with Sheldon Ross' best-selling book A First Course in Probability, and this book has the same focus on elegant and illustrative examples and problems. Most books covering these topics require a lot of prerequisite study of many mathematical details, and the really interesting stuff doesn't get presented until much later. This book takes the reader far into exciting territory from the very beginning. It's not exhaustive by any means, but it tries to be interesting and lively and give alternative or nonstandard points of view.

ISBN: 9780979570407
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So this book belongs in a Mathematics collection? A Business collection?
Any research university should find this book fits into its collection well. Most mathematics, engineering, or science libraries at universities already have many other books by Sheldon Ross. This new book would be the perfect complement to any collection of statistics-related books. A university without a dedicated mathematics library but with some graduate or advanced undergraduate level books on statistics in the main collection would find this fits into the collection. It is especially designed as a book for self-study or reference.

How did you get the idea to write this book?
I recently had a sabbatical in the Department of Statistics at Harvard University where I taught an advanced course in probability theory for graduate students. I found that most of the students in the class wanted exposure to the advanced material but did not want to go on and specialize in it. I also wanted the course to be intuitive, alternative, and exciting. Most books on this subject are written for real specialists, and it requires so much background that you miss the forest for the trees. You end up trudging around and focusing on little tiny details, and you don't see the real beauty of it all. Most books have you go step-by-step; they give you one grain of rice at a time leading you along to some big feast, and you don't get to see what's going on until the end.

I have a high standard for entertainment. I'm very easily bored, and so I wanted to make a course that starts off doing the most interesting things and sort of takes you on this path through all the mundane stuff just skirting past it all. You cover a bunch of really exciting topics and if you really like the subject you can go back and study it more. MBA students are very "why do we need to know this"-type people, and I try to engage the audience and bring it to the really technical subject. Most people who write on this topic don't have that angle at all.

Can you talk about the experience of writing it and getting it published?
Writing the book was a lot of fun. Sheldon Ross and I actually never spoke about starting this project or anytime during the project --- it was all by email. I was planning to teach the course again at Harvard and I started writing the first chapter of a potential book. When I sent my co-author a copy of what I was writing, he wrote back with suggestions. Then over the course of one year we corresponded daily back-and-forth about what we were writing. I have wanted to write a book with Sheldon Ross ever since the very first time I read his book Stochastic Processes while I was a graduate student. In some sense this is the achievement of a lifelong goal for me.

We had several mainstream publishers approach us and express interest in publishing the book while we were writing it, but we decided to self-publish the book through Lightning Source. Sheldon Ross has many other books through other publishers (and I have one in development with a mainstream publisher), but we decided to see if we could go it alone and market the book ourselves. The quality of the book seems identical to what you get through mainstream publishers, but self publishing enables us to maintain editorial control and to sell the book at a lower price.

Do students come to you with complaints about the prices of textbooks or course books?
Definitely that's the main pushback from students. And faculty that I've shown the book to say "well how much is it?" They don't want students to get upset, and most books like this cost over a hundred dollars and the authors get less than ten dollars per book. So we're selling it for a lot less and we can boost the appeal of it by the pricing.

What were some of the challenges in putting it together?
The biggest challenge was in turning it from an evolving manuscript into a finished product. My co-author is very experienced with this and he was great to work with. Towards the end when you've written most of the interesting stuff, there is a lot of tedious work involved with checking/rechecking and so forth -- but he was experienced enough with this process to help see it through and know when to stop.

It was also challenging to come up with completely new ways of explaining these traditional topics. Most books on the topic explain everything in the traditional way -- using notation that requires lots of energy to follow. Our goal was to make it light and lively and so we had to rethink many things.

I've looked through the book: there are a lot of Greek formulas there, but I can tell (even though I'm completely unfamiliar with any of the subject matter) that the tone is very playful.
Right; it's supposed to be. We spent a lot of time trying to think of ways to make it interesting even though it's not the traditional way to teach this one topic. Typically it's taught with all the technical details, and it turns out dry and mundane. We tried to re-think everything so that we could teach it in the most artistic way. This approach is pretty rare in high-level books.

In your section on the Poisson approximation and Le Cam's theorem (p. 61), you include a remark that the result is "beautiful." I've always wanted to know what it means for math to be beautiful. Is it the way it looks on paper, or is it conceptual?
It's conceptual -- the same way a poem or story is beautiful. We are storytellers, and the beauty of this book lies in the way we tell the story. The beauty of a poem often stems from having a simple phrase that instantly and elegantly summarizes a complex emotion or situation. For example, a love poem may contain a short phrase that conveys the complex emotion of love. In the most beautiful mathematics you often start with a very complex setting and the mathematics gives you an unexpected and very simple way to summarize it elegantly --- so that you still appreciate the complexity surrounding it. Probably the most famous example of beautiful mathematics is Einstein's E = mc squared formula, which is so simple and unexpected but explains so much about the world.

Le Cam's theorem we present there is beautiful because something very complex, on the left side of the equation, is related to something very simple, on the right side of the equation. The derivation is not obvious, and during the steps of the derivation the complexities almost magically seem to melt away to reveal the simplicity below.

Here's another way to summarize it: "Beauty in mathematics is seeing the truth without effort."-George Polya

The difficulty many people have with seeing the beauty in mathematics is that its language of expression requires some prerequisite study. I have read that it's difficult to appreciate the real beauty of the Koran unless you first learn Arabic. Mathematics is the same way -- to appreciate the beauty of one of mankind's most impressive achievements requires first learning a new language.

You're working on a new project: The Manager's Common Sense Guide to Statistics. Can you tell a bit about this one?
This book is going to appear through the publisher WH Freeman, and it's a "no formulas" treatment of business statistics using basically just words and pictures. The strength is that almost every problem or example is motivated by a real study or business situation. The book is a non-technical first course in statistics for undergraduate and graduate students in business.

It's easy to read whereas most books on this subject say "a block of cheese has a weight of 25 oz, calculate the weight of the average cheese blocks" and you're already sleeping by the time the question's over because nobody wants to work on a cheese block, and that's not why they're in school and the problems are very tedious. My magic secret, my competitive edge is that I have culled through all these sources like Harvard Business Review, and Business Week, and Wall St Journal, where they have people like you, literary people, looking for exciting things for business people; little angles or tidbits that business people would be interested in, and then I just take their setting and present that in the book. So I feel like I have this professional staff of interesting-problem-gatherers for me.

So it's practical
It's practical and it also takes examples from the mainstream business media. A lot of people take the view that they're either totally skeptical of all numbers, or they are just completely gullible, and both of those types of people are equally missing out on the truth. The purpose of my book is to educate the consumer of statistics and the consumer of numbers so they know when someone's massaging the numbers. So I focus on what can happen, what can surprise you, what can trick you if you do this or someone does that.

This has been quite an interesting morning with you, and I have just one last question: if typical statistics books are so dry and mundane and tedious, and your personality is clearly the opposite, how did you ever end up in this field: what is it about these numbers that keep you slogging through the material?
Probability is a beautiful subject, but many authors get so swept up in their art that they can have trouble communicating the beautiful parts to newcomers and tend to focus on the more dry prerequisites. Knowledge of the rules of spelling and grammar are important prerequisites to becoming a good creative writer, but the beauty of the art of creative writing usually is not revealed in these rules-which can seem mundane and tedious to newcomers. I remember taking a writing class where the instructor became so obsessed with the poor grammar and style of the students in the class that it was difficult for us to see the beauty of writing--it seemed more like tax accounting with many arcane rules and special cases. It's only after you understand the beauty of creative writing that you can appreciate the need for all the rules of spelling and grammar -- and they may even seem beautiful too, after you understand they are tools for artistic expression. Most people who study introductory mathematics in school usually never get past the tedious prerequisites for seeing the beautiful artistic parts that motivated the creation of the subject.

One thing that caught my attention about mathematics at the beginning is how a very important piece of work can be extremely short -- sometimes it can be expressed in a single page or paragraph of writing. A work that may have taken many years to complete on stacks and stacks of scratch paper can end up as a single page and can be viewed as extremely influential, novel, elegant, and beautiful. I was fascinated by this and I wanted to see how this was possible. I have always been a fan of art that was not readily accessible. Though I like Madonna and Cold Play like everyone else, I'm also a fan of atonal jazz music.

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