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# New and Noteworthy Titles on our Bookshelf

June/July 2023

The probability of random events can go against our intuition and have surprising outcomes. Two famous examples of this are the Monty Hall problem and the birthday problem, although examples can be found in all aspects of life. A better understanding of probability can help us reconcile the counterintuitive nature of the randomness we encounter.

One inherent obstacle when thinking about random outcomes is that while probability is a statement about the long run, we experience the outcomes of randomness as individual events. How can we relate the long run with these single occurrences? Elliott terms this complicated duality as the individual versus the collective. He identifies this as one of the five sources of tension that are fundamental to probability which create a barrier to understanding it. Each of the five dualities is clarified through varied examples. For instance, the individual versus collective dichotomy is explained in terms of vaccines, crime statistics, and music, to name a few.

Written for general audiences, this book is extremely engaging and filled with relevant examples of the misuse of probability that immediately draw the reader in. Each section starts with easy to state probability questions that challenge our intuition, after which, various probability concepts are introduced and discussed. The end of each section gives the solution to the problem stated at the beginning, making use of the ideas developed throughout the section. The book emphasizes intuition over technical reasoning, although where technical arguments would enhance the reader’s understanding, the explanations are boxed off and clearly marked so that the reader knows that what follows will be more rigorous. This is an excellent and inviting book for anyone looking to hone their knowledge of probability.

Zeta-3 is the value of the Riemann–Euler zeta function at 3, While the zeta function is most famous for its role in the Riemann hypothesis, there are many open questions surrounding various aspects of it. For example, there is no known symbolic representation for . where is a positive, odd integer (in contrast with when is a positive even integer). Nahin focuses specifically on the attempts to find this representation for Zeta-3 has a number of applications in physics and engineering, which appeals to the author as an electrical engineer. .

In its treatment of this book draws on background covered in the calculus sequence. In particular, infinite series, integration techniques, and multivariable integration feature prominently. The preface contains a brief introduction to mathematical induction which is utilized throughout the book and is also there to ensure that the reader’s mathematical maturity is at a level to engage with the mathematics in the book. Each section contains multiple challenge questions, the solutions to which are included. Additionally, MATLAB code that accompanies the calculation being discussed is often provided. ,

Nahin’s writing style is welcoming and approachable; he easily draws the reader in with his storytelling ability and sense of humor. This book is accessible to anyone with a good grasp of second semester calculus and may be of particular interest to math, physics, or engineering majors. Mathematicians looking for a light math read will also find this engaging and worth picking up!