Have you read a wonderful book about mathematics or statistics? Share the book and your review with the FYMSiC community! 🙂
Latest Good Reads
♦ Introduction to the Theory of Optimization in Euclidean Space by Samia Challal
Recommended by Samia Challal (York University – Glendon Campus)
The book provides students with a robust background in Optimization. It is a self-contained resource for the instructor and for the student. The main theoretical theorems are provided with detailed proofs and followed with examples for illustrations. At the end of each section, some questions are suggested with complete solutions. Depending on the students’ mathematics background, one can skip the detailed proofs and direct the students’ attention to:
- focus on the intuitive ideas,
- practice into acquiring the new strategies needed through solving optimization problems, and
- discover different applications where optimization is involved.
♦ In pursuit of zeta–3: the world’s most mysterious unsolved math problem by Paul J. Nahin
Recommended by Tim Sibbald (Nipissing University)
This book is well suited to enrichment or encouragement for students who are interested in the field of mathematics. It is suitable for undergraduate students and somewhat accessible at the grade 12 level. The strength of the book is that it surveys many results from the rich topic of Riemann’s zeta function while being respectful for, but not bogged down by, rigour. It steers clear of the Riemann Hypothesis and focuses on the mysterious value of the zeta function at three. The value is known to be irrational, but an exact value is not known in spite of evidence suggesting it is likely to be a rational multiple of pi cubed. Within this milieu many results are discussed relating to the zeta function, gamma function, and Euler sums that arise naturally from the overall focus. The coverage of the book is well suited to undergraduate students because of the mix of infinite sums, integrals, products, and Fourier series—yet all topics are addressed in an accessible manner.
Personally, I visited many of the topics in this book when I was in grade 13. That shows my age, but also speaks to how one does not need a fully developed sense of calculus to enjoy the book. I recall being challenged by a variety of the concepts I found in the book in a good way. Revisiting the topic through this book pointed to some aspects that are new to me and serve as provocation to investigate recent findings.
Previous Good Reads Mentioned
♦ Aesthetics of Interdisciplinarity: Art and Mathematics by the editors Kristóf Fenyvesi and Tuuli Lähdesmäki
Recommended by Amenda Chow (York University)
This book dives into the interplay between art and mathematics by showcasing a wide-ranging collection of articles written by various experts. Many of the articles include a selection of thoughtful, complementary, and artistic figures. Some topics discussed are:
- geometry of India’s ancient temple cave art;
- drawings containing a hidden image (known as anamorphosis drawings);
- mathematical modelling influencing scientific discoveries like DNA and viruses;
- African weaving patterns in mats and baskets;
- designs with optical effects and visual illusions; and
- meaning and societal impact of geometry-based monuments.
There is much more in the book, and to begin, the first chapter is a discussion about the aesthetics of interdisciplinarity, which is a term created by the editors of the book to refer to the broad and deep relationship between art, mathematics, science, and technology. This introductory section also includes an overview of the global community that has evolved around the common enthusiasm and intrigue for the aesthetics of interdisciplinarity. Lastly, just a small note: overall, the focus of the book is on the art, with mathematics as a well-placed backdrop.
Why I liked the book? I was introduced to ideas, connections, people, and art pieces that make me now see the world differently. For this I am grateful, and quite inspired. I feel more prepared to teach my upcoming first-year calculus course and my introduction to proofs course because it has given me insights on how to inspire my students’ learning. Many of the ideas and images in the book mesmerized me, and in the middle of reading it, I also felt happily nostalgic and tried out my spiragraph set after a nearly thirty-year long absence. As I child, I remember finding these spiragraph designs to be beautiful and hypnotizing, but at the time, I didn’t realize the underlying mathematical principles. Now I am in awe realizing math and art were part of my life from a young age. Above are some examples of sketches using a spiragraph.
Thank you to Professor Eva Knoll from Université du Québec à Montréal for suggesting I read this book.
♦ Inclusive Teaching by Kelly A. Hogan and Viji Sathy
Recommended by Zack Wolske (University of Toronto)
This book is based on their work towards a more inclusive environment using high-structure, flipped classes to teach introduction to biology and statistics at a large research university with limited institutional support and free rein to decide how to teach.
If you are looking to make incremental changes to teach more inclusively; if you would ask “who might be left behind, and how can we invite them in?” about your teaching; if you are reflecting and looking for questions; if you seek data and transparency with students, TAs, and faculty about your practices; if you want to see specific examples of syllabi, interactions in and out of the classroom, and instructor checklists for high structure courses; if the authors’ situation resonates with you; check out this book.
You can find examples and book club prompts at inclusifiED.com, and hear the authors discuss the book on the Teaching in Higher Ed podcast, episode 425 (and 365, 272, or 197 for some overlapping work).
Also recommended by Rachael A. Lewitzky (George Brown College) & Asia Majeed (University of Toronto)
This book explores teaching strategies the authors use to foster a sense of inclusion in their college classrooms. Two questions guide the authors’ approach to fostering an inclusive environment: 1) Who might be left behind as a result of my practice? 2) How can I invite those students in? The book provides insight about how each author’s teaching practice has evolved – the challenges they have faced and the successes they have experienced. Topics include course structure, class design and facilitation, inclusive practices within and beyond the classroom, as well as reflection on teaching practices.
As introductory science, technology, engineering, and math (STEM) course instructors, they explain the challenges of feeling the need to include an abundance of content in a limited amount of time. They highlight the value of identifying the skills and outcomes of a course and working backwards to determine what content, ideas, and concepts to include in the course. The authors describe what their courses look like from start to finish. From how they structure their course syllabi and activities they complete at the beginning of the term (e.g., opportunities for student-instructor and student-student interactions; creating conditions where it is safe to make mistakes; presenting societal and personal relevance in course) to structured small group and large group discussions, to demystifying the purpose of office hours, the authors provide suggestions and strategies.
The personable way in which this book is written makes it feel like sitting down with a friend and talking about how to learn and grow as an educator. We enjoyed reading this book and sharing our thoughts with one another about how we could employ some approaches discussed in the book. Inclusive Teaching provides readers with the chance to reflect on their own teaching philosophy and highlights opportunities for creating a more inclusive learning environment.
♦ Making a grade: Victorian examinations and the rise of standardized testing by James Elwick
Recommended by Tim Sibbald (Associate Professor, Schulich School of Education, Nipissing University)
This is a remarkable book that explains how the emergence of statistics as an academic field fueled the Victorian simplicity of an educational assembly line. The book explains how standardized testing emerged and was viewed as testing competence and moral character. The latter led to a (then) divisive view that anyone could complete testing to demonstrate ability, but that moral character was different for different segments of society—most notably women. Throughout the book various other issues are addressed within the historical context.
Personally, I found this book insightful because it shows that the issues discussed in conjunction with standardized testing today have been around for a long time. It offers a clarity that the issues are directly tied to the conception of standardized testing. In that sense it provides a strong conceptual portrait of the emergence of standardized testing that is directly connected to current issues.
♦ Shape by Jordan Ellenberg
Recommended by Sean Fitzpatrick (Instructor III, University of Lethbridge)
Superficially, Shape is a book about geometry. It is not a book from which one can learn geometry. However, it is more of a love letter to the subject, and a description of the many ways in which it is woven throughout our daily lives. Recurring themes include the structure of games, and mathematical modelling in biology, including the spread of infectious diseases. Ellenberg does a great job of keeping things entertaining using historical perspective and stories of the personalities involved.
The book ends with a fascinating chapter on the efforts by both mathematicians and politicians to tackle partisan gerrymandering, and describe precisely what would make an electoral map fair. It is a great look under the hood at the process of mathematical thinking.
The book is written with the non-expert in mind, but anyone teaching undergraduate mathematics is sure to find a nugget or two they can use in their classrooms.
♦ The Calculus of Friendship: What a Teacher and a Student Learned about Life While Corresponding about Math by Steven Strogatz
Recommended by Julie Plante (CEGEP Instructor, Vanier College)
A teacher and his student will stay in touch for over 30 years, always united by their love of Calculus, discussing mathematical problems, their lives, everything … Very touching. A must read for any Math teacher…
♦ How Not to be Wrong by Steven Strogatz
Recommended by Wes Maciejewski (Red Deer Polytechnic)
I went to the bookstore to buy Shape (see Sean Fitzpatrick’s review) by Ellenberg and this, his first, sat next to it. I picked up both. I wanted Shape because I’ve been on this kick lately, thinking about how topology and contemporary notions of “shape” might be infused in K-12, and lower-level university, education. Turns out, How Not to be Wrong is the book I needed to read. Why should I be bothered about curriculum? Really: it’s a desire to tell better, more interesting, more relevant stories. How Not to be Wrong does that; it’s the finest example of mathematical storytelling. Stories I, and perhaps you, haven’t heard.
Ellenberg narrates in 5 themes: Linearity, Inference, Expectation, Regression, Existence. Each is a winding path through mathematics used and abused, often wrongly, and often to mislead, intentionally or haphazardly. He brings together wild stories of dead fish, decoding the Torah, the poor economics of the Laffer curve, and voting (among others) and deftly brings forth the underlying mathematics: people think too much and too often in terms of lines; we’d like to use mathematics as a crystal ball when it isn’t; probability and expectation remain hard to comprehend; we search for causes when there might not be any; and consensus is not so easy to discern. Ellenberg is to math as James Burke is to the history of science and technology: he makes connections and guides us to rethink what we take as known. He does this through his own brand of engaging narration.
Going back to how this might be relevant to you, the educator. If we ever only read the same, yellowed texts, we squeeze them dry of all their inspiration. Our stories – the heart of good teaching – become impotent. Read better stories to tell better stories. Read How Not to be Wrong. Make math interesting again.
♦ The Housekeeper and the Professor by Yōko Ogawa
Recommended by Julie Plante (CEGEP Instructor, Vanier College)
A wonderful novel written about Mathematics as much as mathematicians… The novel is very appreciated by non-mathematicians as well as mathematicians. A female house-keeper is introduced to basic number theory by an old professor. The beauty of pure Mathematics is extraordinarily put in words in this writing.
♦ Things to Make and Do in the Fourth Dimension: A Mathematician’s Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More by Matt Parker
Recommended by Asia Matthew (Mathematics Tutor, Quest University)
See Asia’s Review in the March Issue of Crux:
♦ Mathematics for Human Flourishing by Francis Su
Recommended by Sean Fitzpatrick (Instructor III, University of Lethbridge)
This is a book about mathematics, and leading a fulfilling human existence, and how the former helps with the latter. Su examines the role of mathematics in our lives through the lens of a series of human virtues, including exploration, play, truth, beauty, struggle, and justice. A unique feature of the book is the inclusion of some of Su’s correspondence with Christopher Jackson, an inmate in a US federal penitentiary, who wants to become a mathematician. The book is a rewarding read for both mathematicians and the math-averse. It is an excellent choice for an assigned reading in any class containing math-anxious students. The end of the book contains a collection of prompts for reading responses, with further prompts and other resources available on Su’s website.