We spent a delightful hour discussing his book, his love of math and magic, and the inspiration behind writing the book. Plus, Dr. Mulcahy shares a few challenges listeners might enjoy chewing on, sprinkled throughout the interview. And, we discuss Martin Gardner, who Colm Mulcahy knew for the last decade of his life and met with several times.
You may also enjoy Shecky's text interview with Colm Mulcahy at Math Tango.
About Colm Mulcahy
Colm Mulcahy is professor of mathematics at Spelman College, in Atlanta, where he has taught since 1988. He trained in algebra, and has also written papers on CAGC and wavelets. Over the last decade, he has been at the forefront of publishing original "mathemagical" principles and effects, particularly in his long-running bi-monthly Card Colm for the Mathematical Association of America (MAA). He also blogs at the Aperiodical and the Huffington Post.
He's particularly active in Gathering for Gardner and the associated Celebration of Mind initiative, and getting more involved in Maths Week Ireland and Julia Robinson Mathematics Festival outreach activities.
In 1997, Dr. Mulcahy received the MAA's Allendoerfer Award for excellence in expository writing, for an article on wavelets from Mathematics Magazine (Dec 1996). His interests include algebra, number and geometry. He earned a B.Sc. and M.Sc. in mathematical science from University College Dublin, in his native Ireland, and a Ph.D. from Cornell University for research in the abstract algebraic theory of quadratic forms.
Celebration of Mind
About Mathematical Card Magic: Fifty-Two New Effects
Mathematical card effects offer both beginning and experienced magicians an opportunity to entertain with a minimum of props. Featuring mostly original creations, Mathematical Card Magic: Fifty-Two New Effects presents an entertaining look at new mathematically based card tricks.
Each chapter contains four card effects, generally starting with simple applications of a particular mathematical principle and ending with more complex ones. Practice a handful of the introductory effects and, in no time, you’ll establish your reputation as a "mathemagician." Delve a little deeper into each chapter and the mathematics gets more interesting. The author explains the mathematics as needed in an easy-to-follow way. He also provides additional details, background, and suggestions for further explorations.
Suitable for recreational math buffs and amateur card lovers or as a text in a first-year seminar, this color book offers a diverse collection of new mathemagic principles and effects.
When I interviewed Ken Fan of Girls' Angle I learned about Kiki and her wonderful work. Kiki is passionate about improving people's relationships to computers, beyond basic literacy to programming and understanding how computers think. While our interview was largely about computers and not math, we both realized that at the core of both is a blend of logical and creative thinking.
Kiki's passion for changing experiences, especially those of young girls, is contagious. Listen and tell us if you agree.
About Kiki Prottsman
Having dedicated her life to showing women how impressive they are, Kiki is an active role model on FabFems. Her enthusiasm for science and technology become contagious as she introduces under-represented participants to unlikely subjects.
With experience using both sides of her brain, Kiki came to computer science for the artistry of problem solving. She spends her days not only as the Executive Director and Founder of Thinkersmith, but also teaching computer science to undergraduates at the University of Oregon.
Here is a fun question at Quora:
There are some remarkably geeky answers. Those of you who write code might enjoy the second answer, by Anders Kaseorg.
Welcome to Carnival of Mathematics #99. Wikipedia provides some nice trivia about the number 99.
99 is the ninth repdigit, a palindromic number and a Kaprekar number. It is the sum of divisors of the first eleven positive integers.
99 is the sum of the cubes of three consecutive integers:
99 = 2^3 + 3^3 + 4^3
And, I personally like that 99 is the difference of two squares: 99=10^2-1^2.
Now, onto the carnival articles.
John Cook shares Recognizing numbers. For Python users, SymPy is a symbolic math package that "takes a floating point number and tries to simplify it: as a fraction with a small denominator, square root of a small integer, an expression involving famous constants, etc."
Mike Thayer, in Algebra and Geometry, asks this question: "I teach algebra 1, to 9th and 10th graders, mainly. I also teach geometry to the same age group. I'm wondering the following: Why is it that the conversations in geometry are so much more interesting, generally?"
Peter Rowlett takes a break from PhD preparation to explore Ox Block probabilities. "I'm not blogging much in the run up to my PhD thesis deadline, but my curiosity got the better of me with this one. Having seen (via Twitter) that it was being played at a Maths Jam, I bought an old game called Ox Blocks, which offers “Noughts and Crosses[/Tic Tac Toe] with a novel twist”. Here, I investigate the probabilities of rolling an unusual die."
Thomas Woolley writes Egg shells to turtle shells. "No matter how you initially orient the gömböc it will always wobble and rotate itself to finish standing upright. Importantly, the gömböc is made of only one material, so its density is uniform. Mathematically, the gömböc is known as a mono-monostatic body. This simply means that it has exactly one stable and one unstable equilibrium point."
Tony, a university maths professor in London, in My favorite equation considers whether there's a more interesting formula than Euler's formula. "So McKay's formula may not be as immediately beautiful as Euler's, but it has something of the same spirit (and perhaps even importance). It demonstrates a very deep connection between group theory and modular forms; it's mysterious and hard to understand, and it's inspiring important mathematics. And it says a lot about the serendipity which lies behind insights even in a subject as apparently logical and rigorous as mathematics."
Simon Gladman wonders what pendulum waves might sound like in The Sweet Sound of Pendulum Waves - in Glorious Stereo! "I had a little play with Pendulum Waves the other day and since then I've been wondering what sort of sound they would make if I played a tone as each pendulum reached its apex."
Have you ever wondered Why are determinants defined the weird way they are? If you've ever wondered why, whether or not you've studied linear algebra, you might enjoy this article. It'll give you some great material for your next party conversation!
Yao-Hong Kok is a Master's student studying control theory. Math, Control Theory and Two Issues invites interested parties into a discussion. "Control theory is one of those fields that requires a lot of mathematics. I have been in the field for roughly 2 years now and I have realized that they are 2 big issues within control theory, namely: (i) identity of a control engineer/theorist, and (ii) stagnation of fundamental theory advancements. In this post, I would like to relate mathematics to the above issues and perhaps generate some discussions."
Maria Droujkova shares Math dreams meeting May 20, 2013. "Curriculum developers' elephant in the room is a simple question: "Who wants that stuff, anyway?" We decided to ask parents what do they want for their kids, in math. Deep is the chasm between what parents want, and what existing curricula provide..."
Shecky Riemann, inspired by Martin Gardner's passing to start his blog, writes Remembering... Gardner three years after his death. "Not to take anything away from our Veterans, but this is a math blog, and I'll use the opportunity of Memorial Day to once again remember Martin Gardner, whose death just over 3 years ago inspired me to start this endeavor (with no idea it would still be up-and-running 3 years later!!)."
Herminio Lopez examines an interesting puzzle in A black (and red) hole. "Thanks to a prize consisting on the proceeds of a football match, we learn about some numbers that attract the others, which can't escape from them. Mathematical sequences which lead to mathematical black holes."
In Demystifying the Möbius, Burkard and Marty take readers on a nice journey through the many twists and turns that one can take with these paper treats.
Predicting Sums is a fun article at Grey Matters. It shows a nice math trick one can perform with a little knowledge of digital roots (aka nine's complements).
Math Munch is a great blog for children of all ages that describes itself as "A Weekly Digest of the Mathematical Internet." Their latest edition is Solitons, Contours, and Thinking Sdrawkcab. Check it out if you've not yet discovered this blog.
The Aperidical is another of my favorite blogs. They describe themselves as "a meeting-place for people who already know they like maths and would like to know more. It was begun by Katie Steckles, Christian Perfect and Peter Rowlett as a shared blogging outlet and grew out of our desire to have a place on the web where we could keep up to date with what’s going on elsewhere, and to share the mathematical things we do." You might also recognize Aperiodical as the stewards of this Math Carnival. Christian authored this fun piece, Integer sequence review: A000959.
If you've ever wondered what math and the meaning of life were related, check out 42 at Calculus Humor. This article deserves to go viral. Really.
Finally, I'll share one of my own favorite recent articles, Ken Fan: Inspired by Math #29. It's a podcast interview where Ken and I had a nice informal chat without much preparation before-hand.
A friendly reminder:
I'll be hosting the next Carnival of Mathematics. Please check out this URL to learn more about the carnival, to vist past carnivals, or to submit your blog article for #99. Submission deadline is 6/1/13.
I'll be hosting the next Carnival of Mathematics. Please check out this URL to learn more about the carnival, to vist past carnivals, or to submit your blog article for #99. Submission deadline is 6/1/13.
Math contests can be a lot of fun. SIAM, the Society for Industrial and Applied Mathematics, puts on a contest every year for teams of high school juniors and seniors to propose a solution to a pressing real world problem. The contest promotes lots of hard work, collaboration, and smart thinking. And, the winners get a bunch of scholarship money along with a hefty dose of glory. My two podcast guests have key roles in running the contest. It's a great thing that Michelle Montgomery and Katie Fowler are doing to prepare future generations to take on the world's challenges.
About Michelle Montgomery
Michelle Montgomery wrote the initial proposal and is project director for Moody’s Mega Math (M 3) Challenge. This is an extension of her work as director of marketing for the Society for Industrial and Applied Mathematics (SIAM). Her responsibilities focus on fulfilling the mission of SIAM, which includes inspiring young people to study and pursue careers in applied mathematics and computational science.
Since joining the staff in 1988, Michelle has been involved in promoting SIAM publications, conferences, and membership -- all of which are focused on high level applications of math. The M3 Challenge is SIAM’s biggest outreach to students in high school. Other outreach efforts include series of interesting vignettes that explain the math behind everyday life, interesting research being done, and generally highlight the value of computational sciences to our world. These efforts go under the names “Math Matters” and “Nuggets” on the SIAM Public Awareness pages.
Moving forward, Michelle hopes to participate in changing the way students, teachers, and the public look at math education through integration of more math modeling activities in STEM/STEAM curriculum, and more public awareness efforts to demonstrate the importance of work being done by computational professionals.
Michelle lives in the suburbs of Philadelphia with her two teenage children, with whom she spends much of her free time. She is passionate about literacy and education, and serves on the board of trustees for her local public library.
About Katie Fowler
Katie Fowler joined the Department of Mathematics at Clarkson University in the fall of 2003 having graduated from North Carolina State University with a PhD in Computational Applied Mathematics. Her efforts as a mathematician are split between the scientific community and service to the campus and local communities, including educational outreach grants bringing over $3M to northern New York. She co-directs an integrated math-physics roller coaster engineering camp for 50+ local 7-12 grade students every summer.
Katie received the Clarkson University Outstanding New Teacher award in 2005, and in 2010 the Mathematical Association of America honored her with the Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member. The most rewarding part of being a professor to her is mentoring students, including supervising undergraduate projects. She has co-authored eight peer-reviewed papers with undergraduate research students in the last ten years.
Her research focus is applied optimization with an emphasis on developing hybrid derivative-free techniques for simulation-based engineering problems. Although her work has spanned multiple disciplines including psychology, polymer processing, and biology, she is most passionate about environmental applications. She has developed algorithims to tackle remediation of contaminated groundwater and is currently working on sustainable water practices for the agricultural management.
In her spare time, Katie enjoys running, cooking, travelling (to eat new things), and trying to convince her two girls to broaden their culinary experiences.
The Society for Industrial and Applied Mathematics (SIAM) is an international community of over 13,000 individual members. Almost 500 academic, manufacturing, research and development, service and consulting organizations, government, and military organizations worldwide are institutional members.
SIAM fosters the development of applied mathematical and computational methodologies needed in these various application areas. Applied mathematics in partnership with computational science is essential in solving many real-world problems. Through publications, research, and community, the mission of SIAM is to build cooperation between mathematics and the worlds of science and technology. More ...
About Moody’s Mega Math Challenge
The M3 Challenge spotlights applied mathematics as a powerful problem-solving tool, as a viable and exciting profession, and as a vital contributor to advances in an increasingly technical society. Scholarship prizes total $115,000. The Challenge is entirely Internet-based and there are no registration or participation fees. Each high school may enter up to two teams of three to five junior and/or senior students. More ...
This podcast is an experimental one in that I didn't script the questions the way I usually do. My guest, Ken Fan, and I both decided in advance that we'd go with the flow. And, in my judgment, this is the best podcast I've done -- it felt very natural. Ken is a great guy with a sincere desire to improve girls' experience of math education. And, he's created an organization to manifest his great vision. I absolutely love it when a PhD level mathematician decides that high school education is important enough to dedicate himself to it.
If you've never heard of Ken or Girls' Angle you're in for a treat.
About Ken Fan
Ken Fan is the president and founder of Girls' Angle, a nonprofit math club for girls based in Cambridge, Massachusetts (www.girlsangle.org). He received a doctoral degree in mathematics from MIT under the supervision of George Lusztig and was a Benjamin Peirce assistant professor of mathematics at Harvard before leaving academia to pursue a career as an oil painter. To pay the bills, he began freelancing in math educational publishing in various capacities. His experiences as a freelancer as well as an opportunity to volunteer for Science Club for Girls inspired him to create a comprehensive math educational program for girls. He may be reached at girlsangle "at" gmail.com.
P vs. NP is a problem at the forefront of computer science. Until now there hasn't been a book written for a general audience that introduces the problem and its importance. Lance Fortnow has authored such a book. Lance I discuss the problem, the book, why he wrote it, and what it takes to write such a book in a way that doesn't scare most of us away. And, we take a few detours into talks about computer science and programming early microcomputers.
About Lance Fortnow
From the author's web-site:
Lance Fortnow is professor and chair of the School of Computer Science of the College of Computing at the Georgia Institute of Technology. His research focuses on computational complexity and its applications to economic theory. He also holds an adjoint professorship at the Toyota Technological Institute at Chicago.
Fortnow received his Ph.D. in Applied Mathematics at MIT in 1989 under the supervision of Michael Sipser. Before he joined Georgia Tech in 2012, Fortnow was a professor at Northwestern University, the University of Chicago, a senior research scientist at the NEC Research Institute and a one-year visitor at CWI and the University of Amsterdam.
Fortnow's research spans computational complexity and its applications, most recently to micro-economic theory. His work on interactive proof systems and time space lower bounds for satsifability have led to his election as a 2007 ACM Fellow. In addition he was an NSF Presidential Faculty Fellow from 1992-1998 and a Fulbright Scholar to the Netherlands in 1996-97.
Among his many activities, Fortnow served as the founding editor-in-chief of the ACM Transaction on Computation Theory, served as chair of ACM SIGACT and currently sits on the Computing Research Association board of directors and the council of the Computing Community Consortium. He served as chair of the IEEE Conference on Computational Complexity from 2000-2006. Fortnow originated and co-authors the Computational Complexity weblog since 2002, the first major theoretical computer science blog. He has thousands of followers on Twitter.
Fortnow's survey The Status of the P versus NP Problem is CACM's most downloaded article. Fortnow has written a popular science book The Golden Ticket: P, NP and the Search for the Impossible loosely based on that article.
About "The Golden Ticket"
From the Princeton University Press web-site:
The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives.
The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.
Mary O'Keeffe has an article in the Albany Area Math Circle blog expanding on some of the discussion in our recent podcast. And, her daughter Catherine created a transcript of the recording. The transcript is annotated with comments that may be of interest to listeners.
Mary's article, Doing justice to describing the work of other math circles that have inspired us elaborates on the contributions and inspiration that Ken Fan and many others have made to help her math circle to thrive.
I'll be interviewing Ken Fan for the "Inspired by Math!" series. And, I plan to seek out the other people who have inspired the folks in the Albany Area and shine the spotlight on those who are willing.