Strongly Connected Components Episode 10: Richard Stanley
Feb 3rd
Samuel Hansen caught up with professor Richard Stanley at the Joint Mathematics Meetings in San Francisco, where they talked about the colloquium lectures he was to give, over 100 different definitions of the Catalan Numbers, and just what the path is from wanting to be a ventriloquist to becoming a mathematician. You can find Professors Stanly’s foundational book on Enumerative Combinatorics here and find out more about him at his website.
History of Mathematics Journal: 2
Jan 31st
I am here with another entry from my weekly write-up of topics talked about in my History of Mathematics class. This one is a bit longer:
We started this week with a reading of a few section from chapter two of our book, The History of Mathematics by Roger Cooke, specifically those dealing with the mathematical history of India and the Maya. The mathematical history of India is itself, removed from any external context such as the over-all study of the history of mathematics, incredibly interesting.
One of the oldest cultures in the world the history of Indian mathematics reaches, of course, well into BCE. As is common with mathematics of that time, the math seems to be mostly concerned with geometry and artimetics. In fact, according to Cooke, sometime between 800 to 500 BCE the Sulva Sutras, who’s root words come from measure and cord, a collection of mathematically based verses were inserted into the Vedas. These verses, and the idea that the content probably springing from the maintenance of altars, are intimately tied to a conversation that we had in class on Tuesday: The importance that culture and religion have on studies, and mathematics in particular.
Professor Bhatnagar brought up the semester he spent at the University of Nizwa in Oman, and the perspective the students there brought to their education, specifically that they came into classes expecting to be able to memorize their way through instead of learning basic concepts and then extrapolating from there to solve here to fore unseen problems. Professor Bhatnagar then posited that there was a good reason for this and someone else from the class spoke up that it could have something to do with the practice of memorizing large section of the Qur’an for recitation, a hypothesis that was quickly seconded by many in the class and was agreed with by our Professor. Of course it does simply end there because, as our Professor quite rightly pointed out, it is also a great honor to be one chosen to do the recitation and because of that the students were not only well practiced in memorization but have a large respect for the method.
There is no reason to stop the speculation on the effect that religion and culture have on mathematics there though, let me spend a second talking about mathematics in the United States. As we spoke about on Thursday after the USA declared its independence from the Untied Kingdom way back in 1774 it was not only in governing that we decided to break away from the British model. We also changed our education system quite a but as well, so much so in fact that there is very little in common with the two systems now only 236 years since independence. The United States university system tends to function on the idea of: If more than one person wants to study it, it is probably worth studying as opposed to a more track based system such as that in the United Kingdom. While I can not say I agree completely with this idea, I am proud to say that I am a product of a system that does, for some reason that eludes even my radically liberalized mind, offer underwater basket weaving as a for-credit course in more than one university.
Strongly Connected Components Episode 9: Steve Strogatz
Jan 26th
Samuel Hansen spoke with Steven Strogatz from Cornell University at the Joint Mathematics Meeting in San Francisco where Professor Strogatz presented a talk about his fantastic(review soon to come) new book The Calculus of Friendship. They spoke about: Breadth versus Depth, what a friendship based on mathematics can be, and Samuel even gets Steven to retell a Radio Lab story. To find out more about Steven Strogatz please visit his website.
History of Mathematics Journal: 1
Jan 24th
For my History of Mathematics Course this Semester the Professor is having us write up weekly summaries of what we discuss in class. I have decided to post what I write. Here is the 1st entry.
I found myself in the odd position of missing the second class of the semester and therefore missing the first real lecture of the year, as well as losing my change to gain an insight into how the class was going to be approached. Not that I wasted the time I should have been spending in class adsorbing the material. Instead I found myself in San Francisco at the Joint Mathematics Meetings. The second conference that I have attended and, thankfully, the second at which I presented. It was a radically different experience though as the first was a Graph Theory and Combinatorics conference with approximately 300 attendees, rather a smaller amount than the, at least, 5,500 people who made it to the JMM this year. I would be lying if I said it was not surreal scooting past Ron Rivest in a lecture hall or rubbing shoulders with Donald Knuth, sharing the same air with such luminaries of mathematics reminded once again the importance and gravity of our chosen subject. With my presentation, and the ones that I attended, I remembered the mutating and growing nature that is mathematics which really helps to put the challenge of studying its history in perspective. Also speaking to, and interviewing for my podcast, people like Richard Stanley from M.I.T., Steve Strogatz from Cornell, and Joseph Gallian from Duluth I was able to learn just how much mathematics can change in a short period of time. In the end though it was not all work for me in San Francisco, as I was able to spend a lot of time just talking to other mathematicians near my age. Therefore I was able to revel in the companionship that only the shared knowledge of such an exalted subject can bring.
All of this made the first chapter of the book slightly surreal. I had spent four days immersed in a sea mathematicians wearing name tags so then reading about people of whom we only have the vaguest of grasps bordered on spooky. To then leave the realm of certainty in class to talk about whether numbers were created or discovered was an even greater departure but not an unwelcome one. It is that kind of question, along with how does a child perceive mathematics and what is the intersection of mathematics and art that I feel that most mathematicians tend to avoid because they are so called soft questions. Just as what the History of Mathematics is seen to be. To not ask these questions though is rather obviously a mistake in my mind. As we learn more about the mathematics of the ancients through archeology or finding something someone else missed, we can get a more precise image of the mistakes they made and, more vitally, how they succeeded. Through these stories of achievement and failure we will come to gaze on the story of our discipline and better see where and how to move forward.
Strongly Connected Components Episode 8: Olga Holtz
Jan 18th
Olga Holtz is a professor at University of California Berkley and Technischen Universität Berlin. Samuel Hansen spoke with Professor Holtz at the 2010 Joint Mathematics Meeting in San Francisco, California where she was an invited speaker. They discussed: her talk in Zonotopal Algebra, the difference between working in the USA and Germany, and the bottleneck of communication. You can find out more about Professor Holtz by visiting her webpage.
Joint Mathematics Meeting
Jan 12th
Very early tomorrow morning I will be boarding a plane to take me to San Francisco so that I can attend the Joint Mathematics Meeting. I will be presenting a talk about the effect the internet is having on mathematics at 1 PM on Thursday, so if you will be at the JMM and you have the time free I would love to see you at my talk after which please make sure you say hello. If you do not have the opportunity to see my talk please send me a message on the ACMEScience twitter or come to the JMM Tweetup on Thursday 2030 , 14 Jan 2010 in the San Francisco Marriott Lobby. In other ACMEScience news I have lined up a few interviews at the conference with mathematicians you want to hear for Strongly Connected components so check your feed for those over the next few weeks. Hope to see you there.
Combinations and Permutations Episode 34: Diff-E-Freeze
Jan 5th
On this today’s episode Samuel Hansen, Cody Palmer, and the Juan(Man Show) Mariscal discuss: differential equations, stormtroopers, the best mall restaurants, and develop a plan for the best slurpee franchise ever.
Combinations and Permutations Episode 33: Chopping Down the Trees of Ignorance
Dec 22nd
Leigh Anne Duncan, Brandon Metz, Cody Palmer, and your host Samuel Hansen get together at the end of another semester to talk about exams: what they like about them, what types there are, but mostly what they hate about examinations.
We do not like these
Even the Young Ones understand Collaboration is Important
This Exam sucks more than any other
Probably the Best One
Math is This
Dec 9th
There are some people out there who are just fantastic at writing about mathematics. Mark Chu-Caroll of Good Math Bad Math is one of those people. While I imagine most people who will read this already regularly read his blog, if you do not, or if you just happened to miss this post, you have to read Chu-Caroll’s post about “What is Math“:
To me, math is the study of how to create, manipulate, and understand abstract structures. I’ll pick that apart a bit more to make it more comprehensible, but to me, abstract structures are the heart of it. Math can work with numbers: the various different sets of numbers are examples of one of the kinds of abstract structures that we can work with. But math is so much more than just numbers. It’s numbers, and sets, and categories, and topologies, and graphs, and much, much more.
What math does is give us a set of tools for describing virtually anything with structure to it. It does it through a process of abstraction. Abstraction is a way of taking something complicated, focusing in on one or two aspects of it, and eliminating everything else, so that we can really understand what those one or two things really mean.
…
Math is unavoidable. It’s a deeply fundamental thing. Without math, there would be no science, no music, no art. Math is part of all of those things. If it’s got structure, then there’s an aspect of it that’s mathematical.(Read the rest)
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