Without a strong research question, your collaborative research project is going to lack momentum and result in a weak response from students. In order to make sure you are taking your students in the right direction, carefully facilitate the selection of the research problem to be addressed, whether it is one you choose or one that your students come to through consensus. It may take some time and effort, but finding the “right” problem for a particular learning community is essential.
Japanese mathematician claims to have solved a notorious maths problem, but nobody understands it
What happens when someone claims to have proved a famous conjecture? Well, it depends. When a paper is submitted, the journal editor will pass it off to a respected expert for examination. That referee will then scan the paper looking for a significant new idea. If there isn’t one, then the whole argument is unlikely to get much more scrutiny.
A puzzle that has long flummoxed computers and the scientists who program them has suddenly become far more manageable.
A new algorithm efficiently solves the graph isomorphism problem, computer scientist László Babai announced November 10 at a Combinatorics and Theoretical Computer Science seminar at the University of Chicago. The problem requires determining whether two separate sets of interconnected points, known as graphs, are linked in the same way even if the graphs look very different. In practice, existing algorithms can do the job in reasonable time, but it was possible that extremely complex graphs would make the problem intractable. Not anymore.
The most important thing that a young mathematician needs to learn is of course mathematics. However, it can also be very valuable to learn from the experiences of other mathematicians. The ﬁve contributors to this article were asked to draw on their experiences of mathematical life and research, and to oﬀer advice that they might have liked to receive when they were just setting out on their careers. (The title of this entry is a nod to Sir Peter Medawar’s well-known book, Advice to a Young Scientist.)
Given a graph and a starting point, we select a neighbor of it at random, and move to this neighbor; then we select a neighbor of this point at random, and move to it etc. The (random) sequence of points selected this way is a random walk on the graph.
A random walk is a ﬁnite Markov chain that is time-reversible (see below). In fact, there is not much diﬀerence between the theory of random walks on graphs and the theory of ﬁnite Markov chains; every Markov chain can be viewed as random walk on a directed graph, if we allow weighted edges. Similarly, time-reversible Markov chains can be viewed as random walks on undirected graphs, and symmetric Markov chains, as random walks on regular symmetric graphs. In this paper we’ll formulate the results in terms of random walks, and mostly restrict our attention to the undirected case.
This new concept comes from the communication of information between agencies of government. The Department of Homeland Security of USA was created in 2003 in response to the weaknesses discovered in the transfer of classiﬁed information after the September 11, 2001 terrorist attacks. Ericksen made the following observation: An unanticipated aftermath of those deadly attacks was the realization that law enforcement and intelligence agencies couldn't communicate with each other through their regular channels, from radio systems to databases. The technologies utilized were separate entities and prohibited shared access, meaning that there was no way for oﬃcers and agents to cross check information between various organizations.
پروفسور گادزیل در صحبت هایی با تاکید بر ویژگی های منحصر به فرد نرم افزار متن باز SAGE به تمامی محققان و دانشجویان توصیه کردند تا برای انجام پروژه های تحقیقاتی و آموزشی خود در حوزه ریاضی و به خصوص نظریه جبری گراف ها از این نرم افزار استفاده کنند.
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Results matter, whether you are a mathematician, scientist, or engineer. The time that you
spend doing tedious mathematical calculations could be spent in more productive ways. Sage is an open-source mathematical software system that helps you perform many mathematical tasks. ادامه خواندن Continue reading