?What Makes a Good Research Problem

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.

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ABC Conjecture


Japanese mathematician claims to have solved a notorious maths problem, but nobody understands it

This article was written by Kevin Knudson from the University of Florida, and was originally published by The Conversation.

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.

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New algorithm cracks graph problem


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.

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Advices to young mathematicians

Bilder for Det Norske Videnskaps-akademi. Abel-prisen.

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.)

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Random Walks on Graphs

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.

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Rainbow connections of graphs

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.

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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.

فایل ارائه ایشان در زیر قابل دسترسی می باشد.

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در ضمن ایشان در حال تهیه کتابی با عنوان "Exploring Algebraic Graph Theory With Sage" می باشند که انتظار می رود در این کتاب بر کاربردهای خاص این نرم افزار تکیه شود.

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