Can you copyright data? I was reading this link and it says at the bottom that: The panel data are copyrighted by the Initiative on Global Markets and are being analyzed for an article to appear in a leading peer-reviewed journal. I also read that data is not copyrightable, as stated here. I suspect the latter is true but I am not sure - if so, is the former not legally enforceable?
My remarks pertain only to US Law. Laws vary in other countries. Subject matter eligible for copyright protection in the US must be expressive and creative. To the extent data are merely measurements of observable fact in the world, they are not copyrightable. It may be that the presentation or interpretation of data is eligible for copyright protection (for example, artwork used in charts, graphs, graphics, etc., that is expressive and creative), subject to various equitable use provisions (in particular Fair Use, which is still a legal grey area). The methods by which data are gathered can be considered IP, but is the domain of patents. Methods are not copyrightable (17 USC 102(b)).
The words "proprietary format" are important. Are you sure the format is proprietary? If it is, then it's likely protected in which case they might have grounds to sue (but that does not mean they would definetly win). If the format is not proprietary, and so long as you don't share data which is proprietary then I believe you fine. I'm not a lawyer - but I cite GIF files as an example. They were still protected by the US and some other countries until at least the late 90s and there were various threats to open source linux companies who shared code that used the file format. I'm not aware of anything other than threats and never heard of any company being sued, let alone winning or losing. Another example that comes to mind is the RedHat ISO format. My understanding is RedHat could not stop anyone from sharing open source, but they could prevent folks from sharing the format they assembled and shared the open source. Again, I am not sure if it was ever tested in any court of law anywhere.
If you are utilizing the name of the characters just so users can rate them (by rate - I mean rank, review, critique) you should be fine. Copyrights are subject to "fair use" by the public. For purposes such as review, criticism, and comment - this is generally considered to be fair use. Is the site commercial or for-profit? That could impact the analysis, but only if you are making money flowing from the use of the actual copyrighted material(s), rather than advertising (like Adsense) or something similar (this should not suggest that those type sites cannot violate copyright, but it's part of the analysis). If it is something you are investing money into creating, you may want to get a formal legal opinion. But if the site if for fun, or hobby, you are likely fine if what's described is the only use. http://www.socialmediaexaminer.com/copyright-fair-use-and-how-it-works-for-online-images/ This link is to a great, easy to read and understand article on fair use, what it is and what it allows. Keep in mind each case is fact intensive, however, from what you are describing this seems fine.
Names of people, institutions, and events are not protected by copyright. Things that have occurred at events like math tournaments are facts, and may be recounted, in your own words, with no fear of infringing any copyright. Facts are never protected by copyright, although a particular description of facts could be, and so could a particular selection and arrangement of facts. Specific math techniques and their names are not protected either, and may be described without infringing copyright. The items you mention in the question are: video game / movie references and names No copyright issue here. common integration bee problems No copyright issue here. names of a university / math competition organizers No copyright issue here. integration techniques and formulas No copyright issue here, unless you copy an extensive description of a technique without rewriting it in your mown words.. using someone's Overleaf Latex package to format the book This depends on the license for the package, but there is not likely to be an issue. In short I think you are worrying over issues that are in fact non-issues.
united-states In the United States, information released through the federal Freedom of Information (FoI) process, or any of the various state-level versions of FoI, is considered public information. The person who receives it may share it at will, or publish it. Indeed many such inquiries are made by news reporters who intend to publish the information, and many others are routinely posted to various web sites. I suspect that the law on this point in the UK is similar, but I have not checked it.
These are some thoughts about the state of affairs in the US, I do not know how it works in the UK. In the US it seems to be a legal gray area. Gray enough that I do not think any lawyer could say for certain that the use of the data is legal. The data is stolen. If possessing stolen property is illegal then possessing this data is also likely illegal. Of course experts disagree, Stuart Karle, an adjunct media professor at Columbia University and former general counsel for the Wall Street Journal says: ...the documents have been published by the hackers, they are now public by virtue of being put on the Internet. But Barrett Brown was charged with trafficking in stolen authentication when he forwarded a link to some stolen emails. He signed a plea for acting as an accessory after the fact. He spent more than a year in jail while they sorted it out. In the US there is no law banning the download of hacked documents. In fact Bartnicki v. Vopper 532 US 514 (2001) stands for the rule that journalists can report on illegally obtained information. But contrast that with the Barret Brown prosecution! And decide where a data scientist fits. Also there is the question of whether an illegally recorded conversation is of the same "illegal" nature as hacked personal information.
Those posts are talking about making a modified copy of a copyrighted work. The key word is copy. You are not making a copy. Copyright is not about how a physical embodiment of a copyrighted work is treated. You can burn a book and shred a newspaper. Neither of those actions is making a copy. Also, cutting up a newspaper and pasting a picture on your wall has nothing to do with any “derivative works” issue.
Important story, but BoingBoing also doubts the BBC's wording. It could be an attempted summary of a previous story on BBC Newsnight on 18 July: Lord Porter of Spalding, a former bricklayer, alleged corporations were running tests on the safety of their high-rise building materials but refusing to share the results. Releasing the results could allow residents and local authorities to know if their buildings are at risk of a fire following the Grenfell catastrophe which claimed the lives of at least 80 people. There Lord Porter was talking about results commissioned by private companies including manufacturers, where the labs wouldn't provide information because of 'intellectual property rights' of the client, or presumably commercial confidentiality. Under these situations, it is said the private concerns have no obligation to disclose. If this is what the BBC story was referring to, then at least investigations by government or third parties wanting to reveal characteristics of the products wouldn't have a copyright (or patent etc) problem.