I am an undergraduate student, associated with the Department of Mathematics and the Department of Computer Science. My interests principally lie in the subdisciplines of Automated Theorem-Proving, and, more broadly, Compiler Theory. I am also interested in the Philosophy of Mathematics, paying special attention to Set Theory and some elements of Real Analysis. I was once associated with the Department of Electronic Engineering; this is no longer the case.
Here are some books and third-party on-line resources that I have found helpful, from the perspective of an undergraduate with little mathematical background. Sophisticated readers will probably benefit from denser texts, however the additional oft-extraneous commentary offered by some authors provides a very comfortable introduction to ``proof-based'' mathematics, which is in stark contrast to most (all?) A-level programmes. I will expand this list as I continue to find helpful resources, likely in the direction of 20th Century Pure Mathematics. (I am currently reading Lang's Algebra and Mac Lane's Categories for the Working Mathematician, but I do not feel like they would be a good fit for this list!) I compiled the majority of this list before coming to University or receiving any formal teaching; as such, I generally deem these resources as appropriate for self-study. Most of the books are available in The Library.
* There are large portions of this book that I dislike, but the original philosophy of Down with Determinants is excellent for elementary LA. If you're just getting started, Michael Penn has a wonderful YouTube lecture series about Abstract Linear Algebra, complete with a plethora of examples and counter-examples pertaining to the various algebraic structures. MIT OpenCourseWare has also made available a full Linear Algebra course (18.06), complete with lectures and psets with solutions. For Real Analysis, I'd recommend 18.100A on MIT OCW.
If you would like ``a document'', feel free to e-mail me. I have various ways of finding electronic copies of things that aren't available on the public Internet.
Here are some useful web-sites and fun blogs:
Vocationally, I am interested in systems programming, including
embedded and real-time systems work; I once calculated that I have spent
more time writing C and ARM than I have being married, although that's
probably no longer true (I discovered Complex Analysis...). Readers of
my Programming Support Session scripts can attest to my
pedagogical impairments programmatical superiority.
I maintain a passing hobby in electronic typesetting (particularly for aesthetically intransigent mathematical expressions). I strongly believe that TeX and its various deranged offspring are antiquated and in dire need of replacement with a modern, modular, and programmable solution that can be encoded into generalisable AST-like data structures which lend well to translation-based static analysis. Absolute separation of code and data is easily achievable with modern theory, so why did the evolution of typesetting halt in the 70s?
My University e-mail address should be clear from the URL of this page. Members of the University can access more information about me via the old York Directory, since the new one doesn't work properly. This index page hides a colossal amount of resources (gigabytes) that have accumulated over the years. If I mentioned that something is ``available on my website'', but you cannot find it, please e-mail or telephone me. The structure itself is a web of soft symlinks that is subject to change, so I would advise against crawling under this directory! Cheers.
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