Professor Gowers is a British mathematician, Fields medalist 1998. Besides his many interesting and significant results, Gowers has contributed to the mathematical community in several other valuable ways, for example, by prompting the creation and development of polymath projects, “massively collaborative mathematics“.
His blog is very interesting. Recently, he has been posting on topics that are quite close to the content of our course, starting with his Welcome to the Cambridge Mathematical Tripos. I recommend that you take a look at his recent postings (and their comments), as one of Gowers’s strengths is his clarity of exposition helping one understand how even complicated results can be naturally motivated and proved.
Here is a link to a lecture he gave at the Millennium Meeting on May 2000, On the importance of mathematics, also highly recommended. The lecture is split into a series of short videos and lasts about one hour. I hope you can find the time to watch it on its entirety. Here is a pdf transcript of the talk.
Here is the list of his recent postings on topics relevant to our course:
- Welcome to the Cambridge Mathematical Tripos.
- Basic logic — connectives — AND and OR.
- Basic logic — connectives — NOT.
- Basic logic — connectives — IMPLIES.
- Basic logic — quantifiers.
- Basic logic — relationships between statements — negation.
- Basic logic — relationships between statements — converses and contrapositives.
- Basic logic — tips for handling variables.
- Basic logic — summary.
- Alternative definitions.
The subject of his next few postings will be one of our coming topics, and they all certainly come up in more advanced courses, so it may be useful to read these as well:
- Injections, surjections and all that.
- Domains, codomains, ranges, images, preimages, inverse images.
- Equivalence relations.