The obvious route for self-study is to go through Halmos or Axler and Rudin, plus all additional materials and study aids such as Gelbaum & Olmsted, emulating the most popular Harvard Math 55 incarnation. Another nice Math 55 incarnation covered Hubbard & Hubbard, which is a wonderful book.
Although Math 55 is tough, if you are self-paced and have a bit of mathematical maturity I think it is doable. It's also an excellent pure math bootcamp that gives you a solid foundation to branch into any other pure or advanced math topic.
I have gone through Halmos & Rudin myself, and it is a great experience. However, if your end goals are more geared towards pure CS, an alternative route might be much more appropriate. Very interesting and promising parts of CS, such as formal methods, and the foundations of mathematics themselves depend on abstract algebra and logic: https://ncatlab.org/nlab/show/computational+trinitarianism
A minor problem is that beginner literature is not so polished as it is relatively young. But there are some excellent textbooks nonetheless. Some below. Other suggestions welcome:
Although Math 55 is tough, if you are self-paced and have a bit of mathematical maturity I think it is doable. It's also an excellent pure math bootcamp that gives you a solid foundation to branch into any other pure or advanced math topic.
I have gone through Halmos & Rudin myself, and it is a great experience. However, if your end goals are more geared towards pure CS, an alternative route might be much more appropriate. Very interesting and promising parts of CS, such as formal methods, and the foundations of mathematics themselves depend on abstract algebra and logic: https://ncatlab.org/nlab/show/computational+trinitarianism
A minor problem is that beginner literature is not so polished as it is relatively young. But there are some excellent textbooks nonetheless. Some below. Other suggestions welcome:
* http://www.cs.man.ac.uk/~pt/Practical_Foundations/
* https://www.mta.ca/~rrosebru/setsformath/
* https://github.com/ademinn/ttfv/blob/master/2006.%20Sorensen...
* http://www21.in.tum.de/~nipkow/Concrete-Semantics/
* http://adam.chlipala.net/frap/
* https://softwarefoundations.cis.upenn.edu/