
This second edition continues to provide a clear introduction to formal reasoning which is both relevant to the needs of modern computer science and rigorous enough for practical application. Improvements have been made throughout, with many extra and expanded sections and exercises. The coverage of model-checking has been substantially updated.
* Logic for Computer Scientists by Uwe Schoening
* Logic in Computer Science by M. Huth and M. Ryan
The first one is short, very elegant and doable. The second one is a bit longer, but also at freshman level.
There are PDFs circulating on the Internet. Skim through those before buying a hardcopy.
https://web.mat.bham.ac.uk/R.W.Kaye/logic (not very helpful, lots of broken links, just look at the book instead)
I also like Logic in Computer Science by Huth and Ryan, cited in another comment here. It is much more comprehensive and has a lot more about logic applications in computer science.
* Basic Mathematics by Serge Lang
* Calculus Made Easy by Silvanus Thompson
Then try a DIY bootcamp in the spirit of Harvard Math 55. If you are interested in continuous math:
* Vector Calculus by Hubbard & Hubbard
If you are interested in discrete mathematics and computation:
* Logic in Computer Science by Huth & Ryan
Edit: Perhaps this doesn't qualify as a game per se, but I think it might be a fun activity to work through the proofs together.