Take Claude E. Shannon's Master's thesis, the long version.
Considered by many the most important Master's thesis of last century. It fully introduced the concept of binary / Boolean logic to design of electronic circuits. If you understand the core premise of his work, you understand the core of computers. If you can apply his work, you can design computers.<p>Thesis:<p><a href="https://dspace.mit.edu/handle/1721.1/11173" rel="nofollow">https://dspace.mit.edu/handle/1721.1/11173</a>
<a href="https://www.cs.virginia.edu/~evans/greatworks/shannon38.pdf" rel="nofollow">https://www.cs.virginia.edu/~evans/greatworks/shannon38.pdf</a><p>Go through the theory in the thesis with pen and paper, use the references as needed. Thesis, article on it by Shannon and lots of commentary available freely online. He provided a number of practical applications, with breakdown.<p>Here is the core question you need to answer to understand logic in computers: what can you do with just yes and no, represented as 1 and 0?<p>Why were these numbers reversed in Shannon's thesis?<p>In his thesis, 1+1=1. Why? If you understand postulates, it makes sense for the kind of theory he is developing. If not, you should be very excited: mathematical theory, unlike how it is presented in bad schools, is not about following rules someone has decided on. It is about making sense in accordance with the logic you decide upon! This is as close as you can get to real magic, magic you can prove and make manifest in reality. Contemplate this deeply.<p>What kind of information can you transmit with a lamp and a switch, turning the lamp on and off? (Tip: this is the whole idea behind how the super-modern fiber-optic cables are transmitting information today, with lights blinking on and off, real fast, from one end to the other. Poetically, they are the core of the Internet).<p>Following the hyperlinks and looking up what you need should provide all the information required and more.
<a href="https://en.wikipedia.org/wiki/A_Symbolic_Analysis_of_Relay_and_Switching_Circuits" rel="nofollow">https://en.wikipedia.org/wiki/A_Symbolic_Analysis_of_Relay_a...</a>
I actually just wrote one. Check out Computer engineering for babies. (<a href="https://computerengineeringforbabies.com" rel="nofollow">https://computerengineeringforbabies.com</a>)
Not a textbook (just a book), but still a fun way to intuitively encounter formal logic - <a href="https://en.m.wikipedia.org/wiki/To_Mock_a_Mockingbird" rel="nofollow">https://en.m.wikipedia.org/wiki/To_Mock_a_Mockingbird</a>
Not a book, but I found the logic courses on brilliant.org to really stretch the brain muscle<p><a href="https://brilliant.org/courses/logic-deduction/" rel="nofollow">https://brilliant.org/courses/logic-deduction/</a>
One thing that completely changed my thought process and increased intellectual faculties tremendously was working in IT, precisely in Operations. The amount of problems I had to solve helped me think in a certain way. Some problems were easy, others hard, some at leisure others under pressure, but it's the constant and consistent exercise over the years that unlocked problem solving, reason and logic capacity that I posses now and can apply in any life situation following established patterns.<p>Logic can be described in a book, but I don't think it can be taught in a book. It's a consequence of solving a lot of problems over a long period of time. My suggestion would be to pick up any book/website with programming problems and work on them every day changing the problems every so often, however nothing beats actual work experience where you have someone to explain to you why something is a good approach and why not. Understand what is expected of you, see how it fits in the big picture and start by breaking it down into smaller pieces. It's very simple, just <i>getting it</i> takes time.
I recommend "Introduction to Logic", by Irving Copi and others. It is intended for philosophy majors I think, but works very well for general readers.
If I understand correctly, you're asking for books that will teach you logic, problem solving etc? If yes, check these out:
- Mathematical Circles The Russian Experience (the book is in english)
- How To Solve It by Polya
- brilliant.org
Check the art of problem solving contest books, or project euler. I honestly think the best way to build logical reasoning skills is through real math or cs challenges, rather than some artificially constructed logical reasoning tasks.