What are the prerequisites for learning Boolean Algebra?

[Mikaelochi]

I am asking this question as I have found Boolean Algebra quite intriguing. I have a good understanding of high school level probability and statistics and also Algebra II. Is this enough or do I need more "mathematical maturity"? Anyway, thank you in advance.

 

[fresh_42]

I am asking this question as I have found Boolean Algebra quite intriguing. I have a good understanding of high school level probability and statistics and also Algebra II. Is this enough or do I need more "mathematical maturity"? Anyway, thank you in advance.

As always: Well, it depends.

It depends on what you understand by Boolean Algebra. In its basics it is simply a kind of language to do, e.g. logic. The principles should be easy to understand. How far you are willing to go into applications or special, sometimes pretty abstract concepts depends widely on how much effort you want to put into. Or to put it another way: What's your goal?

I've looked online into the content of a textbook about Boolean Algebra and found some sophisticated subjects far beyond the simple definition of Boolean algebras. Some of which require some abstract understandings in algebra and/or calculus. However, those can be learned as well. They don't conceal hidden secrets, they are just unusual when used to HS math.

What may I tell you is, that you most likely will find always someone here on PF, if you have a question or difficulties in understanding.
But you should be prepared to learn stuff that's (normally) beyond a starter level. I assume that most textbooks require the usual algebraic and/or analytic language without repetition.

I could name you a few if you like, which you could look up on Wikipedia to see, whether it fits you. However, there might be someone around here who has more experience in this special subject.

 

[Mikaelochi]

As always: Well, it depends.

It depends on what you understand by Boolean Algebra. In its basics it is simply a kind of language to do, e.g. logic. The principles should be easy to understand. How far you are willing to go into applications or special, sometimes pretty abstract concepts depends widely on how much effort you want to put into. Or to put it another way: What's your goal?

I've looked online into the context of a textbook about Boolean Algebra and found some sophisticated subjects far beyond the simple definition of Boolean algebras. Some of which require some abstract understandings in algebra and/or calculus. However, those can be learned as well. They don't conceal hidden secrets, they are just unusual when used to HS math.

What may I tell you is, that you most likely will find always someone here on PF, if you have a question or difficulties in understanding.
But you should be prepared to learn stuff that's (normally) beyond a starter level. I assume that most textbooks require the usual algebraic and/or analytic language without repetition.

I could name you a few if you like, which you could look up on Wikipedia to see, whether it fits you. However, there might be someone around here who has more experience in this special subject.

I'm interested in the basics rules and logic of Boolean Algebra. Learning its applications is nice but that is not my main focus. In addition I found a book called Boolean Algebra by R.L. Goodstein. It seems like what I'm looking for.

 

[fresh_42]

I'm interested in the basics rules and logic of Boolean Algebra. Learning its applications is nice but that is not my main focus. In addition I found a book called Boolean Algebra by R.L. Goodstein. It seems like what I'm looking for.

Rather logic sided. If you are interested in logic, why not. It doesn't look like Goodstein uses other concepts than logical ones nor presumes the knowledge of those. (As far as a brief online look into it allowed me to judge.)

Only one advice: Take the technical terms used by Goodstein as being defined in the context. Classes, ideals, lattices and so on may have (usually a similar, but) different meaning in other contexts.

 

[Mikaelochi]

Rather logic sided. If you are interested in logic, why not. It doesn't look like Goodstein uses other concepts than logical ones nor presumes the knowledge of those. (As far as a brief online look into it allowed me to judge.)

Only one advice: Take the technical terms used by Goodstein as being defined in the context. Classes, ideals, lattices and so on may have (usually a similar, but) different meaning in other contexts.

o

Okay. Yeah, I think I see what you mean, I noticed that Goodstein names what seems like sets as classes in the first chapter. Although other terms like union and intersection seem to stay the same. Anyway, thank you very much for the assistance.

 

[jedishrfu]

A practical use of Boolean Algebra which helped me learn it was to start with an idea of a circuit with N inputs and M outputs.

I would first develop a truth table of the circuit and then convert it into Boolean equations, one equation for each output with terms for each time the output was true, that I then simplified down a more concise form and from there constructed a circuit of ANDS and ORS that represented the original truth table.

The basic prerequisites were a solid understanding of ordinary algebra in combination with the Boolean identities like A + A' = 1 where A' was the Boolean inverse of A...

 

[fresh_42]

o

Okay. Yeah, I think I see what you mean, I noticed that Goodstein names what seems like sets as classes in the first chapter. Although other terms like union and intersection seem to stay the same. Anyway, thank you very much for the assistance.

The term classes is used in set theory and logic. I always thought to avoid something like the set of all sets which don't contain itself as element. (see https://en.wikipedia.org/wiki/Russell's_paradox)
However, the truth lies deeper and it isn't that simple. I've been disappointed by Goodstein, too, as I saw that he doesn't explain it. The more that I would have learned something here. Likely Wikipedia will give an explanation why classes are used instead of sets. One reason I could imagine is that members of classes have something (defining) in common, whereas there are no restrictions on sets.

What I meant by different meaning of terms is the following: E.g. an ideal in a ring is something defined by addition and multiplication. Here we have union and intersection instead. It's basically the same, however, still different. Same with lattices. In number theory they really look like ordinary lattices, here it's the same but defined by inclusions. So avoid objecting "but an ideal is something else" if someone is talking about rings which are not Boolean.

 

[Mikaelochi]

A practical use of Boolean Algebra which helped me learn it was to start with an idea of a circuit with N inputs and M outputs.

I would first develop a truth table of the circuit and then convert it into Boolean equations, one equation for each output with terms for each time the output was true, that I then simplified down a more concise form and from there constructed a circuit of ANDS and ORS that represented the original truth table.

The basic prerequisites were a solid understanding of ordinary algebra in combination with the Boolean identities like A + A' = 1 where A' was the Boolean inverse of A...

So, would you say that an understanding of basic set theory is helpful?

 

[fresh_42]

So, would you say that an understanding of basic set theory is helpful?

At the end of chapter I you should have this understanding!