Boolean Algebra in the Context of Mathematics

In summary, The speaker is taking a course on Boolean algebra, which is officially called Mathematical Logic, but they do not see much resemblance to other courses on mathematical logic taught in the US. They have covered topics such as Boolean functions, identities, normal forms, and Shannon's expansion in the course. They are curious about the lack of equivalent courses at American institutions and limited information available online. They mention a textbook by Dr. Monk published in the late 1980s, but it is out of print. They question whether the topic is still being taught as a mathematical course or if it is mainly studied in computer science. Another person mentions briefly learning about it in a ring theory class, but not in depth, and suggests looking in abstract algebra
  • #1
PhotonTrail
13
0
I'm currently taking a course on Boolean algebra. It's officially named "Mathematical Logic", but I really don't see much resemblance between what I'm doing and other courses of mathematical logic that are taught in the US.

It has only been a couple of weeks, but to let you have an inkling of the syllabus, so far we've covered roughly the following content:
  • Boolean functions and formulae
  • Identities of Boolean algebra
  • Representation by schemes of functional elements
  • Disjunctive and conjunctive normal forms
  • Shannon's expansion - simply referred to as the decomposition theorem in my course
  • Algebraic normal form
  • Essential and fictitious variables
What I find rather curious is that I simply cannot find an equivalent course at an American institution. It is also quite impossible to find supplementary information on the internet. For example, when I was confused about Shannon's expansion, all I could find online was stuff about decomposition by one variable, whereas my course covered the more general situation of decomposition by m variables.

So, what's the deal? Is it simply taught under a different guise with completely different terminology in the States? A quick search on the forums brought up an ancient thread that mentioned a textbook by a certain Dr Monk published in the late 1980s, but it seems to be out of print. It probably approaches the subject with way more depth and breadth than I require, too.

Is the topic even being taught today, as a mathematical course? Or are people only concerned about the applied aspects of it in computer science?
 
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  • #2
I took a ring theory class and the textbook was on intro abstract algebra. There was a chapter (maybe even two) that talked about it but we never did it. And yea funny because I was looking around too for a course about it too but couldn't find one. I haven't looked for textbooks in our library though.

Weird title by the way o_0
 
  • #3
Square1 said:
I took a ring theory class and the textbook was on intro abstract algebra. There was a chapter (maybe even two) that talked about it but we never did it. And yea funny because I was looking around too for a course about it too but couldn't find one. I haven't looked for textbooks in our library though.

Weird title by the way o_0

Haha my thread title? I was trying to get across the idea that I'm curious about what's happening on the mathematical side of the pond. I'm quite sure computer scientists do deal with it on a regular basis in some form or another. The most helpful resources I've found on the internet so far came from computer science departments, and largely dealt with logic gates if I remember correctly.
 
  • #4
I see I see. Yeah try looking in abstraact algebra books I guess.
 
  • #5


I can understand your curiosity and confusion regarding the differences in the teaching and availability of Boolean algebra courses between different countries. I am not familiar with the specific curriculum of mathematical logic courses in the US, but it is possible that Boolean algebra is being taught under a different name or as a subset of a larger course. It is also possible that it is not as commonly taught in the US compared to other countries.

However, I can assure you that Boolean algebra is still a relevant and important topic in mathematics, particularly in the field of logic and computer science. It provides a fundamental framework for understanding logical operations and is widely used in the design and analysis of digital circuits and computer algorithms.

It is also worth noting that as with any subject, there may be variations in the depth and breadth of coverage depending on the course and instructor. It is possible that the course you are taking is more focused on the mathematical aspects of Boolean algebra, while others may have a stronger emphasis on its applications in computer science. Both approaches are valid and can provide valuable insights into the subject.

In terms of finding supplementary information, it may be helpful to search for resources specifically on Boolean algebra rather than mathematical logic in general. There are many textbooks and online resources available that cover the topic in depth and can provide a better understanding of the concepts you are studying.

In conclusion, I would say that Boolean algebra is still a relevant and important topic in mathematics, and its applications in computer science make it a valuable subject to study. While there may be differences in how it is taught and approached in different countries, the fundamental principles and concepts remain the same. Keep exploring and learning, and I am sure you will find the answers to your questions.
 

1. What is Boolean Algebra?

Boolean Algebra is a branch of mathematics that deals with the study of logical operations and truth values. It involves the use of variables and logical operators such as AND, OR, and NOT to manipulate and analyze logical statements.

2. How is Boolean Algebra used in mathematics?

Boolean Algebra is used in mathematics to solve problems involving logic and sets. It is also used in computer science and engineering to design and analyze digital circuits and algorithms.

3. What are the basic principles of Boolean Algebra?

The basic principles of Boolean Algebra include the commutative, associative, and distributive laws, as well as the identity, complement, and absorption laws. These laws govern the manipulation and simplification of logical expressions.

4. How is Boolean Algebra different from traditional algebra?

Boolean Algebra differs from traditional algebra in that it deals with logical statements rather than numerical values. It also has a different set of rules and operations, which are based on the principles of logic rather than arithmetic.

5. What are some real-world applications of Boolean Algebra?

Boolean Algebra has various real-world applications, such as designing digital circuits, creating computer programs and algorithms, and analyzing logical systems. It is also used in database systems, control systems, and artificial intelligence.

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