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I was intrigued because there is some indication of a rough but important ordering to the topics in formal maybe antics education. I was interested in seeing wh

by jwdunne 10y ago

I was intrigued because there is some indication of a rough but important ordering to the topics in formal maybe antics education. I was interested in seeing what that order was. I've seen others say that linear algebra is a prerequisite of any kind of maths maturity goal. I think, personally, maths is an incredibly important field and there's a feeling that some degree of comfort with it will help me in more ways than I can imagine. That is, however, an opinion formulate after some self study based on a great interest in the field. It fascinates me that even things we take for granted, such as addition and multiplication, has entire subfields that have generalised the structure of those operations over those types of sets (in what's taken for granted: addition and multiplication over the set of integers). What's even more fascinating is that this work has had an impact on other areas of deep interest e.g category theory and Haskell.

goldenkey 10y ago
Right, in fact the interaction between multiplication and addition is one of the most fundamental forms of chaos due to combining recursive operations. One could say, addition is repeated counting. Multiplication is repeated addition. And the interaction between the two points a finger at the relationship between space and time. And yes I agree. It is glorious that the binary operations that seemed so natural to us formed the basis for groups, rings, and fields. Associativity, commutativity, distributivity of two related operations are quite the pearls :-) Its also interesting as a programmer and from a "properties of functions" perspective to study magmas and semigroups and groupoids..etc.. Knowing more about abstract algebra in terms of special properties of functions has led me to believe that most programmers are missing out on some of the beauty of functions by merely implementing them and not so much understanding the common properties and classifications of them.

by jwdunne 10y ago

goldenkey 10y ago

Right, in fact the interaction between multiplication and addition is one of the most fundamental forms of chaos due to combining recursive operations. One could say, addition is repeated counting. Multiplication is repeated addition. And the interaction between the two points a finger at the relationship between space and time. And yes I agree. It is glorious that the binary operations that seemed so natural to us formed the basis for groups, rings, and fields. Associativity, commutativity, distributivity of two related operations are quite the pearls :-) Its also interesting as a programmer and from a "properties of functions" perspective to study magmas and semigroups and groupoids..etc.. Knowing more about abstract algebra in terms of special properties of functions has led me to believe that most programmers are missing out on some of the beauty of functions by merely implementing them and not so much understanding the common properties and classifications of them.