There are so many mathematical ideas that can be interpreted in multiple ways/ can be used to explain many things with the same theory. For instance, addition in Galois Field of order 2 is same as binary XOR, or that irreducible polynomials exhibit prime number like properties, etc.
I'm sure that there is a general process of consolidation and generalization to come up with better i.e. a more inclusive theory. I am curious if there are books of this kind in mathematics that try to explain to the reader the same concept from different angles?
I am mostly interested in Algebra, but I'll appreciate pretty much any suggestion.
>>> From his quote "You don't understand anything until you learn it more than one way", I am guessing that Minsky might have experienced a similar thing.
I have found the explanation of statistical concepts through the lens of linear algebra immensely intuitive. A simple, short and clear illustration of this is in 'The Geometry of Multivariate Statistics' by Thomas D. Wickens, which I purchased solely based on it's title. It goes through the geometric interpretation of univariate, and multivariate linear regression, then goes into the geometric interpretation of correlation, collinearity impact on prediction, PCAs, and statistical tests. Warning: This book assumes you have some very basic statistical background.
Funnily enough, recently I've been going through Strang's 'Introduction to Linear Algebra' textbook, and he also goes through derivation of mulitvariate statistics in the same fashion. I like the way he builds up the geometric interpretation of regression by building up from a exploration of column/row spaces, orthogonality, projection matrices, and from there, seamlessly introduces solving the LLS as a problem that can be solved with a projection matrix. That being said, I find Wicken does a better job of illustrating his concepts, which is most intuitive modality to interpret this.