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That being said, this is faaaaaar beyond basics. It'd be more appropriate to call this an incomplete (aiming to be comprehensive) guide to almost everything you need to know in computer science (related to math).
Very first sentence of 2.1 is full of notation, symbols and terms that I, as a prospective student, might not understand. So many teachers seem incapable of stepping outside their sphere of knowledge and seeing what they know and others do not. And so much work went into this.
Very first sentence of 2.1 is full of notation, symbols and terms that I, as a prospective student, might not understand. So many teachers seem incapable of stepping outside their sphere of knowledge and seeing what they know and others do not. And so much work went into this.
https://www.amazon.com/gp/product/1466230525 - Mathematical Notation: A Guide for Engineers and Scientists
Very first sentence of 2.1 is full of notation, symbols and terms that I, as a prospective student, might not understand. So many teachers seem incapable of stepping outside their sphere of knowledge and seeing what they know and others do not. And so much work went into this.
It definitely looks more like, "math basics" for x field. Kinda like "automotive basics" for Honda or Ford vehicles. Where it's presumed that you know a lot of automotive lingo to begin with and you just need to know what spark plugs go with what engine. And not, "what is a spark plug?"
Keep in mind it can take an hour, and sometimes way more, to really absorb a single page of a math book like this (do the math). This is more of a reference text.
I love professor gallier! He's an incredible person. That being said, this is faaaaaar beyond basics. It'd be more appropriate to call this an incomplete (aiming to be comprehensive) guide to almost everything you need to know in computer science (related to math).
I love that they have problems you can solve as well at the end of (almost) every chapter. This IS a lot of math (1,962 pages) and it’s missing a preface/introduction which would have been helpful to understand if I need to go linear or if a la carte is okay. At the moment I’d assume each major section is independent. Awesome find! Wonder how It’s used. (One of) the author(s) seems pretty prolific too - http://www.ci…
> a la carte Yeah, I wish we had an online resource (other than Wikipedia) anyone could learn any sort of math from in a systematic way... Oh well.
Very first sentence of 2.1 is full of notation, symbols and terms that I, as a prospective student, might not understand. So many teachers seem incapable of stepping outside their sphere of knowledge and seeing what they know and others do not. And so much work went into this.
Then he wants to define, say, addition of real numbers. So, given two real numbers, x and y, that might be equal, he wants to define x + y.
So, here he wants to regard addition, that is, +, as an operation. Then, as is usual for defining operations, he wants an operation to be just a special case of a function. So, he wants to call + a function. So, + will be a function of two variables, say, x and y. With usual function notation we will have
+(x,y) = x + y
The set of all (x,y) is the domain of the function, and the set of all x + y is the range.
So, that defines the function + except commonly in pure math we want to be explicit about the range and domain of the function.
For function +, the range is just the set of all pairs (x,y) with x and y in R. That set is also the set theory Cartesian product of set R with itself and written R x R. So, the domain of + is R x R. The range is just R. Then to be explicit about the range and domain of function +, we can write
+: R x R --> R
which says that + is a function with range R x R and domain R.
We learned how to add in, what, kindergarten? So, why make this so complicated?
Well, he wants to regard the real numbers as just one example of lots of different algebraic systems, e.g., groups, fields, vector spaces, and much more, with lots of operations and, possibly, more that could be defined. E.g., later in his book he will want to add vectors and matrices, take an inner product of two vectors, and multiply two matrices.
So, back to addition on the real numbers, he wants to regard that as just a special case of an operation on an algebraic system.
IMHO there's not much benefit for making adding two real numbers look so complicated.
Whatever he did in that chapter for defining addition on the reals, soon he is discussing matrix multiplication with no definition at all -- assuming the reader already understands that, that is defined and discussed many pages later in his book.
So, in his notation
+: R x R --> R
and matrix multiplication, he is using material before he has defined it, even before he has motivated, explained, exemplified, indicated the value of, and defined it. In good math writing and in good technical writing more generally, that practice is, in non-technical language, a bummer.
But from the table of contents, it appears that the book has quite a long list of possibly interesting narrow topics. And maybe for the routine material, his proofs and presentation are good -- maybe. I thought enough of the book to keep a copy of the PDF. It's there; if someday I want a discussion of some narrow topic, maybe I'll try his book!
In mathematical writing, it used to be common for the word processing to be much more work than the mathematics! Now with TeX and LaTeX, and I'm assuming that the book used one of these two, the flood gates are open!
Very first sentence of 2.1 is full of notation, symbols and terms that I, as a prospective student, might not understand. So many teachers seem incapable of stepping outside their sphere of knowledge and seeing what they know and others do not. And so much work went into this.
Here's what he is doing. He wants to start with the set of real numbers, intuitively the points on the line, usually denoted by R, maybe typed in some special font. Then he wants to define, say, addition of real numbers. So, given two real numbers, x and y, that might be equal, he wants to define x + y. So, here he wants to regard addition, that is, +, as an operation . Then, as is usual for defining operations, he w…