Re: A good self-study book

On Fri, 31 Oct 2008 11:57:08 -0700 (PDT), MoeBlee
<jazzmobe@xxxxxxxxxxx> wrote:

On Oct 31, 4:35 am, Billiam <tadej.sla...@xxxxxxxxx> wrote:

I'm looking for a book, which takes you right from the beginning -
from the simplest math - proofs, theorems, etc - to those more
complicated ones. In other words, I'm looking for a good self-study
math book which is great for a college student of mathematics.

By the way, the book should cover mathematics fields within college
range.

I wouldn't expect this to be handled by just one book. Since, you
mentioned proof, I'd start with getting a good solid understanding of
working in the predicate calculus (which is a formalization of the
ordinary reasoning for mathematical proof). The best book for that is
Kalish, Montague, and Mar 'Logic: Techinques of Formal Reasoning'.

Then, a set theory textbook (for purposes of other math, it would be
enough for just about half the set theory book - through the
construction of the real numbers) provides a basis for the other main
subjects in math: topology, analysis, and abstract algebra.

Such a course is systematic - starting with the logic, then sets (in
which virtually all of mathematics can be formulated), then onto the
individual subjects in mathematics.

Horses for courses, I suppose; but if /this/ horse were led through
such a course, he would never drink a drop! I'm slowly getting more
interested in logic as I learn more mathematics (and wonder about
the reasoning processes I use apparently so naturally), but it would
never work for me the other way around. At university (many, many
years ago), I did almost completely lose interest in mathematics when
I became convinced that it all had to be founded on a completely
formal language in which set theory could be expressed, before I
could actually go about learning anything interesting.

--
Angus Rodgers
"Out came a creature with a face like Venus: round,
lifeless, and pitted with craters."
.

Relevant Pages

  • Re: Universal grammar
    ... modern math is thought to be expressible using some sort of set theory, ... all of it has an equality, at least on the set level. ... Also set theory must be secured against paradoxa, ... nothing else than real world logic leaking into mathematics. ...
    (sci.lang)
  • Re: How seriously do you take mathematics?
    ... you find some solace in math. ... > Do any mathematics professors take their subject as seriously as they ... > axioms of set theory and philosophize about the continuum hypothesis? ... like physics - what we call axioms are analogous to what ...
    (sci.math)
  • Re: Wheres respect? was Re: Corrective interpretation of real numbers
    ... > proof that e.g. set theory fails, ... > in math you have to accept the definitions of math! ... axioms in order to show failures in mathematics because mathematics ... Mückenheim and me are no philosophers. ...
    (sci.math)
  • Re: How to approach the study of mathematics?
    ... math last summer and got A's in both algebra and trigonometry. ... I've also seen Herman post that analysis should be taught before calculus ... What topics are required to really understand mathematics? ... studied basic set theory? ...
    (sci.math)
  • Re: The point of ur-elements
    ... Zuhair here has proposed a formulation of set theory, ... but let's offer some general comments on ur-elements. ... We practically never apply any abstract set theoretic reasoning ... to anything outside mathematics is when we're doing, say, theoretical ...
    (sci.logic)
Quantcast