There has been an extensive notion
about what young men should or should not do, like drinking is
bad,sex is bad, education is good and making money is good. Here I am
at a stand where I don’t know what to do. Like I was doing this
book called ‘Applied Linear Algebra’ which seemed to give sense
to my life, make my life peaceful,enjoyable and something I could
look forward to, each day I went to study. Since I reached the
seventh chapter,I have started ignoring that book, it feels that I
must complete it. Out of necessity or of the joy of completion, I
must complete it but the problem is I can’t . IT has taught me so
much that I feel like devoting my life to the study of vector spaces
and linear transformations although I still don’t know Jordan
Canonical Form which came in the fourth chapter about which I
seriously feel sorry. Now I need to start some new mathematical text
and complete it or at least manage through a few chapters which will
give me something new to learn or perhaps improve my understanding of
what I already know. In hope of that, I started reading single
variable calculus from many books and also multivariable calculus
from a book and also a book on polynomials another on algebra and one
on analysis. I really don’t know what to do. It is like I
acknowledge that I don’t know single variable calculus to its
intricacies and definitions and perhaps I know more of multivariable
calculus that single variable one. But what exactly should I do?
Should I solve problems or should I read some other text on the same
subject or should I study something else. From my reading of the book
on linear algebra of Sadun I came to realise that you can learn the
old stuff in the better way by doing advanced stuff that uses the old
stuff .That way you also get an appreciation for why the old stuff
is important as well. And I also think that extensive problems at the
end of each section are a big turnoff for me like Tom Apostol does in
his book . You get so much involved in the problems itself that you
lose the flow of writing. Like the definition of open ball and closed
balls are merely to be an extension of the idea of open and closed
set in the field of reals .But then you start giving problems like
Prove that every empty set is an open set and also prove that every
empty set is a closed set? And couple of other such problems in
addition to lot of numericals. What are they if not a turnoff. A
given section must always test the understanding of the reader but
not at the cost of losing the touch of the following material or also
demotivating the reader so as to not let him proceed further. Hence
any section must always be followed with excersies but not so less
but certainly not so many. Learning mathematics is a process in which
the reader’s intuition gets better and better by reading more and
more. Its not like other subjects where you could be a master of
advanced stuff and still gets minute details of your fundamentals
wrong which is of course a consequence of them not being consistent
or maybe topic about which not much is known.But mathematics forms a
self-consistent body of knowledge, you can never be write about the
advanced stuff if your basics are wrong. Hence the basics are built
over and over again as you keep on doing the advanced stuff provided
you already have a knowledge of the preliminary stuff. That’s what
happpend to me in reading that book on linear algebra. But you never
know, I could be wrong because maybe that book was way to easy or
something llike that. So the question comes to what must be the right
book for studying any subject.The pre-requisities must be that the
section are smooth and with optimum number of excersice which wont be
too hard to decide,depending on the audience for which you are
writing , If I were to write, I would do it for a self-reader.
SO what really are the topics I am
considering to start now or probably redo or something like that.
- Analysis by Terence Tao
- Calculus 2 by Apostol
- Calculus 1 by Apostol
- Linear Algebra 1 by Gantmacher
- Statistical Inference by Casella and Berger
- Quantum mechanics by Brandsen and Joachain
- Quantum mechanics in matrix formulation
- Algebra by VInberg
- I don’t know some other random books I keep on hitting upon in the library.
If I were to learn mathematics in my
life properly the natural order of things would be as follows
- Analysis
- Single Variable Calculus
- Linear Algebra
- Multivariable Calculus
- Second course in linear algebra
- Algebra and Group theory
If only I could do
all of these I would die in peace.
Mathematics is a
guy or girl who gives me a hard on when I really understand something
or sometimes a cold strange look when its like who the hell let this
guy let in college.
The state of
affairs suggests and I assert that I am not going to give up whatever
happens . I know biology perfectly well and that;s the reason I wont
do it. I have taken up mathematics as a challenge and also a way of
clear thinking and reasoning.i don’t care what happens to my grades
as long as I stick. Even if I am not successful at it, at least I
would know why. I had this generic notion that I was inherently bad
at things compared to anyone else. I would be happy if it is true but
I knows its not . The only reason I would not be able to learn it
could be my lack of will power and nothing else.
The peak of
abstract thinking and clear reasoning is what makes gods.Able to see
everything clearly and precisely without a blemish of doubt. How
could that day would feel.
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