Some old-school advanced calculus books.

[Hartmann von Aue]

Perspicuous tomes on introductory analysis without problems:

Theory of Functions of the Real Variable, Vol 1, James Pierpont (http://books.google.com/books?id=MBoPAAAAIAAJ)

Vol. 2 (http://books.google.com/books?id=nhkPAAAAIAAJ)

His book on Complex Analysis:

Functions of a Complex Variable (http://books.google.com/books?id=SyiQ5ujLzoYC)

These books by Goursat contain challenging problems, to say the least:

A Course in Mathematical Analysis (http://books.google.com/books?id=7FMSAAAAIAAJ) (Advanced Calculus)

A Course in Mathematical Analysis Part 1 of Vol. II (http://books.google.com/books?id=HB4AAAAAMAAJ) (Complex Analysis)

A Course in Mathematical Analysis Part 2 of Vol. II (http://books.google.com/books?id=Rm8gAAAAMAAJ) (Differential Equations)

[Hartmann von Aue]

"College Algebra" the way it used to be taught, in books by L.E. Dickson, born in rural Iowa in 1874, the first PhD in Mathematics at the University of Chicago, in 1896.

You might call some of the books here Algebra III and IV, to compare to what you had in HS.

College Algebra (http://books.google.com/books?id=PvMGAAAAYAAJ)

Elementary Theory of Equations (http://books.google.com/books?id=2_QGAAAAYAAJ)

First Course in the Theory of Equations (http://books.google.com/books?id=l0AAAAAAMAAJ)

Introduction to Theory of Algebraic Equations (http://books.google.com/books?id=2hgPAAAAIAAJ)

[Macrobius]

Another good source of old Math books:

http://dlxs2.library.cornell.edu/m/math/browse/title/a.php

For example, Hamilton on Quaternions: http://dlxs2.library.cornell.edu/cgi/t/text/text-idx?c=math;cc=math;view=toc;subview=short;idno=05230001
(800pp. on all of Physics and Astronomy -- rambles a bit as the Irish tend to).

Lewis Carroll: Euclid and His Modern Rivals

http://dlxs2.library.cornell.edu/cgi/t/text/text-idx?c=math;cc=math;view=toc;subview=short;idno=03190001

(a dramatic comparison of the original Euclid to the various renditions of Elements
found in the 19th century British schoolroom)

1886 version of Descartes Geometry: http://dlxs2.library.cornell.edu/cgi/t/text/text-idx?c=math;cc=math;view=toc;subview=short;idno=00570001

Or Legendre's famous reworking of Euclid: http://dlxs2.library.cornell.edu/cgi/t/text/text-idx?c=math;cc=math;view=toc;subview=short;idno=04850002

... but there are many others.

[Dan Dare]

Differential and integral calculus were required for the old GCE "O"-level examination in Mathematics, taken by 16 year-olds when I was at grammar school in the UK.

Nowadays, the corresponding examination for 16 year-olds requires no knowledge of calculus whatsoever. In fact, judging by the National Curriculum for Key Stage 4, it struggles to cover even basic trigonometry.

[Macrobius]

Differential and integral calculus were required for the old GCE "O"-level examination in Mathematics, taken by 16 year-olds when I was at grammar school in the UK.

Nowadays, the corresponding examination for 16 year-olds requires no knowledge of calculus whatsoever. In fact, judging by the National Curriculum for Key Stage 4, it struggles to cover even basic trigonometry.

Which raises an interesting point -- why the decline? Laxer standards is an obvious ploy to get more minorities to pass, but the fact is, Whites are dumber and less well educated these days. Anyone have a plausible reason why?

For a while, in the US, the theory was that the Baby Boom was simply too big (there's anti-White wishful thinking for you). But that should have self-corrected with Gen-X. TV? Daycare? Two working parents? Does anyone have actual *evidence* of the root cause? Because it is pretty dramatic as an effect.

[Hartmann von Aue]

This one by Kolmogorov is good introduction by a very great thinker:

http://www.amazon.com/Elements-Theory-Functions-Functional-Analysis/dp/0486406830/ref=pd_bxgy_b_img_b

It is really two books, with two different subjects, measure is covered in the second.

The other book "Introductory Real Analysis" (edited by Silverman) doesn't really follow Kolmogorov's presentation, it incorporates a lot of Kolmogorov and includes some ideas from the Riesz book below. If I had to choose I'd choose the first. (I have both)

This book is worth getting, I've read the first part, it provides an interesting approach to the material:

http://www.amazon.com/Functional-Analysis-Frigyes-Riesz/dp/0486662896/ref=pd_sim_b_title_6

Rudin's Real and Complex Analysis is very good, but it is overpriced. I bought it about 9 years ago from Barnes and Noble online for under $60 (it was about $90 at Amazon back then, now it's $160), I had no idea they upped the price so much. I don't own and have never read Shilov, I glanced through it once and didn't think I needed it, but it would probably be good to have.

Rudin is a very good book, but doesn't really cover in detail a lot of the material you'd be expected to know if taking courses in real and complex. Chapter I is a very nice introduction to an abstract definition of integration, without teaching Lebesgue measure of R^n. Chapter II has a very long and hard proof that is then used to define Lebesgue measure on R^n in a non-standard way.

I recommend getting an introduction by reading Kolmogorov and some other Complex Analysis books, before trying to go through the more sophisticated approach in Rudin. Chapter I, however, is worth reading right away.

[Dan Dare]

Which raises an interesting point -- why the decline? Laxer standards is an obvious ploy to get more minorities to pass, but the fact is, Whites are dumber and less well educated these days. Anyone have a plausible reason why?

For a while, in the US, the theory was that the Baby Boom was simply too big (there's anti-White wishful thinking for you). But that should have self-corrected with Gen-X. TV? Daycare? Two working parents? Does anyone have actual *evidence* of the root cause? Because it is pretty dramatic as an effect.

In the case of the UK, the start of the decline can be dated to the mid-1960s when, as part of its own version of the Great Proletarian Cultural Revolution, the-then Labour Government decided to eliminate selctive secondary education.

This resulted in the demise of the grammar and secondary-modern (vocationally-oriented) schools and their replacement by American-style comprehensive schools where all would receive the same education. This has naturally developed into the 'all shall have prizes' syndrome, with the consequent dilution of standards.

Also of relatively recent provenance is the prevailing expectation that everyone has a right to tertiary education, whether or not they have the ability to benefit from it. In the past forty years the number of diploma mills styling themselves as 'universities' has come to exceed the number of real universities by several-fold.

[Winston]

In the case of the UK, the start of the decline can be dated to the mid-1960s when, as part of its own version of the Great Proletarian Cultural Revolution, the-then Labour Government decided to eliminate selctive secondary education.

This resulted in the demise of the grammar and secondary-modern (vocationally-oriented) schools and their replacement by American-style comprehensive schools where all would receive the same education. This has naturally developed into the 'all shall have prizes' syndrome, with the consequent dilution of standards.

Also of relatively recent provenance is the prevailing expectation that everyone has a right to tertiary education, whether or not they have the ability to benefit from it. In the past forty years the number of diploma mills styling themselves as 'universities' has come to exceed the number of real universities by several-fold.

Do grammar schools no longer exist? I know they still existed until very recently. I nearly went to one myself but decided against it, which is a decision I regret. Were these grammar school which survived long after that 1960's decision heavily watered-down versions?

[Dan Dare]

I'm not really sure of the current state-of-play, but at the time certain very prestigious grammar schools, such as Manchester Grammar, did arrange a form of opt out. The vast majority though, including the one I attended, were subsumed within the comprehensive system.

[Macrobius]

I'm not really sure of the current state-of-play, but at the time certain very prestigious grammar schools, such as Manchester Grammar, did arrange a form of opt out. The vast majority though, including the one I attended, were subsumed within the comprehensive system.

Possibly it is as you say in your comments. That certainly could explain how the good students or elite -- top 10% or 1% say, likely the males, have been ill-served. However, it does not explain why there would be a drop in mean scores for the White population as a whole.

One might argue that below the top 1-10% education is useless anyway, or a matter of diminishing returns, simply to be triaged, but there does seem to be a broader phenomenon here than the elite schools getting gutted by the ravenings of the Socialists. Surely true, surely devastating, and surely not a full explanation.

[Hartmann von Aue]

One might argue that below the top 1-10% education is useless anyway, or a matter of diminishing returns, simply to be triaged, but there does seem to be a broader phenomenon here than the elite schools getting gutted by the ravenings of the Socialists. Surely true, surely devastating, and surely not a full explanation.

I certainly is their policy, a good example is colleges getting rid of merit scholarships.

[Delmac]

It is probably an error to think of the current state of English education as the exception, and the tripartite sytem of blessed memory as the rule. Education for the working and lower middle classes in England was _always_ terrible, whereas education for the upper classes has always been very good, if perhaps a little too heavy on the Classics until recently.

For about a generation after the war, our rulers found that they needed to recruit bright proles into the Outer Party, with the dual purpose of staving off revolution and staffing the expanding civil service; hence the eleven plus, which lifted many a council house kid (including my father-in-law) into the middle class proper.

Once the creaming-off had served its purpose, the drawbridge was raised again, and British education reverted to the "Two Nations" status quo ante. The last chance for an English kid of limited means to get the education that the upper classes can afford was cut off when New Labour abolished the assisted places scheme in 1997.

The VC of Imperial College recently commented to a meeting of the Headmasters' Conference that he was shocked to find 40% of successful applicants to the college came from public shools representing at most 7% of the population. He was not really shocked and neither was his audience; the system is not broken, it is working exactly as intended.


I have oversimplified a lot above of course. In particular, certain counties retain the Tripartite system (for instance Kent and Surrey). Please note that these are precisely the sorts of places where the English ruling classes disproportionately live i.e. where the system's levelling effect will be the smallest.


It is also a mistake to conflate the 11 plus system with Grammar Schools per se. These existed as private day schools for centuries before the tripartite system, and still exist today.

[Helios Panoptes]

I'm reading the Shilov book on complex and real analysis. It's fairly readable for someone with my non-mathematical background (by this I mean that I am not a mathematics student, but I've done Calc 1 and 2, and I know set theory and especially logic), but there aren't enough answers to exercises in the back. In fact, there are hardly any.

[Hartmann von Aue]

I'm reading the Shilov book on complex and real analysis. It's fairly readable for someone with my non-mathematical background (by this I mean that I am not a mathematics student, but I've done Calc 1 and 2, and I know set theory and especially logic), but there aren't enough answers to exercises in the back. In fact, there are hardly any.

In my experience, most don't have them.

You might try Boas' Invitation to Complex Analysis, Schaum's or REA problem solvers.

I think I'll head over to the bookstore and pick up Shilov.

edit: Barnes and Noble didn't have it, I've ordered it from Amazon.

[Hartmann von Aue]

Dedekind's Essays on the Theory of Numbers:

http://books.google.com/books?id=tzYIAAAAIAAJ

[Kodos]

In the case of the UK, the start of the decline can be dated to the mid-1960s when, as part of its own version of the Great Proletarian Cultural Revolution, the-then Labour Government decided to eliminate selctive secondary education.

This resulted in the demise of the grammar and secondary-modern (vocationally-oriented) schools and their replacement by American-style comprehensive schools where all would receive the same education. This has naturally developed into the 'all shall have prizes' syndrome, with the consequent dilution of standards.

Its a terrible system.

[Kodos]

Possibly it is as you say in your comments. That certainly could explain how the good students or elite -- top 10% or 1% say, likely the males, have been ill-served. However, it does not explain why there would be a drop in mean scores for the White population as a whole.

One might argue that below the top 1-10% education is useless anyway, or a matter of diminishing returns, simply to be triaged, but there does seem to be a broader phenomenon here than the elite schools getting gutted by the ravenings of the Socialists. Surely true, surely devastating, and surely not a full explanation.

Education below the top 10% should consist of basic arithmetic, literacy, and that god hates Islam and communism and that all believing in these should be killed. Followed by vocational training.

Advanced math is something I can barely comprehend. I was MUCH better at geometric calculus then things like infinite series and transforms to the frequency domain, and I recall little of it today which is why Im reviewing MIT open courseware (http://ocw.mit.edu/OcwWeb/web/home/home/index.htm)... and my IQ is supposedly 135. Trying to give everyone the same education seems like democratic/progressive madness to me.

[Baron_Corvo]

I think Dan's got it slightly wrong here. Manchester Grammar was a direct grant school, i.e. an independent school which accepted a certain number of pupils on state financed scholarships provided they passed its no doubt stiff entrance exam.

http://en.wikipedia.org/wiki/Manchester_Grammar_School

In the mid-70s this arrangement was ended and MGS, like most direct grant schools, became fully independent. Direct grant schools were quite distinct from state grammar schools, of which mine was one (and is still going), which were fully state financed.

As for "O" levels, I did basic differential calculus for Maths "O" level (which I took in 1973) but not integral calculus. My maths teacher told us that, as opposed to the 6 geometry theorems we had to learn the proofs of, he had to learn 83 when he took the same exam in 1926.

BTW, thanks for the transcriptions. My choice would be a book most Phoraites would probably turn up their noses at; Silvanus P. Thompson's "Calculus Made Easy."

[harjit]

Education below the top 10% should consist of basic arithmetic, literacy, and that god hates Islam and communism and that all believing in these should be killed. Followed by vocational training.

Advanced math is something I can barely comprehend. I was MUCH better at geometric calculus then things like infinite series and transforms to the frequency domain, and I recall little of it today which is why Im reviewing MIT open courseware (http://ocw.mit.edu/OcwWeb/web/home/home/index.htm)... and my IQ is supposedly 135. Trying to give everyone the same education seems like democratic/progressive madness to me.
Hey Kodos, that MIT site is an awesome resource. Thanks for pointing it out.

I've gone through some of the course syllabuses (syllabi?), here is the list of courses it would take for a beginner to learn about signal processing:
http://www.geocities.com/harjit_phora/SignalProcessingStudy.htm

(BTW there's nothing else on that Harjit website so far, I honestly just felt like making that curriculum. :))

A hell of a lot to study there. I did take all those math courses at one time (loooong ago!), but much of it is out the window. As for the physics/electronics courses, I hardly took any of it. Just whatever we learned in high school, plus one first-year intro physics course in university.

I may need to learn something about this subject about for a project coming down the pipes and I'm getting pretty worried.

I wonder if there are any generalized books on Signal Processing. Like Signal Processing for Executives. Or Signal Processing for Dummies. :)

[President Barbicane]

(BTW there's nothing else on that Harjit website so far, I honestly just felt like making that curriculum. )

off topic, I know, but I've been thinking about putting up my own web site for a while. I was thinking of writing a few scripts that would put a blog together. Maybe I should start a thread about it in the technology section.

[Geist]

Mathematics has always been a blind spot for me as I have never known where to begin. I never took to it in school, and was always expected to take up a humanities route (English Literature, History, and languages). However despite dropping Mathematics in University and taking up Philosophy it has always grated me that I abandoned this fundamental. MIT website is a beautiful resource and indispensible for a European for whom logic classes are non-existent at any real level.