- #1
murshid_islam
- 458
- 19
have anyone read "A Course on Pure Mathematics" by G. H. Hardy?
is it a good book?
is it a good book?
matt grime said:Its contents merely reflects the era it was written in. How could any modern introduction to pure maths fail to mention groups either? In anycase, multivariable calc is either a direct generalization of one variable and hence uninteresting for its own sake in an introduction, or it is Stokes' theorem which these days, if ever, hardly counts as pure maths at all unless one considers differential manifolds which are beyond the scope af any introductory book.
"this book has been designed primarily for the use of first year students whose abilities reach or approach something like what is usually described as 'scholarship standard'"
Is that displaying properly for anybody else?benorin said:Here, read it for yourself: http://kr.cs.ait.ac.th/~radok/math/mat11/starter.htm#A%20Course%20of%20Pure%20Mathematics .
benorin said:Try this one: A Course of Pure Mathematics by G.H. Hardy. I found it in the Distributed Digital Library of Mathematical Monographs Collection.
Chrono said:You mean I didn't even need to buy it?
JasonRox said:I rather have something tangible.
fourier jr said:as hardy writes in the preface, (quote omitted)
that's roughly what it would be used for today; pure math in first year would be calc I & II (& maybe some matrix theory). i only thought it might be worth mentioning that there's nothing on calculus of several variables & vector analysis since most big modern books & courant's text all have that stuff in them.
matt grime said:I think I must point out that is certainly not what Hardy would consider scholarship standard if he were alive today. Currently Cambridge considers that at the end of the first year in mathematics that you ought to be conversant in group theory, real and complex analysis (holomorphic and meromorphic stuff, not that they call it that prefering analyticity instead for some historical nonsense), calculus methods such as stokes theorem, discrete mathematics such as posets and generating functions, set theory, geometry, probability. And if you're a good student then you should certainly understand linear algebra (not the basic basis and matrix version, which is taught to all) but proper jordan normal form/idempotet/unipotent stuff over arbitrary fields.
I think they have changed it since I was there and now they may delay some of those topics and teach metric spaces instead, I can't say I'm up to date with the current syllabus
In Hardy's day the emphasis was more on special functions (elliptic things I imagine) and real and complex analysis of one variable. After all, algebraic topology and geometry was yet to be invented.
matt grime said:That is undergraduate mathematics, Jason, certainly not graduate level mathematics.
Currently Cambridge considers that at the end of the first year in mathematics that you ought to be conversant in group theory, real and complex analysis (holomorphic and meromorphic stuff, not that they call it that prefering analyticity instead for some historical nonsense), calculus methods such as stokes theorem, discrete mathematics such as posets and generating functions, set theory, geometry, probability. And if you're a good student then you should certainly understand linear algebra (not the basic basis and matrix version, which is taught to all) but proper jordan normal form/idempotet/unipotent stuff over arbitrary fields.
matt grime said:And no one actually cares about the Peano axioms, do they?
selfAdjoint said:Cambridge is the legendary home of the tripos, which still survives, doesn't it? That means the undergraduate math there is as tough as any in the world and much tougher than some, especially the watered down stuff offered in the USA.
"A Course on Pure Mathematics" is a comprehensive textbook written by G.H. Hardy, a renowned mathematician, that covers topics such as number theory, algebra, geometry, and analysis. It is considered a classic text in the field of pure mathematics and is often used as a reference for undergraduate and graduate courses.
The target audience for "A Course on Pure Mathematics" is undergraduate and graduate students in mathematics, as well as anyone with a strong foundation in mathematics who is interested in studying advanced topics in pure mathematics.
"A Course on Pure Mathematics" is highly regarded for its clear and concise explanations of complex mathematical concepts, as well as its rigorous and thorough approach to proofs. It also includes numerous examples and exercises to help readers develop their problem-solving skills.
While it is recommended to have a strong foundation in mathematics before attempting to study from "A Course on Pure Mathematics", it is possible to use it for self-study. However, it may be more beneficial for students to have access to a professor or mentor who can provide guidance and answer any questions that may arise.
Yes, there are many other resources that can be used in conjunction with "A Course on Pure Mathematics". These may include additional textbooks, online lectures or tutorials, and problem-solving guides. It is important for students to find the resources that best suit their learning style and needs.