best maths books for 1st-year undergraduates at Cambridge?
I just want to 'do the course' for the sake of it...and am not about to go to Cambridge or any university... OK so I've been through the Cambridge course schedules, but each lecture course seems to come with 5-6 recommended books or more. For Part IA, about 50 books are recommended.
What would people recommend as the top 10 or so, covering all the courses?
On my list so far (please suggest crossing off if appropriate) are:
Algebra, including groups, vectors, linear, matrices:
1) Alan Beardon, Algebra and Geometry
2) A O Morris, Linear Algebra - An Introduction
(perhaps
3) T Blyth and E Robertson, Basic Linear Algebra ?)
Analysis:
4) M. Spivak, Calculus
5) T M Apostol, Calculus
6) W Rudin, Principles of Mathematical Analysis
(any comparison of 3-5 would be very welcome)
7) Bartle and Sherbert, Introduction to Real Analysis
8) G H Hardy, A Course of Pure Mathematics
Geometry and Topology:
9) W A Sutherland, Introduction to Metric and Topological Spaces
10) J Roe, Elementary Geometry
11) HJ Munkres, Topology
(perhaps
12) B Szendroi and M Reid, Geometry and Topology ?)
Combinatorics:
13) W Lint, A Course in Combinatorics
(perhaps
14) Graham, Knuth, Patashnik, Concrete Mathematics, but maybe not?)
Number Theory
15) A Baker, A Concise Introduction to the Theory of Numbers
16) G H Hardy and E M Wright, An Introduction to the Theory of Numbers
(comparison?)
Would appreciate any advice on whittling the list down to about 10...
Thanks!
D
What would people recommend as the top 10 or so, covering all the courses?
On my list so far (please suggest crossing off if appropriate) are:
Algebra, including groups, vectors, linear, matrices:
1) Alan Beardon, Algebra and Geometry
2) A O Morris, Linear Algebra - An Introduction
(perhaps
3) T Blyth and E Robertson, Basic Linear Algebra ?)
Analysis:
4) M. Spivak, Calculus
5) T M Apostol, Calculus
6) W Rudin, Principles of Mathematical Analysis
(any comparison of 3-5 would be very welcome)
7) Bartle and Sherbert, Introduction to Real Analysis
8) G H Hardy, A Course of Pure Mathematics
Geometry and Topology:
9) W A Sutherland, Introduction to Metric and Topological Spaces
10) J Roe, Elementary Geometry
11) HJ Munkres, Topology
(perhaps
12) B Szendroi and M Reid, Geometry and Topology ?)
Combinatorics:
13) W Lint, A Course in Combinatorics
(perhaps
14) Graham, Knuth, Patashnik, Concrete Mathematics, but maybe not?)
Number Theory
15) A Baker, A Concise Introduction to the Theory of Numbers
16) G H Hardy and E M Wright, An Introduction to the Theory of Numbers
(comparison?)
Would appreciate any advice on whittling the list down to about 10...
Thanks!
D
5) is a very good reference book for Real Analysis, and the one I tend to reach for when I need to brush up on things in that area, but it can be a little impenetrable when you're starting out and not everyone gets on with it. You might want to try 4) as an alternative, as Apostol has a nice style and generally writes very good textbooks.
8) is a very nice introductory text for metric spaces and topology, and 12) seems to be the standard text on combinatorics. It's a bit weighty, but only because it provides a good coverage of topics and is very accessible.
8) is a very nice introductory text for metric spaces and topology, and 12) seems to be the standard text on combinatorics. It's a bit weighty, but only because it provides a good coverage of topics and is very accessible.
elementary number theory by SUMS is good - Hardy is quite hefty and is much like an encyclopedia [and some things are rather dated] - best used as reference or further reading ina ddition to the SUMS or Bakers book (thought it too only goes into small detail on some sections that are important - but if you read through it he says that is basically what he used to teach at Cambridge).
Where would you recommend buying book 4 as its £200+ on most websites, anyone find anywhere cheaper?
Original post by davidne
I just want to 'do the course' for the sake of it...and am not about to go to Cambridge or any university... OK so I've been through the Cambridge course schedules, but each lecture course seems to come with 5-6 recommended books or more. For Part IA, about 50 books are recommended.
What would people recommend as the top 10 or so, covering all the courses?
On my list so far (please suggest crossing off if appropriate) are:
Algebra, including groups, vectors, linear, matrices:
1) Alan Beardon, Algebra and Geometry
2) A O Morris, Linear Algebra - An Introduction
(perhaps
3) T Blyth and E Robertson, Basic Linear Algebra ?)
Analysis:
4) M. Spivak, Calculus
5) T M Apostol, Calculus
6) W Rudin, Principles of Mathematical Analysis
(any comparison of 3-5 would be very welcome)
7) Bartle and Sherbert, Introduction to Real Analysis
8) G H Hardy, A Course of Pure Mathematics
Geometry and Topology:
9) W A Sutherland, Introduction to Metric and Topological Spaces
10) J Roe, Elementary Geometry
11) HJ Munkres, Topology
(perhaps
12) B Szendroi and M Reid, Geometry and Topology ?)
Combinatorics:
13) W Lint, A Course in Combinatorics
(perhaps
14) Graham, Knuth, Patashnik, Concrete Mathematics, but maybe not?)
Number Theory
15) A Baker, A Concise Introduction to the Theory of Numbers
16) G H Hardy and E M Wright, An Introduction to the Theory of Numbers
(comparison?)
Would appreciate any advice on whittling the list down to about 10...
Thanks!
D
What would people recommend as the top 10 or so, covering all the courses?
On my list so far (please suggest crossing off if appropriate) are:
Algebra, including groups, vectors, linear, matrices:
1) Alan Beardon, Algebra and Geometry
2) A O Morris, Linear Algebra - An Introduction
(perhaps
3) T Blyth and E Robertson, Basic Linear Algebra ?)
Analysis:
4) M. Spivak, Calculus
5) T M Apostol, Calculus
6) W Rudin, Principles of Mathematical Analysis
(any comparison of 3-5 would be very welcome)
7) Bartle and Sherbert, Introduction to Real Analysis
8) G H Hardy, A Course of Pure Mathematics
Geometry and Topology:
9) W A Sutherland, Introduction to Metric and Topological Spaces
10) J Roe, Elementary Geometry
11) HJ Munkres, Topology
(perhaps
12) B Szendroi and M Reid, Geometry and Topology ?)
Combinatorics:
13) W Lint, A Course in Combinatorics
(perhaps
14) Graham, Knuth, Patashnik, Concrete Mathematics, but maybe not?)
Number Theory
15) A Baker, A Concise Introduction to the Theory of Numbers
16) G H Hardy and E M Wright, An Introduction to the Theory of Numbers
(comparison?)
Would appreciate any advice on whittling the list down to about 10...
Thanks!
D
Original post by Bioxoxo
Where would you recommend buying book 4 as its £200+ on most websites, anyone find anywhere cheaper?
Amazon, £35.99.
For buying books I would recommend ABE books which has a lot of ex-library copies going cheap. More recent books are usually more expensive but often easier to read.
That Munkres Topology book is pretty great (single-handedly got me through my topology module!).
That Munkres Topology book is pretty great (single-handedly got me through my topology module!).
I am from morroco I love math But i have not money to come to america for studying
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