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synthetic.
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"The Greats" - and more.
[Edit: I have likely posted this in the wrong forum - any Mods are welcome to move it to a more apt location, apologies]
I'm forming a reading list (Undergrad) for myself comprising of modern texts and "classics" by those such as Euclid and Euler.
Advice often offered to Maths students is "read the greats" - so, suggest which texts constitute work by the Greats and should be read by students. That is, texts which are reasonably applicable today and offer wonderful insight to the respective subject.
I have only two of the aforementioned on my list thus far;
Euclid - Elements (All thirteen)
Gauss - Disquisitiones Arithmeticae
What other works by Greats should i have? And what are the opinions on the two listed above?
Ontop of;
General:
The Princeton Companion To Mathematics
Calculus:
Introduction to Calculus and Analysis - Courant
Calculus - Spivak
Elementary Differential Equations and Boundary Value Problems - Boyce & DiPrima
and Apostol's texts (but at £100+ each they can wait)
Algebra:
Elementary Linear Algebra: Applications Version - Anton & Rorres
Elementary Linear Algebra with Applications - Kollman & Hill
Pure Maths/ Numb Theory:
How to Prove It: A Structured Approach - Daniel J. Velleman (Author)
Concise Introduction to Pure Mathematics - Liebeck
Topology:
Introduction to Topology - Mendelson
First Concepts of Topology - W.G. Chinn (Author), N.E. Steenrod (Author)
Introduction to Topology and Modern Analysis - Simmons
Probability/Statistics:
A Modern Introduction to Probability and Statistics: Understanding Why and How - F.M. Dekking (Author), et al.
I only have a few opinions on any of these texts, i am here for more insight and any other suggestions. Indeed, warning me off of any texts is welcome also.
Oh, and also, for anyone suggesting/advocating texts - would it be possible for you to indiciate the pre-requisites for reading said text?
Thanks.
P.S. - I have already read through a lot of Mathwonks thread and taken a few suggestions from it ("who wants to be a . . ").
[Edit: I have likely posted this in the wrong forum - any Mods are welcome to move it to a more apt location, apologies]
I'm forming a reading list (Undergrad) for myself comprising of modern texts and "classics" by those such as Euclid and Euler.
Advice often offered to Maths students is "read the greats" - so, suggest which texts constitute work by the Greats and should be read by students. That is, texts which are reasonably applicable today and offer wonderful insight to the respective subject.
I have only two of the aforementioned on my list thus far;
Euclid - Elements (All thirteen)
Gauss - Disquisitiones Arithmeticae
What other works by Greats should i have? And what are the opinions on the two listed above?
Ontop of;
General:
The Princeton Companion To Mathematics
Calculus:
Introduction to Calculus and Analysis - Courant
Calculus - Spivak
Elementary Differential Equations and Boundary Value Problems - Boyce & DiPrima
and Apostol's texts (but at £100+ each they can wait)
Algebra:
Elementary Linear Algebra: Applications Version - Anton & Rorres
Elementary Linear Algebra with Applications - Kollman & Hill
Pure Maths/ Numb Theory:
How to Prove It: A Structured Approach - Daniel J. Velleman (Author)
Concise Introduction to Pure Mathematics - Liebeck
Topology:
Introduction to Topology - Mendelson
First Concepts of Topology - W.G. Chinn (Author), N.E. Steenrod (Author)
Introduction to Topology and Modern Analysis - Simmons
Probability/Statistics:
A Modern Introduction to Probability and Statistics: Understanding Why and How - F.M. Dekking (Author), et al.
I only have a few opinions on any of these texts, i am here for more insight and any other suggestions. Indeed, warning me off of any texts is welcome also.
Oh, and also, for anyone suggesting/advocating texts - would it be possible for you to indiciate the pre-requisites for reading said text?
Thanks.
P.S. - I have already read through a lot of Mathwonks thread and taken a few suggestions from it ("who wants to be a . . ").
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