Favourite university maths books?

It could be undergraduate book or a graduate book.

As no-one has answered I'll get the ball rolling:

GALLIAN - Contemporary Abstract Algebra - found this long after I was a student and think it a highly approachable read.

DO CARMO - Differential Geometry of Curves and Surfaces - remembering reading this cover to cover one summer. Can't say I've done that with many maths books.

COXETER - Non-Euclidean Geometry - rather old school now but the book that made me decide to be a geometer

WILLARD - General Topology - very well written and incredibly comprehensive without being tome-like.

KLINE - Mathematical Thought from Ancient to Modern Times - as a teenager I think Batley library had all of two maths books. Thankfully this was one of them - think I was the only person ever taking it out.

Reply 2

Gregorius

Original post by ζ(z)

It could be undergraduate book or a graduate book.

Dudley: Real Analysis and Probability.

Reply 3

ζ(z)

@RichE Some interesting titles you've mentioned. I've heard someone else give high praise of the abstract algebra book you mentioned. I've many favourite books on different areas, but strangely not abstract algebra, and I love algebra. I'm gonna have a look at this book next time I see it.

Reply 4

ζ(z)

Original post by Gregorius

Dudley: Real Analysis and Probability.

As someone ignorant of probably theory but likes analysis, I may have a look at this.

Reply 5

RichE

Original post by ζ(z)

I'm sorry to say most (new) editions of Gallian are very expensive, so seek out a library or second hand copy. It seemed to me such a refreshing change from the "classic" dense texts of Herstein or Halmos.

Reply 6

ζ(z)

Original post by RichE

Ah, it's shame how expensive maths books tend to be these days! My first experience with abstract algebra was a Herstein text (Topics in Algebra). It was okay, but I didn't see what the hype was about. Didn't like Finite Dimensional Vector Spaces either, which I'm guessing is the Halmos text you're referring to. I absolutely hated Axler's book: I felt like I understood everything, but at the same time learned nothing (it's all like look what I can do without determinants). The only classic abstract/linear algebra book that met the hype was Hoffman-Kunze.

Reply 7

ThatPerson

Original post by ζ(z)

It could be undergraduate book or a graduate book.

Probability with Martingales by David Williams

Algebra: Chapter 0 by Paolo Aluffi

Reply 8

Gregorius

Original post by ThatPerson

Probability with Martingales by David Williams

Yes! That's an excellent introduction to martingales.

Reply 9

Gregorius

Original post by Gregorius

Dudley: Real Analysis and Probability.

Let's expand my single item list! These are books that I have found to be especially readable.

Silverman & Tate: Rational Points on Elliptic Curves.
Cox, Little, O'Shea: Ideals, Varieties and Algorithms.
Spivak: Comprehensive Introduction to Differential Geometry.
Kolmogorov & Fomin: Introductory Real Analysis.
Enderton: Elements of Set Theory.
Cutland: Computability.
Rose: A Course in Number Theory.
Arnold: Ordinary Differential Equations.
Milnor: Morse Theory (plus anything by Milnor).
Davison: Statistical Models.
Stillwell: Mathematics & its History (plus anything by Stillwell).
Wegert: Visual Complex Functions.
Schilling: Measures, Integrals and Martingales.

Reply 10

RichE

Original post by Gregorius

Very interesting list - I especially agree with your views on Stillwell and Milnor and really ought to have put

STILLWELL - Geometry of Surfaces
STILLWELL - The Real Numbers

on my own list.

Also remember fondly the Cutland book.

Never been a fan of ROSE though. It's encylopaedic as a reference, but would not have liked to learn number theory from it.

Reply 11

Gregorius

Original post by RichE

Never been a fan of ROSE though. It's encylopaedic as a reference, but would not have liked to learn number theory from it.

I've never been a "natural" at number theory, finding it a hard grind. So maybe Rose appealed to me as it lays it all out in an encyclopedic fashion!

Reply 12

Muttley79

I enjoyed 'An introduction to Graph Theory' by Robin Wilson.

Reply 13

Ljg2015

Original post by ζ(z)

It could be undergraduate book or a graduate book.

Fleisch - A Students Guide to Vectors and Tensors Stroud - Engineering Mathematics

Reply 14

Kummer

•

Primes of the Form x^2+ny^2 - Cox.

•

A classical introduction to modern number theory - Ireland/Rosen.

•

Number Fields - Marcus.

•

Elementary Methods in Number Theory - Nathanson.

•

Rational Points on Elliptic Curves - Silverman/Tate.

•

Complex Algebraic Curves - Frances Kirwan.

•

A course in Arithmetic - Serre.

•

Field and Galois Theory - Morandi.

•

Class Field Theory - Nancy Childress.

•

Introduction to Cyclotomic Fields - Lawrence Washington.

•

Topological/Smooth/Riemannian Manifolds (3 volumes) - Lee.

•

Heights in Diophantine Geometry - Enrico Bombieri.

Reply 15

username1162972

What is the contents of Topological/Smooth/Riemann Manifokds by Lee?

Original post by Kummer

[ul]
[li]Primes of the Form x^2+ny^2 - Cox.[/li]
[li]A classical introduction to modern number theory - Ireland/Rosen.[/li]
[li]Number Fields - Marcus.[/li]
[li]Elementary Methods in Number Theory - Nathanson.[/li]
[li]Rational Points on Elliptic Curves - Silverman/Tate.[/li]
[li]Complex Algebraic Curves - Frances Kirwan.[/li]
[li]A course in Arithmetic - Serre.[/li]
[li]Field and Galois Theory - Morandi.[/li]
[li]Class Field Theory - Nancy Childress.[/li]
[li]Introduction to Cyclotomic Fields - Lawrence Washington.[/li]
[li]Topological/Smooth/Riemannian Manifolds (3 volumes) - Lee.[/li]
[li]Heights in Diophantine Geometry - Enrico Bombieri. [/li]
[/ul]

Reply 16

Mr M

Study Forum Helper

Original post by Muttley79

I enjoyed 'An introduction to Graph Theory' by Robin Wilson.

This would surely be a contender were the title of the thread 'Favourite university maths books authored by the son of a former Prime Minister'.

Reply 17

Muttley79

Original post by Mr M

This would surely be a contender were the title of the thread 'Favourite university maths books authored by the son of a former Prime Minister'.

It was the course recommended book. I also had a good Linear Algebra book - can't remember the author because I lent it to a colleague and it was never returned; I know it had a red cover :biggrin: