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A Cumulative List of Math Textbooks

by lase
Tags: cumulative, list, math, textbooks
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lase
#1
Aug7-11, 09:30 PM
P: 22
I'm putting together a list to hopefully help those who are seeking a textbook to use.
Please feel free to offer suggestions/corrections/etc. I'm starting with math and physics
for now but will branch out into other subjects after having a solid foundation. At some
point in the future, I hope to have reviews or descriptions about each book, but that
could take a while.

Math

Calculus:
  • Calculus - Volume 1 and 2 - Tom Apostol
  • Calculus - Michael Spivak
  • Calculus on Manifolds - Michael Spivak
  • Differential and Integral Calculus (Volumes 1 and 2) - Richard Courant
  • Calculus: An Intuitive and Physical Approach - Morris Kline
  • Calculus: Early Transcendentals - James Stewart
  • Calculus (Early/Late Transcendentals) - Howard Anton, Irl Bivens, Stephen Davis
  • Vector Calculus - Jerrold Marsden, Anthony Tromba

Linear Algebra:
  • Linear Algebra - Kenneth Hoffman, Ray Kunze
  • Linear Algbera - Serge Lang
  • Linear Algebra Done Right - Sheldon Axler
  • Linear Algebra - Georgi Shilov
  • Introduction to Linear Alebra - Gilbert Strang
  • Advanced Linear Algebra - Steven Roman

Differential Equations:
  • Elementary Differential Equations and Boundary Value Problems - William Boyce, Richard
    DiPrima
  • An Introduction to Ordinary Differential Equations - James Robinson
  • Partial Differential Equations for Scientists and Engineers - S. Farlow
  • Lectures on Partial Differential Equations - I. G. Petrovsky
  • Lectures on Partial Differential Equations - Vladimir Arnold

Analysis:
  • Introductory Real Analysis - A. N. Kolmogorov, S. V. Formin
  • Principles of Mathematical Analysis - Walter Rudin
  • Real and Complex Analysis - Walter Rudin
  • Real Analysis - N. L. Carothers
  • Counterexamples in Analysis - B. R. Gelbaum, J. M. H. Olmsted
  • Real Analysis - McShane, E.J. Botts

Algebra:
  • Algebra - Serge Lang
  • Abstract Algebra - David Dummit, Richard Foote
  • Algebra - Michael Artin
  • Modern Algebra with Applications - William Gilbert
  • Topics in Algebra - I. N. Herstein
  • Noncommutative Rings - I. N. Herstein
  • Galois Theory - Emil Artin
  • Algebra - Larry Grove
  • Algebra - B. L. Van der Waerden
  • Commutative Algebra - O. Zariski, Pierre Samuel
  • Homology - MacLane
  • Abstract Algebra - Pierre Antoine Grillet
  • Algebra - Thomas Hungerford
  • Algebra - MacLane and Birkhoff

Topology:
  • Topology - James Munkres
  • General Topology - John Kelley
  • Introduction to Topology - Bert Mendelson
  • Topology - Dugundji
  • General Topology - Willard
  • Topology - Janich

Geometry:
  • Geometry Revisited - H.S.M. Coxeter, S.L. Greitzer
  • Introduction to Geometry - H.S.M. Coxeter
  • Elements - Euclid
  • Geometry, Euclid and Beyond - Robin Hartshorne

Graph Theory:
  • Modern Graph Theory - Bollobas
  • Graph Theory - Diestel
  • Graph Theory - Tutte

Number Theory:
  • Number Theory - Helmut Hasse
  • Elementary Number Theory - Charles Vanden Eynden
  • Introduction to Number Theory - Trygve Nagell

Differential Geometry
  • A Comprehensive Introduction to Differential Geometry (vol 1-5) - Michael Spivak
  • Notes on Differential Geometry - Noel Hicks
  • Differential Geometry - Erwin Kreyszig

---

If you have anything to add, please post it! I will add more later.
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wisvuze
#2
Aug7-11, 10:41 PM
P: 367
Please add:

Real Analysis - McShane and E.J. Botts


Abstract Algebra - Pierre Antoine Grillet
Algebra - Thomas Hungerford
Algebra - Mac Lane and Birkhoff

Advanced Linear Algebra - Steven Roman

Topology - Dugundji
General Topology - Willard
Topology - Janich

Graph Theory - Diestel
Graph Theory - Tutte

More later
lase
#3
Aug8-11, 09:10 AM
P: 22
Thank you for those contributions, wisvuze :) Are there any categories for math that anyone would like to see added?

hamsterpower7
#4
Aug26-11, 01:35 PM
P: 43
A Cumulative List of Math Textbooks

do you have to see the books in the following order?
for example
calculus --> linear algebra--->differential equation??
can you read one or two books from each categories?
lase
#5
Aug27-11, 11:52 AM
P: 22
Quote Quote by hamsterpower7 View Post
do you have to see the books in the following order?
for example
calculus --> linear algebra--->differential equation??
can you read one or two books from each categories?
You don't need calculus before starting linear algebra, however I believe the general consensus is that you take calculus before linear algebra. It would not be smart, however, to try and do differential equations without first learning calculus :P You also don't need linear algebra before you start differential equations. It varies from college to college I suppose as to the actual sequence.
wisvuze
#6
Aug27-11, 12:20 PM
P: 367
For a full and "accurate" coverage of differential equations, you should definitely see calculus AND linear algebra first. ( Unless you want to learn them simultaneously )
micromass
#7
Aug27-11, 12:48 PM
Mentor
micromass's Avatar
P: 18,061
Here are some great books you've missed

Calculus
Practical Analysis in One Variable - Esteb

Linear Algebra
Linear algebra - Friedberg
Finite-dimensional Vector spaces - Halmos

Analysis
Principles of Real Analysis - Aliprantis, Burkinshaw
Real Analysis - Yeh
Understanding Analysis - Abbott
Treatise on Analysis - Dieudonne

Functional Analysis
Analysis Now - Pedersen
A course in functional analysis - Conway
Introductory functional analysis with applications - Kreyszig
Lectures and Exercises on Fucnctional analysis - Helemskii
Linear Operators - Dunford, Schwartz
Functional Analysis - Lax

Algebra
Galois Theory - Stewart
A book on abstract algebra - Pinter
Groups and symmetry - Armstrong
Commutative algebra with a view on algebraic geometry - Eisenbud
Introduction to commutative algebra - Atiyah, McDonald

Topology
Counterexamples in Topology - Steen, Seebach
Introduction to Topological Manifolds - Lee

Differential geometry
Introduction to Smooth manifolds - Lee
vici10
#8
Aug27-11, 01:50 PM
P: 41
Quote Quote by lase View Post
Are there any categories for math that anyone would like to see added?
I would add set theory:
Kunen "Set Theory An Introduction To Independence Proofs"
Jech "Set theory"

Also, I would add to Topology section:
Engelking "General topology"
micromass
#9
Aug27-11, 02:05 PM
Mentor
micromass's Avatar
P: 18,061
Quote Quote by vici10 View Post
I would add set theory:
Kunen "Set Theory An Introduction To Independence Proofs"
Jech "Set theory"
Add to that Hrbacek and Jech "introduction to set theory"
doodle_sack
#10
Aug28-11, 09:50 PM
P: 69
A little advanced topics, pardon me if I am re-posting the same titles as above.

Algebra
Basic Algebra I & II, Nathan Jacobson
Introduction to Non-Commutative Rings, Lam
Further Algebra, Cohn
Introduction to Commutative Algebra, Atiyah & MacDonald

Analysis
Real Analysis - Modern Techniques & Their Applications, Folland
Real Analysis - Measure Theory, Integration & Hilbert Spaces, Stein & Shakarchi
Real Variables, Torchinsky
Complex Analysis, Conway
Elementary Theory of Analytic Functions of One or Several Complex Variables, Cartan
Complex Analysis, Stein & Shakarchi
Introduction to Functional Analysis, Taylor & Lay

Topology
Fiber Bundles, Husemuller
Algebraic Topology, Harcher
Homology Theory, Vick
Algebraic Topology, Greenberg & Harper
jbunniii
#11
Aug28-11, 10:20 PM
Sci Advisor
HW Helper
PF Gold
jbunniii's Avatar
P: 3,186
A few more analysis books, off the top of my head:

Pugh - Real Mathematical Analysis
Bartle - Elements of Real Analysis
Bartle - The Elements of Integration and Lebesgue Measure
Knapp - Basic Real Analysis
Knapp - Advanced Real Analysis
Thomson, Bruckner, and Bruckner - Elementary Real Analysis
Bruckner, Bruckner, and Thomson - Real Analysis
Jones - Lebesgue Integration on Euclidean Space
Berberian - Fundamentals of Real Analysis
Hardy - A Course of Pure Mathematics
Hardy - Inequalities
Whittaker and Watson - A Course of Modern Analysis
Wheeden and Zygmund - Measure and Integral
Royden - Real Analysis
Stromberg - Introduction to Classical Real Analysis
Hewitt and Stromberg - Real and Abstract Analysis
Lang - Real and Functional Analysis
Lang - Undergraduate Analysis
Rosenlicht - Introduction to Analysis
Halmos - Measure Theory
qspeechc
#12
Aug29-11, 12:08 PM
P: 792
I don't see how naming 20 textbooks on one subject is going to help anyone. Are you trying to name every book available on every subject? 2 or 3 for each subject at each level would be much more helpful.


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