A Cumulative List of Math Textbooks

lase

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.

wisvuze

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

Thank you for those contributions, wisvuze :) Are there any categories for math that anyone would like to see added?

hamsterpower7

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

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

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

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

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

Add to that Hrbacek and Jech "introduction to set theory"

doodle_sack

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

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

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.