1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Cumulative List of Math Textbooks

  1. Aug 7, 2011 #1
    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.



    • 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
    • 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

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

    • 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.
    Last edited: Aug 8, 2011
  2. jcsd
  3. Aug 7, 2011 #2
    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
  4. Aug 8, 2011 #3
    Thank you for those contributions, wisvuze :) Are there any categories for math that anyone would like to see added?
  5. Aug 26, 2011 #4
    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?
  6. Aug 27, 2011 #5
    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.
  7. Aug 27, 2011 #6
    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 )
  8. Aug 27, 2011 #7
    Here are some great books you've missed

    Practical Analysis in One Variable - Esteb

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

    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

    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

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

    Differential geometry
    Introduction to Smooth manifolds - Lee
  9. Aug 27, 2011 #8
    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"
  10. Aug 27, 2011 #9
    Add to that Hrbacek and Jech "introduction to set theory"
  11. Aug 28, 2011 #10
    A little advanced topics, pardon me if I am re-posting the same titles as above.

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

    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

    Fiber Bundles, Husemuller
    Algebraic Topology, Harcher
    Homology Theory, Vick
    Algebraic Topology, Greenberg & Harper
  12. Aug 28, 2011 #11


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
  13. Aug 29, 2011 #12
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook