A Cumulative List of Math Textbooks

  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.

    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.
     
    Last edited: Aug 8, 2011
  2. jcsd
  3. 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. Thank you for those contributions, wisvuze :) Are there any categories for math that anyone would like to see added?
     
  5. 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. 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. 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. micromass

    micromass 18,532
    Staff Emeritus
    Science Advisor

    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
     
  9. 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. micromass

    micromass 18,532
    Staff Emeritus
    Science Advisor

    Add to that Hrbacek and Jech "introduction to set theory"
     
  11. 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
     
  12. jbunniii

    jbunniii 3,353
    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. 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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