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