A Cumulative List of Math Textbooks

In summary: Stromberg - Real and Abstract AnalysisGoffman - Real FunctionsRudin - Real and Complex AnalysisRudin - Fourier Analysis on GroupsRudin - Harmonic Analysis on SemigroupsRudin - Functional AnalysisRudin - Functional AnalysisRiesz and Nagy - Functional AnalysisBrezis - Functional Analysis, Sobolev Spaces, and Partial Differential EquationsYosida - Functional AnalysisHille and Phillips - Functional Analysis and Semi-GroupsLax - Functional AnalysisDunford and Schwartz - Linear OperatorsRudin - Operator TheoryConway - A Course in Functional AnalysisReed and Simon - Methods of Modern Mathematical PhysicsReed
  • #1
lase
22
0
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:
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  • #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
 
  • #3
Thank you for those contributions, wisvuze :) Are there any categories for math that anyone would like to see added?
 
  • #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?
 
  • #5
hamsterpower7 said:
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.
 
  • #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 )
 
  • #7
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
 
  • #8
lase said:
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"
 
  • #9
vici10 said:
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"
 
  • #10
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
 
  • #11
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
 
  • #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.
 

What is "A Cumulative List of Math Textbooks"?

"A Cumulative List of Math Textbooks" is a comprehensive list of all the math textbooks that have been published over the years. It includes textbooks from various levels, such as elementary, middle school, high school, and college, and covers a wide range of topics in mathematics.

What is the purpose of "A Cumulative List of Math Textbooks"?

The purpose of "A Cumulative List of Math Textbooks" is to serve as a reference guide for students, teachers, and researchers who are looking for specific math textbooks. It can also be used to track the evolution of math education and the development of new teaching methods and approaches.

How often is "A Cumulative List of Math Textbooks" updated?

The list is updated regularly, with new textbooks being added as they are published. However, it may not include every single math textbook that has ever been published, as some may have gone out of print or are not easily accessible.

Can "A Cumulative List of Math Textbooks" be used to find textbooks for a specific math topic?

Yes, the list is organized by topic, making it easy to find textbooks on a specific math concept or subject. It also includes information on the level, publisher, and publication year of each textbook, making it easier to choose the most appropriate one.

Is "A Cumulative List of Math Textbooks" limited to textbooks in English?

No, the list includes textbooks in various languages, such as Spanish, French, and German. However, the majority of the textbooks are in English, as it is the most widely used language in math education.

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