What Topics Does Hassani Cover in His Favorite Mathematical Book?

[micromass]

Abstract Algebra
Aluffi - Algebra: Chapter 0
Artin - Algebra
Dummit, Foote - Abstract Algebra
https://www.physicsforums.com/showthread.php?t=704700
https://www.physicsforums.com/showthread.php?t=704865
https://www.physicsforums.com/showthread.php?t=672385
Herstein - Topics in Algebra
Hungerford - Algebra
Isaacs - Algebra: A Graduate Course
https://www.physicsforums.com/showthread.php?t=704702
https://www.physicsforums.com/showthread.php?t=669162
Knapp - Advanced Algebra
https://www.physicsforums.com/showthread.php?t=672085
Lang - Algebra
https://www.physicsforums.com/showthread.php?t=666712
Pinter - A book of Abstract Algebra

Algebraic Geometry
Harris - Algebraic Geometry: A First Course
Hartshorne - Algebraic Geometry
Miranda - Algebraic Curves and Riemann Surfaces

Analysis
https://www.physicsforums.com/showthread.php?t=669335
https://www.physicsforums.com/showthread.php?t=666087
https://www.physicsforums.com/showthread.php?t=666447
Brown, Churchill - Complex Variables and Applications
Carothers - Real Analysis
Cohn - Measure Theory
Demidovich - Problems in Mathematical Analysis
https://www.physicsforums.com/showthread.php?t=669579
https://www.physicsforums.com/showthread.php?t=704973
https://www.physicsforums.com/showthread.php?t=672082
Knapp - Basic Real Analysis
https://www.physicsforums.com/showthread.php?t=671469
Kreyszig - Introductory Functional Analysis with Applications
Lang - Complex Analysis
Lang - Real and Functional Analysis
Lang - Undergraduate Analysis
Marsden, Hoffman - Basic Complex Analysis
Markushevich - Theory of Functions of a Complex Variable
Mattuck - Introduction to Analysis
Mitrinovic - Calculus on Residues
Needham - Visual Complex Analysis
https://www.physicsforums.com/showthread.php?t=666715
https://www.physicsforums.com/showthread.php?t=672386
Reed, Simon - Functional Analysis
https://www.physicsforums.com/showthread.php?t=704968
Riesz, Sz.-Nagy - Functional Analysis
https://www.physicsforums.com/showthread.php?t=669334
Ross - Elementary Analysis: The Theory of Calculus
Rudin - Principles of Mathematical Analysis
Rudin - Real and Complex Analysis
Simmons - Introduction to Topology and Modern Analysis
Spivak - Calculus on Manifolds
Stein, Shakarchi - Complex Analysis
https://www.physicsforums.com/showthread.php?t=666754
Stein, Shakarchi - Functional Analysis: Introduction to Further Topics in Analysis
https://www.physicsforums.com/showthread.php?t=666756
Volkovyskii, Lunts, Aramanovich - A Collection of Problems on Complex Analysis
https://www.physicsforums.com/showthread.php?t=671467
Zimmer - Essential Results of Functional Analysis

Applied Mathematics and Mathematical Methods
Arfken, Weber, Harris - Mathematical Methods for Physicists
Boas - Mathematical Methods in the Physical Sciences
Courant, Hilbert - Methods of Mathematical Physics
https://www.physicsforums.com/showthread.php?t=665605
https://www.physicsforums.com/showthread.php?t=666390

Calculus
Angenent, Maxim, Robbin - UW Calculus
Anton - Calculus Series
Apostol - Calculus
Comenetz - Calculus: The Elements
Courant - Differential and Integral Calculus
Inouye - Introductory Calculus For Infants
Keisler - Elementary Calculus: An Approach Using Infinitesimals
https://www.physicsforums.com/showthread.php?t=704967
Hubbard, Hubbard - Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach
Hughes-Hallett et al. - Calculus: Single and Multivariable
Kline - Calculus: An Intuitive and Physical Approach
Lang - A First Course in Calculus
https://www.physicsforums.com/showthread.php?t=666704
Larson - Calculus Series
Salas, Etgen, Hille - Calculus: One and Several Variables
https://www.physicsforums.com/showthread.php?t=666396
Spivak - Calculus
Stewart - Calculus Series
https://www.physicsforums.com/showthread.php?t=704965
Thompson - Calculus Made Easy
Varberg, Purcell, Rigdon - Calculus

Classical Geometry
Apostol, Mnatsakanian - New Horizons in Geometry
Coxeter, Greitzer - Geometry Revisited
Euclid - Elements
Hartshorne - Geometry: Euclid and Beyond
Lang, Murrow - Geometry
Moise - Elementary Geometry from Advanced Standpoint

Differential Equations and Dynamical Systems
Arnold - Ordinary Differential Equations
https://www.physicsforums.com/showthread.php?t=665417
Bleecker, Csordas - Partial Differential Equations
https://www.physicsforums.com/showthread.php?t=665418

Differential Geometry
Burke - Applied Differential Geometry
Do Camera - Introduction to Gaussian Geometry
Do Carmo - Riemannian Geometry
Hall - Lie Groups, Lie Algebras and Representation: An Elementary Introduction
Isham - Modern Differential Geometry for Physicists
Lang - Fundamentals of Differential Geometry
Lee - Introduction to Smooth Manifolds
Lee - Riemannian Manifolds: An Introduction to Curvature
https://www.physicsforums.com/showthread.php?t=704698
https://www.physicsforums.com/showthread.php?t=704697
Spivak - A Comprehensive Introduction to Differential Geometry

Discrete Mathematics
Graham, Knuth, Patashnik - Concrete Mathematics: A Foundation for Computer Science
https://www.physicsforums.com/showthread.php?t=669573
https://www.physicsforums.com/showthread.php?t=665387
https://www.physicsforums.com/showthread.php?t=669580

Foundations: Proofs, Logic and Set Theory
Halmos - Naive Set Theory
Houston - How to Think Like a Mathematician: A Companion to Undergraduate Mathematics
https://www.physicsforums.com/showthread.php?t=667713
Kamke - Theory of Sets
Smith - A Transition to Advanced Mathematics

High-School Mathematics
Lang - Basic Mathematics
https://www.physicsforums.com/showthread.php?t=668628
Loney - The Elements of Coordinate Geometry
https://www.physicsforums.com/showthread.php?t=665359
https://www.physicsforums.com/showthread.php?t=704864

Linear Algebra
https://www.physicsforums.com/showthread.php?t=666081
Anton - Elementary Linear Algebra
Axler - Linear Algebra Done Right
Bretscher - Linear Algebra with Applications
Friedberg, Insel, Spence - Linear Algebra
Halmos - Finite-Dimensional Vector Spaces
Hefferon - Linear Algebra
https://www.physicsforums.com/showthread.php?t=666472
Lang - Introduction to Linear Algebra
Lang - Linear Algebra
Poole - Linear Algebra: A Modern Introduction
Roman - Advanced Linear Algebra
Shilov - Linear Algebra
Strang - Introduction to Linear Algebra

Number Theory
Hardy, Wright - An Introduction to the Theory of Numbers
https://www.physicsforums.com/showthread.php?t=668635
https://www.physicsforums.com/showthread.php?t=665362

Probability and Statistics
Bean - Probability: The Science of Uncertainty
https://www.physicsforums.com/showthread.php?t=704843
https://www.physicsforums.com/showthread.php?t=704838
https://www.physicsforums.com/showthread.php?t=704844
Feller - An Introduction to Probability Theory and Its Applications
Hamilton - Time Series Analysis
https://www.physicsforums.com/showthread.php?t=704841
https://www.physicsforums.com/showthread.php?t=704847
Moore - The Basic Practice of Statistics
Ross - A First Course in Probability
https://www.physicsforums.com/showthread.php?t=704839
https://www.physicsforums.com/showthread.php?t=665777
https://www.physicsforums.com/showthread.php?t=665558
Tsokos - Probability for Engineering, Mathematics and Sciences
https://www.physicsforums.com/showthread.php?t=704845
https://www.physicsforums.com/showthread.php?t=704846

Topology
Bott, Tu - Differential Forms in Algebraic Topology
Lee - Introduction to Topological Manifolds
Mendelson - Introduction to Topology
Milnor - Topology from the Differentiable Viewpoint
Munkres - Topology
Simmons - Introduction to Topology and Modern Analysis
Steen, Seebach - Counterexamples in Topology
https://www.physicsforums.com/showthread.php?t=665466

Varia
https://www.physicsforums.com/showthread.php?t=678827
Andreescu, Andrica - Complex Numbers from A to ...Z
https://www.physicsforums.com/showthread.php?t=666925
Courant - What is Mathematics? An Elementary Approach to Ideas and Methods
https://www.physicsforums.com/showthread.php?t=666393
https://www.physicsforums.com/showthread.php?t=666397
Lipschutz, Spiegel, Liu - Schaum's Outline of Mathematical Handbook of Formulas and Tables
Loyd - Sam Loyd's Cyclopedia of 5000 Puzzles tricks and Conundrums with Answers
https://www.physicsforums.com/showthread.php?t=672682

 

[Vinay080]

I think you guys should add old calculus books, like that of L'Hopital's, Leibniz's collected works, Maclaurin's (Method of fluxions), Newton's (2 treatises of..quadrature..and analysis of infinite..); those are the books which speak of real matter along with the diluted one's of the more modern one's.

 

[Geofleur]

How about Sadri Hassani's book, Mathematical Physics? It could go under the applied mathematics / mathematical methods heading. It contains so much, on both the classical and the modern methods, and it's well written.

 

[vanhees71]

Hassini's book is one of my favorites. It is not only very well written, but also shows a great love of the author to his subject, giving also historical and biographical details on the mathematicians/physicists, who discovered the math needed to formulate and solve problems in theoretical physics.