What Topics Does Hassani Cover in His Favorite Mathematical Book?

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Discussion Overview

The discussion centers around the topics covered in a favorite mathematical book mentioned by a participant named Hassani. It encompasses a wide range of mathematical fields, including abstract algebra, algebraic geometry, analysis, applied mathematics, calculus, classical geometry, differential equations, differential geometry, discrete mathematics, foundations of mathematics, high-school mathematics, linear algebra, number theory, probability and statistics, topology, and various other mathematical subjects.

Discussion Character

  • Exploratory
  • Technical explanation

Main Points Raised

  • Some participants list various mathematical texts across multiple disciplines, such as Aluffi's "Algebra: Chapter 0" and Artin's "Algebra" in the field of abstract algebra.
  • Others mention notable works in algebraic geometry, including Harris's "Algebraic Geometry: A First Course" and Hartshorne's "Algebraic Geometry."
  • In analysis, participants reference texts like Brown and Churchill's "Complex Variables and Applications" and Rudin's "Principles of Mathematical Analysis."
  • Applied mathematics is represented by books such as Arfken, Weber, and Harris's "Mathematical Methods for Physicists."
  • Calculus is covered with titles like Apostol's "Calculus" and Stewart's "Calculus Series."
  • Participants also highlight works in differential equations, such as Arnold's "Ordinary Differential Equations," and differential geometry, including Do Carmo's "Riemannian Geometry."
  • Discrete mathematics is represented by Graham, Knuth, and Patashnik's "Concrete Mathematics: A Foundation for Computer Science."
  • Foundational texts like Halmos's "Naive Set Theory" and Houston's "How to Think Like a Mathematician" are also mentioned.
  • Several participants provide links to discussions or threads related to these texts, indicating a collaborative exploration of the subject matter.

Areas of Agreement / Disagreement

There is no consensus on a single favorite book or topic, as participants present a variety of texts and subjects, indicating multiple competing views and preferences.

Contextual Notes

The discussion reflects a broad interest in various mathematical areas without delving into specific methodologies or applications of the texts mentioned. The lack of detailed exploration into each book's content leaves open questions about their comparative significance or relevance to different mathematical concepts.

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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
 
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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.
 
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.
 
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.
 
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