### Post by Angelino Desmet on Oct 18, 2018 15:08:12 GMT

Source: github.com/ystael/chicago-ug-math-bib (which I found on Reddit)

What follows are

Elementary math ([HASH]elementary_math)

[HASH]algebra

[HASH]geometry

[HASH]foundations

[HASH]problemsolving

[HASH]calculus

Intermediate math ([HASH]intermediate_math)

[HASH]foundations

[HASH]abstract_algebra

[HASH]linear_algebra

[HASH]number_theory

[HASH]combinatorics [HASH]discrete_math

[HASH]multivariable_calculus [HASH]calculus

[HASH]differential_equations [HASH]calculus

[HASH]real_analysis

[HASH]complex_analysis

[HASH]point_set_topology

[HASH]geometry

[HASH]differential_geometry

Advanced math ([HASH]advanced_math)

[HASH]foundations

[HASH]problem_solving

[HASH]abstract_algebra

[HASH]group_theory

[HASH]ring_theory

[HASH]commutative_algebra [HASH]homological_algebra

[HASH]number_theory

[HASH]combinatorics [HASH]discrete_math

[HASH]measure_theory

[HASH]probability

[HASH]functional_analysis

[HASH]complex_analysis

[HASH]harmonic_analysis

[HASH]differential_equations

[HASH]differential_topology

[HASH]algebraic_topology

[HASH]differential_geometry

[HASH]geometric_measure_theory

[HASH]algebraic_geometry

This is an annotated bibliography of books that may be useful to undergraduates in pure mathematics. I wrote the original version, with the help of some classmates, during my final year (1997-98) at the University of Chicago. To my great surprise, it has been useful to many people over the intervening years, and I am now maintaining it and accepting contributions on Github.

*only*the books mentioned, so make sure to also read the additional remarks on the former web page before reading or buying.Elementary math ([HASH]elementary_math)

[HASH]algebra

- Gelfand - Algebra: www.goodreads.com/book/show/2140100.Algebra
- Gelfand, Glagoleva, Shnol - Functions and graphs: www.goodreads.com/book/show/946674.Functions_and_Graphs
- Gelfand, Glagoleva, Kirillov - The method of coordinates: www.goodreads.com/book/show/4603880-the-method-of-coordinates

[HASH]geometry

- Euclid - The elements: www.goodreads.com/book/show/214441.Euclid_s_Elements
- Coxeter - Geometry revisted: www.goodreads.com/book/show/207954.Geometry_Revisited

[HASH]foundations

- Rucker - Infinity and the mind: www.goodreads.com/book/show/274050.Infinity_and_the_Mind

[HASH]problemsolving

- Larson - Problem solving through problems: www.goodreads.com/book/show/2146185.Problem_Solving_Through_Problem
- Pólya - How to solve it: www.goodreads.com/book/show/192221.How_to_Solve_It
- Pólya - mathematics and plausible reasoning, I and II: www.goodreads.com/book/show/19943982-mathematics-and-plausible-reasoning-v1-2

[HASH]calculus

- Spivak - Calculus: www.goodreads.com/book/show/4426208-calculus
- Spivak - The hitchhiker's guide to calculus: www.goodreads.com/book/show/862643.The_Hitchhiker_s_Guide_to_Calculus
- Hardy - A course of pure mathematics: www.goodreads.com/book/show/573330.A_Course_of_Pure_Mathematics
- Courant - Differential and integral calculus: www.goodreads.com/book/show/2298338.Differential_And_Integral_Calculus
- Apostol - Calculus:

www.goodreads.com/book/show/282035.Calculus_Volume_1,

www.goodreads.com/book/show/53798.Calculus_Volume_2

Intermediate math ([HASH]intermediate_math)

[HASH]foundations

- Halmos - Naive set theory: www.goodreads.com/book/show/558194.Naive_Set_Theory
- Fraenkel - Abstract set theory: www.goodreads.com/book/show/3146579-abstract-set-theory
- Kunen - Set theory: An introduction to independence results: www.goodreads.com/book/show/558199.Set_Theory
- Ebbinghaus, Flum, Thomas - Mathematical logic: www.goodreads.com/book/show/1768355.Mathematical_Logic
- Enderton - A mathematical introduction to logic: www.goodreads.com/book/show/250872.A_Mathematical_Introduction_to_Logic
- Chang, Keisler - Model theory: www.goodreads.com/book/show/20128440-model-theory
- Landau - Foundations of analysis: www.goodreads.com/book/show/53742.Foundations_of_Analysis

[HASH]abstract_algebra

- Dummit, Foote - Abstract algebra: www.goodreads.com/book/show/264543.Abstract_Algebra
- Herstein - Topics in algebra: www.goodreads.com/book/show/1264762.Topics_in_Algebra
- Artin - Algebra: www.goodreads.com/book/show/20063154-algebra
- Jacobson - Basic algebra I: www.goodreads.com/book/show/7812046-basic-algebra-i
- Hungerford - Algebra: www.goodreads.com/book/show/264515.Algebra_Graduate_Texts_in_Mathematics_
- Lang - Algebra: www.goodreads.com/book/show/79780.Algebra
- Mac Lane, Birkhoff - Algebra: www.goodreads.com/book/show/534605.Algebra

[HASH]linear_algebra

- Halmos - Finite dimensional vector spaces: www.goodreads.com/book/show/692030.Finite_Dimensional_Vector_Spaces
- Curtis - Abstract linear algebra: www.goodreads.com/book/show/3222801-abstract-linear-algebra
- Greub - Linear algebra: www.goodreads.com/book/show/3703166-linear-algebra
- Greub - Multilinear algebra: www.goodreads.com/book/show/4548514-multilinear-algebra

[HASH]number_theory

- Ireland, Rosen - A classical introduction to modern number theory: www.goodreads.com/book/show/585557.A_Classical_Introduction_to_Modern_Number_Theory_Graduate_Texts_in_Mathematics_
- Burn - A pathway into number theory: www.goodreads.com/book/show/1977970.A_Pathway_Into_Number_Theory
- Hardy, Wright - An introduction to the theory of numbers theory: www.goodreads.com/book/show/585623.An_Introduction_to_the_Theory_of_Numbers
- Chandrasekharan - Introduction to analytic number theory: www.goodreads.com/book/show/15911641-introduction-to-analytic-number-theory
- Apostol - Introduction to analytic number theory: www.goodreads.com/book/show/241408.Introduction_to_Analytic_Number_Theory

[HASH]combinatorics [HASH]discrete_math

- Graham, Knuth, Patashnik - Concrete mathematics: www.goodreads.com/book/show/112243.Concrete_Mathematics

[HASH]multivariable_calculus [HASH]calculus

- Spivak - Calculus on manifolds: www.goodreads.com/book/show/328647.Calculus_On_Manifolds
- Do Carmo - Differential forms and applications: www.goodreads.com/book/show/233053.Differential_Forms_and_Applications

[HASH]differential_equations [HASH]calculus

- Arnold - Ordinary differential equations: www.goodreads.com/book/show/1115400.Ordinary_Differential_Equations
- Hurewicz - Lectures on ordinary differential equations: www.goodreads.com/book/show/3637626-lectures-on-ordinary-differential-equations

[HASH]real_analysis

- Rudin - Principles of mathematical analysis: www.goodreads.com/book/show/292079.Principles_of_Mathematical_Analysis
- Apostol - Mathematical analysis: www.goodreads.com/book/show/53800.Mathematical_Analysis
- Gelbaum, Olmsted - Counterexamples in analysis: www.goodreads.com/book/show/818070.Counterexamples_in_Analysis
- Kolmogorov, Fomin - Introductory real analysis: www.goodreads.com/book/show/218517.Introductory_Real_Analysis
- Haaser, Sullivan - Real analysis: www.goodreads.com/book/show/3459109-real-analysis
- Hewitt, Stromberg - Real and abstract analysis: www.goodreads.com/book/show/3992197-real-and-abstract-analysis
- Dieudonné - Foundations of modern analysis: www.goodreads.com/book/show/6520344-foundations-of-modern-analysis
- Rudin - Real and complex analysis: www.goodreads.com/book/show/1039015.Real_and_Complex_Analysis
- Lang - Real and functional analysis: www.goodreads.com/book/show/3395988-real-and-functional-analysis-graduate-texts-in-mathematics
- Royden - Real analysis: www.goodreads.com/book/show/218522.Real_Analysis

[HASH]complex_analysis

- Ahlfors - Complex analysis: www.goodreads.com/book/show/2437190.Complex_Analysis
- Conway - Functions of one complex variable I: www.goodreads.com/book/show/19318638-functions-of-one-complex-variable-i
- Narasimhan - Complex analysis in one variable: www.goodreads.com/book/show/18565987-complex-analysis-in-one-variable
- Rudin, Real and complex analysis: www.goodreads.com/book/show/1039015.Real_and_Complex_Analysis
- Palka - An introduction to complex function theory: www.goodreads.com/book/show/1825029.An_Introduction_to_Complex_Function_Theory

[HASH]point_set_topology

- Munkres - Topology: a first course: www.goodreads.com/book/show/1894071.Topology
- Willard - General topology: www.goodreads.com/book/show/116423.General_Topology
- Kelley - General topology: www.goodreads.com/book/show/2118994.General_Topology
- Steen, Seebach - Counterexamples in topology: www.goodreads.com/book/show/116419.Counterexamples_in_Topology
- Dugundji - Topology: www.goodreads.com/book/show/1503831.Topology
- Armstrong - Basic Topology: www.goodreads.com/book/show/10149070-basic-topology
- Simmons - Introduction to Topology and Modern Analysis: www.goodreads.com/book/show/208761.Intro_Topology_Modern_Analysis

[HASH]geometry

- Coxeter - Introduction to geometry: www.goodreads.com/book/show/207951.Introduction_to_Geometry
- Hilbert - Foundations of geometry: www.goodreads.com/book/show/1635912.The_Foundations_of_Geometry
- Hartshorne - Geometry: Euclid and beyond: www.goodreads.com/book/show/214443.Geometry

[HASH]differential_geometry

- Guillemin, Pollack - Differential topology: www.goodreads.com/book/show/1246834.Differential_Topology
- Do Carmo, Differential geometry of curves and surfaces: www.goodreads.com/book/show/211190.Differential_Geometry_of_Curves_and_Surfaces
- Spivak - A comprehensive introduction to differential geometry, 1 and 2:

www.goodreads.com/book/show/211192.A_Comprehensive_Introduction_to_Differential_Geometry_Vol_1,

www.goodreads.com/book/show/410814.A_Comprehensive_Introduction_to_Differential_Geometry_Volume_2?ac=1&from_search=true

Advanced math ([HASH]advanced_math)

[HASH]foundations

- Mac Lane - Categories for the working mathematician: www.goodreads.com/book/show/1088482.Categories_for_the_Working_Mathematician
- Jech - Set Theory: www.goodreads.com/book/show/558195.Set_Theory
- Foreman, Kanamori, et al - Handbook of Set Theory: www.goodreads.com/book/show/6698683-handbook-of-set-theory-3-volume-set

[HASH]problem_solving

- Pólya, Szegö - Problems and theorems in analysis I and II:

www.goodreads.com/book/show/1894050.Problems_and_Theorems_in_Analysis_I,

www.goodreads.com/book/show/1874241.Problems_and_Theorems_in_Analysis_II

[HASH]abstract_algebra

- Jacobson - Basic algebra II: www.goodreads.com/book/show/20681530-basic-algebra-ii

[HASH]group_theory

- Alperin, Bell - Groups and representations: www.goodreads.com/book/show/2855410-groups-and-representations
- Rotman - Introduction to the theory of groups: www.goodreads.com/book/show/558480.An_Introduction_to_the_Theory_of_Groups
- Gorenstein - Finite groups: www.goodreads.com/book/show/11495195-finite-groups
- Humphreys - Introduction to Lie algebras and representation theory: www.goodreads.com/book/show/1825026.Introduction_to_Lie_Algebras_and_Representation_Theory
- Fulton, Harris - Representation theory: a first course: www.goodreads.com/book/show/585309.Representation_Theory

[HASH]ring_theory

- Kaplansky - Fields and rings: www.goodreads.com/book/show/2604440-fields-and-rings
- Anderson, Fuller - Rings and categories of modules: www.goodreads.com/book/show/2074932.Rings_and_Categories_of_Modules
- Morandi - Field and Galois theory: www.goodreads.com/book/show/241206.Field_and_Galois_Theory
- Lam - A first course in noncommutative rings: www.goodreads.com/book/show/5736258-a-first-course-in-noncommutative-rings

- Atiyah, Macdonald - Introduction to commutative algebra: www.goodreads.com/book/show/1549790.Introduction_To_Commutative_Algebra
- Matsumura - Commutative ring theory: www.goodreads.com/book/show/2304602.Commutative_Ring_Theory
- Eisenbud - Commutative algebra with a view toward algebraic geometry: www.goodreads.com/book/show/1969546.Commutative_Algebra
- Kaplansky - Commutative rings: www.goodreads.com/book/show/3423833-commutative-rings
- Weibel - An introduction to homological algebra: www.goodreads.com/book/show/1331929.An_Introduction_to_Homological_Algebra

[HASH]number_theory

- Weil - Basic number theory: www.goodreads.com/book/show/587109.Basic_Number_Theory
- Narkiewicz - Introduction to the elementary and analytic theory of algebraic numbers: www.goodreads.com/book/show/1788180.Elementary_and_Analytic_Theory_of_Algebraic_Numbers
- Silverman - The arithmetic of elliptic curves: www.goodreads.com/book/show/174316.The_Arithmetic_of_Elliptic_Curves
- Koblitz - p-adic numbers, p-adic analysis, and zeta functions: www.goodreads.com/book/show/753815.p_adic_Numbers_p_adic_Analysis_and_Zeta_Functions_Graduate_Texts_in_Mathematics_
- Fröhlich, Taylor - Algebraic number theory: www.goodreads.com/book/show/3460031-algebraic-number-theory

- Lovasz - Combinatorial problems and exercises: www.goodreads.com/book/show/2382199.Combinatorial_Problems_and_Exercises_AMS_Chelsea_Publishing_
- Stanley - Enumerative combinatorics I: www.goodreads.com/book/show/18791495-enumerative-combinatorics
- Bollobás - Modern graph theory: www.goodreads.com/book/show/388048.Modern_Graph_Theory

[HASH]measure_theory

- Halmos - Measure theory: www.goodreads.com/book/show/743983.Measure_Theory
- Federer - Geometric measure theory: www.goodreads.com/book/show/2278402.Geometric_Measure_Theory

[HASH]probability

- Feller - Introduction to probability theory and its applications:

www.goodreads.com/book/show/2378167.An_Introduction_to_Probability_Theory_and_Its_Applications_Volume_1

www.goodreads.com/book/show/746145.An_Introduction_to_Probability_Theory_and_Its_Applications_Volume_II

[HASH]functional_analysis

- Conway - A course in functional analysis: www.goodreads.com/book/show/1472955.A_Course_in_Functional_Analysis
- Dunford, Schwartz - Linear operators:

www.goodreads.com/book/show/2195562.Linear_Operators_Part_1,

www.goodreads.com/book/show/2195563.Linear_Operators_Part_2,

www.goodreads.com/book/show/2195561.Linear_Operators_Part_3 - Kadison, Ringrose - Fundamentals of the theory of operator algebras:

www.goodreads.com/book/show/1710331.Fundamentals_of_the_Theory_of_Operator_Algebras_Volume_I,

www.goodreads.com/book/show/1710329.Fundamentals_of_the_Theory_of_Operator_Algebras_Volume_II,

www.goodreads.com/book/show/8179519-fundamentals-of-the-theory-of-operator-algebras-volume-iii,

www.goodreads.com/book/show/1710336.Fundamentals_of_the_Theory_of_Operator_Algebras_Volume_IV - Kreyszig - Introductory functional analysis with applications: www.goodreads.com/book/show/241452.Introductory_Functional_Analysis_with_Applications
- Zimmer - Essential Results of Functional Analysis: www.goodreads.com/book/show/5440626-essential-results-of-functional-analysis

[HASH]complex_analysis

- Andersson - Topics in complex analysis: www.goodreads.com/book/show/3516869-topics-in-complex-analysis
- Gunning, Rossi - Analytic functions of several variables: www.goodreads.com/book/show/7147564-analytic-functions-of-several-complex-variables
- Whitney - Complex analytic varieties: www.goodreads.com/book/show/31297342-complex-analytic-varieties
- Narasimhan - Compact Riemann surfaces: www.goodreads.com/book/show/3913058-compact-riemann-surfaces
- Jost - Compact Riemann surfaces: www.goodreads.com/book/show/2581888-compact-riemann-surfaces
- Weyl - The concept of a Riemann surface: www.goodreads.com/book/show/6206794-the-concept-of-a-riemann-surface

[HASH]harmonic_analysis

- Katznelson - An introduction to harmonic analysis: www.goodreads.com/book/show/600474.An_Introduction_to_Harmonic_Analysis
- Rudin - Fourier analysis on groups: www.goodreads.com/book/show/148572.Fourier_Analysis_on_Groups
- Hewitt, Ross - Abstract harmonic analysis: www.goodreads.com/book/show/5852764-abstract-harmonic-analysis
- Stein, Weiss - Introduction to Fourier analysis on Euclidean spaces: www.goodreads.com/book/show/30082488-introduction-to-fourier-analysis-on-euclidean-spaces-pms-32-volume-32
- Helgason - Groups and geometric analysis: www.goodreads.com/book/show/4481022-groups-and-geometric-analysis-integral-geometry-invariant-differential

[HASH]differential_equations

- Taylor - Partial differential equations I: basic theory: www.goodreads.com/book/show/6715867-partial-differential-equations-i
- Evans, Partial differential equations: www.goodreads.com/book/show/7993898-partial-differential-equations
- Hörmander - The analysis of linear partial differential operators I: www.goodreads.com/book/show/2720260-the-analysis-of-linear-partial-differential-operators-i
- Olver - Equivalence, invariants and symmetry: www.goodreads.com/book/show/3353230-equivalence-invariants-and-symmetry

[HASH]differential_topology

- Hirsch - Differential topology: www.goodreads.com/book/show/1688091.Differential_Topology
- Lang - Differential and Riemannian manifolds: www.goodreads.com/book/show/737509.Differential_and_Riemannian_Manifolds
- Warner - Foundations of differentiable manifolds and Lie groups: www.goodreads.com/book/show/12428059-foundations-of-differentiable-manifolds-and-lie-groups

[HASH]algebraic_topology

- Massey - A basic course in algebraic topology: www.goodreads.com/book/show/116424.A_Basic_Course_in_Algebraic_Topology
- Fulton - Algebraic topology: a first course: www.goodreads.com/book/show/1076691.Algebraic_Topology
- Bott, Tu - Differential forms in algebraic topology: www.goodreads.com/book/show/1246831.Differential_Forms_in_Algebraic_Topology
- Spanier - Algebraic topology: www.goodreads.com/book/show/4113534-algebraic-topology
- Rotman - An introduction to algebraic topology: www.goodreads.com/book/show/2324277.An_Introduction_to_Algebraic_Topology
- Stillwell - Classical topology and combinatorial group theory: www.goodreads.com/book/show/1669283.Classical_Topology_and_Combinatorial_Group_Theory
- Bredon - Topology and geometry: www.goodreads.com/book/show/1748333.Topology_and_Geometry

[HASH]differential_geometry

- Spivak - A comprehensive introduction to differential geometry, 3-5:

www.goodreads.com/book/show/2252071.A_Comprehensive_Introduction_to_Differential_Geometry_Volume_3,

www.goodreads.com/book/show/676934.A_Comprehensive_Introduction_to_Differential_Geometry_Volume_4,

www.goodreads.com/book/show/643246.A_Comprehensive_Introduction_to_Differential_Geometry_Volume_5 - Helgason - Differential geometry, Lie groups, and symmetric spaces: www.goodreads.com/book/show/1585857.Differential_Geometry_Lie_Groups_and_Symmetric_Spaces
- Kobayashi, Nomizu - Foundations of differential geometry:

www.goodreads.com/book/show/211193.Foundations_of_Differential_Geometry_Volume_1,

www.goodreads.com/book/show/6984384-foundations-of-differential-geometry-volume-2 - Rosenberg - The Laplacian on a Riemannian manifold: www.goodreads.com/book/show/2324280.The_Laplacian_on_a_Riemannian_Manifold
- Do Carmo - Riemannian geometry: www.goodreads.com/book/show/233052.Riemannian_Geometry
- Boothby - Introduction to differentiable manifolds and Riemannian geometry: www.goodreads.com/book/show/683585.An_Introduction_to_Differentiable_Manifolds_and_Riemannian_Geometry_Revised

[HASH]geometric_measure_theory

- Morgan - Geometric measure theory: a beginner's guide: www.goodreads.com/book/show/6455214-geometric-measure-theory
- Mattila - Geometry of sets and measures on Euclidean spaces: www.goodreads.com/book/show/558168.Geometry_of_Sets_and_Measures_in_Euclidean_Spaces
- Federer - Geometric measure theory: www.goodreads.com/book/show/2278402.Geometric_Measure_Theory
- Falconer - The geometry of fractal sets: www.goodreads.com/book/show/558112.The_Geometry_of_Fractal_Sets

[HASH]algebraic_geometry

- Harris - Algebraic geometry: a first course: www.goodreads.com/book/show/1861684.Algebraic_Geometry
- Shafarevich - Basic algebraic geometry 1: www.goodreads.com/book/show/1642686.Basic_Algebraic_Geometry_Volume_1
- Mumford - Algebraic geometry I: complex projective varieties: www.goodreads.com/book/show/2017827.Algebraic_Geometry_I
- Griffiths, Harris - Principles of algebraic geometry: www.goodreads.com/book/show/1690529.Principles_of_Algebraic_Geometry
- Hartshorne - Algebraic geometry: www.goodreads.com/book/show/338302.Algebraic_Geometry