### Post by Priem19 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

Algebra

Geometry

Foundations

Problemsolving

Calculus

Intermediate math

Foundations

Abstract algebra

Linear algebra

Number theory

Combinatorics, discrete math

Multivariable calculus

Differential equations

Real analysis

Complex analysis

Point set topology

Geometry

Differential geometry

Advanced math

Foundations

Problem solving

Abstract algebra

Group theory

Ring theory

Commutative algebra, Homological algebra

Number theory

Combinatorics, discrete math

Measure theory

Probability

Functional analysis

Complex analysis

Harmonic analysis

Differential equations

Differential topology

Algebraic topology

Differential geometry

Geometric measure theory

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

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

Geometry

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

Foundations

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

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

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

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

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

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

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

Combinatorics, discrete math

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

Multivariable 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

Differential equations

- 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

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

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

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

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

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

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

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

Abstract algebra

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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