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	Index using M.A.A. Basic Library List

Here are the top-level areas of mathematics and related fields classified according to the Mathematical Association of America for the construction of their "Basic Library List". (Accompanying that list is a collection of selected texts and reference works for the different areas, usually at the undergraduate level.)

Note that this system is not necessarily geared towards complete coverage of advanced mathematics; indeed, several of the areas are not really distinct areas of mathematics at all but introductions to the applications of certain mathematical techniques to various other fields of study. The system used more commonly among mathematicians is the Mathematics Subject Classification (MSC) scheme, which is the basis for the organization of materials at this site; some of the topics below will then not correspond very closely to any of the index pages here.

[No links are yet provided from the list below to the index pages at this site; sorry.]

Major Headings:

• General
• Reference
• History
• Recreational Mathematics
• Education
• Calculus and Precalculus
• Differential Equations
• Analysis
• Foundations and Mathematical Logic
• Discrete Math
• Number Theory
• Linear Algebra
• Algebra
• Geometry
• Topology
• Vocational and Technical Mathematics
• Business Mathematics
• Number Analysis
• Modeling and Operations Research
• Probability
• Statistics
• Computer Science
• Applications to Life Sciences
• Applications to Physical Sciences
• Applications to Social Sciences

General

• General Anthologies
• Elementary Exposition
• Advanced Surveys
• Mathematics Appreciation Texts
• Fiction, Aphorisms, Epigrams
• Miscellany

Reference

• Dictionaries
• Handbooks
• Encyclopedias
• Bibliographies
• Indexes
• Reviews
• International Congresses

History

• Surveys
• Biographies
• Source Books
• Classic Works
• Ancient and Medieval
• Modern
• Numbers
• Algebra
• Calculus and Analysis
• Geometry
• Probability and Statistics
• Computers
• Physics and Astronomy

Recreational Mathematics

• Surveys
• Games and Puzzles
• Puzzle Collections
• Contests and Problems
• Martin Gardner
• Miscellany

Education

• Policy
• Philosophy
• Psychology
• Culture
• History
• Curriculum and Instruction
• Elementary Education
• Secondary Education
• Undergraduate Education
• Minorities and Women
• Problem Solving
• Research and Research Summaries
• Studies and Assessment
• Computers and Technology

Calculus and Precalculus

• School Mathematics
• Precalculus
• Elementary Calculus
• Advanced Calculus
• Supplementary Resources

Differential Equations

• Introductory Texts
• Ordinary Differential Equations
• Dynamical Systems
• Partial Differential Equations
• Boundary Value Problems
• Special Topics

Analysis

• Foundations of Analysis
• Elementary Real Analysis
• Advanced Real Analysis
• Fourier Analysis
• Fractals
• Introductory Complex Analysis
• Advanced Complex Analysis
• Functional Analysis
• Operator Theory
• Calculus of Variations
• Inequalities
• Harmonic Analysis
• Lie Groups and Symmetric Spaces
• Nonstandard Analysis
• Special Functions

Foundations and Mathematical Logic

• Surveys
• Logic
• Mathematical Logic
• Philosophy of Mathematics
• Set Theory
• Computability
• Model Theory
• Nonclassical Logic
• Special Topics

Discrete Mathematics

• Discrete Mathematics
• Finite Mathematics
• Introductory Combinatorics
• Advanced Combinatorics
• Graph Theory
• Coding Theory
• Special Topics

Number Theory

• Introductory Texts
• Expositions
• Elementary Monographs
• Primes and Factors
• Algebraic Number Theory
• Analytic Number Theory
• Modular Forms
• P-adic Fields
• Special Topics

Linear Algebra

• Elementary
• Advanced
• Matrix Theory
• Special Topics

Algebra

• Introductory Surveys
• Constructive and Computational Algebra Applied Algebra
• Advanced Surveys
• Group Theory
• Rings and Ideals
• Fields and Galois Theory
• Commutative Algebra
• Homological Algebra
• Category Theory
• Lie Algebras
• Universal Algebra
• Special Topics

Geometry

• General
• Surveys
• School Geometry
• Euclidean and Non-Euclidean Geometry Polyhedra, Tilings, Symmetry
• Geometric Transformations
• Projective Geometry
• Computational Geometry
• Discrete and Combinatorial Geometry
• Differential Geometry
• Algebraic Geometry
• Special Topics

Topology

• General Topology
• Geometric Topology
• Algebraic Topology
• Differential Topology

Vocational and Technical Mathematics

• Industrial Mathematics
• Mathematics for Trades
• Health Sciences
• Data Processing
• Electronics
• Chemical Technology
• Engineering Technology

Business Mathematics

• Basic Skills
• Algebra and Finite Mathematics
• Business Statistics
• Business Calculus
• Finance
• Management
• Introductory Actuarial Mathematics
• Advanced Actuarial Mathematics

Numerical Analysis

• Introductory Texts
• Advanced Surveys
• Differential Equations
• Numerical Linear Algebra
• Approximation Theory
• Computer Methods
• Special Topics

Modeling and Operations Research

• General
• Mathematical Modeling
• Stochastic Modeling and Dynamic Programming Game Theory
• Linear Programming
• Nonlinear Programming
• Integer Programming
• Queueing Theory
• Simulation
• Control Theory

Probability

• General
• Elementary
• Advanced
• Stochastic Processes
• Foundations
• Measure Theory
• Fuzzy Sets
• Special Topics

Statistics

• General
• Introductory Texts
• Elementary
• Intermediate
• Advanced
• Data Analysis
• Bayesian Methods
• Computational Statistics
• Linear Models and Regression Analysis Multivariate Analysis
• Nonparametric Statistics
• Experimental Design
• Sampling and Survey Design
• Quality Control
• Time Series
• Special Topics

Computer Science

• Computer Literacy
• Computers and Society
• Introductory
• Data Structures
• Database Systems
• Programming
• Programming Languages
• Algorithms
• Theory of Computation
• Software Systems
• Artificial Intelligence
• Communications
• Mathematical Typography
• Software Engineering
• Automata
• Compilers and Translators
• Computer Architecture
• Computer Graphics

Applications to Life Sciences

• General
• Ecology
• Epidemiology
• Genetics
• Population Biology
• Physiology
• Medicine
• Special Topics

Applications to Physical Sciences

• General
• Introductory Texts
• Advanced Surveys
• Elasticity and Solid Mechanics
• Quantum Mechanics
• Mechanics
• Relativity
• Cosmology and Celestial Mechanics
• Fluids
• Waves
• Tensor Analysis
• Information Theory
• Special Topics

Applications to Social Sciences

• General
• Economics
• Political Science
• Psychology
• Sociology

Copyright ©1998 The Mathematical Association of America