United States

Course Title:

MATHEMATICS AND STATISTICS

Course Definition:

Instructional programs that focus on the systematic study of logical symbolic language and its applications.

Course Sub Families Description:

For description refer the sub course(s)

#### Mathematics, General.

A general program that focuses on the analysis of quantities, magnitudes, forms, and their relationships, using symbolic logic and language. Includes instruction in algebra, calculus, functional analysis, geometry, number theory, logic, topology and other mathematical specializations.

##### Connected Careers

#### Algebra and Number Theory.

A program that focuses on the expression of quantities and their relationships by means of symbols, vectors, matrices, and equations, and the properties of integers. Includes instruction in algebraic structures, quadratic and automorphic forms, combinatorics, linear algebra, and algebraic geometry.

##### Connected Careers

#### Analysis and Functional Analysis.

A program that focuses on the properties and behavior of equations, multivariate solutions, functions, and dynamic systems. Includes instruction in differential equations, variation, approximations, complex variables, integrals, harmonic analysis and wavelet theory, dynamic systems, and applications to mathematical physics.

##### Connected Careers

#### Geometry/Geometric Analysis.

A program that focuses on the properties, measurements, and relationships pertaining to points, lines, angles, surfaces, and solids. Includes instruction in global analysis, differential geometry, Euclidian and Non-Euclidian geometry, set theory, manifolds, integral geometry, and applications to algebra and other topics.

##### Connected Careers

#### Topology and Foundations.

A program that focuses on the properties of unaltered geometric configurations under conditions of continuous, multi-directional transformations. Includes instruction in mathematical logic, proof theory, model theory, set theory, combinatorics, continua, homotopy, homology, links, and transformation actions.

##### Connected Careers

#### Mathematics, Other.

Any program in mathematics not listed above.

##### Connected Careers

For description refer the sub course(s)

#### Applied Mathematics, General.

A program that focuses on the application of mathematics to the solution of functional problems in fields such as engineering and the applied sciences. Includes instruction in natural phenomena modeling continuum mechanics, reaction-diffusion, wave propagation, dynamic systems, numerical analysis, controlled theory, asymptotic methods, variation, optimization theory, inverse problems, and applications to specific scientific and industrial topics.

##### Connected Careers

#### Computational Mathematics.

A program that focuses on the application of mathematics to the theory, architecture, and design of computers, computational techniques, and algorithms. Includes instruction in computer theory, cybernetics, numerical analysis, algorithm development, binary structures, combinatorics, advanced statistics, and related topics.

##### Connected Careers

#### Computational and Applied Mathematics.

A program that focuses on the application of a broad range of mathematical and computational methods to modeling, analysis, algorithm development, and simulation for the solution of complex scientific and engineering problems. Includes instruction in numerical analysis, discrete mathematics, operations research, optimization, differential equations, statistics, scientific computation, and applications to specific scientific and industrial topics.

##### Connected Careers

#### Financial Mathematics.

A program that focuses on the application of mathematics and statistics to the finance industry, including the development, critique, and use of various financial models. Includes instruction in probability theory, statistical analysis, numerical methods, computation and simulation methods, stochastic processes, economics, and financial markets and applications.

##### Connected Careers

#### Mathematical Biology.

A program that focuses on the application of mathematics to genomics, molecular modeling, structural biology, ecology, evolutionary biology and systems of analysis of neurobiology, physiology, and metabolism. Includes instruction in computational mathematics, chaos and nonlinear systems, perturbation methods, evolutionary biology, molecular biology, bioinformatics, and neurobiology.

##### Connected Careers

#### Applied Mathematics, Other.

Any instructional program in applied mathematics not listed above.

##### Connected Careers

For description refer the sub course(s)

#### Statistics, General.

A general program that focuses on the relationships between groups of measurements, and similarities and differences, using probability theory and techniques derived from it. Includes instruction in the principles in probability theory, binomial distribution, regression analysis, standard deviation, stochastic processes, Monte Carlo method, Bayesian statistics, non-parametric statistics, sampling theory, and statistical techniques.

##### Connected Careers

#### Mathematical Statistics and Probability.

A program that focuses on the mathematical theory underlying statistical methods and their use. Includes instruction in probability theory parametric and non-parametric inference, sequential analysis, multivariate analysis, Bayesian analysis, experimental design, time series analysis, resampling, robust statistics, limit theory, infinite particle systems, stochastic processes, martingales, Markov processes, and Banach spaces.

##### Connected Careers

#### Mathematics and Statistics.

A program with a general synthesis of mathematics and statistics or a specialization which draws from mathematics and statistics. Includes instruction in calculus, linear algebra, numerical analysis and partial differential equations, discrete mathematics, probability theory, statistics, computing, and other related topics.

##### Connected Careers

#### Statistics, Other.

Any instructional program in statistics not listed above.

##### Connected Careers

For description refer the sub course(s)

#### Applied Statistics, General.

A program that focuses on the application of statistics to the solution of functional problems in fields such as business, engineering, medicine, and the applied sciences. Includes instruction in the principles in inference, probability theory, regression analysis, descriptive statistics, stochastic processes, Monte Carlo method, Bayesian statistics, non-parametric statistics, sampling theory, statistical computing, and statistical techniques.

##### Connected Careers

For description refer the sub course(s)

#### Mathematics and Statistics, Other.

Any instructional program in mathematics and statistics not listed above.

##### Connected Careers

Note* - Course Data Adopted from the Classification of Instructional Programs (CIP)