Department of Mathematics

# Bachelor of Arts in Mathematics and Economics

Students on Summer 2019, Fall 2019, or Spring 2020 requirements MATHECONBA

The interdepartmental major in economics and mathematics is designed to enable students to model economic questions mathematically, and to analyze and solve those models. Students must meet the following course requirements. Any course may be replaced by the honors equivalent.

## Requirements

The major requires at least 40 credit hours*, including the requirements listed below.

**Mathematics courses.****Calculus I.**One (1) course:- MATH-M 211 Calculus I
- MATH-S 211

# MATH-M 211 Calculus I

- Credits
- 4
- Prerequisites
- None
- Notes
- R: To be successful, students will demonstrate mastery of two years of high school algebra, one year of high school geometry, and pre-calculus, and trigonometry as indicated by an appropriate ALEKS score or completion of MATH-M 027
- Description
- Limits, continuity, derivatives, definite and indefinite integrals, applications.
- Repeatability
- A student may receive credit for only one of the following: MATH-J 113, MATH-M 119, MATH-V 119, MATH-M 211, or MATH-S 211.

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**Calculus II.**One (1) course:- MATH-M 212 Calculus II
- MATH-S 212 Honors Calculus II

# MATH-M 212 Calculus II

- Credits
- 4
- Prerequisites
- MATH-M 211 or MATH-S 211; or consent of department
- Description
- Techniques of integration (by parts, trigonometric substitutions, partial fractions), improper integrals, volume, work, arc length, surface area, infinite series.
- Repeatability
- Credit given for only one of MATH-M 120 or MATH-M 212.

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# MATH-S 212 Honors Calculus II

- Credits
- 4
- Prerequisites
- MATH-S 211 or consent of department
- Description
- Includes material of MATH-M 212 and supplemental topics. Designed for students of outstanding ability in mathematics.
- Repeatability
- Credit given for only one of MATH-M 120, MATH-M 212, or MATH-S 212.

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**Linear Algebra.**One (1) course:- MATH-M 301 Linear Algebra and Applications
- MATH-M 303 Linear Algebra for Undergraduates
- MATH-S 303 Honors Course in Linear Algebra

# MATH-M 301 Linear Algebra and Applications

- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212; or MATH-M 211 and CSCI-C 241; or MATH-S 211 and CSCI-C 241
- Description
- Solving systems of linear equations, matrix algebra, determinants, vector spaces, eigenvalues and eigenvectors. Selection of advanced topics. Applications throughout. Computer used for theory and applications.
- Repeatability
- Credit given for only one of MATH-M 301 or MATH-M 303.

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# MATH-M 303 Linear Algebra for Undergraduates

- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212; or MATH-M 211 and CSCI-C 241; or MATH-S 211 and CSCI-C 241
- Description
- Introduction to the theory of real vector spaces. Coordinate s, linear dependence, bases. Linear transformations and matrix calculus. Determinants and rank. Eigenvalues and eigenvectors.
- Repeatability
- Credit given for only one of MATH-M 301, MATH-M 303, or MATH-S 303.

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# MATH-S 303 Honors Course in Linear Algebra

- Credits
- 3
- Prerequisites
- Consent of department
- Description
- Honors version of MATH-M 303. For students with unusual aptitude and motivation.
- Repeatability
- Not open to those who have had MATH-M 301 or MATH-M 303.

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**Calculus III.**One (1) course:- MATH-M 311 Calculus III
- MATH-S 311 Honors Course in Calculus III

# MATH-M 311 Calculus III

- Credits
- 4
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Elementary geometry of 2, 3, and n-space; functions of several variables; partial differentiation; minimum and maximum problems; multiple integration.

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# MATH-S 311 Honors Course in Calculus III

- Credits
- 4
- Prerequisites
- MATH-S 212 or consent of instructor; and MATH M-301, MATH M-303, or MATH S-303
- Description
- Honors version of MATH-M 311, covering geometry of 2, 3, and n-space; functions of several variables; partial differentiation; minimum and maximum problems; and multiple integration. For students with unusual aptitude and motivation.
- Repeatability
- Credit given for only one of MATH-M 311 or MATH-S 311.

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**Mathematics Area.**Two (2) courses, including at least one at the 400–499 level, from the following lists of courses, grouped by mathematics area (Students who qualify for honors may use MATH-S 499 to replace the second course in a mathematical area with approval of the Department of Mathematics):- Analysis
- MATH-M 312 Calculus IV
- MATH-M 413 Introduction to Analysis I
- MATH-M 414 Introduction to Analysis II
- MATH-M 415 Elementary Complex Variables with Applications
- MATH-M 420 Metric Space Topology
- MATH-M 420 Metric Space Topology
- MATH-S 312 Honors Course in Calculus IV
- MATH-S 413 Honors Course in Analysis I
- MATH-S 414 Honors Course in Analysis II
- MATH-S 415 Honors Elementary Complex Variables

# MATH-M 312 Calculus IV

- Credits
- 3
- Prerequisites
- MATH-M 311 or MATH-S 311
- Description
- Differential calculus of vector-valued functions, transformation of coordinates, change of variables in multiple integrals. Vector integral calculus: line integrals, Green\'s theorem, surface integrals, Stokes\' theorem. Applications.
- Repeatability
- Credit given for only one of MATH-M 312 or MATH-S 312.

# MATH-M 413 Introduction to Analysis I

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311
- Description
- Modern theory of real number , limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics.

# MATH-M 414 Introduction to Analysis II

- Credits
- 3
- Prerequisites
- MATH-M 413 or MATH-S 413
- Description
- Continuation of MATH-M 413. Functions of several variables, Taylor series, extreme values. Manifolds in Euclidean space, Implicit Function Theorem, Inverse Function Theorem. Divergence Theorem and other classical theorems of vector calculus. Special topics.
- Repeatability
- Credit given for only one of MATH-M 414 or MATH-S 414.

# MATH-M 415 Elementary Complex Variables with Applications

- Credits
- 3
- Prerequisites
- MATH-M 311, MATH-S 311, or consent of instructor
- Description
- Algebra and geometry of complex numbers, elementary functions of a complex variable, power series, integrations, calculus of residues, conformal mapping. Application to physics.
- Repeatability
- Credit given for only one of MATH-M 415 or MATH-S 415.

# MATH-M 420 Metric Space Topology

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Topology of Euclidean and metric spaces. Limits and continuity. Topological properties of metric spaces, including separation properties, connectedness, and compactness. Complete metric spaces. Elementary general topology.

# MATH-M 420 Metric Space Topology

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Topology of Euclidean and metric spaces. Limits and continuity. Topological properties of metric spaces, including separation properties, connectedness, and compactness. Complete metric spaces. Elementary general topology.

# MATH-S 312 Honors Course in Calculus IV

- Credits
- 3
- Prerequisites
- MATH-S 311 or consent of instructor
- Description
- For students with unusual aptitude and motivation.
- Repeatability
- Credit given for only one of MATH-M 312 or MATH-S 312.

# MATH-S 413 Honors Course in Analysis I

- Credits
- 3
- Prerequisites
- MATH-S 312; or consent of instructor
- Description
- Differentiable transformations defined on Euclidean space, inverse and implicit function theorems. Lebesgue integration over Euclidean space and transformation of integrals. Exterior algebra, measure and integration on manifolds. Stokes\' theorem. Closed and exact forms.

# MATH-S 414 Honors Course in Analysis II

- Credits
- 3
- Prerequisites
- MATH-S 413; or consent of instructor
- Description
- Differentiable transformations defined on Euclidean space, inverse and implicit function theorems. Lebesgue integration over Euclidean space and transformation of integrals. Exterior algebra, measure and integration on manifolds. Stokes\' theorem. Closed and exact forms.
- Repeatability
- Credit given for only one of MATH-S 414 or MATH-M 414.

# MATH-S 415 Honors Elementary Complex Variables

- Credits
- 3
- Prerequisites
- MATH-S 311; or consent of instructor
- Description
- For students with unusual aptitude and motivation. Algebra and geometry of complex numbers, elementary functions of a complex variable, power series, contour integrals, calculus of residues, conformal mapping.
- Repeatability
- Credit given for only one of MATH-M 415 or MATH-S 415.

- Differential Equations
- MATH-M 343
- MATH-M 344
- MATH-M 441 Introduction to Partial Differential Equations with Applications I
- MATH-M 442 Introduction to Partial Differential Equations with Applications II
- MATH-S 343 Honors Course in Differential Equations
- MATH-S 344 Honors Course in Differential Equations II

# MATH-M 441 Introduction to Partial Differential Equations with Applications I

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311; and MATH-M 343 or MATH-S 343
- Notes
- R: MATH-M 312 or MATH-S 312
- Description
- Derivation and methods of solution of classical partial differential equations of mathematical physics: heat, wave, and Laplace equations. Separation of variables, Fourier series, Sturm-Liouville theory, special functions, Green\'s functions, Fourier transform, first order equations, characteristics and special topics.

# MATH-M 442 Introduction to Partial Differential Equations with Applications II

- Credits
- 3
- Prerequisites
- MATH-M 441
- Description
- Derivation and methods of solution of classical partial differential equations of mathematical physics: heat, wave, and Laplace equations. Separation of variables, Fourier series, Sturm-Liouville theory, special functions, Green\'s functions, Fourier transform, first order equations, characteristics and special topics.

# MATH-S 343 Honors Course in Differential Equations

- Credits
- 3
- Prerequisites
- MATH-S 212 or consent of instructor
- Description
- Introduction, with historical examples, first order ordinary differential equations (ODEs) and applications, second order linear ODEs, linear ODEs of higher order, series solutions to linear ODEs, and numerical methods for ODEs. In addition, some theoretical aspects will be studied in detail such as the Picard existence/uniqueness theorem for initial-value problems, convergence of series solutions, and the matrix exponential exp(tA).

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# MATH-S 344 Honors Course in Differential Equations II

- Credits
- 3
- Prerequisites
- MATH-M 212 or MATH-S 212; and MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-S 343
- Description
- Covers the topics of MATH-M 344, in addition to more theoretical material, which may include topics such as the uniqueness theorem for the inversion of the Laplace transform, introduction to the theory of distributions, derivation of the heat and wave equations, eigenvalues of Sturm-Liouville boundary problems, and oscillation theory applied to special functions. Meets with MATH-M 344, and the additional material will be incorporated in weekly homework sets. Exams will include some of this additional material.
- Repeatability
- Credit given for only one of MATH-M 344 or MATH-S 344.

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- Applied Mathematics
- MATH-M 371 Elementary Computational Methods
- MATH-M 447 Mathematical Models and Applications I
- MATH-M 451
- MATH-M 471 Numerical Analysis I
- MATH-M 472 Numerical Analysis II

# MATH-M 371 Elementary Computational Methods

- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Interpolation and approximation of functions, solution of equations, numerical integration and differentiation. Errors, convergence, and stability of the procedures. Students write and use programs applying numerical methods.

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# MATH-M 447 Mathematical Models and Applications I

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311
- Notes
- P or C: MATH-M 365
- Description
- Formation and study of mathematical models used in the biological, social, and management sciences. Mathematical topics include games, graphs, Markov and Poisson processes, mathematical programming, queues, and equations of growth.

# MATH-M 471 Numerical Analysis I

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311; and MATH-M 343 or MATH-S 343
- Notes
- Knowledge of a computer language such as FORTRAN, C, C++, etc., is essential for success in this course. Students with other programming backgrounds should consult the instructor
- Description
- Interpolation and approximation of functions, numerical integration and differentiation, solution of nonlinear equations, acceleration and extrapolation, solution of systems of linear equations, eigenvalue problems, initial and boundary value problems for ordinary differential equations, and computer programs applying these numerical methods.

# MATH-M 472 Numerical Analysis II

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311; and MATH-M 343 or MATH-S 343
- Notes
- Knowledge of a computer language such as FORTRAN, C, C++, etc., is essential for success in this course. Students with other programming backgrounds should consult the instructor.
- Description
- Interpolation and approximation of functions, numerical integration and differentiation, solution of nonlinear equations, acceleration and extrapolation, solution of s of linear equations, eigenvalue problems, initial and boundary value problems for ordinary differential equations, and computer programs applying these numerical methods.

- Probability and Statistics
- MATH-M 463 Introduction to Probability Theory I
- MATH-M 464 Introduction to Probability Theory II
- MATH-S 463 Honors Course in Probability Theory I

# MATH-M 463 Introduction to Probability Theory I

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311
- Description
- The meaning of probability. Random experiments, conditional probability, independence. Random variables, expected values and standard deviations, moment generating functions. Important discrete and continuous distributions. Poisson processes. Multivariate distributions, basic limit laws such as the central limit theorem.
- Repeatability
- Credit given for only one of MATH-M 463 or MATH-S 463.

# MATH-M 464 Introduction to Probability Theory II

- Credits
- 3
- Prerequisites
- MATH-M 463 or MATH-S 463
- Description
- Conditional distributions and expectation, linear and nonlinear regression; simple stochastic processes: Poisson process, process with independent increments, random walk, Markov chain with finite state space; information theory.

# MATH-S 463 Honors Course in Probability Theory I

- Credits
- 3
- Prerequisites
- MATH-S 303 and MATH-S 311; or consent of instructor
- Description
- Honors version of MATH-M 463. For students of outstanding ability in mathematics.

- Analysis

**Economics courses.**- One (1) course:
- ECON-B 251 Fundamentals of Economics for Business I
- ECON-E 201 Introduction to Microeconomics
- ECON-E 251 Fundamentals of Economics I
- ECON-S 201 Introduction to Microeconomics: Honors

# ECON-B 251 Fundamentals of Economics for Business I

- Credits
- 3
- Prerequisites
- None
- Description
- First course in a two-course sequence that introduces business students to essential economic concepts. Examines the economic notions of cost and gains from trade, determinants of economic growth, consumer and firm behavior in competitive and non-competitive environments, the effects of taxation, externalities, moral hazard and adverse selection, and basic game theory.
- Repeatability
- Credit given for only one of ECON-B 251 or ECON-E 251.

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# ECON-E 201 Introduction to Microeconomics

- Credits
- 3
- Prerequisites
- None
- Description
- Scarcity, opportunity cost, competitive and non-competitive market pricing, and interdependence as an analytical core. Individual sections apply this core to a variety of current economic policy problems, such as poverty, pollution, excise taxes, rent controls, and farm subsidies.

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# ECON-E 251 Fundamentals of Economics I

- Credits
- 3
- Prerequisites
- None
- Description
- First course in a two-course sequence that lays the foundations for a solid understanding of economics. Examines the economic notions of cost and gains from trade, determinants of economic growth, consumer and firm behavior in competitive and non-competitive environments, the effects of taxation, externalities, moral hazard and adverse selection, and public policy applications.
- Repeatability
- Credit given for only one of ECON-E 251 or ECON-B 251.

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# ECON-S 201 Introduction to Microeconomics: Honors

- Credits
- 3
- Prerequisites
- Honors student
- Description
- Designed for students of superior ability. Covers same core materials as ECON-E 201 and substitutes for ECON-E 201 as a prerequisite for other courses.

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- One (1) course:
- ECON-B 252 Fundamentals of Economics for Business II
- ECON-E 202 Introduction to Macroeconomics
- ECON-E 252 Fundamentals of Economics II
- ECON-S 202 Introduction to Macroeconomics: Honors

# ECON-B 252 Fundamentals of Economics for Business II

- Credits
- 3
- Prerequisites
- ECON-B 251
- Description
- Continuation of Fundamental of Economics for Business I. After a review of the major types of markets, explores macroeconomic concepts, beginning with measurement and the National Income Accounts, and then moving to cycle fluctuations and performance of stock markets. Concludes with microeconomic and macroeconomic perspectives in two areas: labor markets and globalization will applications in business contexts.
- Repeatability
- Credit given for only one of ECON-B 252 or ECON-E 252.

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# ECON-E 202 Introduction to Macroeconomics

- Credits
- 3
- Prerequisites
- ECON-E 201 or ECON-S 201
- Description
- Measuring and explaining aggregate economic performance, money, monetary policy, and fiscal policy as an analytical core. Individual sections apply this core to a variety of current economic policy problems, such as inflation, unemployment, and economic growth.

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# ECON-E 252 Fundamentals of Economics II

- Credits
- 3
- Prerequisites
- ECON-E 251 or ECON-B 251
- Description
- Continuation of Fundamental of Economics I. After a review of the major types of markets, explores macroeconomic concepts, beginning with measurement and the National Income Accounts, and then moving to cycle fluctuations and performance of stock markets. Concludes with microeconomic and macroeconomic perspectives in two areas: labor markets and globalization.
- Repeatability
- Credit given for only one of ECON-E 252 or ECON-B 252.

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# ECON-S 202 Introduction to Macroeconomics: Honors

- Credits
- 3
- Prerequisites
- ECON-S 201 or ECON-E 201; Honors student
- Description
- Designed for students of superior ability. Covers same core material as ECON-E 202 and substitutes for ECON-E 202 as a prerequisite for other courses.

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- One (1) course:
- ECON-E 321 Intermediate Microeconomic Theory
- ECON-S 321 Intermediate Microeconomic Theory: Honors

# ECON-E 321 Intermediate Microeconomic Theory

- Credits
- 3
- Prerequisites
- ECON-B 251 or ECON-E 251; and MATH-J 113, MATH-M 119, MATH-V 119, MATH-M 211, or MATH-S 211
- Description
- Develops economic models of both consumer and firm behavior, including non-strategic and strategic interactions. Models of market structure and behavior focus on price and output determination and include circumstances in which markets may succeed or fail to deliver socially beneficial outcomes.
- Repeatability
- Credit given for only one of ECON-E 321 or ECON-S 321.

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# ECON-S 321 Intermediate Microeconomic Theory: Honors

- Credits
- 3
- Prerequisites
- ECON-B 251 or ECON-E 251; and MATH-J 113, MATH-M 119, MATH-V 119, MATH-M 211, or MATH-S 211
- Description
- Designed for students of superior ability. Covers same core material as ECON-E 321.
- Repeatability
- Credit given for only one of ECON-E 321 or ECON-S 321.

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- One (1) course:
- ECON-E 322 Intermediate Macroeconomic Theory
- ECON-S 322 Intermediate Macroeconomic Theory: Honors

# ECON-E 322 Intermediate Macroeconomic Theory

- Credits
- 3
- Prerequisites
- ECON-E 252 or ECON-B 252; and ECON-E 321 or ECON-S 321
- Description
- National income accounting; theory of income, employment, and price level. Countercyclical and other public policy measures.

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# ECON-S 322 Intermediate Macroeconomic Theory: Honors

- Credits
- 3
- Prerequisites
- ECON-E 252 or ECON-B 252 and ECON-E 321 or ECON-S 321; Hutton Honors student
- Description
- Designed for students of superior ability. Covers same core material as ECON-E 322 and substitutes for ECON-E 322 as a prerequisite for other courses.
- Repeatability
- Credit given for only one of ECON-S 322 or ECON-E 322.

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**Electives.**Three (3) additional economics courses numbered above ECON-E 322, including at least one at the 400–499 level. ECON-E 370, ECON-E 496, and ECON-X 373 cannot be used to meet this requirement.

- One (1) course:
**Statistics.**One (1) course:- ECON-E 370 Statistical Analysis for Business and Economics
- ECON-S 370 Statistical Analysis for Business and Economics: Honors
- MATH-M 365 Introduction to Probability and Statistics

# ECON-E 370 Statistical Analysis for Business and Economics

- Credits
- 3
- Prerequisites
- MATH-M 118, MATH-S 118, or MATH-V 118
- Notes
- R: ECON-E 252 or ECON-B 252 and MATH-M 119
- Description
- Lectures emphasize the use of basic probability concepts and statistical theory in the estimation and testing of single parameter and multivariate relationships. In computer labs, using Microsoft Excel, each student calculates descriptive statistics, probabilities, and least squares regression coefficients in situations based on current business and economic events.
- Repeatability
- Credit given for only one of ANTH-A 306, CJUS-K 300, ECON-E 370, ECON-S 370, MATH-K 300, MATH-K 310, POLS-Y 395, PSY-K 300, PSY-K 310, SOC-S 371, SPEA-K 300, SPH-Q 381, STAT-K 310, STAT-S 300, STAT-S 301, or STAT-S 303.

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# ECON-S 370 Statistical Analysis for Business and Economics: Honors

- Credits
- 3
- Prerequisites
- MATH-M 118, MATH-S 118, or MATH-V 118; and Hutton Honors student
- Notes
- R: MATH-M 119 and ECON-E 252 or ECON-B 252
- Description
- Honors course. Designed for students of superior ability. Covers same core material as ECON-E 370.
- Repeatability
- Credit given for only one of ANTH-A 306, CJUS-K 300, ECON-E 370, ECON-S 370, MATH-K 300, MATH-K 310, POLS-Y 395, PSY-K 300, PSY-K 310, SOC-S 371, SPEA-K 300, SPH-Q 381, STAT-K 310, STAT-S 300, STAT-S 301, or STAT-S 303.

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# MATH-M 365 Introduction to Probability and Statistics

- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Elementary concepts of probability and statistics. Combinatorics, conditional probability, independence, random variables, discrete and continuous distributions, moments. Statistical inference, point estimation, confidence intervals, test of hypotheses. Applications to social, behavioral, and natural sciences.
- Repeatability
- Credit given for only one of MATH-M 360 or MATH-M 365.

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**Major GPA, Hours, and Minimum Grade Requirements.**- At least 18 credit hours in the major must be completed in courses taken through the Indiana University Bloomington campus or an IU-administered or IU co-sponsored Overseas Study program.
- At least 18 credit hours in the major must be completed at the 300–499 level.
- Except for the GPA requirement, a grade of C- or higher is required for a course to count toward a requirement in the major.
- A GPA of at least 2.000 for all courses taken in the major—including those where a grade lower than C- is earned—is required.
- Exceptions to major requirements may be made with the approval of the department's Director of Undergraduate Studies, subject to final approval by the College of Arts and Sciences.

Notes

The Bachelor of Arts degree requires at least 120 credit hours, to include the following:

**College of Arts and Sciences Credit Hours.**At least 100 credit hours must come from College of Arts and Sciences disciplines.**Upper Division Courses.**At least 42 credit hours (of the 120) must be at the 300–499 level.**College Residency.**Following completion of the 60th credit hour toward degree, at least 36 credit hours of College of Arts and Sciences coursework must be completed through the Indiana University Bloomington campus or an IU-administered or IU co-sponsored Overseas Study program.**College GPA.**A cumulative grade point average (GPA) of at least 2.000 is required for all courses taken at Indiana University.**CASE Requirements.**The following College of Arts and Sciences Education (CASE) requirements must be completed:- CASE Foundations
- CASE Breadth of Inquiry
- CASE Culture Studies
- CASE Critical Approaches: 1 course
- CASE Foreign Language: Proficiency in a single foreign language through the second semester of the second year of college-level coursework
- CASE Intensive Writing: 1 course
- CASE Public Oral Communication: 1 course

**Major.**Completion of the major as outlined in the Major Requirements section above.

Most students must also successfully complete the Indiana University Bloomington General Education program.