Department of Mathematics
Bachelor of Arts in Mathematics
Students on Summer 2022, Fall 2022, or Spring 2023 requirements MATHBA
Requirements
The major requires at least 30 credit hours, including the requirements listed below.
- 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.
- Summer 2025CASE MMcourseSpring 2025CASE MMcourseFall 2024CASE MMcourse
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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.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
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.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
- Advanced Electives. Five (5) courses from at least two (2) different areas
- 400–499 Level Requirement. Two (2) courses:
- Algebra and Number Theory
- MATH-M 403 Introduction to Modern Algebra I
- MATH-M 404 Introduction to Modern Algebra II
- MATH-M 405 Number Theory
- MATH-M 409 Linear Transformations
- MATH-S 403 Honors Course in Modern Algebra I
- MATH-S 404 Honors Course in Modern Algebra II
MATH-M 403 Introduction to Modern Algebra I
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Study of groups, rings, field extensions, with applications to linear transformations.
MATH-M 404 Introduction to Modern Algebra II
- Credits
- 3
- Prerequisites
- None
- Notes
- Open only to graduate students
- Description
- Study of groups, rings, field extensions, with applications to linear transformations.
MATH-M 405 Number Theory
- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Numbers and their representation, divisibility and factorization, primes and their distribution, number theoretic functions, congruences, primitive roots, diophantine equations, quadratic residues, sums of squares.
MATH-M 409 Linear Transformations
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- The study of linear transformations on a finite dimensional vector space over the complex field. Canonical forms, similarity theory; inner products and diagonalization of normal transformations.
MATH-S 403 Honors Course in Modern Algebra I
- Credits
- 3
- Prerequisites
- MATH-S 303; or consent of instructor
- Notes
- For students of outstanding ability in mathematics
- Description
- Theory of groups, rings, integral domains, fields, and modules.
MATH-S 404 Honors Course in Modern Algebra II
- Credits
- 3
- Prerequisites
- MATH-S 403; or consent of instructor
- Description
- For students of outstanding ability in mathematics. Theory of groups, rings, integral domains, fields, and modules.
- Analysis
- MATH-M 413 Introduction to Analysis I
- MATH-M 414 Introduction to Analysis II
- MATH-M 415 Elementary Complex Variables with Applications
- 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 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-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.
- Applied Mathematics
- 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 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.
- Differential Equations
- MATH-M 441 Introduction to Partial Differential Equations with Applications I
- MATH-M 442 Introduction to Partial Differential Equations with Applications 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.
- Geometry and Topology
- MATH-M 420 Metric Space Topology
- MATH-M 435 Introduction to Differential Geometry
- MATH-M 436 Introduction to Geometries
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 435 Introduction to Differential Geometry
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311
- Description
- An introduction to the geometry of curves and surfaces. Topics will include arc length, torsion, Frenet formulae, metrics, curvatures, and classical theorems in these areas.
MATH-M 436 Introduction to Geometries
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Non-Euclidean geometry, axiom systems. Plane projective geometry, Desarguesian planes, perspectivities, coordinates in the real projective plane. The group of projective transformations and subgeometries corresponding to subgroups. Models for geometries. Circular transformations.
- Logic
- MATH-M 482 Modal Logic
MATH-M 482 Modal Logic
- Credits
- 3
- Prerequisites
- CSCI-C 241, CSCI-H 241, MATH-M 303, MATH-S 303, or MATH-M 384; or consent of instructor
- Description
- Introduction to modal logic with emphasis on systems of modal logic which apply to philosophy and computer science. Includes epistemic logic, temporal logic, deontic logic, and logics for reasoning about space. Covers primarily the semantics of these systems, and secondarily the standard results about them.
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- Mathematics Education and History
- MATH-T 403 Modern Algebra for Secondary Teachers
MATH-T 403 Modern Algebra for Secondary Teachers
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 391
- Description
- Introduction to the basic concepts of groups, rings, and fields with an emphasis on the theory of equations as it underlies the basic ideas of high school algebra.
- 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.
- Additional course with approval of the director of undergraduate studies
- Algebra and Number Theory
- Advanced Electives. Three (3) additional courses:
- Algebra and Number Theory
- MATH-M 353 Discrete Mathematics
- MATH-M 403 Introduction to Modern Algebra I
- MATH-M 404 Introduction to Modern Algebra II
- MATH-M 405 Number Theory
- MATH-M 409 Linear Transformations
- MATH-S 403 Honors Course in Modern Algebra I
- MATH-S 404 Honors Course in Modern Algebra II
MATH-M 353 Discrete Mathematics
- Credits
- 3
- Prerequisites
- MATH-M 212 or consent of instructor
- Description
- Covers fundamental topics chosen from enumerative combinatorics and graph theory. Possible topics include permutations, combinations, pigeonhole principle, inclusion-exclusion, generating functions, recurrence relations, Pólya theory, spanning trees, Eulerian paths, Ramsey theory, graph coloring, flow problems, Hamiltonian paths and cycles, electrical networks, random graphs.
MATH-M 403 Introduction to Modern Algebra I
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Study of groups, rings, field extensions, with applications to linear transformations.
MATH-M 404 Introduction to Modern Algebra II
- Credits
- 3
- Prerequisites
- None
- Notes
- Open only to graduate students
- Description
- Study of groups, rings, field extensions, with applications to linear transformations.
MATH-M 405 Number Theory
- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Numbers and their representation, divisibility and factorization, primes and their distribution, number theoretic functions, congruences, primitive roots, diophantine equations, quadratic residues, sums of squares.
MATH-M 409 Linear Transformations
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- The study of linear transformations on a finite dimensional vector space over the complex field. Canonical forms, similarity theory; inner products and diagonalization of normal transformations.
MATH-S 403 Honors Course in Modern Algebra I
- Credits
- 3
- Prerequisites
- MATH-S 303; or consent of instructor
- Notes
- For students of outstanding ability in mathematics
- Description
- Theory of groups, rings, integral domains, fields, and modules.
MATH-S 404 Honors Course in Modern Algebra II
- Credits
- 3
- Prerequisites
- MATH-S 403; or consent of instructor
- Description
- For students of outstanding ability in mathematics. Theory of groups, rings, integral domains, fields, and modules.
- 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-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-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.
- 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.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
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.
- 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).
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
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.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
- Geometry and Topology
- MATH-M 321 Intuitive Topology
- MATH-M 420 Metric Space Topology
- MATH-M 435 Introduction to Differential Geometry
- MATH-M 436 Introduction to Geometries
MATH-M 321 Intuitive Topology
- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Intuitive description of topology, including networks and maps, topological equivalence, classification of surfaces, spheres with handles, knot theory, Jordan curve theorem, transformations, and fixed-point theorems.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
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 435 Introduction to Differential Geometry
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311
- Description
- An introduction to the geometry of curves and surfaces. Topics will include arc length, torsion, Frenet formulae, metrics, curvatures, and classical theorems in these areas.
MATH-M 436 Introduction to Geometries
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Non-Euclidean geometry, axiom systems. Plane projective geometry, Desarguesian planes, perspectivities, coordinates in the real projective plane. The group of projective transformations and subgeometries corresponding to subgroups. Models for geometries. Circular transformations.
- Logic
- MATH-M 384 Logic
- MATH-M 385 Mathematics from Language
- MATH-M 391 Introduction to Mathematical Reasoning
- MATH-M 482 Modal Logic
MATH-M 384 Logic
- Credits
- 3
- Prerequisites
- CSCI-C 241, MATH-M 303, or MATH-S 303
- Description
- Construction and study of formal mathematical languages. Definitions of, and relationships between, the notions of truth and provability of a formal sentence. Proof systems for logical systems such as propositional logic and syllogistic logic. Soundness, completeness, and decidability.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
MATH-M 385 Mathematics from Language
- Credits
- 3
- Prerequisites
- MATH-M 118, MATH-S 118, or equivalent
- Description
- Discrete mathematics. Topics in math motivated by linguistics, chosen from formal approaches to syntax and semantics, and from statistical and computational linguistics.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
MATH-M 391 Introduction to Mathematical Reasoning
- Credits
- 3
- Prerequisites
- (A) MATH-M 212, MATH-M 213, or MATH-S 212; or CSCI-C 241 and MATH-M 211; or CSCI-C 241 and MATH-S 211; and (B) MATH-M 301, MATH-M 303, or MATH-S 303
- Notes
- Recommended for students with insufficient background for 400-level courses and for students in education
- Description
- Elementary logic, techniques of proof, basic set theory, functions, relations, binary operations, number systems, counting. Bridges the gap between elementary and advanced courses.
- Repeatability
- Not open to students who have received credit for MATH-M 403, MATH-M 413, or MATH-M 420.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
MATH-M 482 Modal Logic
- Credits
- 3
- Prerequisites
- CSCI-C 241, CSCI-H 241, MATH-M 303, MATH-S 303, or MATH-M 384; or consent of instructor
- Description
- Introduction to modal logic with emphasis on systems of modal logic which apply to philosophy and computer science. Includes epistemic logic, temporal logic, deontic logic, and logics for reasoning about space. Covers primarily the semantics of these systems, and secondarily the standard results about them.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
- Mathematics Education and History
- MATH-M 380 History of Mathematics
- MATH-T 336 Topics in Euclidean Geometry
- MATH-T 403 Modern Algebra for Secondary Teachers
MATH-M 380 History of Mathematics
- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Brief study of the development of algebra and trigonometry; practical, demonstrative, and analytic geometry; calculus, famous problems, calculating devices; famous mathematicians and chronological outlines in comparison with outlines in the sciences, history, philosophy, and astronomy.
- Repeatability
- Credit given for only one of HPSC-X 380 or MATH-M 380.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
MATH-T 336 Topics in Euclidean Geometry
- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- A study of the central aspects of two-dimensional Euclidean geometry from historical and axiomatic points of view as well as through hands-on and/or computer-based explorations of geometric concepts and constructions.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
MATH-T 403 Modern Algebra for Secondary Teachers
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 391
- Description
- Introduction to the basic concepts of groups, rings, and fields with an emphasis on the theory of equations as it underlies the basic ideas of high school algebra.
- Probability and Statistics
- MATH-M 365 Introduction to 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 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.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
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.
- Algebra and Number Theory
- 400–499 Level Requirement. Two (2) courses:
- Major GPA, Hours, and Minimum Grade Requirements.
- Major GPA. 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.
- Major Minimum Grade. Except for the GPA requirement, a grade of C- or higher is required for a course to count toward a requirement in the major.
- Major Upper Division Credit Hours. At least 18 credit hours in the major must be completed at the 300–499 level.
- Major Residency. 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.
- College Breadth. At least 58 credit hours must be completed in courses from College of Arts and Sciences disciplines outside of the major area.
Major Area Courses
-
Unless otherwise noted below, the following courses are considered in the academic program and will count toward academic program requirements as appropriate:
- Any course at the 100–499 level with the
MATH
subject area prefix—as well as any other subject areas that are deemed functionally equivalent - Any course contained on the course lists for the academic program requirements at the time the course is taken—as well as any other courses that are deemed functionally equivalent—except for those listed only under Addenda Requirements
- Any course directed to a non-Addenda requirement through an approved exception
- Any course at the 100–499 level with the
Exclusions
The following courses cannot be applied toward major requirements or the College Breadth requirement:
- Any MATH-A 100–199
- Any MATH-B 100–199
- Any MATH-D 100–199
- Any MATH-E 100–499
- Any MATH-J 100–199
- Any MATH-K 100–499
- Any MATH-M 100–199 except MATH-M 119; MATH-M 120
- MATH-M 330 Exploring Mathematical Ideas
- Any MATH-S 100–199
- Any MATH-T 100–199
- Any MATH-V 100–199
- Any MATH-X 100–199
- MATH-X 373 Internship in Professional Practice
MATH-M 330 Exploring Mathematical Ideas
- Credits
- 3
- Prerequisites
- MATH-M 211 or MATH-S 211
- Notes
- Does not count toward major requirements
- Description
- An experimental course to illustrate important ideas in major areas of mathematics, including number theory, group theory, topology, geometry, and probability. Additional topics may include newly emerging fields, such as chaos theory.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
MATH-X 373 Internship in Professional Practice
- Credits
- 1–3 credit hours
- Prerequisites
- Consent of department
- Description
- Professional work experience involving significant use of mathematics or statistics. Evaluation by employer and Department of Mathematics. Does not count toward major requirements.
- Repeatability
- May be repeated once with approval of Department of Mathematics for a maximum of 6 credit hours in MATH-X 373 and MATH-Y 398.
- Grading
- S/F grading
Restrictions
The following restrictions apply to the minimum credit hours required in the major:
- Only three credit hours may apply toward major:
- MATH-M 380 History of Mathematics
- MATH-T 336 Topics in Euclidean Geometry
- MATH-T 403 Modern Algebra for Secondary Teachers
- May be repeated for a maximum of 6 credit hours:
- MATH-X 170 Service Learning in Mathematics: Community Outreach
- May be repeated once with approval of Department of Mathematics for a maximum of 6 credit hours:
- MATH-X 373 Internship in Professional Practice
- May be repeated for a maximum of 12 credit hours:
- MATH-X 390 Readings and Research
MATH-M 380 History of Mathematics
- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Brief study of the development of algebra and trigonometry; practical, demonstrative, and analytic geometry; calculus, famous problems, calculating devices; famous mathematicians and chronological outlines in comparison with outlines in the sciences, history, philosophy, and astronomy.
- Repeatability
- Credit given for only one of HPSC-X 380 or MATH-M 380.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
MATH-T 336 Topics in Euclidean Geometry
- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- A study of the central aspects of two-dimensional Euclidean geometry from historical and axiomatic points of view as well as through hands-on and/or computer-based explorations of geometric concepts and constructions.
- Summer 2025CASE NMcourseSpring 2025CASE NMcourseFall 2024CASE NMcourse
MATH-T 403 Modern Algebra for Secondary Teachers
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 391
- Description
- Introduction to the basic concepts of groups, rings, and fields with an emphasis on the theory of equations as it underlies the basic ideas of high school algebra.
MATH-X 170 Service Learning in Mathematics: Community Outreach
- Credits
- 1
- Prerequisites
- MATH-M 211, MATH-S 211, or consent of instructor
- Corequisites
- Current enrollment in another mathematics course
- Description
- Students will work within the community to foster interest, knowledge, and appreciation in mathematics. Assignments will include assisting with activities designed for primary and secondary school levels, documenting those activities in a parental guide, and suggesting related activities for children to pursue at home.
- Repeatability
- May be repeated for a maximum of 6 credit hours in MATH-X 170 and MATH-Y 201
- Grading
- S/F graded.
MATH-X 373 Internship in Professional Practice
- Credits
- 1–3 credit hours
- Prerequisites
- Consent of department
- Description
- Professional work experience involving significant use of mathematics or statistics. Evaluation by employer and Department of Mathematics. Does not count toward major requirements.
- Repeatability
- May be repeated once with approval of Department of Mathematics for a maximum of 6 credit hours in MATH-X 373 and MATH-Y 398.
- Grading
- S/F grading
MATH-X 390 Readings and Research
- Credits
- 1–3 credit hours
- Prerequisites
- Consent of supervising member of Mathematics faculty
- Description
- Supervised problem solving.
- Repeatability
- May be repeated for a maximum of 12 credit hours in MATH-M 295 and MATH-X 390.
This program of study cannot be combined with the following:
- Bachelor of Arts in Economics and Mathematics (ECONMATHBA)
- Bachelor of Arts in Mathematics and Economics (MATHECONBA)
- Bachelor of Science in Mathematics (MATHBS)
- Bachelor of Science in Mathematics Program I (MATHBS1)
- Bachelor of Science in Mathematics Program II (MATHBS2)
- Minor in Mathematics (MATHMIN)
Exceptions to and substitutions for major requirements may be made with the approval of the unit's Director of Undergraduate Studies, subject to final approval by the College of Arts and Sciences.
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 College grade point average (GPA) of at least 2.000 is required.
- 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.
Subject areas
- Any AAAD course that carries degree credit
- Any AAST course that carries degree credit
- Any ABEH course that carries degree credit
- Any AFRI course that carries degree credit
- Any AMST course that carries degree credit
- Any ANTH course that carries degree credit
- Any ARTH course that carries degree credit
- Any ASCS course that carries degree credit
- Any AST course that carries degree credit
- Any BIOC course that carries degree credit
- Any BIOL course that carries degree credit
- Any BIOT course that carries degree credit
- Any CEUS course that carries degree credit
- Any CHEM course that carries degree credit
- Any CJUS course that carries degree credit
- Any CLAS course that carries degree credit
- Any CLLC course that carries degree credit
- Any CMLT course that carries degree credit
- Any COGS course that carries degree credit
- Any COLL course that carries degree credit
- Any EALC course that carries degree credit
- Any EAS course that carries degree credit
- Any ECON course that carries degree credit
- Any ENG course that carries degree credit
- Any EURO course that carries degree credit
- Any FOLK course that carries degree credit
- Any FRIT course that carries degree credit
- Any GEOG course that carries degree credit
- Any GER course that carries degree credit
- Any GLLC course that carries degree credit
- Any GNDR course that carries degree credit
- Any HHC course that carries degree credit
- Any HISP course that carries degree credit
- Any HIST course that carries degree credit
- Any HON course that carries degree credit
- Any HPSC course that carries degree credit
- Any HUBI course that carries degree credit
- Any IMP course that carries degree credit
- Any INST course that carries degree credit
- Any INTL course that carries degree credit
- Any JSTU course that carries degree credit
- Any LAMP course that carries degree credit
- Any LATS course that carries degree credit
- Any LING course that carries degree credit
- Any LTAM course that carries degree credit
- Any MATH course that carries degree credit
- Any MELC course that carries degree credit
- Any MEST course that carries degree credit
- Any MLS course that carries degree credit
- Any MSCH course that carries degree credit
- Any NEUS course that carries degree credit
- Any OVST course that carries degree credit
- Any PACE course that carries degree credit
- Any PHIL course that carries degree credit
- Any PHYS course that carries degree credit
- Any POLS course that carries degree credit
- Any PSY course that carries degree credit
- Any REEI course that carries degree credit
- Any REL course that carries degree credit
- Any RMI course that carries degree credit
- Any SEAS course that carries degree credit
- Any SGIS course that carries degree credit
- Any SLAV course that carries degree credit
- Any SLHS course that carries degree credit
- Any SLST course that carries degree credit
- Any SOAD course that carries degree credit
- Any SOC course that carries degree credit
- Any STAT course that carries degree credit
- Any THTR course that carries degree credit