Bachelor of Arts in Mathematics
The Bachelor of Arts in Mathematics is for a student who likes to be challenged; enjoys solving puzzles; has other interests and talents outside of math; desires flexibility and choice in major requirements; has strong analytical skills and wants to develop them further; and wants to keep options open for a variety of career fields.
Students choosing this major should carefully consider the different types of courses available and how different areas of math may complement her/his interests and goals. Math B.A. majors take courses in at least two areas (see "coursework" below). Math B.A. majors gain general analytical and problem-solving skills that are both useful and marketable. They also gain a broad perspective of the power and beauty of mathematics.
Requirements
- 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.
- Fall 2024CASE MMcourseSummer 2024CASE MMcourse
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
- 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
- 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.
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
- 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
- Advanced Electives. One (1) of the following options:
- Option 1: Two Areas.
- Course A. One (1) course from any area:
- 400–499 Level Algebra and Number Theory Area
- 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.
- 400–499 Level Analysis Area
- 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.
- 400–499 Level Applied Mathematics Area
- MATH-M 447 Mathematical Models and Applications I
- MATH-M 451 The Mathematics of Finance
- 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 451 The Mathematics of Finance
- Credits
- 3
- Prerequisites
- MATH-M 311 or MATH-S 311; and MATH-M 365 or MATH-M 463 or MATH-S 463
- Description
- Course covers probability theory, Brownian motion, Ito\'s Lemma, stochastic differential equations, and dynamic hedging. These topics are applied to the Black-Scholes formula, the pricing of financial derivatives, and the term theory of interest rates.
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.
- 400–499 Level Differential Equations Area
- 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.
- 400–499 Level Geometry and Topology Area
- 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.
- 400–499 Level Logic Area
- 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
- 400–499 Level Mathematics Education and History Area
- 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.
- 400–499 Level Probability and Statistics Area
- 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.
- 400–499 Level Algebra and Number Theory Area
- Course B. One (1) course from the Course A list above, but in a second area different from the course selected to fulfill the Course A requirement.
- Additional Courses. Three (3) additional courses:
- MATH-M 353 Discrete Mathematics
- MATH-M 312 Calculus IV
- MATH-S 312 Honors Course in Calculus IV
- MATH-M 371 Elementary Computational Methods
- MATH-M 343 Introduction to Differential Equations with Applications I
- MATH-M 344 Introduction to Differential Equations with Applications II
- MATH-S 343 Honors Course in Differential Equations
- MATH-S 344 Honors Course in Differential Equations II
- MATH-M 321 Intuitive Topology
- MATH-M 384 Logic
- MATH-M 385 Mathematics from Language
- MATH-M 391 Introduction to Mathematical Reasoning
- MATH-M 380 History of Mathematics
- MATH-T 336 Topics in Euclidean Geometry
- MATH-M 365 Introduction to Probability and Statistics
- 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 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 447 Mathematical Models and Applications I
- MATH-M 451 The Mathematics of Finance
- MATH-M 471 Numerical Analysis I
- MATH-M 472 Numerical Analysis II
- MATH-M 441 Introduction to Partial Differential Equations with Applications I
- MATH-M 442 Introduction to Partial Differential Equations with Applications II
- MATH-M 420 Metric Space Topology
- MATH-M 435 Introduction to Differential Geometry
- MATH-M 436 Introduction to Geometries
- MATH-M 482 Modal Logic
- MATH-T 403 Modern Algebra for Secondary Teachers
- 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
- One (1) of the following:
- CSCI-A 201 INTRODUCTION TO PROGRAMMING I
- CSCI-C 200 Introduction to Computers and Programming
- CSCI-C 211 Introduction to Computer Science
- Additional course from outside the Department of Mathematics that has significant mathematical content with approval of the Department of Mathematics Director of Undergraduate Studies
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 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-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-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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-M 343 Introduction to Differential Equations with Applications I
- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Notes
- R: MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Ordinary differential equations and methods for their solution, including series methods and the Laplace transform. Applications of differential equations. s, stability, and numerical methods. Partial differential equations of mathematical physics, Fourier series.
- Repeatability
- Credit given for only one of MATH-M 343 or MATH-S 343.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-M 344 Introduction to Differential Equations with Applications II
- Credits
- 3
- Prerequisites
- One of MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 343 or MATH-S 343
- Description
- Ordinary differential equations and methods for their solution, including series methods and the Laplace transform. Applications of differential equations. Systems, stability, and numerical methods. Partial differential equations of mathematical physics, Fourier series.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
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).
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
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.
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
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.
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
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.
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.
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 451 The Mathematics of Finance
- Credits
- 3
- Prerequisites
- MATH-M 311 or MATH-S 311; and MATH-M 365 or MATH-M 463 or MATH-S 463
- Description
- Course covers probability theory, Brownian motion, Ito\'s Lemma, stochastic differential equations, and dynamic hedging. These topics are applied to the Black-Scholes formula, the pricing of financial derivatives, and the term theory of interest rates.
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.
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-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.
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.
- Fall 2024CASE NMcourseSummer 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-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.
CSCI-A 201 INTRODUCTION TO PROGRAMMING I
- Credits
- 3–4 credit hours
- Prerequisites
- None
- Description
- None
CSCI-C 200 Introduction to Computers and Programming
- Credits
- 4
- Prerequisites
- High school precalculus math
- Description
- This course is an introduction, broadly, to algorithmic thinking and, specifically, to programming. It teaches the basics of programming using real world applications in natural, physical and social sciences. Students will develop ability to program by identifying problems in real world and then creating a program that solves the problem.
- Repeatability
- Credit given for only one of CSCI-C 200, CSCI-C 211, CSCI-H 211, or CSCI-A 591.
CSCI-C 211 Introduction to Computer Science
- Credits
- 4
- Prerequisites
- High school precalculus math
- Description
- A first course in computer science for those intending to take advanced computer science courses. Introduction to programming and to algorithm design and analysis. Using the Scheme programming language, the course covers several programming paradigms. Lecture and laboratory.
- Repeatability
- Credit given for only one of CSCI-C 200, CSCI-C 211, CSCI-H 211, or CSCI-A 591.
- Course A. One (1) course from any area:
- Option 2: Three or More Areas.
- Course A. One (1) course from any area:
- 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-S 312 Honors Course in 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 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-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-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 371 Elementary Computational Methods
- MATH-M 447 Mathematical Models and Applications I
- MATH-M 451 The Mathematics of Finance
- 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.
- Fall 2024CASE NMcourseSummer 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 451 The Mathematics of Finance
- Credits
- 3
- Prerequisites
- MATH-M 311 or MATH-S 311; and MATH-M 365 or MATH-M 463 or MATH-S 463
- Description
- Course covers probability theory, Brownian motion, Ito\'s Lemma, stochastic differential equations, and dynamic hedging. These topics are applied to the Black-Scholes formula, the pricing of financial derivatives, and the term theory of interest rates.
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 Introduction to Differential Equations with Applications I
- MATH-M 344 Introduction to 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
- MATH-M 442 Introduction to Partial Differential Equations with Applications II
MATH-M 343 Introduction to Differential Equations with Applications I
- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Notes
- R: MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Ordinary differential equations and methods for their solution, including series methods and the Laplace transform. Applications of differential equations. s, stability, and numerical methods. Partial differential equations of mathematical physics, Fourier series.
- Repeatability
- Credit given for only one of MATH-M 343 or MATH-S 343.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-M 344 Introduction to Differential Equations with Applications II
- Credits
- 3
- Prerequisites
- One of MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 343 or MATH-S 343
- Description
- Ordinary differential equations and methods for their solution, including series methods and the Laplace transform. Applications of differential equations. Systems, stability, and numerical methods. Partial differential equations of mathematical physics, Fourier series.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
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).
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
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 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.
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 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.
- Fall 2024CASE NMcourseSummer 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
- Course B. One (1) course from the Course A list above, but in a second area different from the course selected to fulfill the Course A requirement.
- Course C. One (1) course from the Course A list above, but in a third area different from the courses selected to fulfill the Course A and Course B requirement.
- Additional Courses. Two (2) additional courses:
- Additional course(s) from the Course A lists above
- One (1) of the following:
- CSCI-A 201 INTRODUCTION TO PROGRAMMING I
- CSCI-C 200 Introduction to Computers and Programming
- CSCI-C 211 Introduction to Computer Science
- Additional course from outside the Department of Mathematics that has significant mathematical content with approval of the Department of Mathematics Director of Undergraduate Studies
CSCI-A 201 INTRODUCTION TO PROGRAMMING I
- Credits
- 3–4 credit hours
- Prerequisites
- None
- Description
- None
CSCI-C 200 Introduction to Computers and Programming
- Credits
- 4
- Prerequisites
- High school precalculus math
- Description
- This course is an introduction, broadly, to algorithmic thinking and, specifically, to programming. It teaches the basics of programming using real world applications in natural, physical and social sciences. Students will develop ability to program by identifying problems in real world and then creating a program that solves the problem.
- Repeatability
- Credit given for only one of CSCI-C 200, CSCI-C 211, CSCI-H 211, or CSCI-A 591.
CSCI-C 211 Introduction to Computer Science
- Credits
- 4
- Prerequisites
- High school precalculus math
- Description
- A first course in computer science for those intending to take advanced computer science courses. Introduction to programming and to algorithm design and analysis. Using the Scheme programming language, the course covers several programming paradigms. Lecture and laboratory.
- Repeatability
- Credit given for only one of CSCI-C 200, CSCI-C 211, CSCI-H 211, or CSCI-A 591.
- 400–499 Level Requirement. At least two (2) of the courses used to fulfill requirements a-d above must be at the 400–499 level.
- Course A. One (1) course from any area:
- Option 1: Two Areas.
- 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
Exclusions
The following courses cannot be applied toward major requirements or the College Breadth requirement:
- MATH-E 201 Linear Algebra for Data Science
- MATH-E 265 Introduction to Probability and Statistics for Data Science
- MATH-E 449 Advanced Undergraduate Engineering Mathematical Methods
- MATH-D 116 Introduction to Finite Mathematics I
- MATH-D 117 Introduction to Finite Mathematics II
- MATH-J 110 Introductory Problem Solving
- MATH-J 111 Introduction to College Mathematics I
- MATH-J 112 Introduction to College Mathematics II
- MATH-J 113 Introduction to Calculus with Applications
- MATH-M 106 The Mathematics of Decision and Beauty
- MATH-M 118 Finite Mathematics
- MATH-M 125 Pre-Calculus Mathematics
- MATH-M 126 Trigonometric Functions
- MATH-M 127 Pre-Calculus with Trigonometry
- MATH-M 330 Exploring Mathematical Ideas
- MATH-S 118 Honors Finite Mathematics
- MATH-T 101 Mathematics for Elementary Teachers I
- MATH-T 103 Mathematics for Elementary Teachers III
- MATH-V 118 Finite Mathematics with Applications
- MATH-V 119 Applied Brief Calculus I
- MATH-X 125 Supplemental instruction for MATH-M 125 Precalculus
- MATH-X 170 Service Learning in Mathematics: Community Outreach
- MATH-X 373 Internship in Professional Practice
MATH-E 201 Linear Algebra for Data Science
- Credits
- 3
- Prerequisites
- MATH-M 211 or MATH-S 211
- Description
- Introduces the basic theory and techniques of linear algebra, emphasizing the topics that have applications in data science.
- Repeatability
- Credit given for only one of MATH-E 201, MATH-M 301, or MATH-M 303.
MATH-E 265 Introduction to Probability and Statistics for Data Science
- Credits
- 3
- Prerequisites
- MATH-M 211, CSCI-C 200, or CSCI-A 201
- Description
- Covers elementary concepts of probability and statistics for data science, including combinatorics, conditional probability, independence, random variables, discrete and continuous distributions, moments, statistical inference, point estimation, quantiles, confidence intervals, test of hypotheses, and related topics. Introduces the application of data analysis to the social and natural sciences.
MATH-E 449 Advanced Undergraduate Engineering Mathematical Methods
- Credits
- 3
- Prerequisites
- MATH-M 343 or MATH-S 343
- Description
- Provides essential mathematical concepts and methods for solving problems encountered in many engineering fields. Topics selected from multivariable and vector calculus, coordinate transformations, infinite series, scaling and dimensional analysis, partial differential equations, integral transforms, linear algebra, discrete mathematics, and numerical methods.
MATH-D 116 Introduction to Finite Mathematics I
- Credits
- 2
- Prerequisites
- Mastery of two years of high school algebra as indicated by an ALEKS score of 40 or higher; or MATH-M 014, MATH-M 018, or MATH-J 111.
- Description
- MATH-D 116 and MATH-D 117 is a two-course sequence that covers sets, counting, basic probability, including random variables and expected values, linear systems, matrices, linear programming, and applications.
- Repeatability
- Credit given for only one of MATH-A 118, MATH-M 118, MATH-S 118, MATH-V 118; or MATH-D 116 and MATH-D 117.
MATH-D 117 Introduction to Finite Mathematics II
- Credits
- 2
- Prerequisites
- MATH-D 116 or consent of the department
- Notes
- MATH-D 116 and MATH-D 117 is a two-course sequence
- Description
- Topics for the course are taken from MATH-M 118. Credit for the College of Arts and Sciences Foundations requirement in Mathematical Modeling or the College's N&M Breadth of Inquiry requirement will be given only upon completion of both MATH-D 116 and MATH-D 117 with a passing grade.
- Repeatability
- Credit given for only one of MATH-A 118, MATH-M 118, MATH-S 118, MATH-V 118; or MATH-D 116 and MATH-D 117.
- Fall 2024CASE MMcourseSummer 2024CASE MMcourse
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-J 110 Introductory Problem Solving
- Credits
- 2
- Prerequisites
- Consent of department
- Notes
- Not counted toward any College of Arts and Sciences distribution requirement nor toward the College of Arts and Sciences fundamental skills requirement in mathematics
- Description
- Emphasizes problem solving and the development of logical reasoning skills. Topics include elementary logic, set theory, measurement of geometric figures, and translating English statements into algebraic equations.
MATH-J 111 Introduction to College Mathematics I
- Credits
- 3
- Prerequisites
- None
- Notes
- R: To be successful, students will have been exposed to two years of high school algebra. For Groups students only
- Description
- A review of basic algebra.
MATH-J 112 Introduction to College Mathematics II
- Credits
- 3
- Prerequisites
- MATH-J 111 with a grade of C- or higher; or consent of department
- Notes
- For Groups students only. Not counted toward any College of Arts and Sciences Breadth of Inquiry requirement or toward the College of Arts and Sciences Foundations requirement in Mathematical Modeling
- Description
- A continuation of MATH-J 111 that includes functions, exponential functions, and logarithmic functions.
MATH-J 113 Introduction to Calculus with Applications
- Credits
- 3
- Prerequisites
- MATH-J 112 with a grade of C- or higher; or consent of department
- Notes
- For Groups students only. MATH-J 113 can count toward the College of Arts and Sciences Foundations requirement in mathematical modeling and the College of Arts and Sciences natural and mathematical sciences Breadth of Inquiry requirement for Groups students
- Description
- A survey of calculus.
- Repeatability
- Credit given for only one of MATH-J 113, MATH-M 119, MATH-V 119, MATH-M 211, or MATH-S 211.
- Fall 2024CASE MMcourseSummer 2024CASE MMcourse
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-M 106 The Mathematics of Decision and Beauty
- Credits
- 3
- Prerequisites
- Mastery of two years of high school algebra as indicated by an ALEKS score of 35 or higher, or successful completion of MATH-M 014, MATH-M 018, or MATH-J 111.
- Description
- Mathematics of art (symmetry and perspective), music (scales, tuning and rhythm), and decision-making (voting, game theory, graph theory). Emphasis on conceptual and geometric modes of mathematical reasoning, with group- and activity-based learning in a smaller class format.
- Fall 2024CASE MMcourseSummer 2024CASE MMcourse
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-M 118 Finite Mathematics
- Credits
- 3
- Prerequisites
- None
- Notes
- R: To be successful, students will demonstrate mastery of two years of high school algebra as indicated by an appropriate ALEKS score or completion of MATH-M 014, MATH-M 018, or MATH-J 111
- Description
- Sets, counting, basic probability, including random variables and expected values. Linear systems, matrices, linear programming, and applications.
- Repeatability
- Credit given for only one of MATH-A 118, MATH-M 118, MATH-S 118, MATH-V 118; or MATH-D 116 and MATH-D 117.
- Fall 2024CASE MMcourseSummer 2024CASE MMcourse
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-M 125 Pre-Calculus Mathematics
- Credits
- 3
- Prerequisites
- None
- Notes
- R: To be successful, students will demonstrate mastery of two years of high school algebra and one year of high school geometry as indicated by an appropriate ALEKS score or completion of MATH-M 14.
- Description
- Algebraic operations; polynomial, exponential, and logarithmic, functions and their graphs; conic sections; systems of equations; and inequalities.
- Repeatability
- Credit given for only one of MATH-M 125 or MATH-M 025.
MATH-M 126 Trigonometric Functions
- Credits
- 2
- Prerequisites
- None
- Description
- Designed to develop the properties of the trigonometric, exponential, and logarithmic functions and to prepare for course in calculus.
MATH-M 127 Pre-Calculus with Trigonometry
- Credits
- 5
- Prerequisites
- None
- Notes
- R: To be successful, students will demonstrate mastery of two years of high school algebra and one year of high school geometry as indicated by an appropriate ALEKS score or completion of MATH-M 014
- Description
- This course is designed to prepare students for calculus. Subject matter includes polynomial, rational, exponential, logarithmic, and trigonometric functions and their application.
- Repeatability
- Credit given for only one of MATH-M 127 or MATH-M 027.
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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-S 118 Honors Finite Mathematics
- Credits
- 3
- Prerequisites
- Hutton Honors College membership
- Notes
- R: To be successful students will demonstrate mastery of two years of high school algebra as indicated by an appropriate ALEKS score or completion of MATH-M 014, MATH-M 018, or MATH-J 111
- Description
- Designed for students of outstanding ability in mathematics. Covers all material of MATH-M 118 and additional topics from statistics and game theory. Computers may be used in this course, but no previous experience is assumed.
- Fall 2024CASE MMcourseSummer 2024CASE MMcourse
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-T 101 Mathematics for Elementary Teachers I
- Credits
- 3
- Prerequisites
- MATH-M 014, MATH-M 018, or a score of at least 35 on the Indiana University Bloomington ALEKS mathematics placement test
- Notes
- Only open to elementary education majors
- Description
- Elements of set theory, counting numbers. Operations on counting numbers, integers, rational numbers, and real numbers.
MATH-T 103 Mathematics for Elementary Teachers III
- Credits
- 3
- Prerequisites
- EDUC-N 101 or MATH-T 101 with a grade of C or better; or consent of department
- Notes
- Only open to elementary education majors
- Description
- Descriptions and properties of basic geometric figures. Rigid motions. Axiomatics. Measurement, analytic geometry, and graphs of functions. Discussion of modern mathematics.
MATH-V 118 Finite Mathematics with Applications
- Credits
- 3
- Prerequisites
- None
- Notes
- R: To be successful, students will demonstrate mastery of two years of high school algebra as indicated by an appropriate ALEKS score or completion of MATH-M 014, MATH-M 018, or MATH-J 111
- Description
- Sets, counting, basic probability, linear modelling, and other discrete topics. Applications to various areas depending on topic. Possibilities include social and biological sciences and consumer mathematics.
- Repeatability
- Credit given for only one of MATH-A 118, MATH-M 118, MATH-S 118, MATH-V 118; or MATH-D 116 and MATH-D 117.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-V 119 Applied Brief Calculus I
- Credits
- 3
- 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 as indicated by an appropriate ALEKS score or completion of MATH-M 025 or MATH-M 027
- Description
- Introduction to calculus. Variable topic course with emphasis on non-business topics and applications. The topic(s) will be listed in the Schedule of Classes each semester.
- Repeatability
- A student may receive credit for only one of the following: MATH-J 113, MATH-M 119, MATH-M 211, MATH-S 211, or MATH-V 119.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-X 125 Supplemental instruction for MATH-M 125 Precalculus
- Credits
- 2
- Prerequisites
- None
- Corequisites
- MATH-M 125
- Description
- This course supplements the instruction in MATH-M 125 Precalculus by reviewing carefully selected skills as the corresponding topics are being studied in M125.
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
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
- MATH-Y 201
- May be repeated once with approval of Department of Mathematics for a maximum of 6 credit hours:
- MATH-X 373 Internship in Professional Practice
- MATH-Y 398
- May be repeated for a maximum of 12 credit hours:
- MATH-M 295
- MATH-X 390 Readings and Research
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)
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.