Department of Mathematics
Bachelor of Science in Mathematics Program I (Bachelor of Science in Mathematics)
Students on Summer 2021, Fall 2021, or Spring 2022 requirements MATHBS1
Bachelor of Science in Mathematics students study in depth the complex relationships between ideas in mathematics. This degree provides rigorous in-depth training suitable for graduate programs in mathematics.
Requirements
The major requires at least 39 credit hours, including the requirements listed below.
- Linear Algebra. One (1) course:
- MATH-M 303 Linear Algebra for Undergraduates
- MATH-S 303 Honors Course in Linear Algebra
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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 2024CASE NMcourse
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 NMcourseSpring 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 2024CASE NMcourse
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 NMcourseSpring 2024CASE NMcourse
- Calculus IV. One (1) course:
- MATH-M 312 Calculus IV
- MATH-S 312 Honors Course in Calculus IV
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.
- Differential Equations or Probability and Statistics. One (1) course:
- MATH-M 343 Introduction to Differential Equations with Applications I
- MATH-M 365 Introduction to Probability and Statistics
- MATH-S 343 Honors Course in Differential Equations
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 NMcourseSpring 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 NMcourseSpring 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 NMcourseSpring 2024CASE NMcourse
- Analysis I. One (1) course:
- MATH-M 413 Introduction to Analysis I
- MATH-S 413 Honors Course in Analysis I
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-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.
- Analysis II. One (1) course:
- MATH-M 414 Introduction to Analysis II
- MATH-M 415 Elementary Complex Variables with Applications
- MATH-S 414 Honors Course in Analysis II
- MATH-S 415 Honors Elementary Complex Variables
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 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.
- Modern Algebra I. One (1) course:
- MATH-M 403 Introduction to Modern Algebra I
- MATH-S 403 Honors Course in Modern Algebra I
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-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.
- Modern Algebra II. One (1) course:
- MATH-M 404 Introduction to Modern Algebra II
- MATH-M 405 Number Theory
- MATH-M 409 Linear Transformations
- MATH-M 453 Cryptography
- MATH-S 404 Honors Course in Modern Algebra II
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-M 453 Cryptography
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- The course covers encryption and decryption in secure codes. Topics include cryptos and their cryptanalysis, Data Encryption Standard, cryptanalysis, Euclidean algorithm, Chinese remainder theorem, RSA crypto, primality testing, factoring algorithms, EI Gamal crypto, discrete log problem, other public key cryptos, signature schemes, hash functions, key distribution and key agreement.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 2024CASE NMcourse
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.
- Electives.
- 400–599 Level Electives. At least two (2) additional courses:
- MATH-M 404 Introduction to Modern Algebra II
- MATH-M 405 Number Theory
- MATH-M 409 Linear Transformations
- MATH-M 414 Introduction to Analysis II
- MATH-M 415 Elementary Complex Variables with Applications
- MATH-M 420 Metric Space Topology
- MATH-M 435 Introduction to Differential Geometry
- MATH-M 436 Introduction to Geometries
- MATH-M 441 Introduction to Partial Differential Equations with Applications I
- MATH-M 442 Introduction to Partial Differential Equations with Applications II
- MATH-M 447 Mathematical Models and Applications I
- MATH-M 451 The Mathematics of Finance
- MATH-M 453 Cryptography
- MATH-M 463 Introduction to Probability Theory I
- MATH-M 464 Introduction to Probability Theory II
- MATH-M 466 Introduction to Mathematical Statistics
- MATH-M 471 Numerical Analysis I
- MATH-M 472 Numerical Analysis II
- MATH-M 482 Modal Logic
- MATH-M 491 Putnam Exam Seminar
- MATH-M 490 Problem Seminar (Departmental consent required)
- MATH-S 404 Honors Course in Modern Algebra II
- MATH-S 414 Honors Course in Analysis II
- MATH-S 415 Honors Elementary Complex Variables
- MATH-S 463 Honors Course in Probability Theory I
- MATH-S 499 Reading for Honors (Departmental consent required)
- MATH 500-599 (graduate level) course with approval from the Director of Undergraduate Studies
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-M 414 Introduction to Analysis II
- Credits
- 3
- Prerequisites
- MATH-M 413 or MATH-S 413
- Description
- Continuation of MATH-M 413. Functions of several variables, Taylor series, extreme values. Manifolds in Euclidean space, Implicit Function Theorem, Inverse Function Theorem. Divergence Theorem and other classical theorems of vector calculus. Special topics.
- Repeatability
- Credit given for only one of MATH-M 414 or MATH-S 414.
MATH-M 415 Elementary Complex Variables with Applications
- Credits
- 3
- Prerequisites
- MATH-M 311, MATH-S 311, or consent of instructor
- Description
- Algebra and geometry of complex numbers, elementary functions of a complex variable, power series, integrations, calculus of residues, conformal mapping. Application to physics.
- Repeatability
- Credit given for only one of MATH-M 415 or MATH-S 415.
MATH-M 420 Metric Space Topology
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Topology of Euclidean and metric spaces. Limits and continuity. Topological properties of metric spaces, including separation properties, connectedness, and compactness. Complete metric spaces. Elementary general topology.
MATH-M 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 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 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 453 Cryptography
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- The course covers encryption and decryption in secure codes. Topics include cryptos and their cryptanalysis, Data Encryption Standard, cryptanalysis, Euclidean algorithm, Chinese remainder theorem, RSA crypto, primality testing, factoring algorithms, EI Gamal crypto, discrete log problem, other public key cryptos, signature schemes, hash functions, key distribution and key agreement.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 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-M 466 Introduction to Mathematical Statistics
- Credits
- 3
- Prerequisites
- MATH-M 463, MATH-S 463, or consent of instructor
- Description
- Rigorous mathematical treatment of problems in sampling and statistical inference. Method of maximum likelihood, efficiency, sufficient statistics, exponential family distributions, likelihood ratio tests, most powerful tests, minimum variance unbiased estimators, shortest confidence intervals, linear models and analysis of variance, nonparametric methods.
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 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 NMcourseSpring 2024CASE NMcourse
MATH-M 491 Putnam Exam Seminar
- Credits
- 1
- Prerequisites
- Consent of the director of undergraduate studies
- Description
- The Putnam Examination is a national mathematics competition for college undergraduates at all levels of study. It is held in December each year. This problem seminar is designed to help students prepare for the examination.
- Repeatability
- May be repeated for a maximum of 3 credit hours.
MATH-M 490 Problem Seminar
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303 or MATH-S 303; and consent of instructor
- Notes
- R: MATH-M 343 or MATH-S 343, and MATH-M 441; and MATH-M 471
- Description
- Introduction to research techniques for advanced undergraduate and beginning graduate students, based on problems from parts of the regular curriculum, such as linear algebra, topology, probability, and analysis. Emphasis will be on problems of both current and historical interest but usually not in the standard literature.
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-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-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.
MATH-S 499 Reading for Honors
- Credits
- 1–12 credit hours
- Prerequisites
- Approval of departmental honors committee
- Description
- None
- Repeatability
- May be repeated for a maximum of 12 credit hours.
- 300–599 Level Electives. Additional courses, as needed, to complete remaining requirements:
- Additional courses from the 400-599 Level Electives list
- MATH-M 301 Linear Algebra and Applications
- MATH-M 321 Intuitive Topology
- MATH-M 330 Exploring Mathematical Ideas
- MATH-M 343 Introduction to Differential Equations with Applications I
- MATH-M 344 Introduction to Differential Equations with Applications II
- MATH-M 348 Discrete Mathematical Models
- MATH-M 353 Discrete Mathematics
- MATH-M 365 Introduction to Probability and Statistics
- MATH-M 371 Elementary Computational Methods
- MATH-M 380 History of Mathematics
- MATH-M 384 Logic
- MATH-M 385 Mathematics from Language
- MATH-M 391 Introduction to Mathematical Reasoning
- MATH-S 343 Honors Course in Differential Equations
- MATH-S 344 Honors Course in Differential Equations II
- MATH-X 373 Internship in Professional Practice
- MATH-X 390 Readings and Research
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 NMcourseSpring 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 NMcourseSpring 2024CASE NMcourse
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 NMcourseSpring 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 NMcourseSpring 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 NMcourseSpring 2024CASE NMcourse
MATH-M 348 Discrete Mathematical Models
- Credits
- 3
- Prerequisites
- MATH-M 118 or equivalent
- Description
- Introduction to the development and use of discrete mathematical models in the social, life, and management sciences; emphasis on models involving Markov chains, game theory, graph theory, and evolutionary systems.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 2024CASE NMcourse
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 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 NMcourseSpring 2024CASE NMcourse
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 NMcourseSpring 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 NMcourseSpring 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 NMcourseSpring 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.
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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.
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MATH-S 343 Honors Course in Differential Equations
- Credits
- 3
- Prerequisites
- MATH-S 212 or consent of instructor
- Description
- Introduction, with historical examples, first order ordinary differential equations (ODEs) and applications, second order linear ODEs, linear ODEs of higher order, series solutions to linear ODEs, and numerical methods for ODEs. In addition, some theoretical aspects will be studied in detail such as the Picard existence/uniqueness theorem for initial-value problems, convergence of series solutions, and the matrix exponential exp(tA).
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MATH-S 344 Honors Course in Differential Equations II
- Credits
- 3
- Prerequisites
- MATH-M 212 or MATH-S 212; and MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-S 343
- Description
- Covers the topics of MATH-M 344, in addition to more theoretical material, which may include topics such as the uniqueness theorem for the inversion of the Laplace transform, introduction to the theory of distributions, derivation of the heat and wave equations, eigenvalues of Sturm-Liouville boundary problems, and oscillation theory applied to special functions. Meets with MATH-M 344, and the additional material will be incorporated in weekly homework sets. Exams will include some of this additional material.
- Repeatability
- Credit given for only one of MATH-M 344 or MATH-S 344.
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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.
- 400–599 Level Electives. At least two (2) additional 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.
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 200–499 level with the
MATHsubject 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:
- 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-M 330 Exploring Mathematical Ideas
- MATH-M 333
- MATH-M 347
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-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.
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Restrictions
The following restrictions apply to the minimum credit hours required in the major:
- 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 (MATHBA)
- Bachelor of Arts in Mathematics and Economics (MATHECONBA)
- Bachelor of Science in Mathematics (MATHBS)
- 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 Science 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 36 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
- Diversity in the United States: 1 course
- Global Civilizations and Cultures: Not required
- CASE Critical Approaches: 1 course
- CASE Foreign Language: Proficiency in a single foreign language through the first 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.