Department of Mathematics

# Minor in Mathematics

Students on Summer 2022, Fall 2022, or Spring 2023 requirements MATHMIN

The Minor in Mathematics is intended for students interested in the logical thinking and problem solving skills that are gained in studying mathematics. This minor provides students with mathematical preparation that may be applied to their major field of study and that may enhance their career preparation.

## Requirements

The minor requires at least 16 credit hours, including the requirements listed below.

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

# MATH-M 211 Calculus I

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

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# MATH-S 211 Honors Calculus I

- Credits
- 4
- Prerequisites
- Hutton Honors College membership or consent of department
- 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
- Designed for students of outstanding ability, who are considering further study in mathematics. Limits, continuity, derivatives, definite and indefinite integrals, applications, with emphasis placed on theory.
- Repeatability
- Credit given for only one of MATH-J 113, MATH-M 119, MATH-M 211, MATH-S 211, or MATH-V 119.

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

# MATH-M 212 Calculus II

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

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# MATH-S 212 Honors Calculus II

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

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**Electives.**Additional courses, with approval of the director of undergraduate studies for Mathematics, to fulfill remaining requirements:- MATH-M 301 Linear Algebra and Applications
- MATH-M 303 Linear Algebra for Undergraduates
- MATH-M 311 Calculus III
- MATH-M 312 Calculus IV
- 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-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-M 413 Introduction to Analysis I
- MATH-M 414 Introduction to Analysis II
- MATH-M 415 Elementary Complex Variables with Applications
- MATH-M 420 Metric Space Topology
- MATH-M 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 490 Problem Seminar
- MATH-M 491 Putnam Exam Seminar
- MATH-S 303 Honors Course in Linear Algebra
- MATH-S 311 Honors Course in Calculus III
- MATH-S 312 Honors Course in Calculus IV
- MATH-S 343 Honors Course in Differential Equations
- MATH-S 344 Honors Course in Differential Equations II
- MATH-S 403 Honors Course in Modern Algebra I
- MATH-S 404 Honors Course in Modern Algebra II
- MATH-S 413 Honors Course in Analysis I
- 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
- MATH-T 336 Topics in Euclidean Geometry
- MATH-T 403 Modern Algebra for Secondary Teachers

# MATH-M 301 Linear Algebra and Applications

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

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# MATH-M 303 Linear Algebra for Undergraduates

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

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# MATH-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-M 312 Calculus IV

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

# MATH-M 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.

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# 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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# 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.

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# 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.Â Applications of differential equations.Â Systems, stability, and numerical methods.Â Partial differential equations of mathematical physics, Fourier series.

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# 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.

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# 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, PÃ³lya 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.

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# MATH-M 371 Elementary Computational Methods

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

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# MATH-M 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.

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# 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.

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# 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-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-M 413 Introduction to Analysis I

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

# MATH-M 414 Introduction to Analysis II

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

# MATH-M 415 Elementary Complex Variables with Applications

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

# MATH-M 420 Metric Space Topology

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

# MATH-M 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.

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# 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.

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# 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-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-S 303 Honors Course in Linear Algebra

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

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# MATH-S 311 Honors Course in Calculus III

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

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# MATH-S 312 Honors Course in Calculus IV

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

# MATH-S 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-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-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-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.

# 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.

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# 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.

**Minor GPA, Hours, and Minimum Grade Requirements.****Minor GPA.**A GPA of at least 2.000 for all courses taken in the minor—including those where a grade lower than C- is earned—is required.**Minor 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 minor.**Minor Upper Division Credit Hours.**At least 9 credit hours in the minor must be completed at the 300–499 level.**Minor Residency.**At least 9 credit hours in the minor must be completed in courses taken through the Indiana University Bloomington campus or an IU-administered or IU co-sponsored Overseas Study program.

##### Minor 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
`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 minor 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 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.

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 I (MATHBS1)
- Bachelor of Science in Mathematics Program II (MATHBS2)

Exceptions to and substitutions for minor 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.