## Course Descriptions

- MATH-J 10 Introduction to Algebra (2 cr.) P: Consent of department. For Groups students only. A review of pre-algebra mathematics. Topics include operations on integers and rational numbers, exponents, evaluating algebraic expressions, and translating English statements into algebraic equations. Emphasis is on problem solving. Credit may not be applied toward a degree. Fulfills no distribution or fundamental skills requirement in the College of Arts and Sciences.

- MATH-M 14 Basic Algebra (4 cr.) P: One year of high school algebra. Designed to provide algebraic skills needed for future mathematics courses, such as M118 or M119. Operations with fractions, exponents, linear equations, inequalities, elementary graphs. Credit may not be applied toward a degree in the College of Arts and Sciences, the School of Education, the Kelley School of Business, or the School of Public and Environmental Affairs. I Sem., II Sem., SS.

- MATH-X 15 Introductory Algebra (2 cr.) P: One year of high school algebra. Designed to provide basic algebraic skills needed for the study of higher-level algebra courses such as X019 or M025: linear and quadratic equations, operations on polynomials, graphs of lines. Credit may not be applied toward a degree in the College of Arts and Sciences; the School of Education; the School of Health, Physical Education, and Recreation; the Kelley School of Business; or the School of Public and Environmental Affairs. I Sem., II Sem., SS.

- MATH-M 18 Basic Algebra for Finite Mathematics (2 cr.) P: One year of high school algebra. Designed to provide algebraic skills needed for the study of finite mathematics: linear equations and inequalities and their graphs, systems of equations, sets, and basic counting. Credit may not be applied toward a degree in the College of Arts and Sciences; the School of Education; the School of Health, Physical Education, and Recreation; the Kelley School of Business; or the School of Public and Environmental Affairs. I Sem., II Sem., SS.

- MATH-M 19 Brief Pre-Calculus Mathematics (2 cr.) P: Two years of high school algebra or M014, and one year of high school geometry. Designed to prepare students for M119. Algebraic operations; polynomial, exponential, and logarithmic functions and their graphs; and inequalities. Credit may not be applied toward a degree in the College of Arts and Sciences. I Sem., II Sem.

- MATH-M 25 Precalculus Mathematics (3 cr.) P: Two years of high school algebra or M014, and one year of high school geometry. Designed to prepare students for M119. Algebraic operations; polynomial, exponential, and logarithmic functions and their graphs; conic sections; systems of equations; and inequalities. Credit may not be applied toward a degree in the College of Arts and Sciences. I Sem., II Sem., SS. (course webpage)

- MATH-M 26 Trigonometric Functions (2 cr.) P or C: M025 or equivalent. Designed to prepare students for M211. Trigonometric functions; identities. Graphs of trigonometric and inverse trigonometric functions. Credit hours may not be applied toward a degree in the College of Arts and Sciences. I Sem., II Sem., SS. (course webpage)

- MATH-M 27 Precalculus with Trigonometry (4 cr.) P: Two years of high school algebra or M014, and one year of high school geometry. This course is designed to prepare students for M211 Calculus. The general content of both M025 and M026 is included, with emphasis placed on exponential, logarithmic, and trigonometric functions at a more sophisticated level and pace. Credit may not be applied toward a degree in the College of Arts and Sciences. Non-College of Arts and Sciences students should see their advisor about appropriate mathematics selection. I Sem., II Sem. (course webpage)

- MATH-T 101 Mathematics for Elementary Teachers I (3 cr.) P: M014, M018 or a score of at least 35 on the Indiana University Bloomington ALEKS mathematics placement test. Elements of set theory, counting numbers. Operations on counting numbers, integers, rational numbers, and real numbers. Only open to elementary education majors. I Sem., II Sem.

- MATH-T 103 Mathematics for Elementary Teachers III (3 cr.) P: T101 with a grade of C or higher; students may enroll concurrently in T102 and T103 with the approval of a School of Education advisor. Descriptions and properties of basic geometric figures. Rigid motions. Axiomatics. Measurement, analytic geometry, and graphs of functions. Discussion of modern mathematics. Only open to elementary education majors. I Sem., II Sem.

- MATH-M 106 The Mathematics of Decision and Beauty (3 cr.)
**CASE MM, CASE N&M**P: Two years of high school algebra or M014. Mathematics of art (symmetry and perspective), music (scales, tuning and rhythm), and decision-making (voting systems, game theory, graph theory). Emphasis on conceptual and geometric modes of mathematical reasoning, with group- and activity-based learning in a smaller class format.

- MATH-J 110 Introductory Problem Solving (2 cr.) P: Two years of high school algebra or permission of department. 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. Not counted toward any College of Arts and Sciences distribution requirement nor toward the College of Arts and Sciences fundamental skills requirement in mathematics.

- MATH-J 111 Introduction to College Mathematics I (3 cr.) P: Consent of department. For Groups students only. A review of basic algebra. Not counted toward any College of Arts and Sciences distribution requirement or toward the College of Arts and Sciences fundamental skills requirement in mathematics.

- MATH-J 112 Introduction to College Mathematics II (3 cr.) P: MATH-J 111 with a grade of C- or higher, or consent of department. For Groups students only. A continuation of J111 that includes functions, exponential functions, and logarithmic functions. 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.

- MATH-J 113 Introduction to Calculus with Applications (3 cr.)
**CASE MM, CASE N&M**P: MATH-J 112 with a grade of C- or higher, or consent of department. For Groups students only. A survey of calculus. J113 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. A student may receive credit for only one of the following: M119, V119, M211, S211, or J113.

- MATH-D 116 Introduction to Finite Mathematics I (2 cr.) P: Two years of high school algebra or M014 or M018. D116-D117 is a two-course sequence that satisfies the College of Arts and Sciences Foundations Requirement in Mathematical Modeling and counts toward the College Natural and Mathematical Sciences Breadth of Inquiry requirement. Topics for the course are taken from M118. Credit for the Foundations requirement in Mathematical Modeling or the N&M Breadth of Inquiry requirement will be given only upon completion of both D116 and D117 with a passing grade. Credit given for only one of the following: the sequence D116-D117, M118, A118, V118, or S118.

- MATH-D 117 Introduction to Finite Mathematics II (2 cr.)
**CASE MM, CASE N&M**P: Two years of high school algebra or M014 or M018, and D116. Topics for the course are taken from M118. 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 D116 and D117 with a passing grade. Credit given for only one of the following: the sequence D116-D117, M118, V118, S118, or A118.

- MATH-M 118 Finite Mathematics (3 cr.)
**CASE MM, CASE N&M**P: Two years of high school algebra or M014 or M018. Sets, counting, basic probability, including random variables and expected values. Linear systems, matrices, linear programming, and applications. Credit given for only one of M118, V118, S118, the sequence D116-D117, or A118.

- MATH-S 118 Honors Finite Mathematics (3 cr.)
**CASE MM, CASE N&M**P: Mastery of two years of high school algebra. Designed for students of outstanding ability in mathematics. Covers all material of M118 and additional topics from statistics and game theory. Computers may be used in this course, but no previous experience is assumed. I Sem.

- MATH-V 118 Finite Mathematics with Applications (3 cr.)
**CASE MM, CASE N&M**P: Two years of high school algebra or M014. 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. Credit given for only one of A118, M118, S118, V118, or the sequence D116-D117.

- MATH-M 119 Brief Survey of Calculus I (3 cr.)
**CASE MM, CASE N&M**P: Two years of high school algebra or M014. Introduction to calculus. Primarily for students from business and the social sciences. A student may receive credit for only one of the following: M119, V119, M211, S211, or J113. I Sem., II Sem., SS.

- MATH-V 119 Applied Brief Calculus I (3 cr.)
**CASE N&M**P: Two years of high school algebra or M014. Introduction to calculus. Primarily for students from the life sciences. A student may receive credit for only one of the following: M119, V119, M211, S211, or J113.

- MATH-M 120 Brief Survey of Calculus II (3 cr.)
**CASE N&M**P: M119 or V119. A continuation of M119 covering topics in elementary differential equations, calculus of functions of several variables and infinite series. Intended for non-physical science students. Credit not given for both M212 and M120. I Sem., II Sem., SS.

- MATH-X 170 Service Learning in Mathematics: Community Outreach (1 cr.) P: M211. C: Current enrollment in another mathematics course. 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. S/F graded. May be repeated for a maximum of 6 credit hours in X170 and Y201.

- MATH-M 211 Calculus I (4 cr.)
**CASE MM, CASE N&M**P: Two years of high school algebra, one year of high school geometry, precalculus math (or its equivalent), and trigonometry; or both M025 and M026. Limits, continuity, derivatives, definite and indefinite integrals, applications. A student may receive credit for only one of the following: M119, V119, M211, S211, or J113.

- MATH-S 211 Honors Calculus I (4 cr.)
**CASE MM, CASE N&M**P: High achievement in one or more of the following: a) two years of high school algebra, one year of high school geometry, precalculus math (or its equivalent), and trigonometry; b) both M025 and M026, or M027; c) one year of calculus in high school. 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. Credit given for only one of S211, M211, M119, V119, or J113. Credit not given for both S211 and X201.

- MATH-M 212 Calculus II (4 cr.)
**CASE N&M**P: M119 and X201, or M211. Techniques of integration (by parts, trigonometric substitutions, partial fractions), improper integrals, volume, work, arc length, surface area, infinite series. A student may receive credit for only one of M120 and M212. I Sem., II Sem., SS.

- MATH-S 212 Honors Calculus II (4 cr.)
**CASE N&M**P: M211 and consent of mathematics department. Includes material of M212 and supplemental topics. Designed for students of outstanding ability in mathematics. I Sem., II Sem.

- MATH-M 213 Accelerated Calculus (4 cr.)
**CASE MM, CASE N&M**P: Placement by examination. Designed for students with one year of calculus in high school. Review of material covered in M211 followed by an intensive study of all material in M212. Students completing M213 with a final grade of A or B may receive credit for M211. Credit not given for both M213 and M212.

- MATH-M 247 Mathematical Contest in Modeling Preparation (1 cr.) P: MATH-M 211 or equivalent. The Mathematical Contest in Modeling (MCM) is an annual contest where teams of undergraduates use mathematical modeling to present their solutions to real world problems. Solutions take the form of 20-25 page reports, an executive summary, and a summary for an audience of nonexperts. In this course, students will train for the contest by preparing solutions to two past MCM problems. May be repeated for a maximum of 3 credit hours.

- MATH-M 298 Careers in Mathematics (1 cr.) P: Major in mathematics. R: Sophomore or junior standing. Invited speakers provide perspectives from a variety of fields. Helps match student skills and interests to the requirements of a chosen career. How to use campus career development resources, write a resume and cover letter, and develop interviewing and networking skills for the job market. Options to prepare for professional or graduate education.

- MATH-S 299 Honors Reading and Research (1-3 cr.) Supervised problem solving. Admission only with permission of a member of the mathematics faculty who will act as supervisor. I Sem., II Sem., SS.

- MATH-M 301 Linear Algebra and Applications (3 cr.)
**CASE N&M**P: M212 or both M211 and CSCI C241. R: M212. 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. Credit not given for both M301 and M303.

- MATH-M 303 Linear Algebra for Undergraduates (3 cr.)
**CASE N&M**P: M212 or both M211 and CSCI C241. R: M212. Introduction to the theory of real vector spaces. Coordinate systems, linear dependence, bases. Linear transformations and matrix calculus. Determinants and rank. Eigenvalues and eigenvectors. Credit not given for both M301 and M303. I Sem., II Sem., SS.

- MATH-S 303 Honors Course in Linear Algebra (3 cr.)
**CASE N&M**P: Consent of department. Honors version of M303. For students with unusual aptitude and motivation. Not open to those who have had M301 or M303. II Sem.

- MATH-M 311 Calculus III (4 cr.)
**CASE N&M**P: M212, M213 or consent of department. Elementary geometry of 2, 3, and n-space; functions of several variables; partial differentiation; minimum and maximum problems; multiple integration. I Sem., II Sem., SS.

- MATH-S 311 Honors Course in Calculus III (4 cr.)
**CASE N&M**P: M212 or M213, and consent of department. Honors version of M311. For students with unusual aptitude and motivation. Credit not given for both M311 and S311. I Sem.

- MATH-M 312 Calculus IV (3 cr.) P: M311. 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’s theorem. Applications. I Sem., II Sem.

- MATH-S 312 Honors Course in Calculus IV (3 cr.) P: M311 or consent of instructor. For students with unusual aptitude and motivation. Credit not given for both M312 and S312. II Sem.

- MATH-M 321 Intuitive Topology (3 cr.)
**CASE N&M**P: M212 or consent of instructor. 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. II Sem.

- MATH-M 330 Exploring Mathematical Ideas (3 cr.)
**CASE N&M**P: M211 or consent of the department. 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. Does not count toward major requirements.

- MATH-T 336 Topics in Euclidean Geometry (3 cr.)
**CASE N&M**P: M212. 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. I Sem.

- MATH-M 343 Introduction to Differential Equations with Applications I (3 cr.)
**CASE N&M**P: M212. 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. M343, I Sem., II Sem., SS; M344, II Sem.

- MATH-M 344 Introduction to Differential Equations with Applications II (3 cr.)
**CASE N&M**P: M301 or M303, and M343. 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. M343, I Sem., II Sem., SS; M344, II Sem.

- MATH-S 343 Honors Course in Differential Equations (3 cr.)
**CASE N&M**P: M212 and consent of department. 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).

- MATH-S 344 Honors Course in Differential Equations II (3 cr.)
**CASE N&M**P: S343 or M343, M212, M301 or M303, and consent of the department. Covers the topics of M344, 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 M344, and the additional material will be incorporated in weekly homework sets. Exams will include some of this additional material.

- MATH-M 348 Discrete Mathematical Models (3 cr.)
**CASE N&M**P: M118 or equivalent. 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.

- MATH-M 353 Discrete Mathematics (3 cr.) P: MATH M212 or permission of instructor. 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 (3 cr.)
**CASE N&M**P: M212. 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. Credit not given for both M365 and M360. The sequence M365-M366 is not recommended. I Sem., II Sem., SS.

- MATH-M 371 Elementary Computational Methods (3 cr.)
**CASE N&M**P: M212. Some computer programming experience is helpful, but not required. 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.

- MATH-X 373 Internship in Professional Practice (1-3 cr.) P: Approval of Department of Mathematics. S/F grading. Professional work experience involving significant use of mathematics or statistics. Evaluation by employer and Department of Mathematics. Does not count toward major requirements. May be repeated once with approval of Department of Mathematics for a maximum of 6 credit hours in X373 and Y398.

- MATH-M 380 History of Mathematics (3 cr.)
**CASE N&M**P: M212 or S212. 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. Credit given for only one of MATH-M380 and HPSC-X380.

- MATH-M 384 Logic (3 cr.)
**CASE N&M**P: MATH-M 303 or CSCI-C241; or consent of the instructor. 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.

- MATH-M 385 Mathematics from Language (3 cr.)
**CASE N&M**P: M118 or equivalent. Discrete mathematics. Topics in math motivated by linguistics, chosen from formal approaches to syntax and semantics, and from statistical and computational linguistics.

- MATH-X 390 Readings and Research (1-3 cr.) P: Admission only with permission of a member of the mathematics faculty who will act as supervisor. Supervised problem solving. May be repeated for a maximum of 12 credit hours in X390 and M295. I Sem., II Sem., SS.

- MATH-M 391 Introduction to Mathematical Reasoning (3 cr.)
**CASE N&M**P: M212, or M211 and CSCI C241; M303 or M301. Elementary logic, techniques of proof, basic set theory, functions, relations, binary operations, number systems, counting. Bridges the gap between elementary and advanced courses. Recommended for students with insufficient background for 400-level courses and for students in education. Not open to students who have received credit for M403, M413, or M420.

- MATH-M 403 Introduction to Modern Algebra I (3 cr.) P: M301 or M303. Study of groups, rings, field extensions, with applications to linear transformations. M403, I Sem.; M404, II Sem.

- MATH-M 404 Introduction to Modern Algebra II (3 cr.) P: M301 or M303. Study of groups, rings, field extensions, with applications to linear transformations. M403, I Sem.; M404, II Sem.

- MATH-S 403 Honors Course in Modern Algebra I (3 cr.) P: S303. For students of outstanding ability in mathematics. Theory of groups, rings, integral domains, fields, and modules. S403, I Sem.; S404, II Sem.

- MATH-S 404 Honors Course in Modern Algebra II (3 cr.) P: S303. For students of outstanding ability in mathematics. Theory of groups, rings, integral domains, fields, and modules. S403, I Sem.; S404, II Sem.

- MATH-T 403 Modern Algebra for Secondary Teachers (3 cr.) P: M301 or M303, and M391. 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. I Sem.

- MATH-M 405 Number Theory (3 cr.) P: M212. 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 (3 cr.) P: M301 or M303. 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 (3 cr.) P: M301 or M303, and M311, or consent of instructor. Modern theory of real number system, limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics. M413, I Sem.; M414, II Sem.

- MATH-M 414 Introduction to Analysis II (3 cr.) P: M413. 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. Credit given for only one of M414 or S414.

- MATH-S 413 Honors Course in Analysis I (3 cr.) P: S312 or consent of instructor. 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’s theorem. Closed and exact forms. S413, I Sem.; S414, II Sem.

- MATH-S 414 Honors Course in Analysis II (3 cr.) P: S312 or consent of instructor. 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’s theorem. Closed and exact forms. S413, I Sem.; S414, II Sem.

- MATH-M 415 Elementary Complex Variables with Applications (3 cr.) P: M311 or consent of instructor. Algebra and geometry of complex numbers, elementary functions of a complex variable, power series, integrations, calculus of residues, conformal mapping. Application to physics. Credit given for only one of M415 or S415.

- MATH-S 415 Honors Elementary Complex Variablese (3 cr.) P: S311 or consent of instructor. 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. Credit given for only one of S415 or M415.

- MATH-M 420 Metric Space Topology (3 cr.) P: M301 or M303. 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 (3 cr.) P: M301 or M303, and M311. 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 (3 cr.) P: M301 or M303. 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 (3 cr.) P: M301 or M303, M311, and M343. 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. M441, I Sem.; M442, II Sem.

- MATH-M 442 Introduction to Partial Differential Equations with Applications II (3 cr.) P: M441. 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. M441, I Sem.; M442, II Sem.

- MATH-M 447 Mathematical Models and Applications I (3 cr.) P: M301 or M303, M311, M360 or M365, which may be taken concurrently, or consent of instructor. 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. M447, I Sem.; M448, II Sem.

- MATH-M 448 Mathematical Models and Applications II (3 cr.) P: M301 or M303, M311, M360 or M365, which may be taken concurrently, or consent of instructor. 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. M447, I Sem.

- MATH-M 451 The Mathematics of Finance (3 cr.) P: M311 and M365. R: M343. 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 (3 cr.)
**CASE N&M**P: M301 or M303. The course covers encryption and decryption in secure codes. Topics include cryptosystems and their cryptanalysis, Data Encryption Standard, cryptanalysis, Euclidean algorithm, Chinese remainder theorem, RSA cryptosystem, primality testing, factoring algorithms, EI Gamal cryptosystem, discrete log problem, other public key cryptosystems, signature schemes, hash functions, key distribution and key agreement.

- MATH-M 463 Introduction to Probability Theory I (3 cr.) P: M301 or M303, and M311. 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. I Sem.

- MATH-S 463 Honors Course in Probability Theory I (3 cr.) P: M303 and M311. Honors version of M463. For students of outstanding ability in mathematics. I Sem.

- MATH-M 464 Introduction to Probability Theory II (3 cr.) P: M463. 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. II Sem.

- MATH-M 466 Introduction to Mathematical Statistics (3 cr.) P: M463 or consent of instructor. Rigorous mathematical treatment of problems in sampling and statistical inference. Possible topics include sufficient statistics, exponential distributions, monotone likelihood ratio, most powerful tests, minimum variance estimates, shortest confidence intervals, linear models, maximum likelihood, simultaneous equations, the relationship of theory to practice. II Sem.

- MATH-M 471 Numerical Analysis I (3 cr.) P: M301 or M303, M311, M343, and knowledge of a computer language such as FORTRAN, C, C++, etc. (Students with other programming backgrounds should consult the instructor.) 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. M471, I Sem.; M472, II Sem.

- MATH-M 472 Numerical Analysis II (3 cr.) P: M301 or M303, M311, M343, and knowledge of a computer language such as FORTRAN, C, C++, etc. (Students with other programming backgrounds should consult the instructor.) 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. M471, I Sem.; M472, II Sem.

- MATH-M 482 Mathematical Logic (3 cr.) Construction and study of formal mathematical languages. Definitions of, and relationships between, the notions of “truth” and “probability” of a formal sentence. Capabilities and limitations of first-order languages. Alternative formal systems. Introductions to model theory and the decision problem. Additional topics chosen by the instructor.

- MATH-M 490 Problem Seminar (3 cr.) P: M301 or M303, M413 (M413 may be concurrent), and consent of the instructor. 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 (1 cr.) P: Approval of the director of undergraduate studies. 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. May be repeated twice for credit.

- MATH-S 499 Reading for Honors (1-12 cr.) P: Approval of departmental honors committee. May be repeated for a maximum of 12 credit hours. I Sem., II Sem., SS.