At most one course from mathematics education and history may count toward the five required courses.

With approval of the Department of Mathematics, one course outside of mathematics that has significant mathematical content may count toward the five required courses as long as conditions in number 3 are still satisfied. Computer Science A201 or C211 is recommended.

Recommendations
In addition to studying mathematics courses, all majors are strongly encouraged to study in depth another discipline that uses mathematics.

Majors are also strongly encouraged to take a computer programming course.

Majors interested in professional work or graduate study should take additional mathematics courses at the 300 and 400 level.

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Major in Mathematics—B.S.

Purpose
The B.S. degree is designed to provide students with an extensive background in mathematics. It provides appropriate training for those students who plan to do graduate work in mathematics (Program I), or in related areas such as astronomy, biology, chemistry, computer science, economics, geology, physics, or psychology (Program II).

Requirements

Program I

1. Writing, same as B.A. degree.
2. Foreign language, 3 credit hours (or the equivalent) at or above the second-year level.
3. Arts and humanities, three courses; social and historical studies, three courses; natural sciences, three courses excluding mathematics courses.
4. Concentration requirement, at least 39 credit hours of mathematics, including:
1. M303, M311, and M312;
2. at least one of M343 or M365;
3. at least one of the sequences M413-M414 or M413-M415;
4. at least one of the sequences M403-M404, M403-M405, M403-M409, or M403-M453;
5. two additional courses at the 400 or 500 level excluding M491. M490 may be used with the approval of the director of undergraduate studies.

Program II

1. Writing, same as B.A. degree.
2. Foreign language, 3 credit hours (or the equivalent) at or above the second-year level.
3. Arts and humanities, two courses; social and historical studies, two courses; natural sciences, two courses excluding mathematics courses and those counted in the outside concentration.
4. Concentration requirements, at least 33 credit hours of mathematics, including:
1. M301 (or M303), M311, M312, M343, and M344;
2. at least one of the sequences M413-M414 or M413-M415;
3. at least one of the sequences M441-M442, M463-M464, M463-M466, M467-M468, or M471-M472.
5. Computer science A201 or C211 or another course approved by the mathematics department. This requirement may be waived for students who can demonstrate proficiency in computer programming.
6. Outside concentration: a concentration approved by the department consisting of 9 credit hours in the following departments: Astronomy, Biology, Chemistry, Computer Science, Economics, Geology, Physics, or other departments with approval of the mathematics department.

Language Recommendations
Students preparing for graduate study in mathematics or a science are strongly encouraged to study French, German, or Russian.

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Interdepartmental Major in Mathematics and Economics

Purpose
The interdepartmental major in Mathematics and Economics is designed to enable students to model economic questions mathematically, and to analyze and solve those models.

Requirements
Students must meet the following course requirements. Any course may be replaced by the honors equivalent.

1. Economics: E201, E202, E321, E322 and at least three courses from the following list: E327, E427, E471, E472, and approved sections of E390 and E490. With approval of the Department of Economics, E499 may replace one of these three courses.
2. Mathematics: M211-M212, or M213, M301 or M303, M311 and at least two courses, including one at the 400 level, from one of the following mathematics areas: analysis (M312, M413, M414, M415, M420); differential equations (M343, M344, M441, M442); applied mathematics (M371, M447, M448, M451, M471, M472); or probability and statistics (M366*, M463, M464, M465, M466, M467, M468). *Note: M366 has a prerequisite of M360; see requirement three below. For students who qualify for honors, Mathematics S499 may replace the second course in a mathematical area with approval of the Department of Mathematics.
3. Statistics: The sequence Mathematics M360-M366, or Economics E370, or Mathematics M365.

1. No more than 3 credit hours of Honors Thesis (Economics E499 or Mathematics S499) may be counted toward the major.
2. It is recommended that students planning to pursue a Ph.D. in economics consult with the Department of Economics concerning classes in the areas of analysis, econometrics, and statistics.
3. It is recommended that students in actuarial studies take Mathematics M360, M366, M371, M463, M464, and one course from M466, M467, or Economics E471. It is recommended that these students also consult with the Department of Economics concerning relevant seminar courses. Students should consult the actuarial studies section in mathematics.

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Minor in Mathematics

Requirements
Students must complete at least 16 credit hours that include M212, S212, or M213 as well as at least three courses at the 300 or 400 level. The average grade must be at least 2.0 with no grade lower than C-. Courses selected for the minor must be approved by the director of undergraduate studies. In particular, the courses K300, K305, and K310 cannot be selected for the minor.

Recommendations
M365 or M360-M366 are recommended for business and social science majors. M371 is recommended for computer science majors. M311, M312, and M343 are recommended for physics majors. M311 and M343 are recommended for chemistry majors. M311 and M365 are recommended for biology majors.

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Departmental Honors Program

The honors program of the Department of Mathematics is designed for students with a wide variety of interests and goals. It offers optimal preparation for graduate study and for a career as a professional mathematician. It can be combined with education courses to lead to certification as a secondary school teacher. It prepares those who wish to apply mathematical methods to other fields. The program also includes courses for honors students who are not majoring in science and mathematics.

The program for mathematics majors normally begins with S212. Those who wish to graduate with honors in mathematics are expected to complete courses S303, S311, S312, S403, S413-S414, and at least two 6 credit hour "S" or "M" sequences at the 400 level or above. (S403-S404 may be used to fulfill this requirement.) Students in this program must achieve a minimum grade point average of 3.3 in all their courses and at least a grade point average of 3.5 in their mathematics courses. Students who successfully complete most of the courses above may petition the department to qualify for departmental honors. Qualified nonhonors students may petition the department to take honors mathematics courses beginning with S303 or S311.

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Actuarial Studies

Actuaries use mathematics and financial theory to determine the financial effect that uncertain future events such as birth, death, retirement, fire, earthquake, accident, and sickness have on insurance and other benefit plans. Actuaries may work for insurance companies, employee benefits consulting firms, or the benefits departments of general businesses and government agencies. Although Indiana University Bloomington does not offer a degree in actuarial science, it is possible to design a program of study within the general B.A. or B.S. degree in mathematics that will prepare the graduate for entry into the actuarial profession. For further information, contact the mathematics department's academic advisor, Rawles Hall 117, (812) 855-1589.

To advance in the actuarial profession, one must pass a series of examinations given by the Society of Actuaries (www.soa.org) or the Casualty Actuarial Society (www.casact.org). The Course 1 examination is a four-hour test on calculus and probability. The syllabus of the examination is covered in M211, M212, M311, and M463. The courses M464 and M466 provide preparation for more advanced exams. The Course 1 examination is administered in the mathematics department each fall. For more information, contact the department's academic advisor.

It is recommended that students pursuing actuarial studies take Accounting A201-A202 and Economics E201-E202 as well as Computer Science A201 or C211 or Business K201. It is also suggested that the students take a course in business law, such as Business L201.

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Course Descriptions

In the following list of courses, the first digit indicates the level of difficulty. The middle digit normally indicates the field of mathematics: x0y, algebra; x1y, analysis; x2y, topology; x3y, geometry; x4y, applied mathematics; x6y, probability and statistics; x7y, numerical analysis; x8y, history and foundations.
M014 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.
X015 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.
M018 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.
A025 Computer-Based Precalculus Mathematics P: Two years of high school algebra or M014, and one year of high school geometry. A025 is a self-taught version of M025. Although there are no formal lectures, free tutoring is available at various times during the week. Students will buy a CD-ROM, not a text. The required work may be done on any campus computer cluster, or possibly on a personal computer in a dormitory. Class meets once a week for quizzes or exams. Credit may not be applied toward a degree in the College of Arts and Sciences; and a grade of C- or better is needed to satisfy the College of Arts and Sciences mathematics fundamental skills requirement.
M025 Precalculus Mathematics (3 cr.) P: Two years of high school algebra or M014, and one year high school geometry. Designed to prepare students for M211. 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; and a grade of C- or better is needed to satisfy the College of Arts and Sciences mathematics fundamental skills requirement. I Sem., II Sem., SS.
M026 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.
M027 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; and a minimum grade of C- is needed to satisfy the College of Arts and Sciences mathematics fundamental skills requirement. Non-College of Arts and Sciences students should see their advisor about appropriate mathematics selection. I Sem., II Sem.
T104 Mathematics for Elementary Teachers via Problem Solving (4 cr.) P: M118 or consent of department. Emphasizes mathematical thinking, problem solving, and the development of adult-level perspectives about the nature of the mathematics content taught in the elementary school. Topics include number/numeration, whole number operations, real numbers (particularly integers and rationals), topics in number theory, measurement, and informal geometry. Open only to education majors. I Sem., II Sem.
M110 Excursions into Mathematics (3 cr.) P: One year each of high school algebra and geometry or the equivalent. A course designed to convey the flavor and spirit of mathematics, stressing reasoning and comprehension rather than technique. Not preparatory to other courses; explores topics in the theory of games and in properties of polyhedra. This course does not count toward a major in mathematics.
D116-D117 Introduction to Finite Mathematics I-II (2-2 cr.) P: D116: Two years of high school algebra or M014. D117: Two years of high school algebra or M014, and D116 with a grade of at least C-. D116-D117 is a two-course sequence that satisfies the mathematics fundamental skills requirement in the College of Arts and Sciences. Topics for the course are taken from M118. Any requirement of M118 can also be met by D116 and D117 together. Credit not given for D116 until D116 is completed with a minimum grade of C- and D117 is completed with a passing grade. N & M distribution credit will be given only upon completion of both D116 and D117. Credit given for only one of the following: the sequence D116-D117 or M118 or A118.
A118 Finite Mathematics for the Social and Biological Sciences (3 cr.) N & M P: Two years of high school algebra or M014. Quantitative reasoning (elementary combinatorics and probability; examples of statistical inference), linear modeling, game models of conflict, and methods and theory of social choice. Applications to genetics, medical diagnosis, law, finance, social science research, ecology, and politics. Credit given for only one of A118, M118, or the sequence D116-D117. I Sem., II Sem.
M118 Finite Mathematics (3 cr.) N & M P: Two years of high school algebra or M014. Sets, counting, basic probability, including random variables and expected values. Linear systems, matrices, linear programming, and applications. Credit given for only one of M118, A118, or the sequence D116-D117.
S118 Honors Finite Mathematics (3 cr.) 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.
M119 Brief Survey of Calculus I (3 cr.) 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 cannot receive credit for more than one of the following: M119, M211, or COAS J113. I Sem., II Sem., SS.
M120 Brief Survey of Calculus II (3 cr.) N & M P: M119. 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.
M211-M212 Calculus I-II (4-4 cr.) 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, techniques of integration, infinite series. A student cannot receive credit for more than one of the following: M119, M211, COAS J113; likewise not more than one of M120 or M212. I Sem., II Sem., SS.
S212 Honors Calculus II (4 cr.) 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.
M213 Accelerated Calculus (4 cr.) 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.
M295 Readings 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.
S299 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.
K300 (PSY K300) Statistical Techniques (3 cr.) P: M014 or equivalent. R: M118. An introduction to statistics. Nature of statistical data. Ordering and manipulation of data. Measures of central tendency and dispersion. Elementary probability. Concepts of statistical inference decision: estimation and hypothesis testing. Special topics discussed may include regression and correlation, analysis of variance, non-parametric methods. Credit given for only one of the following: K300, K310; CJUS K300; ECON E370 or S370; SOC S371; or SPEA K300. I Sem., II Sem., SS.
M301 Linear Algebra and Applications (3 cr.) 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.
M303 Linear Algebra for Undergraduates (3 cr.) 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.
S303 Honors Course in Linear Algebra (3 cr.) 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.
K305 Statistical and Mathematical Techniques for Journalism (3 cr.) P: One college-level mathematics course and JOUR J200. R: M118. Intended for journalism majors. An introduction to the mathematical and statistical methods necessary in the practice of journalism. Working with data, measures of central tendency and dispersion. Statistical inference and hypothesis testing. The use of spreadsheets in statistical work. Focus on the exposition of mathematical and statistical results. Credit given for only one of the following: K300, K305, K310; CJUS P291; ECON E370; PSY K300; SOC S371, or SPEA K300.
K310 (PSY K310) Statistical Techniques (3 cr.) P: M119 or equivalent. Introduction to probability and statistics. Elementary probability theory, conditional probability, independence, random variables, discrete and continuous probability distributions, measures of central tendency and dispersion. Concepts of statistical inference and decision: estimation, hypothesis testing, Bayesian inference, statistical decision theory. Special topics discussed may include regression and correlation, time series, analysis of variance, non-parametric methods. Credit given for only one of the following: PSY or MATH K300, K310; CJUS K300; ECON E370 or S370; SOC S371; or SPEA K300. I Sem., II Sem.
M311 Calculus III (4 cr.) 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.
S311 Honors Course in Calculus III (4 cr.) 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.
M312 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.
S312 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.
T321 Intuitive Topology (3 cr.) N & M P: M212 or consent of instructor. Intuitive description of topology, including networks and maps, topological equivalence, classification of surfaces, spheres with handles, Jordan curve theorem, transformations, and fixed-point theorems. II Sem.
M330 Exploring Mathematical Ideas (3 cr.) 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.
T336 Topics in Euclidean Geometry (3 cr.) 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.
M343-M344 Introduction to Differential Equations with Applications I-II (3-3 cr.) N & M P for M343: M212. P for M344: 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.
M347 Discrete Mathematical Models (3 cr.) 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.
M360 Elements of Probability (3 cr.) P: M212 and M311, which may be taken concurrently. Introduction to theory of probability. Probability models, combinatorial problems, conditional probability and independence, random variables, discrete and continuous distributions, repeated Bernoulli trials, gambler's ruin problems, moments, moment generating functions, law of large numbers, central limit theorem and applications. Credit not given for both M360 and M365. I Sem.
M365 Introduction to Probability and Statistics (3 cr.) 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.
M366 Elements of Statistical Inference (3 cr.) P: M360. Introduction to statistical theory. Basic sampling distributions. Order statistics. Point estimation, maximum likelihood estimation, the Cramer-Rao bound, least squares method, confidence intervals, hypothesis-testing concepts, Neyman-Pearson lemma, likelihood ratio tests, linear models, large sample theory, contingency tables, goodness-of-fit tests. II Sem.
M371 Elementary Computational Methods (3 cr.) 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.
M380 History of Mathematics (3 cr.) P: M212. 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.
M385 Mathematics from Language (3 cr.) 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.
M391 Foundations of the Number System (3 cr.) N & M P: M212 or both M211 and CSCI C241. R: M212. Sets, functions and relations, groups, real and complex numbers. 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. II Sem.
Y398 Internship in Professional Practice (1-3 cr.) S/F grading. P: Approval of Department of Mathematics. 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 total of 6 credits.
M403-M404 Introduction to Modern Algebra I-II (3-3 cr.) P: M301 or M303. Study of groups, rings, field extensions, with applications to linear transformations. M403, I Sem.; M404, II Sem.
S403-S404 Honors Course in Modern Algebra I-II (3-3 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.
T403 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.
M405 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.
M409 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.
M413-M414 Introduction to Analysis I-II (3-3 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.
S413-S414 Honors Course in Analysis I-II (3-3 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.
M415 Elementary Complex Variables with Applications (3 cr.) P: M311. Algebra and geometry of complex numbers, elementary functions of a complex variable, power series, integrations, calculus of residues, conformal mapping. Application to physics. II Sem.
M420 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.
M435 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.
H435 Summer Institute for Mathematics Teachers (3 cr.) Intensive four-week seminar/workshop designed for middle and high school mathematics teachers. Topics from Euclidean geometry and probability and statistics will be explored using computer software.
M441-M442 Introduction to Partial Differential Equations with Applications I-II (3-3 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.
H447 Summer Institute in Mathematical Models (4 cr.) S/F grading. P: M303, M365. Introduction to mathematical models and computer tools for modeling. Mathematical topics include games, graphs, queues, growth processes, and optimization. Emphasis on small group problem solving and on topics which can be incorporated into the high school curriculum.
M447-M448 Mathematical Models and Applications I-II (3-3 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.
M451 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.
M453 Cryptography (3 cr.) 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 algorithyms, EIGamal cryptosystem, discrete log problem, other public key cryptosystems, signature schemes, hash functions, key distribution and key agreement.
M463 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.
S463 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.
M464 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.
S464 Honors Course in Probability Theory II (3 cr.) P: S463 or consent of instructor. Honors version of M464. For students of outstanding ability in mathematics.
M466 Introduction to Mathematical Statistics (3 cr.) P: M463 or consent of instructor. Rigorous mathematical treatment of problems in sampling and statistical inference. Sufficient statistics, exponential distributions, monotone likelihood ratio, most powerful tests, minimum variance estimates, shortest confidence intervals, linear models and analysis of variance, non-parametric methods. II Sem.
M467 Advanced Statistical Techniques I (3 cr.) P: M366 or consent of instructor. Statistical techniques of wide application, developed from the least-squares approach: fitting of lines and curves to data, multiple regression, analysis of variance of one-way and two-way layouts under various models, multiple comparison. I Sem.
M468 Advanced Statistical Techniques II (3 cr.) P: M366 or consent of instructor. Analysis of discrete data, chi-square tests of goodness of fit and contingency tables, Behrens-Fisher problem, comparison of variances, nonparametric methods, and some of the following topics: introduction to multivariate analysis, discriminant analysis, principal components. II Sem.
M471-M472 Numerical Analysis I-II (3-3 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.
M482 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.
M490 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.
M491 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.
S499 Reading for Honors (12 cr. max.) P: Approval of departmental honors committee. I Sem., II Sem., SS.

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