# Courses in Mathematics and Statistics

**A MAT 100 Precalculus Mathematics (3)**This course provides a background in those topics that are needed for success in calculus. Topics include graphing techniques, systems of equations, functions, logarithms, and trigonometry. May not be taken for credit by students with credit in any calculus course. Student with credit for the former A MAT 103 (College Algebra) may not take A MAT 100 for credit). Prerequisite(s): three years of high school mathematics or permission of department. May not be offered in 2015-2016.

**A MAT 101 Algebra and Calculus I (3)**An integrated approach to pre-calculus and calculus. Elements of algebra and analytic geometry necessary to study calculus of one variable. Functions, limits, continuity, differentiation of algebraic functions, applications of differentiation. May not be taken for credit by students with credit for A MAT 100, 106, 112, or 118. Prerequisite(s): three years of high school mathematics or permission of the department.

**A MAT 104 Topics in Contemporary Mathematics (3)**An introduction to application of mathematics to everyday life requiring a background of only standard high school mathematics (intermediate algebra and a little Euclidean geometry). Suggested topics include the mathematics of voting, management science through graph theory, and growth and symmetry. Prerequisite(s): two years of high school mathematics.

**A MAT 105 Finite Mathematics (3)**

An introduction to topics of interest to students of the social sciences; sets and logic, partitions and counting, probability, vectors and matrices, theory of games. Prerequisite(s): three years of high school mathematics. May not be offered in 2015-2016.

**A MAT 106 Survey of Calculus (3)**An intuitive approach to differentiation and integration of algebraic and transcendental functions, intended only for students who plan to take no more calculus. Does not yield credit toward the major or minor in mathematics. May not be taken for credit by students with credit for A MAT 111, 112 or 118. Prerequisite(s): three years of high school mathematics.

**A MAT 108 Elementary Statistics (3)**Frequency distributions, measures of central tendency and dispersion, probability and sampling, estimation, testing of hypotheses, linear regression, and correlation. Only one of A MAT 108 and B ITM 220 may be taken for credit. Not open for credit by students who have taken A MAT 308. Prerequisite(s): three years of high school mathematics.

**A MAT 111 Algebra and Calculus II (4)**The second semester of an integrated approach to pre-calculus and calculus; serves as a prerequisite to A MAT 113. Applications of differentiation, the definite integral, anti-derivatives, logarithms, trigonometry, exponential functions. Only one of A MAT 111, 112, 118/118H and T MAT 118 may be taken for credit. Prerequisite(s): A MAT 101.

**A MAT 112 Calculus I (4)**Calculus of one variable. Limits, continuity, differentiation of algebraic functions, applications of differentiation, anti-derivatives, the definite integral, transcendental functions. A MAT 118 is the honors version of A MAT 112 and substitutes for A MAT 112 toward the prerequisite in any course. Only one of A MAT 111, 112, 118/118H and T MAT 118 may be taken for credit. Prerequisite(s): A MAT 100 or precalculus at the high school or college level. Students without precalculus should elect A MAT 101.

**A MAT 113 Calculus II (4)**Techniques of integration, applications of the definite integral, conics, polar coordinates, improper integrals, infinite series. A MAT 119 is the honors version of A MAT 113 and substitutes for A MAT 113 toward the prerequisite in any course. Only one of A MAT 113, 119/119H and T MAT 119 may be taken for credit. Prerequisite(s): A MAT 111 or 112.

**A MAT 118 Honors Calculus I (4)**Honors version of first semester calculus. Same topics as A MAT 112, but topics are covered in greater depth. This course is for students with more than average ability and more than average interest in mathematics. A MAT 118 substitutes for A MAT 112 toward the prerequisite in any course. Only one of A MAT 111, 112, 118/118H and T MAT 118 may be taken for credit. Prerequisite(s): three years of secondary school mathematics and permission of instructor. Offered Spring semester only. May not be offered in 2015-2016.

**A MAT 119 Honors Calculus II (4)**Honors version of second semester calculus. Same topics as A MAT 113, but topics are covered in greater depth. This course is for students with more than average ability and more than average interest in mathematics. A MAT 119 substitutes for A MAT 113 toward the prerequisite in any course. Only one of A MAT 113, 119/119H, and T MAT 119 may be taken for credit. Prerequisite(s): A MAT 118, a grade of

*A*in A MAT 112, or permission of instructor. Offered Fall semester only.

**T MAT 119 (formerly A MAT 119H) Honors Calculus II (4)**T MAT 119 is the Honors College version of A MAT 119. Only one of A MAT 113, 119/119H, and T MAT 119 may be taken for credit. Prerequisite(s): A MAT 118, a grade of

*A*in A MAT 112, or permission of instructor. Offered Fall semester only.

**A MAT 214 Calculus of Several Variables (4)**Curves and vectors in the plane, geometry of three-dimensional space, vector functions in three-space, partial derivatives, multiple integrals, line and surface integrals. Prerequisite(s): A MAT 113 or 119.

**A MAT 218 Honors Calculus of Several Variables (4)**Same topics as A MAT 214, but topics are covered in greater depth. This course is for students with more than average ability and more than average interest in mathematics. A MAT 218 substitutes for A MAT 214 towards the prerequisites in any course. T MAT 218 is the Honors College version of A MAT 218. Only one of A MAT 214, A MAT 218 and T MAT 218 may be taken for credit. Prerequisite(s): A MAT 119 or T MAT 119, or grade of

*A*in A MAT 113, or permission of the instructor. Offered Spring semester only.

**T MAT 218 (formerly T MAT 214) Honors Calculus of Several Variables (4)**Honors version of third semester calculus. Same topics as A MAT 214, but topics are covered in greater depth. This course is for students with more than average ability and more than average interest in mathematics. T MAT 218 substitutes for A MAT 214 towards the prerequisites in any course. T MAT 218 is the Honors College version of A MAT 218. Only one of A MAT 214, A MAT 218 and T MAT 218 may be taken for credit. Prerequisite(s): A MAT 113. Open to Honors College students only. Offered Spring semester only.

**A MAT 220 Linear Algebra (3)**Linear equations, matrices, determinants, finite dimensional vector spaces, linear transformations Euclidean spaces. Prerequisite(s): A MAT 113.

**A MAT 222 Honors Linear Algebra (3)**Honors version of linear algebra. Same topics as A MAT 220, but topics are covered in more depth, with more emphasis on theory. This course is for students with more than average ability and more than average interest in mathematics. A MAT 222 substitutes for A MAT 220 towards the prerequisites in any course. Only one of A MAT 222, T MAT 222, and A MAT 220 may be taken for credit. Prerequisite(s): grade of A in A MAT 113 or A MAT 214, and permission of the instructor, or a grade of B+ in A MAT 119 , T MAT 119, A MAT 218, or T MAT 218. Offered Fall semester only.

**T MAT 222 Honors Linear Algebra (3)**

Honors version of linear algebra. Same topics as A MAT 220, but topics are covered in more depth, with more emphasis on theory. This course is for students with more than average ability and more than average interest in mathematics. T MAT 222 substitutes for A MAT 220 towards the prerequisites in any course. T MAT 222 is the Honors College version of A MAT 222. Only one of A MAT 222, T MAT 222, and A MAT 220 may be taken for credit. Prerequisite(s): grade of A in A MAT 113 or A MAT 214, and permission of the instructor, or a grade of B+ in A MAT 119 , T MAT 119, A MAT 218, or T MAT 218. Open to Honors College students only. Offered Fall semester only.

**T MAT 252W An Introduction to the Great Theorems of Mathematics**This course for the honors College is an introduction to the great theorems of mathematics in geometry, algebra, number theory, analysis and statistics. The course is designed for students of all majors. Students will develop an appreciation for different branches of mathematics. Step-by-step proofs of some theorems of Pythagoras, Euclid, Archimedes, Heron, Cardano, Newton, Fermat, Euler, Gauss and Cantor will be provided by lectures, class discussions, writing projects and class presentations. Students will learn how these theorems fit into the history of mathematics. Pascal's triangle and the binomial theorem, the Chinese remainder theorem, Pell's equations, Wilson's theorem, the bridges of Konigsberg problem, the four color theorem and the central limit theorem will also be discussed. Prerequisites: High school mathematics through pre-calculus. Open to Honors College students only.

**A MAT 287/287Z Topics Involving Mathematics (1-3) **Selected topics in mathematics. The topic of the course will be indicated in the course schedule and in departmental announcements. May be repeated for credit when content varies. May not be offered in 2015-2016.

**A MAT 299 Introduction to Proofs (3)**Introduction to the methods of higher mathematics, with emphasis on how to read, understand, discover, and write proofs. Topics include basic logic, sets, functions, relations, mathematical induction, countable and uncountable sets, and elementary number theory. This course will require a significant amount of written and oral presentation. Students may receive credit for only one of I CSI 221, A MAT 221 and A MAT 299. Prerequisite(s): Mathematics major; one of A MAT 113, 119, 214 or 218 with a grade of

*C*or better. Corequisite: U UNL 299.

**A MAT 301 (= A ECO 351) Theory of Interest (3)**The basic measures of interest, annuities, sinking funds, amortization schedules, bonds, and installment loans. Recommended as preparation for Actuarial Society exam FM. Only one version of A MAT 301 may be taken for credit. Prerequisite(s): A MAT 113.

**A MAT 308 Topics in Statistical Inference (3)**Various statistical techniques such as chi-square tests, multiple regression and correlation; nonparametric statistics, and the analysis of variance as applied to physical, biological, and social sciences. Prerequisite(s): some prior experience with elementary statistics

**.**

**A MAT 311 Ordinary Differential Equations (3)**Linear differential equations, systems of differential equations, series solutions, boundary value problems, existence theorems, applications to the sciences. Prerequisite(s): A MAT 214.

**A MAT 312/312Z Basic Analysis (3)**Theoretical aspects of calculus including construction of the real numbers, differentiation and integration of functions in one variable, continuity, convergence, sequences and series of functions. Only one version of A MAT 312 may be taken for credit. Prerequisite(s): A MAT 214.

**A MAT 314 Analysis for Applications I (3)**Introduction to topics in mathematical analysis which traditionally have been applied to the physical sciences, including vector analysis, Fourier series, ordinary differential equations, and the calculus of variations. Prerequisite(s): A MAT 214 and 220. Offered Fall semester only.

**A MAT 315 Analysis for Applications II (3)**Continuation of A MAT 314. Series solutions of differential equations, partial differential equations, complex variables, and integral transforms. Prerequisite(s): A MAT 314. Offered Spring semester only.

**A MAT 326/326Z Classical Algebra (3)**Elementary number theory. Elementary theory of equations over rational, real, and complex fields. Only one version of A MAT 326 may be taken for credit. Prerequisite(s): A MAT 113.

**A MAT 327/327Z Elementary Abstract Algebra (3)**Basic concepts of groups, rings, integral domains, fields. Only one version of A MAT 327 may be taken for credit. Prerequisite(s): A MAT 220, 326.

**A MAT 328 Introduction to Combinatorics (3)**

The pigeonhole principle. Basic discrete structures and their enumeration: permutations, combinations, partitions, Catalan numbers. Generalizations of the binomial theorem and related identities. The principle of inclusion-exclusion. Recurrence relations and generating functions. Introduction to graph theory: Eulerian walks, Hamiltonian cycles, trees, matchings, coloring maps. Prerequisite(s): A MAT 221 or A MAT 299.

**A MAT 331/331Z Transformation Geometry (3)**Classical theorems of Menelaus, Ceva, Desargues, and Pappus. Isometries, similarities, and affine transformations for Euclidean geometry. Only one version of A MAT 331 may be taken for credit. Prerequisite(s): A MAT 220. Usually offered Spring semester only.

**A MAT 342/342Z Elementary Topology (3)**Networks, map coloring problems, surfaces, topological equivalence, the Euler number, the polygonal Jordan curve theorem, homotopy, the index of a transformation, and the Brouwer Fixed Point Theorem. Only one version of A MAT 342 may be taken for credit. Prerequisite(s): A MAT 214 and 220. Usually offered Fall semester only.

**A MAT 362/362Z Probability for Statistics (3)**Introduction to discrete and continuous probability models, including probability mass functions, density functions, and cumulative distribution functions. Discrete examples will include the binomial, negative binomial, Poisson, and hypergeometric distributions. Continuous distributions will include the normal and exponential distributions, the family of gamma and beta densities, and, if time permits, t and chi-square distributions. Other topics are the probability axioms, equally likely sample spaces (combinatorics), conditional probability, joint distributions, marginal distributions, conditional distributions, covariance, correlation, moment generating functions, and the Central Limit Theorem. Only one version of A MAT 362 may be taken for credit. A MAT 362 constitutes substantial preparation for Actuarial Exam P. A student may not apply both A MAT 362 and A MAT 367 toward any major or minor in mathematics or a minor in statistics. Prerequisite(s): calculus through A MAT 214 or the equivalent.

**A MAT 363/363Z Statistics (3)**A calculus-based introduction to statistics. Confidence intervals and hypothesis tests for means and variances, differences of means and ratios of variances, including P-values, power functions and sample size estimates and involving normal, binomial, t, chi-square, and F distributions. Additional topics may include introductions to simple linear regression, Bayesian statistics, sample survey methods, goodness of fit tests, non-parametric tests, or analysis of variance. Only one version of A MAT 363 may be taken for credit. Students with credit for A MAT 367 but who have not taken A MAT 362 may take A MAT 363 only with permission of instructor. Students with credit for A MAT 368 may not take A MAT 363. Prerequisite(s): A MAT 362.

**A MAT 367/367Z Discrete Probability (3)**Introduction to discrete probability models (including the binomial, negative binomial, Poisson, and hypergeometric distributions, their means, variances and cumulative distribution functions). Other topics include probability axioms, equally likely sample spaces (combinatorics), conditional probability, the gamblers' ruin problem, finite state Markov chains, moment generating functions, joint distributions (including the multinomial distribution), marginal distributions, conditional distributions, covariance and correlation, the weak law of large numbers, and, if time permits, the Central Limit Theorem. Students who intend to take A MAT 363 should take A MAT 362, not A MAT 367. Students who have taken A MAT 367 and who wish to take a first statistics course can take A MAT 308. Actuarial students who need continuous as well as discrete probability, should take A MAT 362 (which constitutes substantial preparation for Actuarial Exam P). A student may not apply both A MAT 362 and A MAT 367 toward any major or minor in mathematics or a minor in statistics. Only one version of A MAT 367 may be taken for credit. Prerequisite(s): A MAT 113 or 119, plus 6 credits at the 200 or higher level in either mathematics or computer science.

**A MAT 369 Statistics and Data Analysis (3)**A topics course whose content will vary somewhat from semester to semester. In the recent past the course has focused on analysis of variance, categorical data analysis, distribution free methods, and survey sampling. Other possible topics include Bayesian statistics, bootstrap methods, log-linear models, lifetime distributions, Meier-Kaplan estimators, and the Mantel-Haenszel test. Topics covered in A MAT 465 (multiple regression and time series) would be avoided. May be repeated for credit with permission of instructor. Prerequisite(s): A MAT 363.

**A MAT 370 Probability and Statistics for Engineering and the Sciences (3)**

Basic probability, conditional probability and independence, families of discrete and continuous random variables, expected values and variances, moment generating functions, bivariate distributions, Bayesian networks, law of large numbers and central limit theorem, normal, t, and chi-square distributions, confidence intervals and hypothesis testing and simple linear regressions. A MAT 370 is a one semester introduction to probability and statistics intended primarily for science or engineering majors who have completed two semesters of calculus. Students cannot apply both A MAT 362 and A MAT 370 or both A MAT 363 and A MAT 370 toward the requirements for a Mathematics major. A MAT 370 fulfills the probability/statistics requirement for the Mathematics BA. A MAT 367 and A MAT 370 can be one of the two sequences required for the B.S. in Mathematics. Students who expect to do graduate work in mathematics or statistics should take both A MAT 362 and A MAT 363, not A MAT 370. Prerequisite(s): A MAT 367 or I CSI 210.

**A MAT 372/372Z Linear Programming and Game Theory (3)**Theory and methods of linear programming, duality theory, and matrix games, including the simplex algorithm and an introduction to interior point methods. A MAT 372Z is the writing intensive version of A MAT 372; only one version may be taken for credit. Prerequisite(s): A MAT 214 and 220. May not be offered in 2015-2016.

**A MAT 374 Operations Research (3)**Operations research techniques and applications, linear programming, queuing theory, including birth and death processes, decision theory, network analysis, simulation. Prerequisite(s): A MAT 362 or 367 or permission of instructor. May not be offered in 2015-2016.

**A MAT 401 Numerical Analysis (3)**Error analysis, numerical solution of nonlinear equations, interpolation and polynomial approximation, numerical differentiation and integration, direct methods for solving linear systems. Not more than one of A MAT 313 or 401 may be taken for credit. Prerequisite(s): A MAT 220. Offered Fall semester only. May not be offered in 2015-2016.

**A MAT 403 Life Contingencies I (3)**Treatment of single and joint lives including mortality functions, various kinds of annuities and life insurance, premiums, reserves and standard actuarial notations for these concepts. Recommended as partial preparation for Actuarial Exam M. Prerequisite(s): A MAT 301, 362, 363.

**A MAT 404 Life Contingencies II (3)**Expansion of A MAT 403 with emphasis on two or more lives in combination and on multiple causes of decrement. Topics include population theory, multi-life statuses, multi-life functions, reversionary annuities, multiple-decrement functions, primary and secondary decrements, and applications of multiple-decrement functions. Prerequisite(s): A MAT 403. May not be offered in 2015-2016.

**A MAT 409 Vector Analysis (3)**Classical vector analysis presented heuristically and in physical terms. Topics include the integral theorems of Gauss, Green, and Stokes. Prerequisite(s): A MAT 214. Offered Spring semester only.

**A MAT 412/412Z Complex Variables for Applications (3)**The elementary functions, differentiation, conformal transformations, power series, integral theorems, Taylor’s theorems, Taylor’s and Laurent’s expansions, applications of residues. Only one version of A MAT 412 may be taken for credit. Prerequisite(s): A MAT 214. Usually offered Fall semester only.

**A MAT 413/413Z Advanced Calculus I (3)**A rigorous presentation of the traditional topics in the calculus of several variables and their applications. Topics include the implicit function theorem, Taylor's theorem, Lagrange multipliers, Stieltjes integral, Stokes' theorem, infinite series, Fourier series, special functions, Laplace transforms. Only one version of A MAT 413 may be taken for credit. Prerequisite(s): A MAT 312. Offered Fall semester only.

**A MAT 414 Advanced Calculus II (3)**A rigorous presentation of the traditional topics in the calculus of several variables and their applications. Topics include the implicit function theorem, Taylor's theorem, Lagrange multipliers, Stieltjes integral, Stokes' theorem, infinite series, Fourier series, special functions, Laplace transforms. Prerequisite(s): A MAT 413. Offered Spring semester only.

**A MAT 416 Partial Differential Equations (3)**The partial differential equations of classical mathematical physics. Separation of variables, eigenvalue problems, Fourier series and other orthogonal expansions. First order equations, Green’s functions, Sturm-Liouville theory, and other topics as time permits. Prerequisite(s): a course in Ordinary Differential Equations.

**A MAT 420 Topics in Abstract Algebra (3)**Topics in abstract algebra chosen by the instructor. The focus of the course will be publicized in departmental announcements. Prerequisite(s): A MAT 327.

**A MAT 424 Advanced Linear Algebra (3)**Duality, quadratic forms, inner product spaces, and similarity theory of linear transformations. Prerequisite(s): AMAT 220 and AMAT 326, or permission of instructor. Offered Fall semester only.

**A MAT 425 Number Theory (3)**Divisibility, congruences, quadratic reciprocity, Diophantine equations, sums of squares, cubes, continued fractions, algebraic integers. Prerequisite(s): A MAT 326. Offered Spring semester only.

**A MAT 432/432Z Foundations of Geometry (3)**Axiomatic development of absolute geometry, theory of parallels, introduction to non-Euclidean geometry, isometries of the Bolyai-Lobachevsky plane. Only one version of A MAT 432 may be taken for credit. Prerequisite(s): A MAT 220 or equivalent. Offered Fall semester only.

**A MAT 441 Introduction to Differential Geometry (3)**Differential geometry of curves and surfaces in Euclidean space, frames, isometries, geodesics, curvature, and the Gauss-Bonnet theorem. Prerequisite(s): A MAT 214 and 220. Offered Spring semester only.

**A MAT 442 Introduction to Algebraic Topology (3)**Two-dimensional manifolds, the fundamental group and Van Kampen’s theorem, covering spaces, graphs, and applications to group theory. Prerequisite(s): A MAT 214 and 220. May not be offered in 2015-2016.

**A MAT 452/452Z History of Mathematics (3)**History of the development of mathematics, emphasizing the contributions of outstanding persons and civilizations. Normally only the writing intensive version of this course is offered

**.**Only one version of A MAT 452 may be taken for credit. Prerequisite(s): A MAT 214, 326, and either 331 or 432. Offered Fall semester only.

**A MAT 464 Applied Stochastic Processes (3)**An overview of stochastic processes with particular emphasis on Markov chains. Introduction to queuing theory. Particular attention given to estimation. Recommended as partial preparation for Actuarial Exams M and C. Prerequisite(s): One of A MAT 362 or 367 or 467. Offered Spring semester only.

**A MAT 465/465Z Applied Statistics (3)**A

**second or third course in statistics, focusing on simple and multiple regression and time series. Course carries VEE credit from the Society of Actuaries in applied statistics. Only one version of A MAT 465 may be taken for credit. Prerequisite(s): A MAT 220 and one of A MAT 308, 363, or 468. Offered Fall semester only.**

**A MAT 467 Continuous Probability and Mathematical Statistics (3)**One and two dimensional calculus applied to probability. Continuous random variables in one and two dimensions, including the normal, bivariate normal, exponential, gamma (including chi-square), and beta. Density functions of transformations of random variables. Moment generating functions, weak law of large numbers, central limit theorems, convergence of random variables. Maximum likelihood and unbiased estimators. Confidence intervals, mainly for normal means and variances. Recommended as partial preparation for Actuarial Exam P. Prerequisite(s): A MAT 214 and 220 and one of A MAT 362 or 367. Offered Fall semester only.

**A MAT 468 Mathematical Statistics (3)**Neyman-Pearson theory (hypothesis testing), type I and II errors, power functions, generalized likelihood ratio tests. Two-sample confidence intervals and hypothesis tests. Sampling distributions, including the t, chi-square and F, all rigorously defined. Sufficient statistics, Fisher information, minimum variance estimators. Introduction to regression and Bayesian estimators. Some listed topics are tested on Actuarial Exam C. Prerequisite(s): A MAT 467. Offered Spring semester only

**.**

**A MAT 469 Actuarial Probability and Statistics (1)**Drill in problem solving for one of the following Actuarial Exams: P, FM or M. May be repeated for credit with permission of instructor. Prerequisites depend on which of the three Actuarial Exams is featured.

*S/U*Graded.

**A MAT 475 Optimization Theory (3)**

Introduction to optimization. Constrained optimization and Lagrange multipliers. Convex sets, convex functions and conjugate functions. Fenchel duality, convex optimization, Lagrange duality, non-linear programming. Karush-Tucker conditions and calculus of variations. Prerequisite(s): A MAT 214 and 220.

**A MAT 482/482Y/482W Senior Seminar (3)**Study of topics in mathematics, chosen at the discretion of the instructor. Only one version of A MAT 482 may be taken for credit. Prerequisite(s): permission of instructor.

**A MAT 487 Topics in Modern Mathematics (3)**Selected topics in mathematics. The topic of the course will be indicated in the course schedule and in departmental announcements. The course may be repeated for credit when content varies. Prerequisites for A MAT 487 will be as indicated on the departmental announcements.

**A MAT 497 Independent Study in Mathematics (1–3)**Individual, independent study of selected topics not covered in a regularly scheduled course. Open only to majors in mathematics. May be repeated for credit. Prerequisite(s): junior or senior standing, and permission of instructor with whom student wishes to study.

**A MAT 499Z Undergraduate Thesis (3)**Individual, independent study leading to an undergraduate thesis under the direction of faculty chosen by the student. The thesis may be used to fulfill the thesis requirement in the honors program with the approval of the department. Prerequisite(s): permission of instructor.