Catalog

Mathematics

After completing one semester of calculus with a grade of C (2.000) or better, no math major may receive credit in any mathematics course numbered below 1300. No student may obtain more than 9 hours of credit in mathematics courses numbered below 1300. A grade of C- or above is required for all prerequisite courses.

MATH 1005-3. Introduction to College Mathematics. Introductory level mathematics course which presents a college level introduction to algebraic functions and their applications. Student with credit for MATH 1005 receives only one additional hour of credit for MATH 1001, 1011 or 1012 or two additional hours of credit for MATH 1150. Course is only offered through the Student Academic Service Center. Meets MAPS requirement for mathematics.

MATH 1011-3. Fundamentals and Techniques of College Algebra. Covers simplifying algebraic expressions, factoring linear and quadratic equations, inequalities, exponentials, logarithms, functions, and graphs, and systems of equations. Credit not granted for this course and MATH 1010, 1020, and 1150. Prereq., one year high school algebra or placement exam score for MATH 1000. Meets MAPS requirement for mathematics. Approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.

MATH 1012-3. Quantitative Reasoning and Mathematical Skills. Promotes mathematical literacy among liberal arts students. Teaches basic mathematics, logic, and problem-solving skills in the context of higher level mathematics, science, technology, and/or society. This is not a traditional math class, but is designed to stimulate interest in and appreciation of mathematics and quantitative reasoning as valuable tools for comprehending the world in which we live. Credit not granted for this course and QRMS 1010. Meets MAPS requirement for mathematics. Approved for arts and sciences core curriculum: mathematical skills.

MATH 1021-2. Numerical and Analytical College Trigonometry. Covers trigonometric functions, identities, solutions of triangles, addition and multiple angle formulas, inverse and trigonometric functions, and laws of sines and cosines. Credit not granted for this course and MATH 1150, 1030 or 1040. Prereqs., MATH 1011 or 1020, or placement exam score for MATH 1030, or 1 1/2 years or high school algebra and 1 year of high school geometry.

MATH 1071-3. Finite Mathematics for Social Science and Business. Discusses systems of linear equations and introduces matrices, linear programming, and probability. Prereq., MATH 1011 or 1000, placement exam score for MATH 1020, or one and a half years of high school algebra. Credit not granted for this course and MATH 1050, 1060 and 1070. Approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.

MATH 1081-3. Calculus for Social Science and Business. Covers differential and integral calculus of algebraic, logarithmic, and exponential functions. Prereq., MATH 1011, 1071, 1010, or 1070 or placement exam score for MATH 1020 or two years high school algebra. Credit not granted for this course and MATH 1080, 1090, 1100, 1300, 1310, APPM 1350, and ECON 1088. Approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.

MATH 1110-3. The Spirit and Uses of Mathematics 1. For liberal arts students and prospective elementary teachers. Includes a study of problem-solving techniques in mathematics, the uses and role of mathematics in our society, and the structure of our familiar number systems. Additional topics are chosen from number theory, ancient numeration systems, computer science, modern geometry and algebra, and elementary logic. Prereq., one year of high school algebra and one year of plane geometry. The combination MATH 1110 and 1120 is approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.

MATH 1120-3. The Spirit and Uses of Mathematics 2. Continuation of MATH 1110. Prereq., one year of high school algebra and one year of plane geometry. The combination MATH 1110 and 1120 is approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.

MATH 1130-3. Mathematics from the Visual Arts. Introduces mathematical concepts through the study of visual arts. In practicum and lectures, students study the symmetry groups of patterns, shibori-like paper cuttings, origami, and mandalas. Also studied are Euler’s characteristics, perspective, golden ratio, computer art, and fractals. Credit not granted for this course and QRMS 1130. Approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.

MATH 1150-4. Precalculus Mathematics. Develops techniques and concepts prerequisite to calculus through the study of trigonometric, exponential, logarithmic, polynomial, and other functions. Prereq., one and a half years of high school algebra. Students having credit for college algebra and trigonometry may not receive additional credit for MATH 1150. Students with credit for college algebra receive only 2 additional hours of credit for MATH 1150. Similar to MATH 1000, 1010, 1020, 1011, 1021, 1030, and 1040. Meets MAPS requirement for mathematics. Approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.

MATH 1300-5. Analytic Geometry and Calculus 1. Topics include limits, derivatives of algebraic and trigonometric functions, applications of the derivative, integration and application of the definite integral. Prereqs., two years high school algebra, one year geometry, and 1/2 year trigonometry or MATH 1150. Credit not granted for this course and MATH 1081, 1310, APPM 1345, 1350, and ECON 1088. Similar to MATH 1080, 1090, and 1100. Approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.

MATH 1310-5. Calculus 1 with Biological Applications. The topics, prerequisites, and credit restrictions are the same as for MATH 1300, but a greater emphasis is placed on synthesizing the geometric, numerical, and algebraic aspects of each concept and on exploring “real world” applications of calculus. Especially recommended for biology majors. Prereq., 2 years high school algebra, 1 year geometry, and 1/2 year trigonometry, or MATH 1150. Credit not granted for this course and MATH 1080, 1081, 1090, 1100, 1300, APPM 1350, or ECON 1088. Approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.

MATH 1410-3. Mathematics for Secondary Educators. Assists students in meeting state mathematics certification requirements. Topics include problem solving, number systems, geometry and measurement, probability and statistics. Enrollment is restricted to students already admitted to or intending to apply for admission to the secondary teacher education program. Prereqs., one year high school algebra, one year geometry. Approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.

MATH 2001-3. Introduction to Discrete Mathematics. Introduces the ideas of rigor and proof through an examination of basic set theory, quantification theory, elementary counting, discrete probability, and additional topics. Prereq., MATH 1300 or APPM 1350.

MATH 2300-5. Analytic Geometry and Calculus 2. Continuation of MATH 1300. Topics include transcendental functions, methods of integration, polar coordinates, conic sections, improper integrals, and infinite series. Prereq., Calculus 1. Credit not granted for this course and MATH 1320 or APPM 1360.

MATH 2380-3. Mathematics for the Environment. An interdisciplinary course where analysis of real phenomena such as acid rain, population growth, and road-killed rabbits in Nevada leads to consideration of various fundamental concepts in mathematics. One-third of the course consists of individual projects chosen by students. Prereq., proficiency in high school mathematics. Credit not granted for this course and QRMS 2380. Approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.

MATH 2400-4. Analytic Geometry and Calculus 3. A continuation of Calculus 2. Topics include vectors, three-dimensional analytic geometry, partial differentiation and multiple integrals, and vector analysis. Prereq., Calculus 2. Credit not granted for this course and APPM 2350.

MATH 2510-3. Introduction to Statistics. Elementary statistical measures. Introduces statistical distributions, statistical inference, and hypothesis testing. Prereq., two years of high school algebra. Credit not granted for this course and MATH 4570/5570 or MATH 3510.

MATH 2520-3. Introduction to Biometry. Introduces the concepts of randomness, confidence and hypothesis tests, then applies these ideas to analysis of variance, linear regression and correlation, all in the context of biology. Credit not granted for this course and any of MATH 2510, 4520, or APPM 4570/5570. Prereq., MATH 1300 or 1310 or APPM 1350.

MATH 3001-3. Analysis 1. Provides a rigorous treatment of the basic results from elementary Calculus. Topics include the topology of the real line, sequences of numbers, continuous functions, differentiable functions, and the Reimann integral. Prereq., MATH 2001, 3000, or 3200.

MATH 3110-3. Introduction to Theory of Numbers. Studies the set of integers, focusing on divisibility, congruences, arithmetic functions, sums of squares, quadratic residues and reciprocity, and elementary results on distributions of primes. Prereq., MATH 2001. Offered each spring.

MATH 3120-3. Functions and Modeling. Engages the students in lab-based activities designed to strengthen and expand knowledge of the topics in secondary mathematics, focusing especially on topics from Precalculus and Calculus. The labs will involve the use of multiple representations, transformations, data analysis techniques, and interconnections among geometry, probability and algebra. A recurrent theme will be building relationships between discrete and continuous reasoning. Prereqs., Calculus I, MATH 2001, or instructor consent.

MATH 3130-3. Introduction to Linear Algebra. Examines basic properties of systems of linear equations, vector spaces, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, and eigenvectors. Prereq., MATH 2300 or APPM 1360. Credit not granted for this course and APPM 3310.

MATH 3140-3. Abstract Algebra 1. Studies the elementary theory of groups, rings, fields, polynomials, group and ring homomorphisms, and isomorphisms. Prereq., MATH 2001 and 3130.

MATH 3170-3. Combinatorics 1. Covers basic methods and results in combinatorial theory. Includes numeration methods, elementary properties of functions and relations, and graph theory. Emphasizes applications. Prereq., MATH 2001.

MATH 3210-3. Euclidean and Non-Euclidean Geometry. Axiomatic systems. Foundations of Euclidean and Lobachevskian geometries. Prereq., MATH 2001 and 3130.

MATH 3510-3. Introduction to Probability and Statistics. Introduces the basic notions of Probability: random variables, expectation, conditioning, and the standard distributions (Binomial, Poisson, Exponential, Normal). This course also covers the Law of Large Numbers and Central Limit Theorem as they apply to statistical questions: sampling from a random distribution, estimation, and hypothesis testing. Prereqs., MATH 2001 and 2300 or APPM 1360. Credit not granted for this course and MATH 2510 or 4510.

MATH 3850-1. Seminar in Guided Mathematics Instruction. Provides Learning Assistants with an opportunity to analyze assessment data for formative purposes, and develop instructional plans as a result of these analyses. These formative assessment analyses will build on the literature in the learning sciences. Students will gain direct experiences interacting with the tools of the trade, especially with actual assessment data and models of instruction. May be repeated up to 3 total credit hours. Restricted to Learning Assistants in MATH. Coreq., EDUC 4800.

MATH 4000-3. Foundations of Mathematics. Focuses on a complete deductive framework for mathematics and applies it to various areas. Presents Goedel’s famous incompleteness theorem about the inherent limitations of mathematical systems. Uses idealized computers to investigate the capabilities and limitations of human and machine computation. Prereq., MATH 2001 plus one of 3001, 3130, 3140, or 3210.

MATH 4001-3. Analysis II. Provides a rigorous treatment of infinite series, sequences of functions, and an additional topic chosen by the instructor (for example, multivariable analysis, the Lebesgue integral, or Fourier analysis). Prereqs., MATH 3001 and 3130.

MATH 4120-3. Introduction to Operations Research. Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation, and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Prereqs., MATH 3130 or APPM 3310. Same as MATH 5120 and APPM 4120.

MATH 4140-3. Abstract Algebra 2. Covers group actions, Sylow theory, Field theory, and some Galois theory. Prereq., MATH 3140.

MATH 4200-3. Introduction to Topology. Introduces the basic concepts of point set topology. Includes topological spaces, metric spaces, homeomorphisms, connectedness, and compactness. Prereqs., MATH 3001 or MATH 4310.

MATH 4210-3. Euclidean and Non-Euclidean Geometry II. Continues the study of Euclidean and non-Euclidean geometry from MATH 3210 and examines a more advanced topic from geometry chosen by the instructor (e.g., projective geometry or three-dimensional geometry). Prereq., MATH 3120.

MATH 4230-3. Geometry of Curves and Surfaces. Introduces the modern differential geometry of plane curves, space curves, and surfaces in space. Computers are used, but no prior knowledge of computer programming is required. Prereqs., Calculus 3 and MATH 3130.

MATH 4320-3. Multivariable Analysis. Instructs students in calculus of several variables. Topics include continuity, differentiation and integration, implicit function theorem, inverse function theorem, and if time permits, Fourier series. Prereqs., MATH 4310, and MATH 3130 or APPM 2360.

MATH 4330-3. Fourier Analysis. The notion of Fourier analysis, via series and integrals, of periodic and nonperiodic phenomena is central to many areas of mathematics. Develops the Fourier theory in depth, and considers such special topics and applications as wavelets, Fast Fourier Transforms, seismology, digital signal processing, differential equations, and Fourier optics. Prereq., MATH 3001 or instructor consent. Same as MATH 5330.

MATH 4430-3. Ordinary Differential Equations. Involves an elementary systematic introduction to first-order scalar differential equations, nth order linear differential equations, and n-dimensional linear systems of first-order differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, basic existence and uniqueness, and numerical solutions. Prereqs., Calculus 3, and MATH 3130 or APPM 2360 (min. grade C). Similar to APPM 2360.

MATH 4440-3. Mathematics of Coding and Cryptography. Gives an introduction, with proofs, to the algebra and number theory used in coding and cryptography. Basic problems of coding and cryptography are discussed; prepares students for the more advanced ECEN 5032 and 5682. Prereq., MATH 3130. Same as MATH 5440.

MATH 4450-3. Introduction to Complex Variables. Theory of functions of one complex variable, including integrals, power series, residues, conformal mapping, and special functions. Available fall semester only. Prereq., MATH 3001.

MATH 4470-3. Partial Differential Equations 1. Studies initial, boundary, and eigenvalue problems for the wave, heat, and potential equations. Solution by separation of variables, Green’s function, and variational methods. Prereq., MATH 4430 or equivalent. Same as MATH 5470.

MATH 4510-3. Introduction to Probability Theory. Studies axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains. Prereqs., MATH 2400, or APPM 2350, and MATH 3130. Credit not granted for this course and APPM 3570, ECEN 3810, or MATH 3510.

MATH 4520-3. Introduction to Mathematical Statistics. Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis. Analyzes variance distribution-free methods. Prereq., MATH 4510 or APPM 3570. Same as MATH 5520 and APPM 4520.

MATH 4540-3. Introduction to Time Series. Stresses basic properties, linear extrapolation, and filtering of stationary random functions. Topics also include spectral analysis and estimation of the power spectrum using computers. Prereqs., MATH 4510/APPM 3570 and MATH 4520/APPM 4520. Same as MATH 5540 and APPM 4540.

MATH 4650-3. Intermediate Numerical Analysis 1. Focuses on numerical solution of nonlinear equations, interpolation, methods in numerical integration, numerical solution of linear systems, and matrix eigenvalue problems. Stresses significant computer applications and software. Prereqs., APPM 3310 or MATH 3130, and knowledge of a programming language. Same as APPM 4650.

MATH 4660-3. Intermediate Numerical Analysis 2. Topics include solution of algebraic and transcendental equations, and linear and nonlinear systems of equations. Highlights interpolation, integration, solution of ordinary differential equations, least squares, sources of error and error analysis, computer implementation of numerical methods, matrix eigenvalue problems, and summation of infinite series. See also MATH 4650. Prereq., MATH 4650. Same as APPM 4660.

MATH 4730-3. Set Theory. Studies in detail the theory of cardinal and ordinal numbers, definition by recursion, the statement of the continuum hypothesis, simple cardinal arithmetic, and other topics chosen by the instructor. Prereq., MATH 2001 plus one upper-division MATH class.

MATH 4820-3. History of Mathematical Ideas. Examines the evolution of a few mathematical concepts (e.g., number, geometric continuum, or proof), with an emphasis on the controversies surrounding these concepts. Begins with Ancient Greek mathematics and traces the development of mathematical concepts through the middle ages into the present. Prereq., two upper division courses in mathematics. Recommended prereq., completion of upper division Written Communication requirement.

MATH 4890 (1-3). Honors Independent Study. Offered for students doing a thesis for departmental honors.

MATH 4900 (1-3). Independent Study.

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