800 Mathematics

TO MEET ANY COURSE PREREQUISITE, GRADE OF C- OR HIGHER IS REQUIRED IN THE PREREQUISITE COURSE.

800:004. Intermediate Algebra -- 3 hrs.
Fundamental mathematical concepts; functions and graphs; solutions of equations; systems of equations and inequalities; matrices and determinants. Successful completion will satisfy the university's high school mathematics requirement. Does not count toward minimum hours required for baccalaureate degree. (Offered Fall and Spring)

800:023. Mathematics in Decision Making -- 3 hrs.
Survey of mathematical ideas of particular use in analyzing information and forming and analyzing hypotheses. Topics include logical statements, probability, statistics, graphs, interest, and matrices. (Offered Fall, Spring, and Summer)

800:030. Mathematics for Elementary Teachers -- 3 hrs.
Mathematics as problem solving, communication, connections, and reasoning with regard to tasks involving numeration, relationships, estimation, and number sense of whole and rational numbers, measurement, and geometry and spatial sense. Activities and models appropriate to elementary school mathematics are used to represent these topics. Prerequisite: UNI and cumulative GPA of 2.50 or better. (Offered Fall, Spring, and Summer)

800:037. Technology for Elementary School Mathematics Teachers -- 3 hrs.
Survey of technologies used to develop mathematical thinking in elementary grades. Technologies addressed include calculators, LOGO, spreadsheets, Geometer’s Sketchpad, other educational software, and the internet. (Offered Fall and Spring)

800:043. Analysis for Business Students -- 3 hrs.
Analysis and interpretation of data using numerical, graphical, and functional viewpoints; linear and exponential functions; modeling data using functions. No credit for students with credit in 800:046 or 800:056. (Offered Fall and Spring)

800:044. Trigonometry -- 2 hrs.
Trigonometric functions, solution of triangles and applications of simple harmonic motions, polar coordinates, and vectors. No credit for students with credit in 800:046. (Offered Spring)

800:046. Elementary Analysis -- 4 hrs.
Pre-calculus mathematics; equations and inequalities; logarithms, exponential and circular functions; analytic trigonometry, analytic geometry, mathematical induction; applications. Credit reduced to one hour for students with credit in 800:043 and to two hours for students with credit in 800:044. (Offered Fall and Spring)

800:048. Condensed Calculus -- 4 hrs.
Survey of analytic geometry and elementary calculus with emphasis on applications. May not be applied to Mathematics major or minor. (Variable)

800:050. Matrices with Applications -- 3 hrs.
Introduction to matrices, systems of linear equations, vector spaces and linear mappings, rank and inverses, determinants, characteristic values and characteristic vectors. Prerequisite: 800:046, or 800:043 and 800:044. Students with credit in 800:076 may not receive credit for 800:050. (Variable)

800:056. Mathematics for Biological Sciences — 3 hrs.
Proportional reasoning, linear functions and linear regression, exponential functions, and logarithmic functions with scientific applications. No credit for students with credit in 800:043 or 800:046. (Offered Fall and Spring)

800:060. Calculus I -- 4 hrs.
The derivatives and integrals of elementary functions and their applications. Prerequisite: 800:046, or 800:043 and 800:044, or equivalent. (Offered Fall, Spring, and Summer)

800:061. Calculus II -- 4 hrs.
Continuation of 800:060. Prerequisite: C- or better in 800:060. (Offered Fall and Spring)

800:062. Calculus III -- 4 hrs.
Continuation of 800:061. Prerequisite: C- or better in 800:061. (Offered Fall and Spring)

800:072. Introduction to Statistical Methods -- 3 hrs.
Descriptive statistics including correlation and curve fitting. Intuitive treatment of probability and inferential statistics including estimations and hypothesis testing. Students with credit in 800:172 should not enroll in 800:072. (Offered Fall, Spring, and Summer)

800:074. Discrete Mathematics -- 3 hrs.
Introduction to mathematical reasoning, sets, relations, and functions with applications in computer science. Prerequisites: 800:050 or 800:060; 810:030 or equivalent. (Variable)

800:076. Linear Algebra for Applications -- 3 hrs.
Gaussian elimination; matrix algebra; vector spaces, kernels, and other subspaces; orthogonal projection; eigenvalues and eigenvectors. Prerequisite: 800:060. (Offered Fall and Spring)

800:080. Mathematics of Finance -- 3 hrs.
Study of mathematics of financial transactions: simple and compound interest, annuities, amortization of indebtedness, bonds, depreciation, life annuities, and death insurance. Of special interest to actuarial and business students. Prerequisite: 800:060. (Offered Spring)

800:090. Mathematical Problem Solving -- 1 hr.
Basic techniques used to solve challenging mathematics problems. Problems considered will come from a broad range of courses. Prepares students to take the William Lowell Putnam Examination and the Iowa Collegiate Mathematics Competition. May be repeated for credit. (Offered Fall and Spring)

800:092. Introduction to Mathematical Modeling -- 3 hrs.
Components of mathematical modeling. Formulation, interpretation, and testing of models. Prerequisite: four years of college preparatory mathematics, or 800:046, or 800:043 and 800:044. (Offered Fall and Spring)

800:096. Technology and Programming for Secondary Mathematics Teachers — 3 hrs.
Introduction to technologies used in grades 7-12 mathematics classrooms. Technologies include LOGO, spreadsheets, Geometer’s Sketchpad and graphing calculators. Prerequisites: 800:060; 800:092. (Offered Fall)

800:111(g). Introduction to Algebraic Thinking for Elementary Teachers -- 4 hrs.
Investigation of problems involving patterns, variables, relations, functions, and their graphs. Exploration and representation of these problems using physical models and technology. Prerequisites: 800:030; 800:037; junior standing. (Offered Spring)

800:112(g). Introduction to Geometry and Measurement for Elementary Teachers -- 3 hrs.
Van Hiele levels of thinking. Investigation of two- and three-dimensional concepts, rigid transformations, symmetry, and spatial sense. Prerequisites: 800:030; 800:037; junior standing. (Offered Fall and Spring)

800:113(g). Topics in Mathematics for Grades K-8 -- 3 hrs.
Investigation of ratio, proportion, percent; number theory; data analysis; patterns; and connections to algebra and geometry. Exploration of topics in the context of the K-8 mathematics curriculum. Prerequisites: 800:030; 800:037; junior standing. (Offered Fall and Spring)

800:114(g). Problem Solving in Mathematics for Elementary Teachers -- 4 hrs.
Strategies for constructing and communicating a mathematics problem-solving process. Analysis of resources and strategies to generate mathematics tasks and to create an effective problem-solving environment. Problem solving as a means of constructing mathematics knowledge. Prerequisites: 800:134; at least one of 800:111, 800:112, 800:113; junior standing. (Offered Fall and Spring)

800:121(g). Applied Statistical Methods for Research — 3 hrs.
Inference about two or more population variances, multiple comparisons, categorical data analysis, linear and logistic regression, design of experiments, analysis of variance and covariance, repeated measures and random effects. Prerequisites: 800:072; junior standing. (Offered Spring)

800:134. Teaching Mathematics in the Elementary School -- 3 hrs.
Effective instructional models and strategies for teaching elementary school mathematics; involves selecting and designing mathematical tasks, creating an environment, and orchestrating discourse. Using and supplementing mathematics materials within a sound psychological framework for making instructional decisions. Prerequisites: 800:030; UNI and cumulative GPA of 2.50 or better. (Offered Fall, Spring, and Summer)

800:137. Action Research for Elementary School Mathematics Teachers -- 1 hr.
Planning, conducting assessments, providing instruction, and evaluating instructional effectiveness for selected mathematics topics in the elementary curriculum. Prerequisite: 800:134 or 800:190. (Offered odd Falls and even Springs)

800:140(g). Intermediate Mathematical Analysis I -- 3 hrs.
Algebraic and topological structure of the reals; limits and continuity; theory of differentiability of functions of a single real variable. Prerequisites: 800:062; 800:076; junior standing. (Offered Fall)

800:141(g). Intermediate Mathematical Analysis II -- 3 hrs.
Riemann integration; sequences and series of functions; introduction to Lebesgue integration. Prerequisites: 800:140; junior standing. (Offered Spring)

800:142(g). Dynamical Systems: Chaos Theory and Fractals — 3 hrs.
Historical background, including examples of dynamical systems; orbits, fixed points, and periodic points; one-dimensional and two-dimensional chaos; fractals: Julia sets, the Mandelbrot set, and fractal dimension; computer programs and dynamical systems. Prerequisites: 800:061; 800:076; junior standing. (Offered odd Falls)

800:143(g). Combinatorics — 3 hrs.
Various ways to enumerate elements of a set. Appropriate for mathematics, mathematics education, computer science, and actuarial science students. Prerequisite: junior standing. (Offered even Falls)

800:144(g). Elementary Number Theory -- 3 hrs.
Topics from properties of integers, prime numbers, congruences, cryptography, Pythagorean triples, Diophantine equations, Fermat’s last theorem, Fibonacci numbers, and the golden rectangle. Also, number theoretic connections to abstract algebra. Prerequisites: 800:160; junior standing. (Offered Fall)

800:146. Actuarial Examination Preparation -- 1-2 hrs.
Strengthening student skills solving computational problems similar to those included on actuarial examinations. Analyzing and practicing appropriate choice of problem solving techniques and strategies. May be repeated for credit for preparation for different examinations. (Offered Spring)

800:149(g). Differential Equations -- 3 hrs.
Elementary theory and applications of first order differential equations; introduction to numerical techniques of solving differential equations; solutions of nth order linear differential equations with constant coefficients. Prerequisites: 800:062; 800:076; junior standing. (Offered Fall)

800:150(g). Partial Differential Equations -- 3 hrs.
Study of applied partial differential equations using heat, wave, and potential equations as basis; Fourier series and integrals; Laplace transformations. Prerequisites: 800:149; junior standing. (Offered odd Springs)

800:152(g). Introduction to Probability -- 3 hrs.
Axioms of probability, sample spaces having equally likely outcomes, conditional probability and independence, random variables, expectation, moment generating functions, jointly distributed random variables, weak law of large numbers, central limit theorem. Prerequisites: 800:061; junior standing. (Offered Fall and Spring)

800:153(g). Actuarial Mathematics — 3 hrs.
Survival distributions and life tables, life insurance, life annuities, benefit premiums. Prerequisites: 800:080; 800:152; junior standing. (Variable)

800:154(g). Introduction to Stochastic Processes -- 3 hrs.
Markov chains, Poisson processes, continuous time Markov chains, renewal processes, Brownian motion and stationary processes. Prerequisites: 800:152; junior standing. (Offered Fall)

800:155(g). Differential Geometry -- 3 hrs.
Analytic study of curves and surfaces in three-dimensional Euclidean space. Prerequisites: 800:062; 800:076; junior standing. (Offered odd Falls)

800:156(g). Introduction to Complex Analysis -- 3 hrs.
Differentiation and integration of functions of a single complex variable; Taylor and Laurent expansions; conformal mapping. Prerequisites: 800:062; junior standing. (Offered even Springs)

800:157(g). Statistical Quality Control -- 3 hrs.
Exploratory data analysis, Shewhart control charts and their variations, process capability analysis, CUSUM charts, EWMA charts, sampling inspection by attributes and by variables, continuous sampling plans, application of design of experiments in quality engineering. Prerequisite: 800:152 or consent of instructor; junior standing. (Variable)

800:158(g). Topics in Actuarial Science -- 3 hrs.
Topics from mathematics of life contingencies, risk theory, survival analysis, construction of actuarial tables, demography, graduation. May be repeated on different topic with consent of instructor. Prerequisites: 800:152; junior standing; consent of instructor. (Offered Fall)

800:160(g). Modern Algebra I -- 3 hrs.
Introduction to study of algebraic systems. Groups, rings, fields, homomorphisms and isomorphisms. Prerequisites: 800:061 or equivalent; 800:076; junior standing. (Offered Fall and Spring)

800:161(g). Linear Algebra I -- 3 hrs.
Vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, canonical forms, inner product spaces. Prerequisites: 800:160; junior standing. (Variable)

800:162(g). Modern Algebra II -- 3 hrs.
Continuation of 800:160. Groups with operators, modules over rings, Sylow theorems, composition series, semi-simple and simple rings, field theory and introduction to Galois theory. Prerequisites: 800:160; junior standing. (Offered Spring)

800:165(g). Introduction to Modern Geometry -- 3 hrs.
Historical survey of Euclidean geometry and examination of its modern formulation; introduction to transformational geometry; elements of hyperbolic non-Euclidean geometry and its models in the Euclidean plane and space. Prerequisites: 800:060 or equivalent; junior standing. (Offered Fall and Spring)

800:167(g). Topology I -- 3 hrs.
Introductory study of metric spaces, completeness, topological spaces, continuous functions, compactness, connectedness, separability, product, and quotient spaces. Prerequisites: 800:062; 800:076; junior standing. (Variable)

800:168(g). Topology II -- 3 hrs.
Continuation of 800:167. Two- and n-dimensional manifolds, orientable manifolds, the fundamental group of a space, free groups, covering spaces, application to geometry and knot theory. Prerequisites: 800:160; 800:167; junior standing. (Variable)

800:169(g). Mathematical Logic -- 3 hrs.
Introduction to semantics and syntax of propositional and predicate calculus; applications to electrical networks and analysis of formal mathematical theories. Prerequisites: 800:060; junior standing. (Offered even Springs)

800:170(g). Loss Models — 3 hrs.
Applied probability methods used in modeling loss. Loss distributions, aggregate loss models, credibility theory and long term models. Prerequisites: 800:152; 800:174; junior standing. (Offered odd Springs)

800:171(g). Spatial Data Analysis -- 3 hrs.
Analysis and interpretation of spatial point processes, area, geostatistical and spatial interaction data. Applications to geographic data in real estate, biology, environmental, and agricultural sciences using S-Plus software. Prerequisites: 800:072 or 980:080; junior standing. (Same as 970:160g.) (Offered odd Springs)

800:172(g). Statistical Methods -- 3 hrs.
Descriptive statistics including graphical representation, central tendency and variation, correlation and regression; elementary probability; problems of estimation and hypothesis testing from an intuitive approach; use of statistical packages such as SAS or SPSS. Students with credit in 800:072 or 800:174 may not enroll in 800:172. Prerequisite: junior standing. (Variable)

800:173. Probability and Statistics -- 3 hrs.
Descriptive statistics and graphical representations, basic concepts of probability and distributions, random variables, expectations, sampling theory, tests of statistical significance. Calculus is employed in developing and applying these ideas. Specific attention devoted to the use of technology in motivating and explaining concepts and techniques. Emphasis on applications appropriate for secondary school probability/statistics courses. No credit with credit in 800:172. Prerequisite: 800:061. (Offered Fall and even Springs)

800:174(g). Introduction to Mathematical Statistics -- 3 hrs.
Sampling distribution theory, point and interval estimation, Bayesian estimation, statistical hypotheses including likelihood ratio tests and chi-square tests, selected nonparametric methods. Prerequisites: 800:062; 800:152; junior standing. (Offered Spring)

800:175(g). Regression Analysis -- 3 hrs.
Regression analysis, analysis of variance, time series methods. Prerequisites: 800:174; junior standing. (Offered Fall)

800:176(g). Numerical Analysis I -- 3 hrs.
Theory and application of standard numerical techniques dealing with nonlinear equations, systems of linear equations, interpolation and approximation, numerical differentiation and integration. Prerequisites: 800:061; 800:076; 810:034 or 810:035 or 810:036, or equivalent; junior standing. (Offered odd Falls)

800:177(g). Linear and Non-Linear Programming -- 3 hrs.
Linear, non-linear, integer, and dynamic programming. Prerequisites: 800:061; 800:050 or 800:076; 810:034 or 810:035 or equivalent; junior standing. (Offered Spring)

800:178(g). Numerical Analysis II -- 3 hrs.
Theory and application of numerical techniques for solution of ordinary and partial differential equations. Advanced topics from interpolation, approximation, numerical linear algebra. Prerequisites: 800:176; junior standing. (Offered odd Falls)

800:180(g). History of Mathematics: To the Calculus -- 3 hrs.
Survey of mathematical activities of mankind to the advent of the calculus in the 17th century. Motives, influences, and methods affecting development of algebra, geometry, and number theory in Mesopotamian, Egyptian, Greek, Islamic, and eastern civilizations. Prerequisite: junior standing. (Offered Fall and even Springs)

800:181(g). Philosophy of Mathematics -- 3 hrs.
Consideration of views on foundations of mathematics and such topics as role and possible limitations of mathematics in scientific investigation; significance of logical constructs in mathematics. Prerequisites: Humanities course; one semester of calculus; at least one additional mathematics course; junior standing. (Variable)

800:182(g). Introduction to Set Theory -- 3 hrs.
Overview of Cantor's set theory. Informal introduction to the axioms of set theory; general relations and functions; order relations; the axiom of choice, Zorn's lemma, and well-ordering; ordinal and cardinal numbers and their arithmetics; the Cantor-Schroeder-Bernstein theorem. Prerequisites: 800:160 or 800:165 or 800:169; junior standing. (Offered even Falls)

800:184(g). Introduction to Automata Theory -- 3 hrs.
Finite automata and their decision problems: perspectives from finite-state machines, neural networks, and regular sets. Introduction to Turing machines, computability, and the halting problem. Students may not earn credit in both 800:184 and 810:181. Prerequisites: 800:061; at least one 100-level mathematics course; junior standing. (Variable)

800:185(g). History of Mathematics: From the Calculus to the 21st Century -- 3 hrs.
Survey of mathematical activities of mankind from development of calculus in the 17th century. Rise of analysis, and development of modern algebra, non-Euclidean geometries, and general axiomatic method in the 19th century. Set theory, topology, mathematical logic, and other integrating developments in 20th century mathematics. Prerequisites: 800:061; junior standing. (Offered Spring)

800:187(g). Formal Languages -- 3 hrs.
Brief comparison of natural languages and formal languages. Grammars and their generated languages; the Chomsky hierarchy and corresponding automata theories; operations on languages; some solvable and unsolvable problems. Students may not earn credit in both 800:187 and 810:182. Prerequisites: 800:184 or 810:181; junior standing. (Same as 810:182g.) (Variable)

800:188. The Teaching of Middle School/Junior High Mathematics -- 3 hrs.
Teaching strategies for grades 5-8; roles of content and methods; participation in a middle school/junior high teaching situation. Prerequisites: 200:128; 200:148; 6 hours of 100-level courses in Mathematics. (Offered Fall and Spring)

800:189(g). Geometric Transformations -- 3 hrs.
Isometries and similarity transformations in the Euclidean plane and Euclidean space; preservation properties of isometries; existence and classification of isometries in the Euclidean plane; applications to concepts and problems in geometry, physics, and modern algebra, and to analysis of congruence and similarity. Prerequisites: 800:076; 800:165; junior standing. (Offered Spring)

800:190. The Teaching of Secondary Mathematics -- 3 hrs.
Teaching strategies for grades 7-12; roles of content and methods; participation in a secondary teaching situation. Prerequisites: 200:128; 200:148; 250:150; 800:160; 800:165; 800:188. (Offered Fall and Spring)

800:191(g). Contemporary Mathematics Curricula -- 1-2 hrs.
Study and evaluation of innovative curriculum materials. Focus on early elementary, middle grades, or high school curriculum. May be repeated for a different curriculum level with consent of department. Prerequisites: 800:134 or 800:188 or 800:190; junior standing. (Offered Summer)

800:192. Mathematics for Elementary Students with Special Needs -- 1 hr.
Assessing, designing, and providing appropriate mathematical tasks for students with special needs. Prerequisite: 800:134 or 800:190. (Offered even Falls and odd Springs)

800:193(g). Linear Algebra II -- 3 hrs.
Inner product spaces, Gram-Schmidt orthonormalization, unitary operators and their matrices, bilinear forms, Hermitian forms, normed linear vector spaces. Prerequisites: 800:161; junior standing. (Variable)

800:194. Senior Mathematics Seminar -- 1 hr.
Researching and writing a paper exploring specific theme, topic, or problem in mathematics, culminating with oral presentation to the class. Prerequisite: senior mathematics major. (Offered Fall and Spring)

800:195. Undergraduate Research in Mathematics -- 3 hrs.
Research on selected topic in mathematics with faculty supervision. Presentation of written paper at departmental seminar. Prerequisite: completion of the major core with minimum GPA of 3.00. (Offered Fall and Spring)

800:196(g). Applied Multivariate Statistical Analysis -- 3 hrs.
Multivariate normal distribution, tests of significance with multivariate data, discrimination and classification, clustering, principal components, canonical correlations, use of statistical computer packages. Prerequisites: 800:076; 800:174; junior standing. (Variable)

800:198. Independent Study.
(Variable)

800:201. Mathematical Analysis I -- 3 hrs.
The real numbers; topology of Cartesian spaces; continuous functions; differentiation in Cartesian spaces. Prerequisite: 800:140 or consent of instructor. (Offered even Springs)

800:202. Mathematical Analysis II -- 3 hrs.
Riemann-Stieltjes and Lebesgue integrals; integration in Cartesian spaces; improper and infinite integrals; infinite series. Prerequisite: 800:201. (Offered even Falls)

800:203. Complex Analysis I -- 3 hrs.
Analyticity; differentiation and integration of functions of one complex variable; power series, Laurent series; calculus of residues. Prerequisites: 800:140; 800:156; or consent of instructor. (Offered odd Springs)

800:204. Complex Analysis II -- 3 hrs.
Analytic continuation; harmonic functions; entire functions; conformal mapping; selected applications. Prerequisite: 800:203. (Offered odd Falls)

800:210. Theory of Numbers -- 3 hrs.
Mathematical study of integers: induction, divisibility, prime numbers, congruences, quadratic reciprocity, multiplicative functions. (Offered even Springs)

800:211. Teaching Algebra in the Middle Grades -- 2 hrs.
Examination of literature and students' thinking related to algebraic concepts. Curriculum issues, teaching strategies, and implications of technology. Prerequisite: 800:215 or consent of department. (Offered Summer)

800:213. Selected Topics in Mathematics for the Middle Grades -- 2 hrs.
Investigation of mathematical topic(s), such as geometry, data analysis, probability, or number sense. Examination of a major mathematical idea including implications of research literature, and examination of relevant curriculum materials. May be repeated once on a different topic with consent of department. Prerequisite: consent of department. (Offered Summer)

800:214. Mathematical Problem Solving in the Middle Grades -- 1 hr.
Solving problems from a variety of mathematical topics such as linear programming, geometry, and probability. Analyzing problem-solving techniques and teaching strategies. Investigating issues related to implementing a problem-solving approach in the classroom. (Offered Summer)

800:215. Teaching Rational Numbers -- 2 hrs.
Examination of literature, problems, and issues related to teaching fractions, decimals, ratios, proportion, and percent in grades 4-8. Exploration of innovative strategies for developing concepts, skills, and proportional reasoning. Implications of research and reform recommendations for the curriculum. (Offered Summer)

800:220. New Developments in Middle Grades Mathematics -- 3 hrs.
Investigation of current recommendations for goals, content, instructional strategies, and curriculum of mathematics programs in grades 4-8. In-depth examination of selected content and implementation of a problem-solving approach to instruction. Focus on application to classroom practice and planning for change for a selected topic. (Offered Summer)

800:221. Mathematics Literacy in an Information Age -- 2 hrs.
Examination of applications and contributions of mathematics to other disciplines, the workplace, personal lives, and society. Investigation of shifting conceptions of mathematics and mathematics literacy in today's world. Diverse uses of mathematics illustrated. Prerequisites: 800:220; 800:236; 800:238. (Offered Summer)

800:222. Issues and Problems in Teaching Mathematics in the Middle Grades -- 2 hrs.
Issues and problems related to current reform in mathematics, including planning curriculum, assessing student learning, managing instruction, and providing for individual needs. Examination of related literature. Prerequisite: 800:220. (Offered Fall)

800:236. Mathematics for the Middle Grades Teachers I -- 3 hrs.
Integrated, historical, and cultural study of development and structure of quantity, data, and chance. Focus on mathematical ways of knowing and verification. (Offered Spring)

800:237. Technology in Middle Grades Mathematics -- 2 hrs.
Uses of technology in teaching and learning mathematics. Examination of research related to incorporating technology in the teaching of mathematics. (Offered Summer)

800:238. Mathematics for the Middle Grades Teacher II -- 3 hrs.
Integrated, historical, and cultural study of development and structure of patterns, functions, relationships, and shapes. Focus on ways of knowing and verification. Prerequisite: 800:236. (Offered Fall)

800:240. Theory of Rings and Modules -- 3 hrs.
Ring theory from factorization in commutative rings, rings of quotients, localization, rings of polynomials and formal power series, and elements of Galois theory. Module theory from exact sequences, free modules, projective and injective modules, tensor products, modules over principal ideal domains, and algebras. Prerequisite: 800:162 or consent of instructor. (Offered even Falls)

800:245. Topics in Algebra -- 3 hrs.
Topics from groups, noncommutative rings and algebras, and linear algebras, introduction to homological, Lie, and linear algebras. May be repeated on different topics with the consent of instructor. Prerequisite: 800:162 or consent of instructor. (Offered odd Springs)

800:246. Topics in the History of Mathematics -- 3 hrs.
Topics from history of algebra, analysis, arithmetic, geometry, number theory, probability, and topology as they appear in the development of Mesopotamian, Greek, Islamic, Indian, Chinese, and western civilizations. May be repeated on different topics with the consent of instructor. Prerequisite: 800:180 or 800:185. (Offered even Falls)

800:263. Topics in Mathematical Logic and Set Theory -- 3 hrs.
Topics from: the predicate calculus and first-order mathematical theories; the Godel completeness and incompleteness theorems; algebraic and many-valued logic; Boolean algebras, lattices, representation theorems, and models in set theory and mathematical logic; independence of the axioms of set theory (including the axiom of choice and the continuum hypothesis). May be repeated on different topics with the consent of instructor. Prerequisite: 800:169 or 800:182, depending on the topic. (Variable)

800:265. Geometric Symmetry -- 3 hrs.
Symmetry groups in the Euclidean plane and the geometric significance of normality. Finite and discrete symmetry groups in the plane: the rosette, frieze, and wallpaper groups. Applications to analysis of Escher-type designs and ornamental designs of Alhambra. Finite symmetry groups in Euclidean space. Prerequisites: 800:160; 800:189. (Offered odd Falls)

800:266. Topics in Geometry -- 3 hrs.
Topics from: geometric convexity, non-Euclidean geometries, the Banach-Tarski paradox, inversions and mappings of the Euclidean sphere, geometric inequalities, the history of geometry, differential manifolds. May be repeated on different topic with consent of instructor. Prerequisite: consent of instructor. (Offered even Springs)

800:273. Topics in Probability and Statistics -- 3 hrs.
Topics chosen from correlation and regression analysis, analysis of variance and co-variance, non-parametric methods, order statistics. May be repeated on different topics with the consent of instructor. Prerequisite: consent of instructor. (Variable)

800:291. Problems and Issues in Teaching High School Mathematics -- 3 hrs.
Course content decided by participants and instructor. Consideration of both mathematics content and methodology of the senior high school. Prerequisite: consent of department. (Variable)

800:293. The Secondary School Mathematics Curriculum -- 3 hrs.
Comparison of current secondary curriculum with national standards, implementation, assessment, and the role of technology. (Variable)

800:299. Research.
(Variable)