216 Mathematics for Elementary and Middle School Teachers II (3)
This is the second course in a two semester sequence designed for elementary, middle school, and special education majors. The purpose is the continuation of the study of mathematical topics from Math 215 with an emphasis on algebraic notation, sets and functions, basic geometric concepts of measurement, length, area, perimeter, surface area, volume, and the Pythagorean Theorem. Some elementary probability and statistics, including some educational statistics, will be included. Every semester. Prerequisites: UTC Math Placement Level 30 or Mathematics 214 or 215 with a grade of C or better or Math ACT 26 or above or approval of the Mathematics Department Head. This course will meet General Education Mathematics requirement, but not General Education Statistics requirement.
245 Introduction to Differential and Difference Equations (3)
First order and second order linear differential and difference equations, systems of equations and transform methods. Every semester. Prerequisite: Mathematics 160 or 161 with a minimum grade of C. Pre- or Corequisite: Mathematics 212 with a minimum grade of C.
255 Multivariable Calculus (3)
Lines, curves, and surfaces; partial derivatives, gradients, divergence and curl; multiple integrals and vector analysis. Every semester. Prerequisites: Mathematics 160 or 161 and 212 with minimum grades of C.
256 Multivariable Calculus Laboratory (1)
Calculator and computer treatment of problems and topics in Math 255 using graphical, numerical, and symbolic methods Spring semester. Laboratory 2 hours. Pre- or Corequisite: Mathematics 255.
300 Foundations of Mathematics (3)
Introductory concepts of sets, functions, equivalence relations, ordering relations, logic, methods of proof, and axiomatic theories with topics from combinatorics, graph theory, or abstract algebra. Fall and spring semesters. Prerequisite: Mathematics 160 or 161 and 162 with minimum grade of C. This course is a prerequisite for Mathematics 321, 350, 403, 410, 412, 422, 430 and 452. Mathematics majors should enroll in it at the end of the sophomore year or beginning of the junior year.
303 Discrete Structures (3)
Concepts and techniques of several areas of discrete mathematics with emphasis on areas often applied to computer science. Topics will include induction, algorithms, combinatorics, graph theory with emphasis on trees, formal language, grammars. Fall and spring semesters. Prerequisites: Mathematics 161/162 and Computer Science 150 with minimum grades of C. Credit not allowed on both Mathematics 303 and 403.
307 Applied Statistics (3)
Introduction to probability and statistical methods with applications to various disciplines. A study of some basic statistical distributions, sampling, testing of hypotheses, and estimation problems. Fall and spring semesters. Prerequisite: Mathematics 160 or 161 with minimum grade of C. Credit not allowed in both Mathematics 307 and 407-408.
321 Introduction to Modern Algebra (3)
Integral domains, rings, fields, groups, elementary number theory, and other selected topics. Prerequisites: Mathematics 212, 300 (or approval of the Mathematics Department Head) with minimum grades of C.
350 Fundamental Concepts in Analysis (3)
Classical treatment of the basic concepts of calculus: limits, continuity, differentiation, Riemann integration, sequences and series of numbers and functions. Prerequisites: Mathematics 255, 300 with minimum grades of C.
401 Mathematics of Interest (3)
Mathematical theory of interest with applications, including accumulated and present value factors, annuities, yield rates, amortization schedules and sinking funds, depreciation, bonds and related securities. Recommended for students planning to take actuarial exams. Prerequisites: Mathematics 160 or 161 with a minimum grade of C, or approval of the Mathematics Department Head.
403 Graph Theory and Combinatorics (3)
Planar graphs, circuits, graph coloring, trees, general counting principles, generating functions, recurrence relations with applications to computer science including tree traversal, grammars, languages, and finite-state machines. Prerequisites: Mathematics 300 with a minimum grade of C, and either Computer Science 118 or 150 or approval of the Mathematics Department Head. Credit not allowed in both Mathematics 403 and 303.
407 Introduction to Probability and Statistics (3)
Introduction to the theory of probability and its applications, counting techniques, sample spaces, random variables and their distributions, mathematical expectation, moment generating functions, binomial, Poisson, and normal distributions, Central Limit Theorem. Prerequisite: Mathematics 255 with a minimum grade of C.
408 Mathematical Statistics (3)
A continuation of Math 407 with an introduction to the theories of point and interval estimation, hypothesis testing, regression and correlation analysis, goodness of fit, chi-square, t and F distributions. Prerequisite: Mathematics 407 with a minimum grade of C.
410 Number Theory (3)
Divisibility, primes, congruencies, Fermat’s Theorem, number theoretic functions, primitive roots and indices, the quadratic reciprocity law. Prerequisite: Mathematics 300 with a minimum grade of C.
412 Linear Algebra and Matrix Theory (3)
Vector spaces, linear transformations, eigenvalue and similarity transformations, orthogonal and unitary transformations, normal matrices, Jordan form. Prerequisites: Mathematics 212, 300 with a minimum grades of C.
414 Operations Research (Linear) (3)
Introduction to linear programming, duality, transportation and assignment problems, integer programming. Prerequisites: Computer Science 118 or 150, Math 212 with a minimum grade of C, or approval of the Mathematics Department Head.
420 Applied Statistical Methods (3)
Intermediate applied statistical analysis and model building. Covers One and Two Factor Analysis of Variance, Simple and Multiple Regression and Correlation, and Time Series Analysis. This course is recommended for students planning to take actuarial exams. Prerequisite: Mathematics 307 or 407 or Engineering 322 with a minimum grade of C, or approval of the Mathematics Department Head.
422 Introduction to Point Set Topology (3)
Introductory set theory, topologies and topological spaces, continuous mappings, compactness, connectedness, separation axioms and metric spaces. Prerequisite: Mathematics 300 with a minimum grade of C.
424 Operations Research (Non-Linear) (3)
Network flows, Markov chains and applications, queuing theory and applications, inventory theory, decision theory, and games. Prerequisites: Computer Science 118 or 150 or equivalent, Mathematics 307 or 407 with minimum grades of C, or approval of the Mathematics Department Head.
428 Packages for Mathematical Computations (3)
The nature of libraries of procedures for solving mathematical problems, including the design parameters, selection of algorithms, problems with reliability and transportation. Several major mathematical packages will be examined in detail, including IMSL, LINPACK, EISPACK, MINPACK. On demand. Prerequisites: Computer Science 118 or approval of the department head; Mathematics 245 and Engineering 225 with minimum grades of C.
430 The Historical Development of Mathematics (3)
Examination of central ideas, major developments, and important issues in mathematics from ancient times to the present. Historical overview of the evolution of the discipline through comparative examination of specific theories and results. Prerequisite: Mathematics 300 with a minimum grade of C.
440 Applied Analysis (3)
Vector analysis through Stokes’ Theorem and the Divergence Theorem. Topics in advanced calculus including implicit functions, Jacobians, interchange of limit processes, and uniform convergence of series of functions; introduction to power series solutions of differential equations. Prerequisites: Mathematics 245, 255 with minimum grades of C.