Mathematics and Statistics Courses

424 Humanities Building

209 Hurt Street

Martin, TN 38238

Ph:

(731) 881-7360

Interim Chair: Thomas E. Eskew

Em:

math@utm.edu


Mathematics and Statistics Courses

Mathematics courses:
          100-110 130 140 160 170 185 191-192 210 251-252 291 310 314 315 320 330 340
          350 410 420 430 451 471-472 481-482 491-492 498-499 710 720 730
Statistic courses:
          325 365 375 385 435 455 461 462 465 491-492 498-499


Departmental Syllabi

Mathematics (MATH) Courses

100-110 Essentials of Algebra Part I, II (4, 4)

Functions and their graphs (including polynomial, rational, exponential, and logarithmic), exponents, roots, radicals, rational expressions, factoring polynomials, zeroes of polynomials, solutions of linear and nonlinear equations and inequalities, systems of equations and inequalities, matrices and determinants, inverse functions. Three hours of lecture and two hours of lab. (In order to proceed to MATH 110, students must complete MATH 100 with a grade of C or better. Math 100 may not be substituted for MATH 110. Math 100 cannot be used to satisfy the general education requirement. Credit may not be received for both MATH 100-110 and MATH 140. Credit may not be received for both Math 100-110 and Math 185.)


130 The Nature of Mathematics (3) Selected topics from algebra, geometry, number theory, logic, probability, statistics, management science, finance, computing and numerical techniques. Modeling and problem solving techniques will be illustrated to give students insight into what mathematics is, what mathematics attempts to accomplish, and how mathematics is used to solve real life problems. May not be used to satisfy degree requirements for the B.S. degree. May not be taken for credit by any student who has successfully completed a higher-numbered mathematics course Prereq: One unit of high school geometry, two units of high school algebra and a satisfactory score on the placement test.

140 College Algebra and Elementary Functions (3) (TBR: MATH 1710) Functions (e.g., polynomial, exponential, and logarithmic). Zeroes of polynomials. Solutions of systems of equations and inequalities. Triangle trigonometry. Selected topics from algebra such as matrices and determinants, and arithmetic and geometric sequences. Prereq: Two units of high school algebra, and appropriate mathematics placement. Credit may not be received for both MATH 140 and MATH 100-110. Credit may not be received for both MATH 140 and MATH 185.

160 Calculus for Business and Life Sciences (3) (TBR: MATH 1830) Average and instantaneous rates. The derivative and its application to curve tracing and max-min theory. Antiderivative, area under a curve, fundamental theorem. Natural logarithm and its application to interest, growth, and decay. Appropriate mathematics placement or a grade of C or better in MATH 110 or 140 or 185.

170 Trigonometry (3) Trigonometric functions, identities, graphs, equations, harmonic motion, trigonometric form of complex numbers, vectors, dot product, and conics. Applications of trigonometric functions. Prereq: EITHER two units of high school algebra, one unit of high school geometry, and appropriate mathematics placement OR completion of MATH 110 or 140 with a grade of C or better. Credit may not be received for both MATH 170 and 185.

185 Precalculus (5) Algebraic properties of real numbers. Solutions of equations and inequalities. Logarithmic and exponential equations. Survey of conics. Trigonometric functions, identities, graphs, and equations. Trigonometric applications. Prereq: Two units of high school algebra, one unit of high school geometry, and appropriate mathematics placement. Credit may not be received for MATH 100-110 or MATH 140 or MATH 170 after completing MATH 185 and credit may not be received for MATH 185 after completing MATH 100-110 or MATH 140 or MATH 170.

191-192 Principles of Mathematics (3, 3) (TBR: MATH 1410-1420) Algorithms for four basic operations, systems of whole numbers and integers. Relations and functions. Greatest common factor and least common multiple. Fractions, decimals, percent, ratio, and proportion. Statistics and probability. Metric system, measurement, area, volume, informal plane and solid geometry. These are manipulative and activity based courses. Courses must be taken in sequence. Prereq: MATH 100-110 or 140 or 185 or 251.

210 Elementary Statistics and Probability (3) (TBR: MATH 1530) Descriptive measures, elementary probability, sampling, random variables. Discrete probability distributions, normal probability distributions, and introduction to inference theory. Prereq: MATH 100-110, or 140, or 185, or 251 or appropriate mathematics placement.

251-252 Calculus I, II (4, 4) (TBR: MATH 1910- 1920) Limits and continuity. Derivatives and integrals of polynomial, exponential, logarithmic, trigonometric, and hyperbolic functions. Techniques of integration, conics, parametric and polar equations, indeterminate forms, and improper integrals. Infinite series, including Taylor's series. Must be taken in sequence. Prereq: Two units of high school algebra, one unit high school geometry, 1/2 unit high school trigonometry, and appropriate mathematics placement OR completion of EITHER Math 170 with a grade of C or better OR MATH 185 with a grade of C or better. A grade of C or better in MATH 251 is required to enroll in MATH 252.

291 Special Topics in Mathematics (1-3) Lectures and/or laboratory work relating to specialized topics in mathematics. Course may be repeated with total credits not to exceed six (6) hours. May be offered on a Pass/Fail basis. Prereq: Departmental approval.

310 Linear Algebra (3) Vectors, matrices, systems of linear equations, determinants, inverses of matrices, vector spaces, linear transformations, eigenvalues and eigenvectors. Prereq: MATH 160 or 251 or 314.

314 Foundations of Mathematics (3) Proof techniques, sets, propositional calculus, functions, relations and properties of integers. Prereq: MATH 140, or 185, or 251.

315 Mathematics and Statistics Career Preparation (1) Formal mathematical and statistical written and verbal communication including, but not limited to, preparing presentations and written papers in the mathematical and statistical sciences. Assistance in preparing resumes and the various requirements, procedures, and guidelines of graduate school applications.Prereq: MATH 314 and MATH 320.

320 Multivariate Calculus (4) (TBR: MATH 2110) Vector-valued functions, functions of several variables. Differentials, gradients, and extremes. Multiple integrals, line and surface integrals. Prereq: A grade of C or better in MATH 252.

330 Differential Equations (3) (TBR: MATH 2120) Setting up and solving first order equations, applications of first order equations. Wronskians, use of operators and the exponential shift theorem, solutions of higher order equations with constant coefficients, systems of first order equations, solutions in series, Laplace transform methods. Prereq: MATH 252.

340 (540) Numerical Analysis (3) Formulation of numerical problems for solution on a digital computer. Error analysis and control, nonlinear equations, differentiation, integration, systems of equations, differential equations, curve fitting and eigenvalue problems. Prereq: CSCI 221 and MATH 252; CSCI 301 or MATH 310. (Same as CSCI 340/540)


350 Number Theory (3) The integers: wellordering, different bases, divisibility, primes, and factoring. The fundamental theorem of arithmetic and the division algorithm. Diophantine equations and applications of congruences. Pseudorandom numbers, pseudoprimes, and cryptography. Prereq: MATH 314.

410 (610) Geometry (3) Euclidean geometry (Birkhoff's and Hilbert's Postulates), non-Euclidean geometries (hyperbolic and elliptic), finite geometries, transformational geometry, and theory of area. Prereq: MATH 314.

420 (620) History of Mathematics (3) Study of the development of mathematics from ancient to modern times through problem solving. The investigation of the lives and works of specific mathematicians with particular attention to the development of ideas, notation, and the influence of mathematics on society. Prereq: MATH 160 or 251.

430 (630) Complex Variables (3) Algebraic operations and geometry of complex numbers, definitions of limit, continuity, and analytic functions, differentiation, mapping of simple functions, line integrals, Cauchy integral formula, Laurent series, evaluation of real integrals using residue theorem. Prereq: MATH 320.

451 (651) Applications and Modeling (3) Practical applications of mathematics including optimization, interpolation and best fit, simulation, dimensional analysis and graph theory. Mathematical model building including problem identification, model construction or selection, fine tuning and validation. Prereq: MATH 310 and 320.

471 (671) Abstract Algebra I
(3) Equivalence relations and partitions. Properties of the integers. Elementary theory of groups and rings. Polynomial rings, integral domains, divisibility, unique factorization domains, fields, vector spaces, and linear transformations. Students are required to submit written work and make an oral presentation. Must be taken in sequence with MATH 472. Prereq: MATH 310 and 314.

472 (672) Abstract Algebra II (3) Equivalence relations and partitions. Properties of the integers. Elementary theory of groups and rings. Polynomial rings, integral domains, divisibility, unique factorization domains, fields, vector spaces, and linear transformations. Students are required to submit written work and make an oral presentation. Must be taken in sequence with MATH 471. Prereq: MATH 310 and 314.

481-482 (681-682) Real Analysis I, II (3, 3) Sets and countability. The real number systems. Sequences, limits, infinite series, metric spaces, continuous functions, uniform continuity, and convergence. Riemann and Lebesgue integration. Students are required to submit written work and make an oral presentation. Must be taken in sequence. Prereq: MATH 314 and 320.

491-492 (691-692) Special Topics (1-3) Selected topics in mathematics, student research, or seminar. Course may be repeated with total credits not to exceed six hours. Prereq: MATH 320 and departmental approval.

498 Undergraduate Research Experience I (2) Introduction to research methodologies and tools including LaTeX and MathSciNet. Presenting mathematics in written and oral formats. Ethics in research. This course includes substantial directed individualized study leading to the preparation of a significant paper. Prereq: consent of the department chair. Cannot receive credit for both Math 498 and Stat 498. Grading on a pass or fail basis.

499 Undergraduate Research Experience II (1) The presentation of mathematics works in both oral and written formats. This course will finalize the significant paper begun in Math/Stat 498 and based on the students’ individual research. This will require that it be presented at a regional or national meeting. Prereq: Math 498 and consent of the department chair. Graded on a pass or fail basis.

710 Selected Topics in Arithmetic for Teachers (3) Selected topics in arithmetic through student research, seminars, or workshops. Prereq: Departmental approval.

720 Selected Topics in Algebra for Teachers (3) Selected topics in algebra through student research, seminars, or workshops. Prereq: Departmental approval.

730 Selected Topics in Geometry for Teachers (3) Selected topics in geometry through student research, seminars, or workshops. Prereq: Departmental approval.



Statistics (STAT) Courses


325 Statistical Methods (3) Basic probability distributions, fundamentals of statistical inference, hypothesis testing, one way classification, analysis of variance, covariance, use of variance components and their estimation, comparative experiments, multiple comparisons, and regression. Prereq: MATH 210.

365 (565) Regression Analysis (3) Measuring the relationship among variables using standard regression techniques. Topics include simple, multiple, and polynomial regression, model fitting, verification of model assumptions, and examination of residuals. Prereq: MATH 251, Math 310, and either STAT 325 or ENGR 311 or department approval. Credit for both MATH 360 and MATH 365 (565) will not be allowed.

375 (575) Sampling Theory (3) Mathematical development of sampling. Consideration of simple probability sampling including simple random, stratified random, cluster and multistage sampling. Deriving estimates and variances of estimates for different sampling designs. Prereq: STAT 325 or ENGR 311 or departmental approval.


385 (585) Nonparametric Methods
(3) Alternatives to normal-theory statistical methods; analysis of categorical and ordinal data, methods based on rank transforms, measures of association, goodness of fit tests, order statistics. Prereqs: Math 251, and either STAT 325 or ENGR 311 or departmental approval.


435 (635) Categorical Data Analysis (3) Analysis of categorical data. Contingency tables, exact tests, loglinear models, analyses involving ordinal variables, binary response models, and multinomial response models. Prereqs: Math 251, and either STAT 325 or ENGR 311 or departmental approval.


455 (655) Design of Experiments
(3) The design and analysis of experiments. Topics include one and two factor analysis of variance, randomized designs, repeated measures, and factorial experiments. Prereq: MATH 251 and either STAT 325 or ENGR 311 or department approval.

461 (661) Probability and Statistics I (3) Discrete and continuous probability spaces, statistical independence, distributions, discrete and continuous random variables, expectations, moment-generating functions, limiting distributions, estimation of parameters, confidence intervals, hypothesis testing with applications, linear regression and correlation, multiple linear regression. Prereqs: MATH 252, either Math 314 or CSCI 301, and either STAT 325 or ENGR 311 or department approval.

462 (662) Probability and Statistics II (3) Discrete and continuous probability spaces, statistical independence,distributions, discrete and continuous random variables, expectations, moment-generating functions, limiting distributions, estimation of Description of Courses - Mathematics 371 Course Descriptions parameters, confidence intervals, hypothesis testing with applications, linear regression and correlation, multiple linear regression. Prereqs: MATH 320 and STAT 461.

465 (665) Statistical Computing (3) Applications of major statistical software packages. Emphasizes the use of computers to perform statistical procedures and the interpretation of statistical output. Either STAT 325 or ENGR 311 or department approval.


491-492 (691-692) Special Topics (1-3) Selected topics in mathematics, student research, or seminar. Course may be repeated with total credits not to exceed six hours. Prereq: MATH 320 and departmental approval.


498 Undergraduate Research Experience I (2) Introduction to research methodologies and tools including LaTeX and MathSciNet. Presenting mathematics in written and oral formats. Ethics in research. This course includes substantial directed individualized study leading to the preparation of a significant paper. Prereq: consent of the department chair. Cannot receive credit for both Math 498 and Stat 498. Grading on a pass or fail basis.

499 Undergraduate Research Experience II (1) The presentation of mathematics works in both oral and written formats. This course will finalize the significant paper begun in Math/Stat 498 and based on the students’ individual research. This will require that it be presented at a regional or national meeting. Prereq: Math 498 and consent of the department chair. Grading on a pass or fail basis.

 

 

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