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# The University of Tennessee, Knoxville

University of Tennessee, Knoxville

Feb 19, 2018

# Course Descriptions

Contract All Courses |

### Registration Notes

(MATH) Mathematics (641)

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### MATH 113 - Mathematical Reasoning

3 Credit Hours
Classical and modern topics in number theory, logic, geometry, and probability with emphasis on problem solving. Consumer mathematics and other real-world applications.

Satisfies General Education Requirement: (QR)

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### MATH 115 - Statistical Reasoning

3 Credit Hours
An introduction to probability and statistics without calculus.

Satisfies General Education Requirement: (QR)
Credit Restriction: Not available for credit to students in the Haslam College of Business.

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### MATH 117 - Honors: Mathematical Reasoning

3 Credit Hours
Topics will be selected from: number theory, logic, geometry, elementary topology, fractals, or probability with an emphasis on problem solving. Consumer mathematics, fair division, voting theory or other real-world applications may be included.

Satisfies General Education Requirement: (QR)
Recommended Background: ACT composite score of 31 or SAT score of 1360.

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### MATH 119 - College Algebra

3 Credit Hours
A review of algebraic functions, equations, and inequalities for students who satisfy the course prerequisites for 123 or 125 but whose placement test scores indicated additional preparation is necessary.

Credit Restriction: Students who receive a grade of C or better in any course numbered 123 or higher (except for 201 or 202) may not subsequently receive credit for 119.
Comment(s): This course should not be taken to remove an entrance requirement.

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### MATH 123 - Finite Mathematics

3 Credit Hours
For students not planning to major in the physical sciences, engineering, mathematics or computer science. Topics include systems of linear equations and matrices, matrix algebra and applications, linear programming and the mathematics of investments and loans.

Satisfies General Education Requirement: (QR)
(RE) Prerequisite(s): 119 or 130 or 125 or 141 or 147.

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### MATH 125 - Basic Calculus

3 Credit Hours
For students not planning to major in the physical sciences, engineering, mathematics, or computer science. Calculus of algebraic, exponential, and logarithmic functions, with applications.

Satisfies General Education Requirement: (QR)
Credit Restriction: Students who receive a grade of C or better in 141, 147, or 152 may not subsequently receive credit for 125.
(RE) Prerequisite(s): 119 or 130 or 123.

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### MATH 130 - Precalculus I

4 Credit Hours
Review of algebraic, logarithmic, exponential, and trigonometric functions.

Credit Restriction: Students who receive a grade of C or better in 141, 147, or 151 may not subsequently receive credit for 130.
(RE) Prerequisite(s): 119 or appropriate placement exam score.
Comment(s): For students who satisfy the course prerequisites for 141 or 151, but whose placement test scores indicate additional preparation is necessary.

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### MATH 141 - Calculus I

4 Credit Hours
Single variable calculus especially for students of science, engineering, mathematics, and computer science. Differential calculus with applications.

Satisfies General Education Requirement: (QR)
(RE) Prerequisite(s): 130.

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### MATH 142 - Calculus II

4 Credit Hours
Single variable calculus especially for students of science, engineering, mathematics, and computer science. Integral calculus with applications.

Satisfies General Education Requirement: (QR)
(RE) Prerequisite(s): 141 or 147.

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### MATH 147 - Honors: Calculus I

4 Credit Hours
Honors version of 141 for well-prepared students.

Satisfies General Education Requirement: (QR)
Credit Restriction: Credit will not be given for both 147 and 141 or 152.
(RE) Prerequisite(s): 130.
Comment(s): Students should have a 32 mathematics ACT score, a 700 quantitative SAT score, or permission from the instructor to enroll.

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### MATH 148 - Honors: Calculus II

4 Credit Hours
Honors version of 142 for well-prepared students.

Satisfies General Education Requirement: (QR)
(RE) Prerequisite(s): 147.
Comment(s): Students should have a 32 mathematics ACT score or a 700 quantitative SAT score and credit for mathematics 141, an AP Calculus score of 5, or permission of the instructor to enroll.

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### MATH 151 - Mathematics for the Life Sciences I

3 Credit Hours
For students majoring in the life sciences. Does not serve as a prerequisite for 231 or 241. Topics include descriptive statistics, linear regression, discrete probability, matrix algebra, difference equations, calculus, and differential equations. Emphasis on applications in the life sciences. Includes computer projects.

Satisfies General Education Requirement: (QR)
(RE) Prerequisite(s): 130.

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### MATH 152 - Mathematics for the Life Sciences II

3 Credit Hours
Continuation of Math 151.

Satisfies General Education Requirement: (QR)
Credit Restriction: Students who receive a grade of C or better in 141 cannot subsequently receive credit for 152.
(RE) Prerequisite(s): 151.

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### MATH 171 - Computer Literacy for Mathematics

3 Credit Hours
Introduction to computers, the Internet, mathematical packages, and programming for prospective mathematics majors.

(RE) Prerequisite(s): 141 or 147.

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### MATH 200 - Matrix Computations

2 Credit Hours
Introduction to matrix calculations, including determinants, eigenvalues, and eigenvectors.

Credit Restriction: Students who have received a grade of C or better in 251 may not subsequently receive credit for 200.
Comment(s): For students in the College of Engineering and statistics majors in the Haslam College of Business.

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### MATH 202 - Probability, Statistics, and Euclidean Geometry

3 Credit Hours
Probabilities in simple experiments. Measures of central tendency and variation. Basic plan and three-space geometry. Congruence and similarity. Constructions with compass and straightedge. Transformations and area and volume measurement. Turtle graphs.

Satisfies General Education Requirement: (QR)

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### MATH 205 - Functions and Modeling for Secondary Math Instruction

3 Credit Hours
Project-based activities to strengthen and expand knowledge of topics in mathematics for secondary math instruction, focusing especially on topics from pre-calculus and the transition to calculus.

(RE) Prerequisite(s): 142 or 148 and Interdisciplinary Programs 120.

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### MATH 231 - Differential Equations I

3 Credit Hours
First course emphasizing solution techniques. Includes first-order equations and applications, theory of linear equations, equations with constant coefficients, Laplace transforms, and series solutions.

(RE) Prerequisite(s): 142 or 148.

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### MATH 237 - Honors: Differential Equations I

3 Credit Hours
Honors version of Math 231.

(RE) Prerequisite(s): 148.

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### MATH 241 - Calculus III

4 Credit Hours
Calculus of functions in two or more dimensions. Includes solid analytic geometry, partial differentiation, multiple integration, and selected topics in vector calculus.

(RE) Prerequisite(s): 142 or 148.

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### MATH 247 - Honors: Calculus III

4 Credit Hours
(RE) Prerequisite(s): 148.
Comment(s): Students should have a 32 mathematics ACT score or a 700 quantitative SAT score and credit for mathematics 142, or permission from the instructor to enroll.

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### MATH 251 - Matrix Algebra I

3 Credit Hours
First course in the algebra of simultaneous linear equations and matrices. Includes Gaussian elimination, determinants, vector spaces, linear transformations, eigenvalues, and eigenvectors.

(RE) Prerequisite(s): 142 or 148.

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### MATH 257 - Honors: Matrix Algebra I

3 Credit Hours
(RE) Prerequisite(s): 148.

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### MATH 299 - Studies in Mathematics

1-3 Credit Hours
Repeatability: May be repeated. Maximum 9 hours.

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### MATH 300 - Introduction to Abstract Mathematics

3 Credit Hours
Algebra of sets, functions, relations, and mathematical induction. Algebraic structure of the real number system, order properties, and completeness.

(RE) Prerequisite(s): 142 or 148.

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### MATH 307 - Honors: Introduction to Abstract Mathematics

3 Credit Hours
Honors version of 300.

(RE) Prerequisite(s): 142 or 148.
Comment(s): For current and prospective math majors, honors students, and well-prepared students.

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### MATH 309 - Putnam Preparation Seminar

1 Credit Hours
Problem-solving activities designed to prepare students for the annual Putnam Exam.

Repeatability: May be repeated. Maximum 4 hours.

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### MATH 323 - Probability and Statistics

3 Credit Hours
Discrete and continuous random variables. Conditional probability, expectation, moment generating functions. Law of large numbers. Central limit theorem. Elements of statistical inference, estimation, and hypothesis testing.

(RE) Prerequisite(s): 241 or 247; 300 or 307.

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### MATH 341 - Analysis I

3 Credit Hours
Introduction to the theory of the real number system. Limits of sequences and functions of a real variable.

(RE) Prerequisite(s): 241 or 247; 300 or 307.

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### MATH 351 - Algebra I

3 Credit Hours
Introduction to abstract algebra emphasizing integers and polynomial rings.

(RE) Prerequisite(s): 251 or 257; 300 or 307.

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### MATH 371 - Numerical Algorithms

3 Credit Hours
Development and application of fundamental algorithms for finding roots of equations, solving systems of linear equations, interpolating, fitting data using least-squares, differentiation, integration, and solving ordinary differential equations.

Credit Restriction: Students may not receive credit for both Mathematics 371 and Computer Science 370.
(RE) Prerequisite(s): 231; 200 or 251 or 257.
Comment(s): Knowledge of high-level programming language required.

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### MATH 397 - Junior Honors Seminar

2 Credit Hours
Preparation for graduate school in mathematics and related fields. Review of the main undergraduate math topics, with emphasis on problem solving.

Registration Restriction(s): Honors mathematics concentration only.

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### MATH 398 - Math Honors Program

0 Credit Hours
Maintain the requirements of the Mathematics Honors Program.

Repeatability: May be repeated. Maximum 3 times.
Registration Restriction(s): Honors mathematics concentration only.

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### MATH 399 - Studies in Mathematics

1-3 Credit Hours
Repeatability: May be repeated. Maximum 9 hours.

•

### MATH 400 - History of Mathematics

3 Credit Hours
Development of major ideas in mathematics from ancient to modern times and the influence of these ideas in science, technology, philosophy, art, and other areas. Includes at least one in-class essay examination and 3,000 words of writing outside the classroom. Writing-emphasis course.

(RE) Prerequisite(s): 251 or 257.
(DE) Prerequisite(s): 300 or 307.

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### MATH 403 - Mathematical Methods for Engineers and Scientists

3 Credit Hours
Matrix computations, numerical methods, partial differential equations, Sturm-Liouville Theory and special functions as used in engineering and science.

(RE) Prerequisite(s): 231; 241 or 247.
Comment(s): Knowledge of high-level programming language required.

•

### MATH 404 - Applied Vector Calculus

3 Credit Hours
Topics from multivariable and vector calculus, including line and surface integrals, the divergence theorem, and the theorems of Gauss and Stokes.

(RE) Prerequisite(s): 241 or 247.

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### MATH 405 - Models in Biology

3 Credit Hours
Difference and differential equation models of biological systems.

(Same as Ecology and Evolutionary Biology 406.)
(RE) Prerequisite(s): 142 or 148 or 152.

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### MATH 411 - Mathematical Modeling

3 Credit Hours
Construction and analysis of mathematical models used in science and industry. Projects emphasized. Writing-emphasis course.

(RE) Prerequisite(s): 231; 241 or 247; 200 or 251 or 257.

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### MATH 421 - Combinatorics

3 Credit Hours
Introduction to problems of construction and enumeration for discrete structures, such as sequences, partitions, graphs, finite fields and geometries, and experimental designs.

(RE) Prerequisite(s): 300 or 307.

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### MATH 423 - Probability

3 Credit Hours
Axiomatic probability, univariate and multivariate distributions, conditional distributions and expectations, moment generating functions, laws of large numbers and central limit theorem.

(RE) Prerequisite(s): 241 or 247; 300 or 307.
(DE) Prerequisite(s): 323.

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### MATH 424 - Stochastic Processes

3 Credit Hours
Markov chains, Poisson processes and Brownian motion. Other topics as selected by instructor.

(RE) Prerequisite(s): 423.

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### MATH 425 - Statistics

3 Credit Hours
Standard statistical distributions, independence of mean and variance for a Gaussian sample, basic limit theorems; point and interval estimation, tests of statistical hypotheses, Neyman-Pearson theorem; likelihood ratio and other parametric and nonparametric tests.

(RE) Prerequisite(s): 423.

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### MATH 431 - Differential Equations II

3 Credit Hours
A second course in ordinary differential equations. Linear systems of differential equations. Frobenius method, Sturm-Liouville eigenvalue problems, and phase plane analysis.

(RE) Prerequisite(s): 231; 200 or 251 or 257.

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### MATH 435 - Partial Differential Equations

3 Credit Hours
Separation of variables, Fourier series, solution of Laplace, wave, and heat equations.

(RE) Prerequisite(s): 231; 241 or 247.

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### MATH 443 - Complex Variables

3 Credit Hours
Introduction to the theory of functions of a complex variable, including residue theory and contour integrals.

(RE) Prerequisite(s): 241 or 247.

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### MATH 445 - Advanced Calculus I

3 Credit Hours
Introduction to the theory of sequences, series, differentiation, and Riemann integration of functions of one or more variables.

(RE) Prerequisite(s): 241 or 247; 300 or 307.

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### MATH 446 - Advanced Calculus II

3 Credit Hours
Continuation of 445.

(RE) Prerequisite(s): 445.

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### MATH 447 - Honors: Advanced Calculus I

3 Credit Hours
Honors version of 445.

(RE) Prerequisite(s): 341.
Comment(s): Or honors mathematics concentration.

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### MATH 448 - Honors: Advanced Calculus II

3 Credit Hours
Continuation of 447.

(RE) Prerequisite(s): 447.

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### MATH 453 - Matrix Algebra II

3 Credit Hours
Advanced topics in matrix theory, including the Jordan canonical form.

(RE) Prerequisite(s): 200 or 251 or 257.

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### MATH 455 - Abstract Algebra I

3 Credit Hours
Introduction to algebraic structures such as groups, rings, fields, vector spaces, and linear transformations.

(RE) Prerequisite(s): 251 or 257; 300 or 307.

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### MATH 456 - Abstract Algebra II

3 Credit Hours
Continuation of 455.

(RE) Prerequisite(s): 455.

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### MATH 457 - Honors: Abstract Algebra I

3 Credit Hours
Honors version of 455.

(RE) Prerequisite(s): 351.

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### MATH 458 - Honors: Abstract Algebra II

3 Credit Hours
Continuation of 457.

(RE) Prerequisite(s): 457.

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### MATH 460 - Geometry

3 Credit Hours
Axiomatic and historical development of neutral, Euclidean, and hyperbolic geometry stressing proof technique and critical reasoning. Models of Non-Euclidean geometries.

(RE) Prerequisite(s): 300 or 307.

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### MATH 462 - Differential Geometry

3 Credit Hours
Classical differential geometry of curves and surfaces: Frenet frames, first and second fundamental forms, Gauss curvature and mean curvature, geodesics and parallel transport, the Gauss-Bonet theorem, geometry of the hyperbolic plane.

(RE) Prerequisite(s): 241 or 247.

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### MATH 467 - Honors: Topology

3 Credit Hours
Includes topology of line and plane, separation properties, compactness, connectedness, continuous functions, homeomorphisms, continua, and topological invariants.

(RE) Prerequisite(s): 300 or 307.
(DE) Prerequisite(s): 241 or 247.

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### MATH 471 - Numerical Analysis

3 Credit Hours
Introduction to computation, instabilities, and rounding. Interpolation and approximation by polynomials and piecewise polynomials. Quadrature and numerical solution of initial and boundary value problems of ordinary differential equations, including stiff systems.

(Same as Computer Science 471.)
(RE) Prerequisite(s): 231; 200 or 251 or 257.
(DE) Prerequisite(s): 371.
Comment(s): Knowledge of high-level programming language required.

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### MATH 472 - Numerical Algebra

3 Credit Hours
Direct and iterative methods for systems of linear equations. Solution of a single nonlinear equation and nonlinear systems. Orthogonal decomposition, least squares, and the algebraic eigenvalue problem.

(Same as Computer Science 472.)
(RE) Prerequisite(s): 231; 200 or 251 or 257.
(DE) Prerequisite(s): 371.
Comment(s): Knowledge of high-level programming language required.

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### MATH 475 - Industrial Mathematics

3 Credit Hours
Modeling, analysis, and computation applied to scientific/technical/industrial problems.

(RE) Prerequisite(s): 231.
Recommended Background: Familiarity with operating system and programming language.

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### MATH 490 - Readings in Mathematics

1-3 Credit Hours
Open to superior students. Independent study with faculty guidance.

Repeatability: May be repeated. Maximum 9 hours.
Comment(s): Consent of faculty mentor to supervise independent work required.
Registration Permission: Consent of department head.

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### MATH 495 - Math Proficiency

0 Credit Hours
Student will demonstrate proficiency in mathematics.

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### MATH 497 - Undergraduate Honors Seminar

2 Credit Hours
Forum for presentation of student theses and other undergraduate research projects.

Comment(s): Other students may register with permission of the instructor.
Registration Restriction(s): Honors mathematics concentration only.

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### MATH 498 - Senior Honors Thesis

1-3 Credit Hours
Students in the mathematics honors program work individually under the direction of a faculty member to write an honors thesis. The thesis must be approved by the departmental honors committee.

Repeatability: May be repeated. Maximum 6 hours.

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### MATH 499 - Seminar in Mathematics

1-3 Credit Hours
Topics vary. Requires out-of-class projects and in-class presentations by students. Students must register for the number of credit hours announced for a particular seminar.

Repeatability: May be repeated. Maximum 9 hours.
Registration Permission: Consent of instructor.

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