# Mathematics

## Mathematics

### 356 Phillips Hall, CB# 3250

(919) 962-0198

## First Session, 2020

### MATH 110 Algebra (3)

Provides a one-semester review of the basics of algebra. Basic algebraic expressions, functions, exponents, and logarithms are included, with an emphasis on problem solving. This course should not be taken by those with a suitable score on the achievement test.

### MATH 118 Aspects of Modern Mathematics (3)

Introduction to mathematical topics of current interest in society and science, such as the mathematics of choice, growth, finance, and shape. The course is intended for the non-science major.

### MATH 119 Introduction to Mathematical Modeling (3)

ONLINE. Provides an introduction to the use of mathematics for modeling real-world phenomena in a nontechnical setting. Models use algebraic, graphical, and numerical properties of elementary functions to interpret data. This course is intended for the non-science major.

### MATH 130 Precalculus Mathematics (3)

*Prerequisite, MATH 110*. Covers the basic mathematical skills needed for learning calculus. Topics are calculating and working with functions and data, introduction to trigonometry, parametric equations, and the conic sections. A student may not receive credit for this course after receiving credit for MATH 231.

### MATH 231 Calculus of Functions of One Variable I (4)

*Prerequisites, MATH 110 and 130*. Requires a grade of C- or better in MATH 130 or placement by the department. Limits, derivatives, and integrals of functions of one variable. Students may not receive credit for both MATH 231 and MATH 241.

### MATH 232 Calculus of Functions of One Variable II (4)

*Prerequisite, MATH 231 or 241*. Requires a grade of C- or better in MATH 231 or 241 or placement by the department. Calculus of the elementary transcendental functions, techniques of integration, indeterminate forms, Taylor’s formula, infinite series.

### MATH 233 Calculus of Functions of Several Variables (4)

*Prerequisite, MATH 232 or 283*. Vector algebra, solid analytic geometry, partial derivatives, multiple integrals.

### MATH 381 Discrete Mathematics (3)

*Prerequisite, MATH 232 or 283*. This course serves as a transition from computational to more theoretical mathematics. Topics are from the foundations of mathematics: logic, set theory, relations and functions, induction, permutations and combinations, recurrence.

### MATH 383 First Course in Differential Equations (3)

*Prerequisite, MATH 233*. Introductory ordinary differential equations, first- and second-order differential equations with applications, higher-order linear equations, systems of first-order linear equations (introducing linear algebra as needed).

### MATH 383L First Course in Differential Equations Laboratory (1)

*Prerequisite, MATH 233; pre- or co-requisite, MATH 383. *Course is computational laboratory component designed to help students visualize ODE solutions in Matlab. Emphasis is on differential equations motivated by Applied Sciences. Some applied linear algebra will appear as needed for computation and modeling purposes.

### MATH 521 Advanced Calculus I (3)

*Prerequisites, MATH 233 and 381*. A grade of A- or better in STOR 215 may substitute for MATH 381. The real numbers, continuity and differentiability of functions of one variable, infinite series, integration.

### MATH 528 Mathematical Methods for the Physical Sciences I (3)

*Prerequisite, MATH 383*. Theory and applications of Laplace transform, Fourier series and transform, Sturm-Liouville problems. Students will be expected to do some numerical calculations on either a programmable calculator or a computer. This course has an optional computer laboratory component: MATH 528L.

### MATH 528L Laboratory for Mathematical Methods for the Physical Sciences I (1)

*Prerequisite, MATH 383*; *pre- or co-requisite, MATH 528*. Training in the use of symbolic and numerical computing packages and their application to the MATH 528 lecture topics. Students will need a CCI-compatible computing device.

### MATH 533 Elementary Theory of Numbers (3)

*Prerequisite, MATH 381*. A grade of A- or better in STOR 215 may substitute for MATH 381. Divisibility, Euclidean algorithm, congruences, residue classes, Euler’s function, primitive roots, Chinese remainder theorem, quadratic residues, number-theoretic function, Farey and continued fractions, Gaussian integers.

### MATH 535 Introduction to Probability (STOR 435) (3)

*Prerequisite, MATH 233.* Introduction to the mathematical theory of probability, covering random variables; moments; binomial, Poisson, normal and related distributions; generating functions; sums and sequences of random variables; and statistical applications.

### MATH 547 Linear Algebra for Applications (3)

MAYMESTER. The algebra of linear combination of vectors has numerous applications in the arts and sciences, most recently as a foundation for data science and artificial intelligence. Vectors can be used to represent visual images, musical scores, or medical cardiograms. Exploring the range of new entities (images, sounds, diagnoses) that can thus be obtained leads to consideration of matrices, linear systems of equations, best approximations, eigenvalues and algorithms for these procedures. This course presents the mathematical framework for linear algebra enhanced by numerous applications, with a focus on treating art images as data that can be processed to identify particular artists or even produce new works in a particular style. No prerequisites are required and computer programming and mathematical calculus concepts are introduced as needed throughout the course.

### MATH 547 Linear Algebra for Applications (3)

*Prerequisite, MATH 233 or 283.* Algebra of matrices with applications: determinants, solution of linear systems by Gaussian elimination, Gram-Schmidt procedure, eigenvalues. MATH 416 may not be taken for credit after credit has been granted for MATH 547.

### MATH 566 Introduction to Numerical Analysis (3)

*Prerequisite, MATH 383*. Requires some knowledge of computer programming. Iterative methods, interpolation, polynomial and spline approximations, numerical differentiation and integration, numerical solution of ordinary and partial differential equations.

## Second Session, 2020

### MATH 110 Algebra (3)

Provides a one-semester review of the basics of algebra. Basic algebraic expressions, functions, exponents, and logarithms are included, with an emphasis on problem solving. This course should not be taken by those with a suitable score on the achievement test.

### MATH 118 Aspects of Modern Mathematics (3)

Introduction to mathematical topics of current interest in society and science, such as the mathematics of choice, growth, finance, and shape. The course is intended for the non-science major.

### MATH 119 Introduction to Mathematical Modeling (3)

Provides an introduction to the use of mathematics for modeling real-world phenomena in a nontechnical setting. Models use algebraic, graphical, and numerical properties of elementary functions to interpret data. This course is intended for the non-science major.

### MATH 130 Precalculus Mathematics (3)

*Prerequisite, MATH 110*. Covers the basic mathematical skills needed for learning calculus. Topics are calculating and working with functions and data, introduction to trigonometry, parametric equations, and the conic sections. A student may not receive credit for this course after receiving credit for MATH 231.

### MATH 231 Calculus of Functions of One Variable I (4)

*Prerequisites, MATH 110 and 130*. Requires a grade of C- or better in MATH 130 or placement by the department. Limits, derivatives, and integrals of functions of one variable. Students may not receive credit for both MATH 231 and MATH 241.

### MATH 232 Calculus of Functions of One Variable II (4)

*Prerequisite, MATH 231 or 241*. Requires a grade of C- or better in MATH 231 or 241 or placement by the department. Calculus of the elementary transcendental functions, techniques of integration, indeterminate forms, Taylor’s formula, infinite series.

### MATH 233 Calculus of Functions of Several Variables (4)

*Prerequisite, MATH 232 or 283*. Vector algebra, solid analytic geometry, partial derivatives, multiple integrals.

### MATH 294 Undergraduate Seminar in Mathematics (1-3)

Permission of the instructor. A seminar on a chosen topic in mathematics in which the students participate more actively than in usual courses.

### MATH 381 Discrete Mathematics (3)

*Prerequisite, MATH 232 or 283*. This course serves as a transition from computational to more theoretical mathematics. Topics are from the foundations of mathematics: logic, set theory, relations and functions, induction, permutations and combinations, recurrence.

### MATH 383 First Course in Differential Equations (3)

*Prerequisite, MATH 233*. Introductory ordinary differential equations, first- and second-order differential equations with applications, higher-order linear equations, systems of first-order linear equations (introducing linear algebra as needed).

### MATH 383L First Course in Differential Equations Laboratory (1)

*Prerequisite, MATH 233; pre- or corequisite, MATH 383. *Course is computational laboratory component designed to help students visualize ODE solutions in Matlab. Emphasis is on differential equations motivated by Applied Sciences. Some applied linear algebra will appear as needed for computation and modeling purposes.

### MATH 521 Advanced Calculus I (3)

*Prerequisites, MATH 233 and 381*. A grade of A- or better in STOR 215 may substitute for MATH 381. The real numbers, continuity and differentiability of functions of one variable, infinite series, integration.

### MATH 547 Linear Algebra for Applications (3)

*Prerequisite, MATH 233 or 283.* Algebra of matrices with applications: determinants, solution of linear systems by Gaussian elimination, Gram-Schmidt procedure, eigenvalues. MATH 416 may not be taken for credit after credit has been granted for MATH 547.