# Undergraduate Mathematics Course Descriptions

**MATH 104** *Elementary Mathematical Modeling* Three Credit Hours

Prerequisites: Two years of high school algebra

This course will introduce students to mathematical models of real world problems. Designed for non-technical majors, this course focuses on basic mathematical functions, modeling using those functions, properties of their graphs, and real-world applications. Functions will include linear, quadratic, higher degree polynomial, exponential, logarithmic, and logistic. Students will solve problems using algebra and a graphing calculator; they will use matrices for solving systems of linear equations, and they will be required to interpret results in writing.

**MATH 105** *Finite Mathematics* Three Credit Hours

Prerequisites: Two years of high school algebra

An introduction to finite mathematics with an emphasis on applications and formulation of problems in mathematical language. Students are taught a variety of topics, including mathematics of finance, counting methods, probability, and statistics. The course also includes lab assignments using a computer software package.

**MATH 106** *Applied Calculus I* Three Credit Hours

Prerequisite: Two years of high school algebra

An introduction to differential and integral calculus of polynomials, exponential, and logarithmic functions with an emphasis on applications to business and the life and social sciences. *Students may not receive credit for both MATH 106 and MATH 131.*

**MATH 107** *Applied Calculus II* Three Credit Hours

Prerequisite: MATH 106 with a grade of “C” or higher, or MATH 131 with a grade of “C” or higher.

A continuation of the calculus introduced in MATH 106. Topics include techniques of integration, applications of integrals, improper integrals, partial derivatives and applications, and a brief introduction to double integrals.

**MATH 118** *College Algebra with Trigonometry* Four Credit Hours

The goal of this course is to prepare students for Precalculus (MATH 119). This course focuses on basic properties of functions that are linear, quadratic, higher degree polynomial, exponential, logarithmic, and trigonometric. Students will have a good understanding of these properties verbally, numerically, graphically and algebraically, and know how to apply these properties in real-world applications and Precalculus.

**MATH 119** *Precalculus* Four Credit Hours

Prerequisite: MATH 118 with a grade of "C" or higher, or a satisfactory score on the Math Placement Exam, or approval of the department head.

The goal of this course is to prepare students majoring in mathematics, sciences, and engineering for the required calculus sequence. Topics include polynomial, rational, exponential, logarithmic, and trigonometric functions and their graphs, with emphasis on conceptual understanding and algebraic skills necessary for success in calculus. Students in the majors above will normally start their mathematics track in Analytic Geometry and Calculus I (MATH 131). Students desiring to enhance their mathematics foundation before taking Analytic Geometry and Calculus I can opt to take this course. Students scoring below baseline on the departmental Mathematics Placement Exam must take this course. *A student who passes MATH 119 and subsequently changes to a major that does not require MATH 131 may substitute MATH 119 for MATH 104. *

**MATH121** *Introduction to the Practice of Mathematics* Three Credit Hours

Prerequisites: None

This course is restricted to the first year mathematics majors.

This three credit course is required of all mathematics majors during the first year. It is intended to provide them with basic skills needed for independent studies and undergraduate research projects in mathematics. Among these skills are effective written and oral mathematical communication and basic facility with modern mathematical software. Instruction in written communication will include the craft of mathematical writing, the use of technology (e.g., LATEX) for the creation of mathematical text, and readings of level-appropriate mathematics articles in undergraduate journals. Attendance at some departmental seminars will be required and models for effective presentations in professional venues will be discussed. An introduction to computational (e.g., MATLAB) and indexing (e.g., MathSciNet) software that will be of use throughout the four-year curriculum will be provided.

**MATH 129** *Calc I wi Func, Part 1, ExCEL *Three Credit Hours

Prerequisite: Score of 16 or greater on the Math Placement Exam.

Differential calculus of functions of one variable, including: limits, continuity, differentiation, and differentiation rules. Problems are evaluated from theoretical, procedural, and engineering perspectives.

**MATH 130** *Calc I wi Func, Part II, ExCEL *Three Credit Hours

Prerequisite: MATH 129.

Applications of derivatives, anti-differentiation, definite and indefinite integrals, and integration by substitution.

**MATH 131** *Analytic Geometry and Calculus I* Four Credit Hours

Prerequisite: MATH 119 with a grade of “C” or higher, a satisfactory score on the placement exam, or approval of the department head

Limits, derivatives, applications of the derivative, antiderivatives and definite integrals.*Students may not receive credit for both MATH 106 and MATH 131.*

**MATH 132** *Analytic Geometry and Calculus II* Four Credit Hours

Prerequisite: MATH 131 with a grade of “C” or higher, or HONR 131 with a grade of “C” or higher

Applications of the integral, transcendental functions, techniques of integration, series and sequences of real numbers, Taylor series, power series, parametric equations, and polar coordinates.

**MATH 206** *Introduction to Discrete Structures* Three Credit Hours

Prerequisite: MATH 131, or HONR 131, or a grade of "C" or higher in MATH 106 or MATH 119

Set algebra including relations and functions, propositional and predicate logic, combinatorics, graphs, and applications of these to various areas of computer science.

**MATH 231** *Analytic Geometry and Calculus III* Four Credit Hours

Prerequisites: MATH 132 or HONR 132

The analytical geometry of two and three dimensions, the differential and integral calculus of functions of two or more variables, and vector differential calculus.

**MATH 234** *Applied Engineering Mathematics I* Four Credit Hours

Prerequisite: MATH 132 or HONR 132

An integrated course in linear algebra and differential equations. Topics include differential equations of the first order and degree, linear differential equations of higher order, systems of differential equations, the Laplace transform, vector spaces, bases, linear transformations, systems of linear equations, algebra of matrices, and determinants.

**MATH 240** *Linear Algebra* Three Credit Hours

Prerequisite: MATH 132, MATH 107, or HONR 132

Systems of linear equations, algebra of matrices, inverses, determinants, vector spaces with an emphasis on Euclidean vector spaces, bases, subspaces, transformations, eigenvalues and eigenvectors, and quadratic forms.

**MATH 290** *Topics in Mathematics* Three Credit Hours

A study of a particular aspect of mathematics or a related area that is of interest to both mathematics major and other majors, but is not on our list of standard mathematics courses. This course assumes no prerequisites.

**MATH 302** *Applied Cryptography* Three Credit Hours

Prerequisites: MATH 206, MATH 234, or MATH 240

In this course the students will learn about the common cryptographic use, for example: security functions (data protection, data integrity, authentication, non-repudiation). The students will learn about symmetric cryptography, public key cryptography (Diffie-Hellman, RSA, El Gamal), the strength and weaknesses of various cryptography models. Finally, students will learn about cryptographic failures including types of attacks (brute force, chosen plaintext, known plaintext, differential and linear cryptanalysis, etc) and implementation failures.

**MATH 303** *Modern Algebra I* and

**MATH 304** *Modern Algebra II* Three Credit Hours Each Semester

Prerequisites: MATH 206 and MATH 240.

A two-semester sequence in the algebraic structures which lie at the foundations of many areas of modern mathematics. Topics are chosen from the theory of groups, rings, integral domains, and fields, coding theory, Galois theory, modules, and Euclidean constructions.

**MATH 305** *Modern Geometry* Three Credit Hours

Prerequisite: MATH 132, MATH 107, or HONR 132

Special topics from axiomatic geometries. Topics include Euclidean geometry, projective geometry, non-Euclidean geometry, and metric projective geometry.

**MATH 335** *Applied Engineering Mathematics II* Three Credit Hours

Prerequisite: MATH 231 and MATH 234

Advanced topics in differential equations and multi-dimensional calculus. Topics include power series solutions of differential equations, line and surface integrals, Fourier series, vector integral calculus, special functions, and an introduction to partial differential equations.

**MATH 343** *Applied Numerical Methods I* Three Credit Hours

Prerequisites: MATH 240 or MATH 234 and a knowledge of a programming language

An introduction to numerical methods. Topics include floating-point computation, finding zeros of functions, direct methods for solving systems of linear equations, interpolation, and numerical differentiation and integration.

**MATH 344** *Applied Numerical Methods II* Three Credit Hours

Prerequisite: MATH 234 and a knowledge of a programming language

A further study of numerical methods. Topics include approximation, numerical solutions of ordinary differential equations, iterative methods for solving systems of linear equations, eigenvalue problems, and error analysis.

**MATH 361** *Image Processing *Three Credit Hours

Prerequisite: MATH 132 or HONR 132

An introduction to mathematical image processing and its applications. Topics include linear filters, mathematical morphology, variational methods, PDE-based methods, image modalities, and machine learning. Some prior computer programming experience would be helpful but is not required.

**MATH 381** *Deterministic Methods of Operations Research* Three Credit Hours

Prerequisites: One semester of calculus

The theory and applications of deterministic models of operations research. Topics include linear programming and the simplex algorithm, transportation and assignment problems, game theory, graphs and network flows, dynamic programming, and sensitivity analysis.

**MATH 382** *Probabilistic Methods of Operations Research* Three Credit Hours

Prerequisites: Two semesters of calculus

The theory and applications of probabilistic models of operations research. Topics include queuing models, birth and death processes, finite-state Markov chains, inventory theory, forecasting, simulation, decision analysis, game theory, and reliability.

**MATH 390** *Topics in Mathematics* Three Credit Hours

A study of a particular aspect of mathematics or a related area at junior level that is of interest to both mathematics major and other majors, but is not on our list of standard mathematics courses. The offering of this course will depend upon the interest of the students, the availability of an instructor, and approval of the department head. Since the content of the course may change, a student may repeat the course for credit with the consent of the department head.

**MATH 399** *Junior Research Project* Three Credit Hours

Open only to junior mathematics majors with a MATH GPA of at least 3.0.

It is required to have a written proposal accepted by the research advisor and the department head.

This course offers a mathematics junior an opportunity to complete research n an area of current interest and importance in mathematics in collaboration with a research advisor. A formal paper is required in this course. Although it is a 300-level course, this course is not approved as a departmental elective. It may be used to fulfill a general elective. This course satisfies the ROTC-fulfillment.

**MATH 403** *Introduction to Analysis I* and

**MATH 404** *Introduction to Analysis II* Three Credit Hours Each Semester

Prerequisites: MATH 231

A two-semester sequence in real analysis. Topics include sets, functions, properties of the ordered field of real numbers, topology of the reals, sequences and series, continuity, differentiation, integration, and sequences and series of functions.

**MATH 405** *Mathematical Statistics* Three Credit Hours

Prerequisites: MATH 132 and STAT 261

Axioms of probability, combinatorial probability, random variables, distribution functions, the law of large numbers, central limit theorem, estimation, maximum likelihood methods, hypothesis testing, confidence intervals, and non-parametric methods.

**MATH 411** *Number Theory* Three Credit Hours

Prerequisite: MATH 132, MATH 107, or HONR 132

The Euclidean algorithm, prime and composite integers, elementary Diophantine equations, Pythagorean triples, Euler's phi-functions, congruences, Euler-Fermat theorems, exponents and primitive roots, and quadratic residues.

**MATH 412** *History of Mathematics* Three Credit Hours

Prerequisite: MATH 132, MATH 107, or HONR 132

A survey of the concepts and methods of mathematics from the time of the ancients to the present. The course includes a research paper on some major mathematician or body of mathematics.

**MATH 414 ***Teaching Secondary Mathematics - The Teaching Cycle *Three Credit HoursPrerequisite: MATH 303

Students examine research-based models of teaching and learning in mathematics. Students also work in Professional Learning Communities (PLCs) within the class to model the ongoing professional development they will be expected to undertake throughout their careers. Topics include: constructing quality assessments, promoting mathematical discourse, thoughtful integration of technology, and issues of equity and access.

**MATH 415** *Teaching Secondary Mathematics - Mathematical Proficiency and Motivation *Three Credit HoursPrerequisite: MATH 303

*Topics include: unpacking the concept of mathematical proficiency in the context of Algebra I, Algebra II, and Geometry; research-based strategies for promoting student motivation; and the role of classroom culture and student identity in teaching and learning. Students will work in Professional Learning Communities (PLCs) within the class to model the ongoing professional development they will be expected to undertake throughout their careers. Students will also gain experience productively observing current in-service teachers, building skills and dispositions that are key to long-term professional growth and development.*

**MATH 422** *Complex Variables* Three Credit Hours

Prerequisite: MATH 231

Topics from complex function theory: complex differentiation and integration, Cauchy theorem, complex series and uniform convergence, harmonic functions.

**MATH 451** *Graph Theory* Three Credit Hours

Prerequisite: MATH 206

A formal introduction to the theory and applications of graphs. Topics include connectivity, trees, Eulerian graphs, Hamiltonian graphs, planarity, graph colorings, matchings, and domination.

**MATH 470** *Mathematical Models and Applications* Three Credit Hours

Prerequisite: MATH 234

An introduction to the theory and practice of building and analyzing mathematical models for real-world situations encountered in the social, biological, and environmental sciences.

**MATH 480** *Readings in Mathematics* Three Credit Hours

Prerequisite: Permission of the instructor

Directed reading on assigned topics in mathematics. The course includes weekly conferences with the instructor and a formal paper. Since the content of the course may change, a student may repeat the course for credit with the consent of the department head.

**MATH 490** *Advanced **Topics in Mathematics* Three Credit Hours

Prerequisite: Permission of the instructor

Selected topics in mathematics. The offering of this course will depend upon the interest of the students, the availability of an instructor, and approval of the department head. Since the content of the course may change, a student may repeat the course for credit with the consent of the department head.

**MATH 495** *Senior Seminar in Mathematics* Three Credit Hours

Open only to senior mathematics majors.

This is a "capstone" course that will cover various topics from the undergraduate mathematics curriculum. Each student will have a substantial term project and will write a paper and make an oral presentation to departmental faculty about that topic. This course satisfies the ROTC-fulfillment requirement.

**MATH 499** *Senior Research Project* Three Credit Hours

Prerequisite: Approval of department head

Open only to senior mathematics majors with a MATH GPA of at least 2.500.

A research project with a required formal paper. Recommended for students planning graduate work. Approval for enrollment based on the acceptance of a written proposal by the instructor and approval of the department head.

This course can be approved as a departmental elective for a student if the following criteria are satisfied:

(1) the student has a MATH GPA of at least 3.0,

(2) the proposed research project is a continutation of a project conducted during the previous semester(s) with at least one oral or poster presentation given at The Citadel Student Excellence Day or a regional conference during the previous semester(s) or submitting at least one journal paper to a known journal in a STEM field, and

(3) the additional research results will be presented at The Citadel Student Excellence Day, at a regional conference, or a known journal in a STEM field during the semester.

This course satisfies the ROTC-fulfillment.