# Morganton Courses

# Common Course Pathways

# Course Videos

Below you will find descriptions for each of the courses offered by the mathematics department. Please note that the instructors for each course vary from year to year. All of our course offerings are aligned with our collaboratively established department beliefs. Be sure to check the NCSSM Course Catalog for your campus to view any prerequisites for the courses.

# Calculus-Related Courses

# MA 4000/4002: Precalculus & Modeling w/ Advanced Topics I & II

These courses are devoted to developing a toolkit of functions that serves as a bridge between mathematics and the world it models. The toolkit includes explicitly defined functions such as exponential, polynomial, logarithmic, and trigonometric functions, as well as functions that are defined recursively and parametrically. Students investigate functions, bivariate data, and models with graphing calculators and computers.

Both graphical and analytical approaches to problem solving are emphasized.

Students also complete lab activities and present their results in formal written reports.

Precalculus & Modeling w/Advanced Topics I/II is a yearlong course. Students must enroll in both semesters when registering.

# MA 4042/4044/4046 Calculus I & Calculus II

MA 4042 Calculus I

This course provides students with an introduction to the concepts of differential calculus and the applications of calculus to mathematical modeling. Through class discussions, problem solving, laboratory experiences, and writing assignments students discover the important concepts of calculus, develop an understanding of these concepts, and use these concepts in solving realistic problems. Topics typically covered include the concept of a limit, the derivative, local linearity of functions, linear approximations, applications of the derivative, L'Hopital's rule, an introduction to integration and integration techniques.

This course generally includes the completion of a substantial mathematical modeling project. Calculators and computers are used as tools in the course.

This is one part of a 2-semester course sequence; students must enroll in both semesters when registering.

MA 4046 Calculus II

This course continues the accelerated study of calculus and its applications to mathematical modeling from Calculus I. Through class discussions, problem solving, laboratory experiences, and writing assignments students discover the important concepts of calculus, develop an understanding of these concepts, and use these concepts in solving realistic problems. Topics typically covered include an introduction to differential equations, slope fields, Euler's method, definite and indefinite integrals, numerical approximations of integrals, advanced integration techniques, applications of integrals, Taylor polynomials, and series (including power series).

This course generally includes the completion of a substantial mathematical modeling project. Calculators and computers are used as tools in the course.

This is the second part of a 2-semester course sequence; students must enroll in both semesters when registering.

MA 4044 Calculus II with AP Exam Prep

This course is identical to Calculus II, except that students enrolled in Calculus II with AP Exam Prep are also enrolled into the Calculus II Exam Prep Co-requisite and plan to take the AP Calculus BC exam.

Students in Calculus II and Calculus II with AP Exam Prep will be in the same classroom for the course. If a student would like to drop Calculus II Exam Prep, then their core course would change to Calculus II without a change in block.

# MA 4050: Modeling with Differential Equations

In this course students examine what differential equations are and how they are used to model real-world phenomena. They also look at different techniques for solving differential equations and interpret their solutions in a real world context. Matrices and vector functions will be utilized to help prepare students for future coursework in Calculus and Linear Algebra.

Analytical methods, geometric methods, and numerical methods are included. Technology is an important component of the course.

If you would like to learn more, check this video!

# MA 4060: Multivariable Calculus

This course includes the theory and application of vector functions and partial derivatives. Topics include a vector approach to regression modeling, the Frenet-Serret equations, continuity and differentiability of functions of several variables, gradients and directional derivatives, and classic optimization problems. Numerical methods such as Newton's Method for solving nonlinear systems and modeling with vector-valued functions of scalar and scalar-valued functions of a vector are included.

If you want to learn more, check this this video!

# Statistics & Data Science Courses

# MA 4110: Foundations of Data Science

This course combines three perspectives: inferential thinking, computational thinking, and real-world relevance. Given data arising from some real-world phenomenon, how does one analyze that data so as to understand that phenomenon? The course teaches critical concepts and skills in computer programming and statistical inference, in conjunction with hands-on analysis of real-world datasets, including economic data, document collections, geographical data, and social networks. It delves into social issues surrounding data analysis such as privacy and design.

If you would like to learn more, check this video!

# Applied Math Courses

# MA 4220: Mathematical Modeling

Students with advanced mathematical knowledge are introduced to the creative and analytic aspects of modeling real-world phenomena. Models from engineering, biology, political science, management science, and everyday life are examined through a variety of techniques. When presented with a situation, students learn to develop, test, and revise an appropriate model. The course is project-oriented and focuses on applying the mathematics students already know. Group work is required, and students present their work in extensive written reports.

# MA 4250: History of Mathematics

This course will provide historical context for the evolution of mathematical thinking from the development of counting systems and early geometry to modern fields of mathematics such as knot theory and abstract algebra. The course will focus on both mathematical concepts and the mathematicians and cultures who discovered them.

# MA 4360: Operations Research

This course is a survey of methods and applications to model and analyze real-world problems, especially in the business realm. Examples of problem areas and solution techniques studied:

Multi-Criteria Decision Making and Decision Trees (making decisions given varied criteria like in choosing a college)

Mathematical Programming (linear, binary, integer) (choosing best production mix given limited resources)

Shortest Paths and Transportation Planning (making delivery routes)

Assignment Problems (pairing customers with suppliers)

Simulations (simulating decisions to find optimal outcomes)

# Pure Math & Research Courses

# MA 4320: Linear Algebra with Applications

This course is a study of systems of linear equations, matrices, vectors, vector spaces, linear transformations, eigenvalues, eigenvectors, orthogonality and matrix decompositions. This course will focus on applications including least-squares solutions, Markov chains, and systems of linear differential equations as well as proof writing.

# MA 4330: Non-Euclidean Geometry

Students will explore and prove conjectures about non-Euclidean geometries, which are geometries in which the parallel postulate does not hold, leading to distinct and interesting properties.

# MA 4345: Low-Dimensional Topology

An introduction to the field of topology, focused on the study of 1, 2, and 3-dimensional spaces. The course will begin by covering the basics of point set topology, including homeomorphisms, embeddings, topological manifolds, and constructions of spaces including quotient spaces, products, and complements. We will then explore the classification of closed surfaces. Our semester will culminate in investigating 3-dimensional spaces, starting with lens spaces and ending with the Lickorish-Wallace theorem that every topological 3-manifold can be constructed by Dehn surgery on some link in the 3-sphere. Each unit will include a project with both a visualization and written component.

# MA 4335: Knot Theory

Knots have fascinated humankind, in addition to being practically useful and beautiful, for millennia. In this course we will study mathematical knots and their properties including knot diagrams and Reidemeister moves, knot colorings and polynomials, crossing and unknotting numbers, and the Seifert genus of a knot. These properties give us ways to quantify knots and understand their differences. Students will work on 3-dimensional visualization skills for manipulating knots and surfaces as well as developing mathematical techniques to distinguish knots. In addition, students will develop basic proof writing skills, and connections with other areas of math and science will be emphasized. Depending on student interest, we may delve into advanced topics such as knot energies, knot groups, fibered knots, the 4-dimensional knot theory of concordance and knotted surfaces, and connections with other sciences. Coursework includes mathematical writing, drawing, and projects.

# MA 4350 Real Analysis

Real Analysis is a formal description of functions on the real numbers. In this course, students will learn the underpinnings of calculus through a study of the real numbers, sequences, series, continuity, and differentiability. Potential additional topics include topology, the Riemann Integral, series and sequences of functions, and measure theory. This course will focus on proof writing and developing the skills for undergraduate and graduate study in mathematics.

# MA 4500: Graph Theory with REX Math

An introduction to formal mathematical proofs and research in mathematics in the field of graph theory. This course develops the theory and application of graphs, a major area of modern mathematics, and also provides an introduction to mathematical proof and research. Students develop their ability to make thoughtful conjectures, and to verify those conjectures with valid mathematical arguments. This is done by considering questions of graph structures and colorings,properties of graphs, and some open questions in the field. Students are then required to investigate an open problem in which they demonstrate their ability to make conjectures and to write concise, complete, and coherent proofs. Strong interest and talent in mathematics are required.

If you would like to learn more, check this video!

# MA 4510: Research in Math

Research in Mathematics

Work in a small research group on an open problem in mathematics. Emphasis will be placed on writing and presenting your research, leading up to our participation in the schoolwide Research Symposium.

Research in Mathematics II

Continue your research project from Research in Mathematics. Students will write a formal mathematics research paper, and if the results warrant, submit it for publication.

If you would like to learn more, check this video !

# For Additional Information:

- Talk with your current math instructor