Current Mathematical Sciences Special Course Offerings
Fall 2024
Support Courses:
MAT 1535 "Precalculus Support" (1 credit)
Are you uneasy about your preparation for Precalculus (MAT 1025)? This course is designed to support student success in MAT 1025 and is for students also enrolled in MAT 1025. This course has an attendance requirement and includes prerequisite and precalculus course content. If you have any questions specifically about this course, please feel free to contact Mrs. Lisa Maggiore at: lm72407@appstate.edu
MAT 1530 "Calculus 1 Support" (1 credit)
Are you uneasy about your preparation for Calculus (MAT 1110)? This course is designed to support student success in MAT 1110 and is for students enrolled in MAT 1110. This course has an attendance requirement and includes prerequisite and calculus content work. If you have received a score of 12 on the "Calculus Readiness Test" you must take MAT 1530 Calculus 1 Support corequisitely during the same semester you take MAT 1110. If you have a higher score on the readiness test or have placed into calculus in some other way you can also enroll in this support course. If you have any questions specifically about this course, please feel free to contact Dr. Katie Mawhinney at: mawhinneykj@appstate.edu
MAT 1005 "Brief Introduction to Mathematics" (1 credit)
STT 1805 "Brief Introduction to Statistics" (1 credit)
Many students transfer in a 3 credit mathematics course which potentially gives them 3 Quantitative Literacy (QL) hours. These coureses, MAT 1005 and STT 1805, are single credit courses intended to give such students their final QL hour in order to fulfill their Gen Ed requirements.
For those transferring a statistics course, MAT 1005 is a good choice. For those transferring in a more traditional math course, STT 1805 (a taste of statistics) is a good choice.
Please note: You need permission from the department to register for either of these courses. Since it turns out that many students will get their final QL hour from a course in their major (making both of these courses uneccesary), we are limiting registration to standing Juniors or Seniors.
If you have any questions about these courses or need permission to enroll, please feel free to contact Astrid Sosa at: sosaa1@appstate.edu
For Honors Courses see the Current Honors Courses page
MAT 4010-101 & MAT 5980-101: "Using AI to Improve Mathematics Teaching and Learning"
We will investigate employing AI to improve mathematics teaching and learning through lesson/activity brainstorming and development, content assessment, lesson development, assessment development, and assessment grading. A focus will be on looking deeply into and assessing the correctness and limitations of the AI-provided mathematics, and considering AI's understanding of mathematical pedagogy.
Meeting Times: Tuesdays at 5pm-7:30pm in Walker Hall room 302
If you have any questions specifically about this course, please feel free to contact Dr. Michael Bossé at: bossemj@appstate.edu
Spring 2024
MAT 4720-101 & MAT 5210-101: "Topic in Abstract Algebra" - Galois Theory
Everyone knows how to solve the quadratic equation. Although much more involved, there are also corresponding cubic and quartic equations. However, it turns out that no such "quintic formula" exists! This was first shown in the 1800's by Abel (and sort of by Ruffini in 1800). In the 1820's Galois developed a complete theory which explains exactly when a polynomial equation is "solvable".
This course will include a review of basic group and ring theory. We will cover some of the theory of vector spaces (linear algebra) and then study field extensions. This will then allow us to show the impossibility of obtaining certain compass-straightedge geometric constructions (eg. trisecting angles, doubling cubes, squaring circles). Next, we will develop the Galois correspondence relating field extensions to (Galois) groups of automorphisms and then show the impossibility of solving certain quintic equations.
If there is time, I also plan on sketching out some of "differential Galois theory" and discuss solvability of differential equations.
Meeting Times: Mondays, Wednesdays, & Fridays at 11-11:50am in Walker Hall room 314
Prerequisite: (Introduction to Modern Algebra) MAT 3110. [Note: Although I will assume everyone has had an introductory course in modern algebra and linear algebra, I will take time to review necessary background material. For example, I will assume that students are familiar with the definition of a ring, but not that they know any ring theory.]
If you have any questions specifically about this course, please feel free to contact Dr. Bill Cook at: cookwj@appstate.eduMAT 5535-101: "Graduate Differential Geometry"
Differential geometry "is intuitive, calculable, useful, interdisciplinary, and, most importantly, interesting... It has a long history and has found new relevance in areas ranging from machinery design to the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA” (Oprea).
We consider the differential geometry of curves, surfaces, and spacetime, including theoretical and computational components, intrinsic and extrinsic viewpoints, and numerous applications. The geometry of space-time will also be considered. We will develop geometric skills and 3-D spatial visualization skills and understand the importance of differential geometry in various scientific fields, including physics. This course will also build off of numerous undergraduate courses, in order to develop a greater appreciation for connections between various disciplines of mathematics as they apply to differential geometry.
Graduate students who are enrolled in this course will attend the undergraduate course MAT 4140 and complete that work as well as extra graduate problems and assignments that make use of the ideal prerequisites below. Graduate students will also research, review and interpret literature related to topics in differential geometry.
Required prerequisites: multivariable calculus and linear algebra at the undergraduate level + at least some of the additional ideal prerequisites of differential equations, real analysis, and analytical physics I and II, all at the undergraduate level.
If you previously took MAT 4140 or its equivalent, then you are not eligible for this class. Two of the three credit hours are in person. Our hybrid class is officially scheduled by the university for our third hour to be a part of the activities between classes.Meeting Times: Mondays & Wednesdays 3-3:50pm in Walker Hall room 309
If you have any questions specifically about this course, please feel free to contact Dr. Sarah Greenwald at: greenwaldsj@appstate.eduMAT 5540-101: "Noncomputability Theory"
This course explores the theoretical limitations of algorithmic computation. The main text is Computability Theory by Rebecca Weber. Introductions to reverse mathematics and Weihrauch reducibility will be included.
Meeting Times: Mondays, Wednesdays, & Fridays at 12-12:50pm in Walker Hall room 308
Prerequisites: This is a graduate course. Undergraduate students who will be seniors and have at least a 3.0 GPA may request permission to enroll.
If you have any questions specifically about this course, please feel free to contact Dr. Jeff Hirst at: hirstjl@appstate.edu
Fall 2023
Support and Fallback Courses:
MAT 1535 "Precalculus Support" (1 credit)
MAT 1530 "Calculus 1 Support" (1 credit)
MAT 1532 "Calculus 2 Support" (1 credit)
Are you uneasy about your preparation for Calculus 2 (MAT 1120)? This support course is for students also enrolled in MAT 1120. This course has an attendance requirement and includes prerequisite and calculus content work. If you have any questions specifically about this course, please feel free to contact Dr. Eric Marland at: marlandes@appstate.edu
MAT 1531 "Intensive Calculus Preparation" (3 credits)
This fallback course is designed for students who meet the requirements to enroll in calculus, but realize they don’t quite have a solid understanding of the prerequisite material needed for calculus. This class starts 5 weeks into the fall semester, meets 3 hours per week and also requires completion of adaptive online precalculus assessments.
If you have any questions specifically about this course, please feel free to contact Dr. Trina Palmer at: palmerk@appstate.edu
MAT 4010-101 & MAT 5530-101: "Calculus 4: An Introduction to Manifold Theory"
We will extend topics introduced in Calculus 3 (MAT 2130). In particular, we will study derivatives (i.e., Jacobian matrices) of functions of several variables and generalize from parameterized curves and surfaces to manifolds covered by a single coordinate chart. Here we also generalize vector fields to differential forms, curl and divergence to the exterior derivative, and our big theorems to the generalized Stokes' theorem. From there we will begin developing the theory of manifolds including concepts such as the tangent bundle, tensor fields, exterior algebras, orientations, and integration on manifolds.
Meeting Times: Mondays, Wednesdays, & Fridays at 11-11:50am in Walker Hall room 302
Prerequisites: Calculus 3 (MAT 2130), Linear Algebra (MAT 2240), and some proof writing background (MAT 2110)
If you have any questions specifically about this course, please feel free to contact Dr. Bill Cook at: cookwj@appstate.eduMAT 4010-102 & MAT 5540-101: "Mathematical Questions from the Classroom"
Countless questions naturally arise during instruction. Some more elementary questions include: "Why can't we divide by zero?" "Why is a negative times a negative a positive?" "Why do we rationalize the denominator and not the numerator?" Other more sophisticated and common questions include algebra, trigonometry, set theory, infinity, complex numbers, calculus, and much more. Effective mathematics educators must have immediate answers to these questions immediately at hand to effectively address student inquiries, promote interest and learning, and continue a positive flow of ideas. We will investigate and develop grade- and course-appropriate responses to hundreds of these questions. We will also investigate mathematical topics that may have been missing in undergraduate or graduate mathematics experiences that are important for the effective teaching of mathematics at any level.
Meeting Time: Tuesdays at 4-6:30pm in Walker Hall room 302 or online [ask instructor]
If you have any questions specifically about this course, please feel free to contact Dr. Michael Bossé at: bossemj@appstate.edu