## Current Mathematical Sciences Honors Course Offerings

### Fall 2023

#### MAT 3510: Applications of Mathematics in Artificial Intelligence [Junior Honors Seminar]

The overarching objective of this course is to understand how mathematics works under the hood of Artificial Intelligence (AI) models. Too many times AI models are referred to

as "black boxes." We will debug this myth by discovering that AI is not magic, instead it's data and science. We will see that an "artificial neural network" is really just a composite function assembled with vectors and matrices (i.e., tensors). We will also see that "backpropagation" which is required to help AI models "learn" involves the application of the chain rule, gradient vectors, and finding minimums using methods learned in an undergraduate mathematics curriculum. Natural Language Processing will be used as the vehicle to help facilitate our explorations and discussions. We will follow the same model development pipeline used by Data Scientists to prepare data (text) and then build, train, and evaluate various types of Recurrent Neural Networks (RNNs) that make predictions based on a temporal sequence of inputs. You will experience an aha moment when you learn how your favorite texting app is able to predict the next words that you will type in your message. We will develop our models using the Python programming language and leverage the computing power of a graphics processing unit (GPU) on Google’s Colaboratory.Meeting Time: MWF at 1-1:50pm (MW synchronous online and F in Walker Hall room 314).

Prerequisite: No prior experience using the Python programing language is required.

MAT 2240 (Linear Algebra)

Helpful background: MAT 2130 (some multivariable calculus) and STT 3250/3850 (some Probability/Statistics)

If you have any questions specifically about this course, please feel free to contact Dr. William Fehlman at: wfehlman@gmail.com

### Spring 2023

#### MAT 2110 Section 410: Techniques of Proof [Honors Section]

There are two ways to learn to write proofs. You can either (1) write incorrect proofs until you discover all the possible ways to make errors, or (2) find out what proofs really are and then write some. We'll take the second approach. This course provides excellent preparation for upper division mathematics courses and is great for people interested in thinking clearly.

This spring Dr. Jeffry Hirst will be teaching the honors section of Techniques of Proof. Dr. J. Hirst is not just an excellent instructor; he is coauthor (with Dr. H. Hirst) of this course's textbook!

Meeting Times: MTWR at 1-1:50pm in Walker Hall room 106.Prerequisites: Calculus II (and status as an honors student in mathematical sciences)

If you have any questions specifically about this course, please feel free to contact Dr. J. Hirst at: hirstjl@appstate.edu#### MAT 3510: Introduction to Measure Theory [Junior Honors Seminar]

Measures are set functions that generalize notions of "size" like length, area, and probability. In this course, we will investigate several formal ways to construct measures toward understanding central challenges and insights in the development of modern probability theory and the Lebesgue integral. Beware the Vitali set!

Meeting Time: MWF at 9-9:50am in Walker Hall room 309.Prerequisite: MAT 1120 (Calculus With Analytic Geometry II) and MAT 2110 (Techniques of Proof)

If you have any questions specifically about this course, please feel free to contact Dr. Noah Williams at: williamsnn@appstate.edu

### Fall 2022

#### MAT 3510: Game Theory [Junior Honors Seminar]

This course is an introduction to the mathematical theory of analyzing games and playing them optimally. Although the concept of a game usually implies fun and leisure, "game theory" is a branch of advanced theoretical mathematics. Games like blackjack, poker, and chess provide obvious examples, but many other situations can be formulated as games. Any situation in which rational people make decisions within a framework of strict and known rules, and where each player gets a payoff based on the decisions of all the players, is a game. Examples include auctions, collective bargaining, political and economic theory, negotiations between countries, and military tactics.

If you have any questions specifically about this course, please feel free to contact Dr. Rick Klima at: kilmare@appstate.edu

### Spring 2022

#### MAT 2110 Section 410: Techniques of Proof [Honors Section]

#### MAT 3510: The Broader Impact of Big Mathematical Ideas [Junior Honors Seminar]

Mathematics is so ubiquitous that many people do not recognize the mathematics they encounter in their daily lives and work. Beyond these encounters, many people and professions — whether overtly or tacitly — intersect with Big Mathematical Ideas (e.g., Pythagorean Theorem, limits, modulo systems, Law of Large Numbers, measurement, error, estimation, statistics, probability, proportions, and linear and exponential growth, and many others).

This course will investigate a variety of mathematical ideas encountered by people working in various professions recognized as seemingly “non-mathematical”. Its focus is on connections, applications, and breadth of numerous mathematical fields rather than on the depth of a small number of topics. Focus will be on students interacting with people and professions in “non-mathematical” fields. This course will be primarily activity based.Meeting Time: T at 3:30-6:00pm in Walker Hall room 302.

Prerequisite: Calculus (and mathematical science honors status)

If you have any questions specifically about this course, please feel free to contact Dr. Michael Bossé at: bossemj@appstate.edu

### Fall 2021

#### MAT 3510: Elementary Stochastic Calculus [Junior Honors Seminar]

In this course, we will explore the basic concepts in stochastic calculus. Stochastic calculus is used to model and solve problems in which Brownian motion is a driving influence. It has been used in modeling a continuous trait through time in biology, the movement of particles in a fluid due to collisions with other atoms or molecules in physics, and the movement of interest rates and the price of financial assets in financial mathematics. Brownian motion was first used to describe the motion of particles suspended in a fluid in the late nineteenth century and later used by Einstein in one of his 1905 papers to indirectly confirm to fellow physicists the existence of atoms and molecules. In this course, we will first need to understand and simulate the process that gives rise to Brownian sample paths. Second, since Brownian sample paths are nondifferentiable, we will study the tools necessary to define an integral with respect to this process. Some of the tools we need require mathematics beyond the level of the course and will be introduced and studied heuristically. We will see that multiple definitions of the integral are possible and focus on two of the more commonly used ones, by Stratonovich and by Ito. The integral by Ito yields a chain rule that is different than what the student sees in elementary calculus. Finally, we will solve some common stochastic differential equations and discuss their meaning.

Meeting Times: MWF at 9-9:50am in Walker Hall room 310.

Corequisite: MAT 2130, Prerequisites: MAT 2240 (and mathematical science honors status)

If you have any questions specifically about this course, please feel free to contact Dr. Shirley at: shirleykl1@appstate.edu