Current Mathematical Sciences Honors Course Offerings
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: MWF at 12-12:50pm in Walker Hall room 304 plus one asynchronous video lecture per week.
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: email@example.com
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: firstname.lastname@example.org
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: email@example.com