Department of Mathematics and Statistics Honors Program

Academically able students who'd like to experience Mathematics, Statistics, or Math Education in greater depth are encouraged to pursue Department Honors. As an Honors student you will have the opportunity to work one-on-one with professors in select classes in the major. You will do original, independent work that takes you beyond the basics and also enjoy the benefits of close supervision and mentorship. Your senior project will be an opportunity to collaborate with a faculty member on a problem that is significant personally and in your discipline. Participating in Department Honors enhances your chances of obtaining fellowships and admission to graduate school and gains you membership in the USU Honors Program. For further information about Math/Stat Department Honors, contact the Honors Advisor, James Powell.

Page Contents: Overview Honors Courses Departmental Honors Requirements Research/Thesis Opportunities Related Interdisciplinary Programs

Sample surface and contour plot produced by Matlab.

Department Honors Advisor: James Powell
Phone: (435) 797-1953
email: powell@math.usu.edu

Overview of Honors in Mathematics and Statistics

The goal of the Honors program in mathematics is to provide an opportunity for Honors students to enhance their mathematical, scientific, and general education. This is accomplished by:

• Offering Honors sections of entry-level mathematics courses with selected instructor and smaller student/teacher ratios,
• Providing advanced Honors course offerings through either individual student contracts or designated upper division classes,
• Advising Honors students on research opportunities, individualized programs of study, and interdisciplinary options which will serve their goals, and
• Providing a broad range of undergraduate research and scholastic opportunities to pursue Honors Thesis work.

Departmental Honors Requirements

GPA Requirements

Honors students with a declared major in Mathematics or Statistics and a cumulative GPA of at least 3.5 are eligible for acceptance. Students must maintain a GPA of 3.5 or better in math and stat courses, and have a cumulative USU GPA of at least 3.3 to graduate with Departmental Honors.

Course Requirements

Fifteen credit hours of Honors coursework are required to graduate with Departmental Honors. These must include:

• At least 6 semester-hours of upper-division (above 3000 level) Honors credit within the Department of Mathematics and Statistics. This will normally be accomplished by arranging for two classes to be taken under Honors contract. For this designation the student and professor meet to discuss requirements to be met in order for Honors credit to be assigned. Example Honors components for existing classes may consist of a paper or project representing Honors-quality work at the upper-division level.
• Complete 3 hours of Senior Thesis (Math 5950 or Stat 5950) credit supervised by a faculty member in Mathematics and Statistics. These credits must also be completed under Honors Contract.
• Complete at least 6 additional semester-hours of upper-division Honors credit, in any department ( Honors Calculus, Math 1220H, is highly recommended, and may be substituted for 3 of the upper division credits. )

Senior Thesis

Each Honors student must enroll in either Math 5950 or Stat 5950 in order to complete an Honors Thesis. The thesis, developed under the direction of a department faculty member, must be presented in a public forum (e.g. an undergraduate colloquium or MAA sectional meeting). Three credits are granted for the senior thesis.

Course Offerings

We offer three classes which are Honors Designated. These are:

Math 1220H Calculus II

Prerequisites: Math 1210, or AP score of at least 4 on calculus AB exam or at least 3 on calculus BC exam. Topics from Math 1220, second semester calculus, will be covered. These include integration techniques and applications, Taylor's theorem, infinite series and the calculus of parametric curves. The curriculum will be augmented by one or more of the following: a rigorous approach to some basic calculus concepts, computer labs, interdisciplinary applications, a written project, field trips, guest lectures, group learning experiences, historical connections, written communication and use of mathematics technology. At instructor's discretion, the class may meet more frequently than the regular section (e.g. in a 3 lectures, 2 hours of lab/week format). Taught by J. Powell, Fall.

Math 2210H, Multivariable Calculus

Prerequisites: Math 1220, or AP score of at least 5 on calculus BC exam. Vector calculus, multiple integration, partial derivatives, line and surface integrals. The theorems of Green, Gauss, and Stokes are covered. The curriculum will be augmented by one or more of the following: a rigorous approach to some basic calculus concepts, computer labs, interdisciplinary applications, a written project, field trips, guest lectures, group learning experiences, historical connections, written communication and use of mathematics technology. At instructor's discretion, the class may meet more frequently than the regular section (e.g. in a 3 lectures, 2 hours of lab/week format). Taught by J. Powell, Spring.

Research/Thesis Opportunities

The Department offers a wealth of research opportunities for undergraduate studnets, from advanced work in theoretical mathematics to applications of mathematics and statistics in biology, physics, and engineering. Examples of currently-available opportunities for undergraduates include:

Connecting Homogenization and Wavelets in a Geological Context

A student would work on the relationship between methods of averaging (formally known as homogenization) and construction of wavelets using a scheme called lifting. Initial work shows there is a direct relationship which can be used to represent the details in a signal. The main application where this will be used is in the characterization of geological formations with specific cases in petroleum reservoirs and aquifers. Research Supervisor: J. Koebbe

Numerical Methods for Shocks and Forcing in Fluids

A student would work on numerical methods for approximately solving hyperbolic conservation laws which model fluid dynamics. Special techniques will be developed and tested for handling forcing terms. Research Supervisor: J. Koebbe

Mathematical Ecology of Bark Beetles

Bark beetles are aggressive herbivores which attack large, robust conifers. Endemic infestations seem to contribute to forest health, but epidemic infestations are capable of laying waste to thousands of acres. A combination of dynamical systems, partial differential equations and numerical simulation is used to address questions relating to prediction and management of bark beetle populations in national forests. Research Supervisor: J. Powell

Analyzing Autonomous Negotiation Systems

Autonomous negotiation techniques are methods by which computerized networks accomplish tasks by bottom-up team building. Areas of application include transportation logistics, scheduling target illumination for an integrated system of radar emitters, and task organization on Beowulf clusters. Dynamical systems techniques are used to predict the emergent properties of networks which use negotiation protocols. Research Supervisor: J. Powell

Projects Related to DOE Laboratory Fellowships

The Department of Energy offers a variety of summer internship opportunities for undergraduates interested in some branch of DOE research. You can get some great ideas (as well as a summer job!) by visiting their Web site: Energy Research Laboratory Fellowships

Recent Honors Graduates

Undergraduates who have recently finished Honors Theses involving Mathematics and Statistics include:

• Sunni Lyn Mumford Dementia-Free Survival Analysis -- Findings from the Cache County Study on Memory in Aging. Advisor: Chris Corcoran
• Lacey LaRie Jones Statistical Visualization on the Web using nViZn. Advisor: Juergen Symanzik
• Zy Biesinger Parameterizing a Model of Mountain Pine Beetle Mass Attack. Advisor: Jim Powell and Jim Haefner (Biology)
• Amanda Brown The History of Fermat's Last Theorem. Advisor: Dan Nakano
• Jason Knight Belnap Gersgorin and Beyond..... Advisor: LeRoy Beasley

Other opportunities are available through the USU Research Experiences for Undergraduates , an National Science Foundation project providing research opportunities for university students. For information on this opportunity, visit the REU Web Site .

Related Interdisciplinary Programs

The Department houses a number of related interdisciplinary programs which may be attractive to Honors Students. These include:

• The BioMath Minor, an interdisciplinary minor program for students in Mathematics, Statistics, Biology, and Biological and Irrigation Engineering.
• Dual Majors in Computatational Math, Math Physics, and Math Engineering.
• A five-year Industrial Master's Program for talented students at USU.
• An NSF-Supported Summer Research Experiences for Undergraduates program. For more information visit the REU Web Site

Any students with questions regarding honors in Mathematics and Statistics should contact James Powell (email: powell@math.usu.edu ). Also visit the home page.