Tag: Mathematics

Scouting for Sierpiński and rummaging for Riesel (Carrie Finch-Smith)

On campus: this project is scheduled to begin on 6/08/2026 and run for 8 weeks, finishing on 7/31/2026.

Project Description

My favorite number is 509203; it’s the smallest known Riesel number. Riesel numbers are found in many other integer sequences, such as the Fibonacci numbers, the sequence of triangular numbers, the set of Ruth-Aaron pairs, and many others… My research group looks for new results in the intersection of interesting integer sequences and the set of Riesel numbers and Sierpiński numbers.

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Prerequisites

Successful applicants must know how to add, subtract, and mutiply, and more importantly, they must be curious, persistant, and willing to fail over and over again!

Special Comments

Project Information (subject to change)

Estimated Start Date: 6/08/2026

Estimated End Date: 7/31/2026

Estimated Project Duration: 8 weeks

Maximum Number of Students Sought: 6

Research Location: On campus

Travel Required? No (If “yes”: )

Contact Information: Carrie Finch-Smith (email: finchc@wlu.edu)

Fibonacci numbers and D-finite numbers (Greg Dresden)

Remote: this project is scheduled to begin on 6/08/2026 and run for 6 weeks, finishing on 7/17/2026.

Project Description

The Fibonacci sequence start with 0,1,1,2,3 and then each number is the sum of the two previous terms. By contrast, a D-finite sequence might start the same but then each number is some polynomial times the previous term(s). There’s a connection between these D-finite sequences, and sums of double-products in Pascal’s triangle. I haven’t figured it out yet, but that’s the plan for the summer!

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Prerequisites

Some math sophistication, and Math 225 or equivalent.

Special Comments

Project Information (subject to change)

Estimated Start Date: 6/08/2026

Estimated End Date: 7/17/2026

Estimated Project Duration: 6 weeks

Maximum Number of Students Sought: 2

Research Location: Remote

Travel Required? No (If “yes”: )

Contact Information: Greg Dresden (email: dresdeng@wlu.edu)

Counting Schreier-Type Sets (Hung Chu)

Remote: this project is scheduled to begin on 6/08/2026 and run for 6 weeks, finishing on 7/17/2026.

Project Description

A finite set F of natural numbers is called a Schreier set if the minimum element of F is at least the cardinality of F. For example, {4,5,11} is a Schreier set because its minimum element is 4, while its cardinality is 3. However, the set {2,4,7} is not a Schreier set because its minimum element is 2, which is smaller than its cardinality, 3. Various connections between Schreier sets and interesting integer sequences have been discovered. A notable result, due to A. Bird, states that the number of Schreier sets whose maximum element is n is equal to the n-th Fibonacci number. In this project, we will study different Schreier-type conditions, count the sets that satisfy these conditions, and explore the integer sequences that arise from this counting.

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Prerequisites

Students should have completed MATH 225 – Bridges to Advanced Mathematics. Completion of an additional proof-based course is strongly preferred.

Special Comments

Project Information (subject to change)

Estimated Start Date: 6/08/2026

Estimated End Date: 7/17/2026

Estimated Project Duration: 6 weeks

Maximum Number of Students Sought: 2

Research Location: Remote

Travel Required? No (If “yes”: )

Contact Information: Hung Chu (email: hchu@wlu.edu)