Mathematics Programs
Program Overview
In this research workshop, the Professor will guide students in original research on generalized Zeckendorf decompositions. In the course of their investigations, students will learn material in number theory, probability, statistics, and combinatorics, as well as develop programming skills. This research workshop focuses on generalized Zeckendorf decompositions, which involve the unique representation of positive integers as the sum of non-adjacent terms from a given sequence. The workshop consists of lectures and discussions, where students will learn about the Fibonacci numbers, Gaussianity questions, and generalizations to other recurrences. Additionally, students will work on original research questions such as finding formulas for terms in a two-dimensional sequence and determining the number and uniqueness of decompositions. Prerequisites include algebra, pre-calculus, and optional calculus.
Eureka Alumni from this program have received admission offers to Princeton University, Massachusetts Institute of Technology (MIT), Stanford University, University of Pennsylvania (UPenn), Cornell University, and many other top US universities. Alumni from this program have gone off to pursue majors in Applied Mathematics, Computer Science, Data Science, Law, and Engineering.
The research experience, training, and skills students receive at the Eureka Mathematics Program have helped students to compete in prestigious math competitions and exams, such as the Regeneron Science Talent Search, Yale Physics Olympiad, American Mathematics Competitions (AMC), American Invitational Mathematics Examinations (AIME), International Science and Engineering Fair (ISEF) and many other programs.
Young scholars that have attended the Eureka Mathematics Program have received many honors and prestigious awards. To just name a few, our students have received awards such as: S.-T. Yau High School Science Award - Economic & Financial Modelling; 2022 MathWorks Math Modeling Challenge Finalist; 2022 Amazon Future Engineer Scholarship; NJ Academy of Science Research Competition - 1st Place in Physics; 3 Time AIME Qualifier; AMC Qualifier; Yale Physics Olympiad 10th Place; President’s Volunteer Service Award (Gold); and other awards in math and science competitions. We are so proud of our students' accomplishments!
The below sections will provide more insight into the students that have attended this program and share their experiences and successes.
College Admission Results
Attended Eureka
2020
High School Name
United World College Changshu China
Admission Offer Received
• Williams College
Eureka Research Title
Generalizations Of The Fibonacci Decomposition
Attended Eureka
2020 Summer
High School Name
George School
Admission Offer Received
• (REA) Princeton University
Eureka Research Title
Mathematics: Generalized Zeckendorf Decompositions - Joint Paper
Attended Eureka
2020 Summer
High School Name
Salisbury School
Admission Offer Received
• University of Pennsylvania (UPenn)
• Cornell University
• Williams College
• Northwestern University
Eureka Research Title
Mathematics: Generalized Zeckendorf Decompositions - Joint Paper
Attended Eureka
2019
High School Name
Phillips Exeter Academy
Admission Offer Received
• Massachusetts Institute of Technology (MIT)
Eureka Research Title
Group Paper: On Fibonacci Sequences
Attended Eureka
2020
High School Name
The Experimental High School Attached To Beijing Normal University
Admission Offer Received
• Massachusetts Institute of Technology (MIT)
Eureka Research Title
Mathematics: Generalized Zeckendorf Decompositions: Group Paper
Attended Eureka
2021
High School Name
Concord Academy
Admission Offer Received
• (REA) Stanford University
• Massachusetts Institute of Technology (MIT)
Eureka Research Title
Group Paper: On The Reciprocal Sums Of Several Generalized Fibonacci Sequences
Attended Eureka
2018
High School Name
Taft School
Admission Offer Received
• Yale University
• Columbia University
• University of Pennsylvania (UPenn)
Eureka Research Title
Gaussian Behavior In Zeckendorf Decompositions From Lattices
Attended Eureka
2021 Summer
High School Name
Shanghai Starriver Bilingual School
Admission Offer Received
• (ED) University of Chicago
Eureka Research Title
On The Reciprocal Sum Of Tribonacci Numbers With Indices In Arithmetic Progression
Attended Eureka
2021
High School Name
High School - Undisclosed
Admission Offer Received
• University of Southern California (USC)
• Columbia University
• Duke University
• Brown University
Eureka Research Title
Group Paper: On Fibonacci Sequences
Attended Eureka
2019 Summer
High School Name
High Technology High School
Admission Offer Received
• Columbia University
Eureka Research Title
Gaps Of Summands Of The Zeckendorf Lattice
Attended Eureka
2020 Spring
High School Name
Admission Offer Received
• University of California - Berkeley (UCB)
Eureka Research Title
Research Topic - Undisclosed
Attended Eureka
2020
High School Name
Jasper High School
Admission Offer Received
• The University of Texas at Austin
Eureka Research Title
Mathematics: Generalized Zeckendorf Decompositions: Group Paper