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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.

Image by Dan Cristian Pădureț

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

Student Experiences

Student's Final Presentation