About the Course
Called "The Queen of Mathematics" by the great mathematician Carl Friedrich Gauss, number theory is the study of the natural number system from which all others are derived. Despite the simplicity of the natural numbers, many accessible problems in number theory remain unsolved. For example, the Goldbach Conjecture, formulated in 1742, which posits that every even integer larger than 2 is the sum of two prime numbers, has defied all proof attempts. In this proof-based course, you'll learn the major ideas of elementary number theory and the historical framework in which they were developed. While strengthening your ability to analyze and construct formal proofs, you and your classmates will explore topics such as the Euclidean Algorithm and continued fractions, Diophantine equations, Fibonacci numbers and the golden ratio, modular arithmetic, Fermat's Little Theorem, and RSA public key cryptography. You'll leave the course with an appreciation for the elegance of theoretical mathematics and the ability to craft rigorous arguments.
Typical Class Size: 16-18
Learning Objectives
- Elaborate, construct, and solve problems of primes using unique factorization, congruences, divisibility, Diophantine equations, primitive roots, and quadratic reciprocity rules
- Elaborate, construct, and solve problems using sums of squares, number-theoretic functions, continued fractions, and apply to public-key encryption, and elliptic curves
- Demonstrate competence with modular arithmetic and apply to Diophantine equations
- Solve Diophantine equations and decide on whether solutions for them exist
- Explain the role of primes, their central role in arithmetic problems and be knowledgeable about primes in number systems other than integers
- Proficient at solving primitive root problems
- Formulate rigorous proofs and defend techniques and theories applied to proofs
About Advanced Enrichment courses
These courses offer above-grade-level material that is presented in a novel context, explored with other advanced learners, and guided by a CTY educator to help prepare students for higher-order thinking and college-style academic challenges. Students work individually and may finish the course early if they complete all requirements before the course end date.
Requirements
CTY courses have grade-level requirements and most require minimum test scores. Some courses may also have prerequisites.
Identification DetailsDates and Tuition
In Person
Johns Hopkins University
Baltimore, MD
Residential Site
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Register by: June 11, 2026
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Register by: July 2, 2026
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Registration Fee and Financial Aid
Tuition and fees will be waived or reduced for students who qualify for financial aid.
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