• Henri Berestycki wins the 2026 Schauder Medal

    Congratulations Henri Berestycki for winning the 2026 Schauder Medal.  This medal is awarded to Henri for his exceptional achievements in nonlinear analysis and for his numerous applications in many other branches of science.  Henri has been spending one semester per year in our department since 2023.  Among many other awards, Henri is an… Read More

  • Doron Levy is elected SIAM Class of 2026 Fellow

    Doron Levy was elected Fellow of the Society for Industrial and Applied Mathematics (SIAM), class of 2026:  https://www.siam.org/publications/siam-news/articles/siam-announces-2026-class-of-fellows.   Dr. Levy is recognized for his amazingly-stellar and sustained distinguished contributions to research and training in mathematical oncology and mathematical biology.  This exceedingly well-deserved award is fantastic for our department and university. Read More

  • Artem Chernikov awarded the Bessel Research Award by the Humboldt Foundation

    This award is given annually to internationally renowned academics from outside of Germany in recognition of their research accomplishments.  This award is named after Bessel and funded by the German ministry of education and research. Congratulations Atrem Chernikov.  https://www.humboldt-foundation.de/en/apply/sponsorship-programmes/friedrich-wilhelm-bessel-research-award  Read More

  • Mapping the Mind

    Junior computer science and mathematics double major Brooke Guo analyzes neural connections to understand the causes of complex brain conditions like schizophrenia.  When Brooke Guo arrived at the University of Maryland as a freshman in 2022, she knew she wanted to help people and work in a health-related field someday.… Read More

  • Four Science Terps Awarded 2025 Goldwater Scholarships

    Four undergraduates in the University of Maryland’s College of Computer, Mathematical, and Natural Sciences (CMNS) have been awarded 2025 scholarships by the Barry Goldwater Scholarship and Excellence in Education Foundation, which encourages students to pursue advanced study and research careers in the sciences, engineering and mathematics.  Over the last 16 years, UMD’s nominations… Read More
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Description

Integers, divisibility, prime numbers, unique factorization, congruences, quadratic reciprocity, Diophantine equations and arithmetic functions.

Prerequisites

1 course with a minimum grade of C- from (MATH240, MATH241, MATH246, MATH340, MATH341, MATH461, MATH243, ENEE290)


Level of Rigor

Standard


Sample Textbooks

Intro to Number Theory w/Cryptography, by Kraft and Washington

Elementary Number Theory and its Applications, by Rosen


Applications

Computer Science (cryptography)


If you like this course, you might also consider the following courses

MATH456, MATH402 or MATH403


Additional Notes

Students interested in grad school in MATH should consider this course. It is a good course to take before Math 403.

Topics

The integers

Divisibility

Prime numbers

Greatest common divisor

Euclidean algorithm

Unique factorization

Congruences

Basic properties

Modular arithmetic

Euler's phi function

Fermat's, Euler's and Wilson's theorems

Chinese remainder theorem

Legendre and Jacobi symbols

Law of quadratic reciprocity (possibility skip proof to allow time for other topics)

Additional Topics, (as time allows)

Diophantine equations: Pythagoras, Fermat, Pell

Primitive roots: Lagrange's Theorem

Primality testing

Factoring

RSA Algorithm

Arithmetic functions, Moebius inversion formula, Mersenne primes

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