• Scott Wolpert to lead NSF-funded project on DEI in mathematics and statistics

    Congratulations to Scott Wolpert, professor emeritus of mathematics, who was named principal investigator of a new project to improve diversity, equity and inclusion in mathematics departments. The project is funded by a $600,000 grant from the NSF, and it will provide DEI training to six representatives of math and statistics departments Read More
  • Abba Gumel Featured in Scientific American Article

    Congratulations to Abba Gumel being featured in a new Scientific American Article. The title is “How Mathematics Can Predict and Help Prevent the Next Pandemic” (link to the article). What a great advertisement to Maryland. It is a great honor to have Abba as our colleagues.   Congratulations Abba! Read More
  • Congratulations to Perrin Ruth and Elliot Kienzle

    Eighteen current students and recent alums of the University of Maryland’s College of Computer, Mathematical, and Natural Sciences (CMNS) received prestigious National Science Foundation (NSF) Graduate Research Fellowships, which recognize outstanding graduate students in science, technology, engineering, and mathematics. Across the university, 34 current students and recent alums were among the Read More
  • Congrats to CMNS' Deven Bowman, 2023 Goldwater Scholar

    Congratulations to Deven Bowman, a junior physics and mathematics dual-degree student, who was named a 2023 Goldwater Scholar! Deven has done research with Eun-Suk Seo and Steve Rolston and studied abroad in Florence with Luis Orozco. This summer he’ll be at Caltech working on LIGO. And, fun fact, both of his parents Read More
  • Maryland finishes fourth in the 2022 Putnam competition

     We are very excited to share the news that the University of Maryland Putnam team ranked fourth among 456 institutions in the 2022 Putnam Competition. This is the best result for our team in more than four decades. The first three teams are MIT, Harvard and Stanford. Our team members, Read More
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Integers, divisibility, prime numbers, unique factorization, congruences, quadratic reciprocity, Diophantine equations and arithmetic functions.


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

Level of Rigor


Sample Textbooks

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

Elementary Number Theory and its Applications, by Rosen


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.


The integers


Prime numbers

Greatest common divisor

Euclidean algorithm

Unique factorization


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


RSA Algorithm

Arithmetic functions, Moebius inversion formula, Mersenne primes

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