Course Learning Outcomes
- Department: Mathematics
- Course number: 34500
- Course title: Theory of Numbers
- Term offered: Varies
- Prerequisite: A grade of C or higher in MATH 30800 or placement by the Department
- Hours and credits: 4 hrs./week and 4 credits
- Date effective: September 7, 2025
- Course coordinator: Gautam Chinta
Catalog description
Divisibility, primes, fundamental theorem of arithmetic, congruences, number theory from an algebraic viewpoint, quadratic reciprocity, number theoretic functions, diophantine equations.
Typical textbooks used
- A friendly introduction to number theory, 4th edition, by Joseph Silverman (Pearson)
Course learning outcomes:
| After taking this course, the students should be able to: | Contributes to Departmental learning outcome(s): |
|---|---|
| 1) Write clear and rigorous proofs (or disproofs) of mathematical statements utilizing basic proof techniques. | e1, e2, f, g |
| 2) Understand statements and proofs of basic number theory results, including Fundamental Theorem of Arithmetic, Chinese Remainder Theorem, Fermat’s Little Theorem, existence of primitive roots mod a prime, and quadratic reciprocity. | e1, e2, f, g |
| 3) Become proficient in using the Euclidean algorithm and solving linear congruence equations. | a, g |
| 4) Collect and use numerical data to form conjectures about the integers. | a, d |
Typical course assessment tools
- Final exam: 40%
- In-class exams, quizzes, homework, attendance: 60%
Departmental learning outcomes:
The mathematics department, in its varied courses, aims to teach students to:
- a) perform numeric and symbolic computations
- b) construct and apply symbolic and graphical representations of functions
- c) model real-life problems mathematically
- d) use technology appropriately to analyze mathematical problems
- e) state (e1) and apply (e2) mathematical definitions and theorems
- f) prove fundamental theorems
- g) construct and present (generally in writing, but, occasionally, orally) a rigorous mathematical argument.