MATH 313
Introduction to Number Theory Spring 2025
Division III Writing Skills Quantitative/Formal Reasoning

Class Details

The study of numbers dates back thousands of years, and is fundamental in mathematics. In this course, we will investigate both classical and modern questions about numbers. In particular, we will explore the integers, and examine issues involving primes, divisibility, and congruences. We will also look at the ideas of number and prime in more general settings, and consider fascinating questions that are simple to understand, but can be quite difficult to answer. This course will include a significant focus on mathematical proof writing and problem solving skills. This includes writing clear and rigorous mathematical proofs, clearly explaining mathematical ideas verbally and in writing, determining how to approach certain types of problems, looking for patterns and making conjectures, and asking good questions about the implications of certain ideas and theorems.
The Class: Format: lecture
Limit: 19
Expected: 19
Class#: 3539
Grading: yes pass/fail option, yes fifth course option
Requirements/Evaluation: Problem sets, project, and exams
Prerequisites: MATH 250 or permission of instructor
Enrollment Preferences: If course is over-enrolled, enrollment preference will be based on answers to a questionnaire. Some preference will be given to students who have not yet had Math 355.
Distributions: Division III Writing Skills Quantitative/Formal Reasoning
WS Notes: Students will complete weekly problem sets, with a strong emphasis on proof writing, as well as 2 5-10 page papers/projects. There will be feedback given on mathematical writing as well as accuracy, and discussion time during class on writing in math.
QFR Notes: This course requires working with various number systems, performing explicit computations, and proving mathematical results using logical reasoning practices.

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