MATH 457
Partition Theory Spring 2024
Division III Quantitative/Formal Reasoning
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The partitions of a positive integer are the different ways of writing it as a sum of positive integers. For example, 5 has seven partitions, three of which are 5=1+1+1+1+1, 5=2+3, and 5=5. (Can you find the rest?) Partition theory is a rich area of combinatorics with applications to algebra and mathematical physics. In this class we will focus on enumerative and bijective methods to answer questions such as: How can we calculate the number of partitions of a number efficiently? Why is the number of partitions of N into strictly odd numbers always the same as the number of its partitions into distinct numbers? Why does a 2-dimensional partition look like a stack of cubes, and what does that have to do with tilings?
The Class: Format: lecture
Limit: 25
Expected: 10
Class#: 3511
Grading: yes pass/fail option, yes fifth course option
Requirements/Evaluation: Written homework; Written/Oral Exams; Project/Presentation
Prerequisites: A course in abstract algebra such as MATH 355, or permission of instructor.
Enrollment Preferences: Priority given to Junior and Seniors, and according to previous experience with subject.
Distributions: Division III Quantitative/Formal Reasoning
QFR Notes: This is an advanced course in mathematics.

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