The Maths of Puzzles

MATH-704

Teacher: Rom Pinchasi

Credits: 2

Duration: 6 weeks, from 17.02. to 26.03.

Language: English

Time and Place: Tuesdays 11:15-13:00 in MAA110,
Thursdays 11:15-13:00 in MAA330

Requirements: The course is suitable for Ph.D. students and graduate students as well as extremely excellent undergraduate students.

PLEASE NOTICE: Despite its attractive name, the course is normally NOT recommended for undergraduate students. Only graduate students and Ph.D. students can register for the course.  

Content

The course ‘ The Math of Puzzles’  will revolve both around different strategies and methods to solve Puzzles and Problems  and at the same time also around some mathematical topics that will be presented through attractive puzzles.
We will have some flexibility with choosing the topics presented in the course. This will depend on the size of the class and on the audience,
Some specific topics that we can choose from are:

  • Invariants and Potential Functions in Math Puzzles
  •  Linear Algebra methods
  • The method of coloring
  • The method of combinatorial Nullstellensatz and Chevalley-Warning
  • Using Hall’s theorem to solve puzzles
  • Advanced applications of the Pigeon-Hole principle
  • The principle of MINIMUM/MAXIMUM in solving puzzles
  • The Polynomial Method
  • Puzzles about Polynomials and Number Theory
  • The Probabilistic Method

Homework

Every week there will be puzzles for homework that the students will have to try and solve (without any help from AI) and present their solution in class. Some open problems will be discussed as well. 

HW problem sets

HW of week #1: HW Week1

HW of week #2: HW Week2

HW of week #3: HW Week3

HW of week #4: HW Week4