Math 400 / COLL 400 Mathematical Connections, Fall 2018
Instructor: Chi-Kwong Li
Meeting time and place: TR 3:30 - 4:50 p.m. Morton 1
Office: Jones 128, Tel: 221-2042
E-mail: ckli@math.wm.edu,
http://cklixx.people.wm.edu
Office hours: TWR. 9:00 - 10:30 a.m., or by
appointments
Course description
Topics concerning how one can connect mathematics to other areas including biology, chemistry,
physics, business, finance, political science, sports, music, literature, education, etc.
will be discussed.
Format
Instructor and students will take turn to discuss material related to the connection of mathematics
to other areas. Speakers are responsible in introducing audience how mathematics is connected to
the topic. Audience are responsible to take active part in the discussion and evaluation of the speakers.
Each student will do two presentations and lead the discussions, and submit a written
report on each presentation.
The discussion can based on any material from textbook, websites, etc.
The speaker should organize the material to get a
coherent presentation and report.
Objectives of the course/expected learning outcome
Student will learn
- connections between mathematics and other subjects;
- to find useful resource;
- to read, understand, and explain mathematics;
- to communicate interesting/useful mathematical ideas in the formats of
presentation, discussion, and writing;
- to stimulate and lead discussion in a seminar setting;
- to work in teams and co-ordinate efforts
to prepare presentations;
- to keep an open mind to suggestions and use them to
improve their work;
- to think critically and provide
constructive feedbacks to classmates.
Assessment
Participation/evaluation/discussion/homework 40 points
Presentation/Leadership of discussion
(evaluated by instructor and audience)
Presentation 1 (30 min.) 15 points
Presentation 2 (55 min.) 15 points
Papers associated with presentation 1 15 points
Papers associated with presentation 2 15 points
Extra credits (inspiring ideas/problems/solutions) 5 points
Letter grades out of the total points:
0 - 60 - 65 - 70 - 75 - 80 - 83 - 87 - 90 - 93 - 105
F D C- C C+ B- B B+ A- A
Talk schedules
- Aug. 30. CK Li. Introduction of the course.
- Sept. 4. CK Li.
Factorization of permutation. See the paper at https://arxiv.org/pdf/1303.3776.pdf
Abstract. The problem of factoring a permutation as a product of special types of transpositions,
namely, those transpositions involving two positions with bounded distances, is
considered. In particular, the minimum number N such that every permutation can be
factored into no more than N special transpositions is investigated. This study is
related to sorting algorithms, Cayley graphs, and genomics.
- Sept. 6. CK Li.
Some mathematical aspect of the combinatorial game Mahjong .
See the paper at https://arxiv.org/pdf/1707.07345.pdf
Abstract.
We study some mathematical aspects of the Mahjong game.
In particular, we use combinatorial theory and write a
Python program to study
some special features of the game. The results confirm
some folklore concerning
the game, and expose some unexpected results. Related
results and possible future
research in connection to artificial intelligence will be mentioned.
- Sept. 11. No class due to hurricane Florance.
- Sept. 13. No class due to hurricane Florance.
- Sept. 18. Chengwu Shen and Hanmi Zou. (A joint 60 min. presentation.)
A Mathematical Model of Maximizing Matching Rate Between Students and Advisors
[
Written report.]
Abstract: Operational Research focuses on how to make an effective mathematical model that is useful for the
allocation of limited resources, such as material, machines etc., to several competing activities, thus
maximizing the optimal solution. People usually use the operational model to improve the decision-making
process. In this talk, we will demonstrate how to use the linear operational model, specifically, the
transportation problem algorithm to optimize the matching between freshman and pre-major advisors, and to
maximize the satisfaction degree between these two groups. The talk will give generally ideas of background
of operational research, details of transportation problem algorithm, and our own modified model based on
the transportation problem algorithm.
- Sept. 20. Talk 1. Kayla Ebright.
Potential Collision Monitoring and Characterization.
[
Written report.]
Abstract. We consider the problem of classifying dead satellites to determine their collision risk.
We will discuss how we can use and expand statistical methods to create a list of
"worst offenders" that should be closely monitored because they have a higher likelihood of collision.
Talk 2.
Xinyao Wang,
Mathematical model of coupled patch model.
[
Written report.]
Abstract: Coupled patch model could be used to analyze the dynamics of populations.
In my presentation, I focus on the two-dimensional spatial model with two parameters.
Since I choose to examine the dynamics of population, my two parameters are growth rate and
dispersal rate. Growth rate refers to the dynamical change of population in the area itself,
while dispersal rate refers to the dynamics of interactions between neighboring areas.
- Sept. 25. Talk 1. Ren He,
Machine learning and music composition.
[
Written report.]
Abstract.
Music composition is considered the most easy kind of art form to be performed by a computer algorithm.
In my presentation, I will describe an immature method I used to assist music composition,
as well as common approaches that are currently being used in the world, including genetic
operator approach and the neural network approach.
Talk 2. Mengting Lei.
Iterated Prisoner's Dilemma on an adaptive network with continuous links
[
Written report.]
Abstract.
Prisoners' Dilemma is a classical example of game theory. In the game,
two suspects of a crime play against each other to minimize their own
penalty by either cooperating or defecting. Previous studies have been
focused on simulating this game in networks with discrete links, where an
agent plays equally against all its opponents in one time step. Such models
could be more realistic if we consider the limited resources of each individual.
Therefore in this research, we examine the game by allowing each agent to divide its
resources into different portions for different opponents. The long-time behavior
of the agents and the distribution of their connections to individual opponents are studied.
- Sept. 27.
Talk 1. Jimmy McLaughlin.
Inventory Modelling Using Simpy
[
Written report.]
Abstract: This presentation will discuss different techniques used in
inventory management policy, as well as a specific problem which examines
the optimal way to manage inventory in a simplified supply chain.
I will talk about SimPy, the python package used to build my model,
as well as how inventory management is used in practice by corporations.
Talk 2. Laura Olliverrie.
The mathematics behind sudoku
[
Written report.]
Abstract:
I will explore the mathematics behind sudoku. Specifically, I will explore enumerating
the number of distinct Sudoku grids, the use of computer algorithms to solve puzzles,
and the application of abstract algebra and graph theory to enumerate
essentially different sodoku grids.
- Oct. 2. Talk 1. Sarah Hardy.
Minimum Toll Booth (MINTB) Problem.
[
Written report.]
Abstract:
In this presentation we will explore the Minimum Toll Booth Problem (MINTB), which aims
to determine the least number of toll booth locations required to create an efficient
transportation network from an origin location to a destination location.
The network is optimized at a Tolled User Equilibrium with the fewest number of toll booths
and we will explore how this can be determined through a Genetic Algorithm, as well as
explore other heuristic methodologies that have been researched.
Will Cranford.
Route Optimization Problems and Google Maps
[
Written report.]
Abstract: The focus of this presentation is the Shortest Path problem as well as the
Travelling Salesman problem. I will consider suitable algorithms to solve these problems,
computational limits on these algorithms, and data-driven approaches to solving these problems.
Outside applications will also be examined.
- Oct. 4. Talk 1. Hanqiu Peng,
Counterintuitive Probability Problems & What Are Behind Them.
[
Written report.]
Abstract:
I will mainly talk about 2 famous counter-intuitive math problem in my presentation: Monty Hall
problem and Birthday Paradox. I will also expand these problems and discuss some variations of them.
Besides, I will illustrate how these math questions are related to other field such as computer science.
Talk 2. Elaina Liu
Mathematical Model for Athletic Training
[
Written report.]
Abstract:
In this presentation we will explore current models for the relationship between human performance and training management, focusing mainly on the Banister model, its flaws along with existing and possible modifications.
- Oct. 9. Charlie Strausser.
Bayesian Connections
[
Written report.]
Abstract: This presentation aims to explore both the Rule of Bayes, exploring its role in psychology and decision making, as well as the ideals of Bayesian Inference, exploring its connections to finance, poker, and machine learning. The goal of this presentation is to explain how modern modeling techniques help us better understand ourselves and the world around us.
- Oct. 11. Joe Brown.
Blackjack: Counting Hands and Counting Cards
[
Written report.]
Abstract: In this presentation we will discuss the rules of Blackjack,
the basic combinatorics needed to partially model games of Blackjack,
the difficulties present in attempts to fully model the game, and the
basics behind counting cards to gain advantage in the game.
- Oct. 16. Fall break.
- Oct. 18. CK Li.
What is 1 + 11 + ... + 11...11? What are scientific facts?
Abstact. We discuss how to obtain a formula 1 + 11 + ... + 11...11,
and the pattern of the digits in the formula. The study will lead to
the question of how to recognize and classify scientific facts.
- Oct. 23. CK Li
Voting systems
Abstract: We describe different voting systems, and disucss how they could be
manipulated.
- Oct. 25. C.K. Li, Quantum mechanics and quantum computing.
Abstract. We will discuss some on line material explaning the interesting phenonmena of
quantum mechanics, and describe some research problems on the topic.
- Oct. 30.
Talk 1 Chengwu Shen
Kidney exchange
[
Written report.]
Talk 2.
Kayla Ebright
Climate Modeling
[
Written report.]
- Nov. 1. Will Cranford
The Math. of Baseball
[
Written report.]
- Nov. 6. He
AI: Optimization to Survive
[
Written report.]
- Nov. 8. Hanmi Zou,
Minimax Algorithm
[
Written report.]
- Nov. 13. Talk 1. Sarah Hardy.
Fractals
[
Written report.]
Talk 2. Elaina Liu
How Credit Card Numbers are Generated.
[
Written report.]
- Nov. 15. Jimmy McLaughlin,
Mathematics behind fingerprinting
[
Written report.]
Joe Brown.
"More Game Enumeration and the Folly of Math"
[
Written report.]
Abstract: In this presentation, we will continue our examination of
the enumeration of card games in a more general sense, discuss
problems regarding best strategies in said games, and link those
problems to classic Fermi Problems and show examples of instances
where strict mathematics may be too complicated or not helpful.
- Nov. 20
Talk 1 Hanqiu Peng.
Introduction to Cryptography.
[
Written report.]
Charles Strausser.
Predicting and Solving Crimes using mathematics.
[
Written report.]
- Nov. 22. Thansksgiving.
- Nov. 27.
Wang,
Reaction and Diffusion System.
[
Written report.]
Lei,
Use of Nighttime Lights for Estimating Gross National Income.
[
Written report.]
- Nov. 29. No meeting.
- Dec. 4.
CK Li.
Abacus.
Laura
Olliverrie.
Understanding symmetries and geometry through dance
[
Written report.]
- Dec. 6.
Ren He,
Tonal Theory and
Composition
Chengwu Shen,
Random Number
Generator
Ellen Wang,
Ouroboros.
Leila Lei. Uparrow notation, and Graham's number.
References:
Knuth's Up-Arrow Notation: https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation
Graham'number: https://en.wikipedia.org/wiki/Graham%27s_number
TREE(3): https://en.wikipedia.org/wiki/Kruskal%27s_tree_theorem#TREE(3)
Homework list
- Homework 1. Due Sept. 4, 5:00 p.m.
Submit (1) A summary of discussion, (2) suggestions of class format and discussion of Aug. 30.
Also, think about possible presentation topics, and try find useful resource.
- Homework 2. Due Sept. 6, 5:00 p.m.
Submit (1) A summary of discussion, (2) evaluation/suggestion of the presentation on Sept. 4.
Evaluation should include comments and suggestions on: (2.a) the preparation, (2.b) the execuation.
Give a score 1 to 5 (best) for (2.a), and a score for (2.b).
- Homework 3. Due Sept. 11, 5:00 p.m.
Submit (1) A summary of discussion, (2) evaluation/suggestion of the prsentation on Sept. 6.
- Homework 4. Due Sept. 25, 5:00 p.m.
Submit (1) A summary of discussion, (2) evaluation/suggestion of the prsentation on Sept. 6.
- Homework 5. Due Sept. 27, 5:00 p.m.
Submit (1) A summary of discussion, (2) evaluation/suggestion of the prsentation on Sept. 6.
- Homework 6. Due Oct. 2, 5:00 p.m.
Submit (1) A summary of discussion, (2) evaluation/suggestion of the prsentation on Sept. 6.
- Homework 7. Due Oct. 4, 5:00 p.m.
Submit (1) A summary of discussion, (2) evaluation/suggestion of the prsentation on Sept. 6.