2014 Summer International Course at Shanghai University
Mathematics in Daily Life
A class photo
Row 3. Junjie Xu, Renteng Huang, Xin Fan, Yinxiang Ma, Zhihao Hu,
Zeyu Xu, Weitao Zhu, Chao Hu.
Row 2. Mengyuan Li, Yao Ge, Jiahui Zong, Ziqian Liu, Zhixia Lin, Sheng Liu, Honggang Hu,
Yong Geng, Jun Zhang, Linfan Wang, Mengge Hu, Tianyu Chen
Row 1. Yajing Ge, Yun Ye, Xiaomei Gao, Chi-Kwong Li, Yinglei Hua, Peiyu Si, Wanting Shi,
Miaomiao
Wang, Siyuan
Nie.
Instructor Chi-Kwong Li
Office/e-mail/homepage F423, math.ckli@gmail.com,
http://cklixx.people.wm.edu/
Meeting Place A 114.
Meeting times
June 16 (8:00-10:00), June 17, 18 (3:00 - 5:00),
June 19, 20
(8:00-10:00).
Office hours June 16 (2:00-5:00), June 17 (1:00 - 2:30), June 18 (9:00-noon),
June 20 (2:00-5:00).
Course Description
This course aims to help students develop the mathematical literacy to see the connections and
applications of mathematics to daily life activities. The course consists of two components:
- introducing different topics of mathematics in daily life such as mathematics in voting,
finance, scheduling, etc,
-
guiding projects on the students' chosen topics of mathematics related to
real life problems or other branches of study.
Format and structure
June 16 (Monday) 1:00-2:00 p.m.
- Li and students will introduce themselves.
- Each person will use 5 minuites to describe their experience in
mathematics, and the use of mathematics in daily life.
- Student should prepare a written statement (typed) and turn in to the
instructor.
- After class: Students should form groups, and prepare
a topic to do 15 minute presentations on Thursday or Friday.
- Students who fail to find partners to form a group will be assigned to
form by group by the instructor.
June 17 (Tuesday) 8:00-9:00 a.m.
- Li gives a sample presentation.
- Students do evaluations, and discuss possible improvement of the presentation
and the evaluation form.
- Students decide topics of discussion by noon.
June 18 (Wednesday) 8:00-9:00 a.m.
- Li gives another presentations.
- Students will further discuss the contents, and styles of presentation.
June 19/20 (Thursday/Friday) 1:00-2:00 p.m.
- Students give 25 minute presentations.
- Students will further discuss the contents, and styles of presentation.
- Students submit a written report on their bopic by 5:00 p.m. Monday.
Objectives of the course/expected learning outcome
As participants, students will learn:
- the connections and applications of mathematics to real
life problems and other branches of study;
- expressing their ideas
verbally in class and in writing (on line discussion and in their reports);
- thinking critically and provide
constructive feedbacks to presentations.
As presenters, students will learn how to:
- read, understand, and explain mathematics;
- stimulate and lead discussion in a seminar setting;
- work in teams and co-ordinate efforts
to prepare presentations;
- keep an open mind to suggestions and use them to
improve their work.
Course work and assessment
[Some notess on
the assessment scheme]
Class participation. 25 points
Evaluations/summary of presentations of other speakers. 25 points
Presentation. 25 points
Written report. 25 points.
Activities
- June 16. 8:00-9:50 a.m. (office hours: 2:00-5:00 pm)
- Li and students will introduce themselves.
- Each person will use 5 minuites to describe their experience in
mathematics, and the use of mathematics in daily life.
Homework due June 17.
- Write a short description of yourself, and your interest in
matheamtics. Optional. Add some comments about the first class, and suggest
improvement if there is any.
- Form a group of 4, and select a topic for presentation.
- June 17. 3:00-4:50 a.m. (1:00-2:30 pm)
Presentation of CK Li: Amidakuji
[pdf file|
A related report|
Evaluation of
presentation and responses.]
Classwork on June 17 and homework due on June 18.
- Do a evaluation of the presentation of CK Li. (Done in class)
- Form 7 groups to do presentations. (Done in class)
- To describe a rough plan/theme of presentations on June 18.
Different groups should think about that tonight and tomorrow morning.
CK Li will be available in his offie F 423 to give suggstions on June 18 morning.
- June 18. 3:00-4:50 a.m. (9:00 - noon)
Presentation of CK Li: Paradox
[pdf file|
Wikipedia article |
Evaluation of
presentation and responses.]
- June 19. 8:00-9:50 p.m. (10:00 - noon)
Presentations:
- Fan, Hu, Hua, Si. Fair Division.
[ppt file|
Report|
Evaluation of
presentation and paper.]
- Hu, Ge, Ge, Zong. Game Theory.
[ppt file|
Report|
Evaluation of
presentation and responses.]
- Gao, Liu, Nie, Ye, Economics and Mathematics.
[ppt
file|
Report|
Evaluation of
presentation and responses.]
- June 20. 8:00-9:50 p.m. (10:00 - noon)
Presentations:
- Chen, Huang, Lin, Liu. Mathematical Magic.
[ppt file|
Report|
Evaluation of
presentation and report.]
- Geng, Li, Ma, Xu. The biggest benefit.
[ppt file|
Report|
Evaluation of
presentation and report.]
- Hu, Si, Wang, Wang. The mathematics behind Prague horloge.
[ppt file|
Report|
Evaluation of
presentation and report.]
- Hu, Xu, Zhu. Calculating Skills.
[ppt file|
Report|
Evaluation of
presentation and report.]
Afterthought about the course (Chi-Kwong Li)
1. Objective of the mini-course
My understanding is that the goal of the mini courses is to provide a variety of
topics for students at SHU to experience different educational models, and gain
some international experience. It is a wonderful idea.
In this connection, my course on ``Mathematics in Daily Life'' is to let students
see that mathematics is not just about formulas and technical proofs. It is related
to different topics and also daily life activities if one can make the connection.
Also, I want to let the students see that one should not passively receive knowledge
in the classroom at the university level. One should learn how to make connections of
of their knowledge acquired from their instructors and textbooks to the outside world.
Nowadays, it is easy to get a lot of information from different sources, one needs to
select useful information, make suitable connections, and make good use of them in
order to be successful in future study and work. This is would help ``break the
four barriers'' emphasized as the spirit of the Shanghai University.
It is also worth pointing out that even though my course does not emphasize
technical mathematics, the discussion can easily lead to study at the research
level. What I want to demonstrate is: one can make the connections according
to his/her own interest and background that will lead to different levels
of appreciating, using, and doing research in mathematics.
2. Students
Most students saw the difference between my course and the mathematics courses in
the past experience. Asking them to change their learning mode, and use English to
communicate is challenging. This obviously move them away from their comfort zone.
In any event, most students have a reasonable command of English. Many of them are
just lacking practice and confidence. Hopefully, they would have more confidence and
understand they can indeed communicate well in English if they have enough practice.
I am happy that students were able to come up with a presentation and a report in a
very short period of time. Of course, there are rooms of improvements, and it is not
the hope that this short course can teach them all the techniequs in communicating
mathematics orally and in writing. Nonetheless, it is the hope that students would
learn from their experience and those of others so that they would be able to improve
themselves continuously in communicating ideas (mathematics or other subjects).
Thus, instead of a learning experience in one course, it will become a life long
educational experience. In fact, in real life, one may indeed have to finish a task
in a short notice of time, and give a presentation with time limits. So, in a sense
the course provides some experience in real life setting. In addition, working with
other team mates, and giving contructive comments to other classmates are also part
of the training related to real life situations. Hopefully, students see that there
are many other skills that will help their future study and work besides technical
knowledge.
3. Possible improvements
I also learn a great deal in this course. There are much could be improved
under the current setting.
a) Before meeting the students, I can put up more sample and proposed projects
on my course website. Then students can choose tentative topics for their
presentations even in day one, and form different groups according to their
common interest.
b) I could set up more meetings with students in the first 3 days so that
students could get guidance for the preparation of their presentations.
c) The idea of teaching buddies is a wonderful idea. But I think that it is
important that the teaching buddy have time to work with the instructor.
(Do not assign a busy professor as a teaching buddy.) Ideally, the teaching
buddy can go to every class with the instructor, giving feedback and sharing
experience with the instructor, helping the instructor with the university
computer system. In fact, instead of treating the duty as a burden, hopefully,
the teaching buddy can also gain some useful useful experience in the process.
d) Hopefully, the Google search engine, and gmail are not blocked. It has huge
negative impact on the teaching for some instructors such as myself who rely
heavily on these websites.
Summary and evaluation
form
Sample presentation and report format
Some suggested topics.
- Graph techniques in solving problems. (Seven bridge problem of Konigsburg.
Traveling problems.) http://en.wikipedia.org/wiki/Graph_theory
- Symmetry patterns in nature. (Flowers, trees, shell.)
http://www.pinterest.com/mytmack/patterns-and-symmetry-in-nature/
- Mathematical games. (Sorting out a fake coin which is lighter by a balance.)
http://en.wikipedia.org/wiki/Mathematical_game
- Mathematics and Arts.
http://en.wikipedia.org/wiki/Mathematics_and_fiber_arts
- Mahtematics and Music.
http://en.wikipedia.org/wiki/Mathematics_and_music
- Mathematics and Sports.
- Ancient mathematical problems.
- Scheduling problems.
- Fibonnaci number. http://en.wikipedia.org/wiki/Fibonnaci_Sequence
- Mathematical
finance. http://en.wikipedia.org/wiki/Mathematical_finance
- Mathematical biology.
http://en.wikipedia.org/wiki/Mathematical_and_theoretical_biology
Some useful references
- COMAP,
For All Practical Purposes (Paper): Mathematical Literacy in Today's
World (Comap, the Consortium for Mathematics and Its
Applications) (Paperback), W. H. Freeman, Seventh or Eighth Edition.
- Liping Ma,
Knowing and teaching elementary mathematics:
Teachers' understanding of fundamental mathematics in China and the
United States.
-
George F. Simmons,
Calculus Gems: Brief Lives and Memorable Mathematics (Paperback),
McGraw-Hill Co., 1992.
- C.K. Li, A website on
mathematical education related topics.
- Wikipedia. Key word search on "Mathematics in nature, music, sports, etc."