# Math 456 Course Info

**Course Meets:** Tues and Thurs 2:30-3:45PM in LGRT 143.

**Instructor**

Michael Sullivan, LGRT 1323G, 545-1909

Office Hours:
Tuesday 1:15-2:15, Thurs 11:00-12:00.
You can also make an appointment or drop by anytime Tues, Thurs, Fri.
I am not on campus Mon and Weds (usually).
If you want help by email instead of in person, a yes/no question is much more likely to receive an answer.

**TA/Grader**

Ling-Chen Bu; bu at math dot umass dot edu, LGRT 1323E (his office) or LGRT 1114 (a small classroom)

Office Hours: In the first part of semester,
they will be 1:45-3:45 one day before HW is due (so either on Monday and Wednesday
since HW is due on Tues or Thurs).
After spring break, if no HW is due that week,
office hours will be on 1:45-345 Weds in case you need help with the final project.
If you have questions about the final project,
please e-mail them to Ling-Chen ahead of time,
to give him time to think about your project.
He can also help with TeX and some programming.

**Prerequisites: ** Math 131, 132, 233, 235. Math 331 and Stats 515 is useful but not necessary.

**Credit:** 3 credit hours

**Textbooks: **
We will mostly use part of use Richard Durrett's Essentials of Stochastic Processes, 2nd or 3rd edition.
But this is only for part of the semester.
Class after that does not follow a particular textbook.
You can download for free from the author's website the
2nd edition.
You can also download the 3rd edition e-book from any Amherst/Mt Holyoke/Smith
campus libraries.

Durrett's book requires parts of Stats 515, which we review at the beginning.
If you do not own the Stats 515 book, you can also legally download, for free,
Introduction to Probability
by Charles M. Grinstead and J. Laurie Snell. American Mathematical Society.

** Overview: **
This course is an introduction to mathematical modeling.
The main goal of the class is to learn how to translate problems from
"real-life" into a mathematical model and how to use mathematics to solve the problem.
Since this is too broad of a topic for one semester, this class will focus on
Markov chains.
There are two parts of this course.
The first half is a more traditional course,
building off of a review of discrete probability and leading into Markov chains.
The second part of the course samples from some very different areas in
mathematical modeling, some of which apply Markov chains
and some of this don't.
Which topics are covered depends on timing and interest.
This course counts towards your Integrative Experience requirement.

** Syllabus: ** (under construction)

Overview (0.5 weeks)

A crash course in discrete probability (1.5 weeks)

Markov chains (5? weeks. Midterm will cover up to here.)

Elections: redistricting and voting preference systems using Markov chains, geometry and game theory (2 week)

Finance: stock volatility and pricing stock options using Markov chains and finite different methods (2 weeks, probably won't finish)

Group Presentations (2-2.5 weeks).

**Grading: **
The grade for the course has four components:
midterm (25%), timely-completion
of homeworks/quizzes (25%), book report (10%), final project (40%)

**Exam: **
The midterm will be closed-book, in-class on ** March 7 **
which is the Thurs before spring break.
Because the exam is in-class, there is ** NO ** make-up midterm except for
family or medical emergency (with proper documentation).
You may bring to the exam one single-sided sheet of hand-written notes.
There is no final exam.
However, if need be, we will use the final exam time
(Friday May 3rd 3:30-5:30) for group presentations.
So be sure to not schedule travel that conflicts with your final exam time.

**Homeworks: ** If attendance starts to drop,
there MAY be several short in-class quizzes that will supplement the homework grade component.
These quizzes will be relatively easy.
Some quizzes may be individual and some group efforts.

**Book Report: ** The book report should be at least 3 pages, writen in TeX (or LaTeX).
You can download the TeXShop version of a compilor for LaTeX
here, although it exists in many other forms.
The report is due Tues Feb 12 in class.
You should pick a book (popular literature, non-fiction) which explores the connections between mathematics and real-life applications.
You can either pick a book from the
Book report list
or suggest your own book.
I will need to approve it if it is not from my list.
Most of the listed books contain little actual mathematics
but can be very informative on mathematical ideas shape social and economical ideas.
Your report needs to at least address the following points.

(1)Explain why you chose your particular book.

(2)Summarize the most important things you learned from the books.

(3)Was it well-written and/or informative?

(4)How did it resonate with what you have learned as a math major.

(5) Can you imagine using any knowledge gained from the book in your future studies,your eventual professional career, and/or your project in this class?

**Final project: ** The final project will be done in groups of 3.
There are four components.
The first is a one-page outline/proposal, submitted as a group to me.
An ungraded draft needs to be submitted by Feb 28.
I may give feedback if necessary.
The graded final 1-page proposal needs to be typed in TeX or LaTex
and is due Tues March 19 in class.
The second is a group update/discussion
and very rough presentation done just for me, outside of class,
sometime during advising week (March 25-29). Each group needs to find times
you all can meet me together.
The third is a polished 20-minute group presentation,
with up to 5 minutes of questions and answers at the end, done in front of class.
You should each talk about something, so divide your presentation into three roughly equal in length parts.
Part of the skill set is mastering clarity and pace.
It is easy to run out of time, and this would factor into your grade.
(Of course if you run out things to say after 10 minutes,
this will also play a factor.)
I highly suggest your group practice beforehand a timed presentation without an audience. Presentations occur
during our last four or five classes (April 16 (maybe), 18, 23, 25, 30), and possibly during our final exam time (May 3) if needed.
The ordering will be randomly assigned a day in advance, so every group
should be prepared to present by April 16.
** Attendance and participation **
as audience members is mandatory for the non-presentors.
If you are absent without excuse when another group is presenting,
your individual final project score will be penalized by a TBD amount.
The fourth and main component is a typed group report, again in TeX or LaTeX.
This is due the last day of class, April 30.
You will also submit a short note assessing the contributions toward the project of the members of your group.