MATH 472 002/992: Numerical Methods With Financial Applications

MATH 472 002/992: Numerical Methods with Financial Applications
Fall 2020
Instructor: Prakash Chakraborty
Class hours: Tuesdays and Thursdays, 11:30 – 13:00, in 170 WEISER (Section 992)
or remotely over zoom
Office hours: (Tentative) Tuesdays and Thursdays 16:00 – 17:30, remotely over zoom
LSA Course Guide: MATH 472 – 002 or MATH 472 – 992
E-mail address: cprakash@umich.edu
Grader: TBA
Course description This is a survey course of basic numerical methods for solving scientific problems,
especially those arising in actuarial and financial applications. The emphasis lies on the analysis of the
methods, their practical applications, and their implementation. Topics intended to be covered are:
• root-finding methods,
• systems of linear equations,
• polynomial interpolation,
• numerical differentiation and integration,
• ordinary differential equations,
• Monte Carlo simulations.
Required textbook Numerical Analysis by Timothy Sauer, third edition, published by Pearson Education
in 2018 (ISBN: 978-0-13-469645-4). The second edition is also acceptable.
Prerequisites For a detailed description consult 400-Level Math Courses

• Required: calculus; multivariable calculus; ordinary differential equations; linear algebra; working
knowledge of MATLAB. In particular, familiarity with the contents of Appendices A and B of the
textbook is assumed.
• Recommended: probability (e.g., MATH 425); mathematical finance (e.g., MATH 423).
Course website If you are registered for the course, you should see “MATH 472 002 FA 2020” or "MATH
472 992 FA 2020" on your dashboard on Canvas (https://umich.instructure.com/). I will post lecture
notes, lecture videos, announcements, homework assignments, and other resources there.
Course recordings Course lectures may be audio/video recorded and made available to other students
in this course. As part of your participation in this course, you may be recorded. If you do not wish to be
recorded, please contact the instructor the first week of class to discuss alternative arrangements. Students
may not record or distribute any class activity without written permission from the instructor, except as
necessary as part of approved accommodations for students with disabilities. Any approved recordings may
only be used for the student’s own private use.
Attendance You are strongly encouraged to attend class. Attendance will be taken for the first two lessons
according to the LSA Class Attendance Policy. The department may give away your place in this course if
you do not attend both of the first two lessons.
1
Grading
Ingredient Date Percentage of final grade
Homework 30%
Midterm exam (tentative) Tuesday, 20 October 30%
Final exam (tentative) Wednesday, 16 December, 16:00 – 18:00 40%
Homework:
• There will be six or seven homework assignments.

• The submission deadlines will be announced when the assignment is posted. You will have approxi-
mately one and a half weeks for each assignment.
• You are encouraged to collaborate with other students on homework problems, but each student must
write up his or her assignment independently. If you worked together with someone on a programming
assignment, you must mention who you worked with.
• The completed homework (preferably typed and in pdf format) should be uploaded to Canvas BEFORE
each deadline. Late or non-submission of a homework set will result in a zero grade for this set, except
in the case of documented family or medical emergency.
• I will drop the lowest homework grade, and the rest homework grades have equal weights.
• You are encouraged to meet me in the office hours for help after you have tried to solve the problems
on your own.
Exams: If you miss the midterm exam, then a zero grade will be assigned, except in the case of documented
family or medical emergency. In such documented circumstances, the midterm exam weight will be merged
to the final exam weight, that is, the final exam grade will account for 70% of your final grade. Please also
bear in mind that future exams might be harder than the earlier ones.
Guaranteed minimum grade: You are guaranteed to get the following grade if your final grade (without
rounding) lies in the corresponding interval.
[97, 100]: A+ [87, 90): B+ [77, 80): C+

[93, 97): A [83, 87): B [73, 77): C [60, 70): D [0, 60): E
[90, 93): A- [80, 83): B- [70, 73): C-
In addition, there might be rounding up, or curving up, or more generous cutoffs if the whole class’ course
grades are significantly lower than the historical data.
Testing accommodations If you think you need an accommodation for a disability, please let me know
as soon as possible. In particular, a Verified Individualized Services and Accommodations (VISA) form must
be provided to me at least two weeks prior to the need for a test/quiz accommodation. The Services for
Students with Disabilities (SSD) Office (G664 Haven Hall; http://ssd.umich.edu/) issues VISA forms.
Academic integrity The University of Michigan community functions best when its members treat one
another with honesty, fairness, respect, and trust. The college promotes the assumption of personal responsi-
bility and integrity, and prohibits all forms of academic dishonesty and misconduct. All cases of academic mis-
conduct will be referred to the LSA Office of the Assistant Dean for Undergraduate Education. Being found
responsible for academic misconduct will usually result in a grade sanction, in addition to any sanction from
the college. For more information, including examples of behaviors that are considered academic misconduct
and potential sanctions, please see https://lsa.umich.edu/lsa/academics/academic-integrity.html.
2
Student’s background In order to better understand the background and the needs of the students
who attend the course, you are kindly requested to fill in the Student data form. This is very useful for
us: knowing that a course is 80% LS&A undergraduates, or 75% Engineering students, allows us to better
construct it to address the needs of those in the course. If you have additional questions about the form,
please see our FAQ.
Classroom Culture of Care LSA is committed to delivering our mission while aiming to protect the
health and safety of the community, which includes minimizing the spread of COVID-19. Our entire LSA
community is responsible for protecting the collective health of all members by being mindful and respectful
in carrying out the guidelines laid out in our Wolverine Culture of Care and the University’s Face Cover-
ing Policy for COVID-19. Individuals seeking to request an accommodation related to the face covering
requirement under the Americans with Disabilities Act should contact the Office for Institutional Equity.
In our classrooms all students are expected to adhere to the required safety measures and guidelines of the
State of Michigan and the University of Michigan, including sanitizing their work areas, maintaining 6 feet
or more of personal distance, wearing a face covering that covers the mouth and nose in all public spaces,
and not coming to class when ill or in quarantine. This course will also limit group gatherings while being
thoughtful about classroom activities and exercises that require collaboration.
Any student who is not able and willing to comply with campus safety measures for this [in-person/hybrid]
course should contact the course instructor or their academic advisor to discuss alternate participation or
course options. Students who do not adhere to these safety measures while in a face-to-face class setting,
and do not have an approved exception or accommodation, may be asked to [participate on a remote basis
or - include if available option] disenroll from the class.
For additional information refer to the LSA Student Commitment to the Wolverine Culture of Care and the
OSCR Addendum to the Statement of Student Rights and Responsibilities on the OSCR website.

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MATH 472 002/992: Numerical Methods with Financial Applications

Prerequisites For a detailed description consult 400-Level Math Courses

Ingredient Date Percentage of final grade

• There will be six or seven homework assignments.

[97, 100]: A+ [87, 90): B+ [77, 80): C+

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