Syllabus for Math 441 (Topics in Actuarial Models)

Spring 2023 Semester at Lycoming College


Course Content

Topics are selected from those covered on the examinations administered by the Society of Actuaries, with the exception of the topics already covered in MATH 325, 332, 333.  The major goal of this course is to provide the student with an overview of some advanced statistical techniques and some applications in a variety of fields, such as business, psychology, sociology, science, etc. This course can count as a capstone course for the actuarial science major or for the mathematics major.  Prerequisite: MATH 325 and MATH 332.



Course Goals

Goals for this course include developing critical thinking skills, and the abilities to apply the techniques of calculus (i.e., derivatives, integration, infinite series), probability theory, interest theory, and the available computer software (e.g., spreadsheets) in applications involving various types of insurance, annuities, and other such financial scenarios.



Who Should be Taking This Course

This course is designed to cover topics on the examinations administered by the Society of Actuaries.  This course can be used as a capstone requirement for the actuarial mathematics major or for the mathematics major.


Disability Support Services

In keeping with the Americans with Disabilities Act (and its amendments) and Section 504 of the Rehabilitation Act, Lycoming College is committed to providing reasonable accommodations for students with documented disabilities that impact their learning experiences. The Office of Academic Services Deans coordinates disability support services (DSS), and students can contact (570) 321-4358 or to set up a confidential conversation about the disclosure and accommodation process. The Office of Academic Services Deans is located in the second floor of the Krapf Gateway Center. Further information regarding DSS is available at:













Find your instructor’s office hours at , and write them here for future reference.



Required Materials

Each student must have

·      a three-ring binder containing copy of this syllabus, the course schedule, the class notes, completed assignments, etc. (Note: Since students will need to use this binder every day in class and might be allowed to use this binder for some exams, the binder should be kept up‑to‑date and complete.)  Although no textbook is required, the material in this course is taken from various textbooks on actuarial science.

·      a calculator (any TI-84 or TI-83 calculator is recommended but not required) – some of the material in class, on homework, and on exams will require heavy use of the calculator.



Course Links


Course Schedule


Some Well-Known Sums and Series


A Useful Trigonometry Review





Point Values and Policies


Homework assignments due on the next class are posted in red on the course schedule.  Late homework is generally not accepted.  Homework counts for 20% of the final grade; however, a student who misses submitting more than 10 homework assignments automatically fails the course.

Semester Tests

Several semester exams are given; specific dates are available from the course schedule.  For each missed test, a grade of zero is recorded, unless (1) the instructor is presented with documented evidence of a medical reason for not completing the test at the scheduled time, and (2) arrangements to make up the test are made within 24 hours of the originally scheduled exam time.  Semester exams count for 40% of the final grade.

Capstone Project

During the semester, each student is required to research a topic and give a poster presentation; see the Poster Presentation section following this section.  This counts for 20% of the final grade.

Final Exam

The final exam (administered during final exam week) counts for 20% of the final grade.


The final course grade percentage is reduced by 4% for each unexcused absence after the third unexcused absence; an absence is considered to be excused when the instructor accepts an email from the student explaining the reason for the absence.  It is the student’s responsibility to find out what was missed in class and keep up with the coursework.  A student with more than 8 unexcused absences automatically fails the course.

The final course letter grade is determined from the course average as follows:


          A = above 93.33%                                A– = 90% to 93.33%                  B+ = 86.67% to 90%


          B = 83.33% to 86.67%                         B– = 80% to 83.33%                  C+ = 76.67% to 80%


          C = 73.33% to 76.67%                         C– = 70% to 73.33%                  D+ = 66.67% to 70%


          D = 63.33% to 66.67%                         D– = 60% to 63.33%                  F = below 60%



Poster Presentation

     Each student is required to give a poster presentation during a poster session held in Pennington Lounge on April 18th from 3-4pm (subject to possible change).  Each student is responsible for picking a topic, researching that topic, creating a poster of the findings, and presenting the findings to those that attend the poster session.  Two important points to note here are that (1) the student must be prepared to discuss the poster not only with math department faculty and math majors, but also with non-math faculty and non-math majors, and (2) students enrolled in MATH 441 need to be simultaneously enrolled in MATH 449 (Colloquium), which is scheduled for Tuesday 3:00-4:00.

     Early in the semester, each student will focus on choosing a topic, after which there will be several one-on-one check-in sessions with the instructor.  During the check-in sessions, we will discuss the progress made on the research topic since the last check-in, as well as the work to be done in preparation for the next check-in.

     Prior to the poster session on April 18th, there will be two poster presentation dry run sessions to help prepare for the actual poster session.  Part of the poster presentation grade takes into account the effort put forth in dry runs.  The research should be completed and the poster mostly done prior to the first dry run session on April 4th.  Completed PowerPoint Poster files are due by email on April 10th and will be used for the second dry run session on April 11th.  The overall grade for the poster presentation will be based on

          how well the student prepared for each check-in session,

          the research the student did on the topic,

          the poster itself (contents, design, layout, etc.), and

          how well the findings and poster were presented to both a math and non-math audience.



MATH Assessment Exam

As part of the Mathematics Department’s capstone requirements, math majors enrolled in a MATH capstone course are required to take the MATH Assessment Exam if they haven’t done so already. The assessment exam will be given towards the end of the semester and it will contain questions from the eight required courses of the mathematics major (MATH 128, CPTR 125, …).



Tips for Success in This Course

(1) Keep up with the homework - understanding every homework assignment as completely as you can is the key to grasping the course material.  Even though there will be some homework assignments that you may not be required to submit, do them anyway, since they will help you master the material.

(2) Keep your binder up-to-date and well-organized, since you might be allowed to use the binder for exams.



General Standards and Policies

          All work submitted must be of professional quality.  All paper must be neat, without ragged edges, rips, tears, smudges, stains, etc.  All answers must be clear, complete, and concise; handwriting must be legible.  If the instructor can't read it, it's wrong.  Assignments may be down-graded if these standards are not met.

          It can be very helpful for some students to work together on daily assignments and to study together; this is encouraged when it does not result in one student simply copying another's work with no understanding.  Acts of academic dishonesty will result in a grade of F for the course, and a letter to the Provost describing the circumstances.  If you are having problems in the course, talk to the instructor; don't involve yourself in academic dishonesty. With each assignment submitted, students are expected to write a short note at the end of the assignment indicating from whom help was received and to whom help was given (but this does not affect the grade for the assignment).  The following is from the FACULTY HANDBOOK in the section titled Student Course Load:


"It is expected that students will spend, in preparation for courses, two hours of study time outside the classroom for every hour of credit in the classroom."


This means that you should be prepared to spend, on average, eight hours per week outside of class working on a four-credit course; however, this will vary from student to student and from course to course.  Your time will be spent reading the text, reviewing class notes, and completing homework exercises.