Capstone Handbook
(As of Academic Year 2023-2024)
1. General Information
What is a Capstone in Applied Mathematics?
According to university-wide policy, a capstone marks the culmination of a student’s curriculum. The capstone is a project that demonstrates the principal learning outcomes and competencies of that curriculum in a meaningful and coherent way. The capstone may also be drawn from relevant extra-curricular activities and practical experience to support the research and realization of the project. The capstone should evidence competency in a primary disciplinary specialization (optionally supported by secondary and tertiary disciplinary areas).
In the Applied Mathematics major, the capstone is to be conducted individually and can take only the form of a written thesis. In extremely rare cases, a student may wish to complete other kinds of projects. However, in such cases an approval by ALL faculty in Applied Mathematics is required.
REMEMBER:
- The capstone should demonstrate the mastery of basic mathematical concepts and the ability to apply those concepts to understand current research literature.
- Original work is not required. In fact, it is rare for an undergraduate thesis in Mathematics to be original and significant.
- You should think very carefully about an appropriate scope of research and production for your proposed capstone. It is important for you to consult early on with your prospective advisor about this.
- Applications which do not demonstrate awareness of the scope and the practicalities needed to realize the capstone may not be approved.
Keep in mind that projects for which there is no current faculty expertise may not be approved. The 2023-2024 full-time faculty in Applied Mathematics hold expertise in the following fields:
- Probabilistic combinatorics,
- Numerical analysis,
- Optimization,
- Financial mathematics,
- Statistics,
- Partial differential equations.
1.1. Eligibility Criteria
To be eligible to apply for the capstone in Applied Mathematics, you must meet the following criteria:
- Major GPA: 3.5
Capstone applicants will be assessed by the major faculty based on the eligibility criteria and the quality of the proposal.
- NOTE: Successful capstone applicants must maintain a 3.5 GPA throughout their senior year to be able to earn an Honors for the capstone. Failure to maintain the required GPA will result in the capstone being capped at Pass.
1.2. Allocation of advisor process
Successful applicants will provide a first choice of primary and secondary advisor and will be accomodated when prudent. If the student’s first or second preference cannot be accommodated due to the necessity of maintaining a fair distribution of faculty workload, the major capstone coordinator will consult with the student to determine an appropriate solution.
1.3. Advising process
The primary advisor is your first point of contact, and should hold expertise relevant to your project, for example, in terms of being a specialist in the project’s disciplinary field. The primary advisor will be the primary reviewer of your work in progress, and as such, will be the person with whom you meet most frequently. Expertise does not need to be regional or topical – an advisor may have a strong grounding in the theory or methodological approaches of the capstone rather than a specific research background in that topic.
The secondary advisor can offer you additional feedback where necessary and may represent a disciplinary field outside of Applied Mathematics (if your project is interdisciplinary). In cases when the primary advisor is unable to continue, the secondary advisor will assume their role.
You should plan to meet with your primary advisor at least once a month, if not more often. You are expected to be proactive in organizing these meetings with your advisors and to follow up on the meetings’ actionable items. The capstone places responsibility on you to be organized and to be responsible in regular communications and submission of work-in-progression to your primary advisor. Failure to do this might lead to a “Fail”.
REMEMBER:
- Respect your advisor’s working hours
- Correspond professionally and courteously
- Use Fulbright email instead of social media platforms
- Respect your professor’s time
- Be prepared at meetings (with materials, questions) and use your time efficiently
- You are responsible for setting up the meetings (and showing up!)
- Expect meetings to be about at leat 30 minutes
OTHER EXPECTATIONS:
- You cannot change your capstone’s topic and format without consulting your advisors and getting their approval
- We expect you to demonstrate and maintain clear communication, a steady work ethic, a capacity for self-organization, and balanced management of your capstone workload with your other coursework
- Try to keep up with your timeline
- Manage your expectations in terms of what you can accomplish
1.4. The Applied Mathematics Capstone Meetings
Approved Capstone students are expected to meet with the advisor(s) regularly (preferably weekly). The students will present any relevant updates on their project and receive active feedback from the advisor(s).
1.5. Capstone I
In Capstone I you will commence research and refine your project proposal and plan. Depending on the project, this will likely include development of a comprehensive bibliography and literature review focusing on background context.
Capstone I will be assessed by a combination of your active participation in the advising processes, and both a midterm and end-of-term submission. The midterm submission must demonstrate clear progression, and will be used to facilitate your advisors in guiding your research moving forward. The end-of-term submission will demonstrate successful progress towards the final capstone submission, and satisfactory completion of the criteria listed in the above paragraph.
What you might be expected to submit for Capstone I:
Midterm submission(s):
- Initial Literature review
- Annotated bibliography
End-of-term submission (very likely a combination of some of the following):
- Revised literature review
- Initial written background
- Preliminary findings
- Other materials to be decided on in consultation with your advisors
1.6. Capstone II
In Capstone II you will focus more on a particular research subject that is actively developed in the mathematics community. At the minimum, you are expected to write a document that summarize these developments with full theoretical justification.
In order to receive honors, you need to demonstrate some originality in the work. This could be (but not limited to) proving a known theorem in a different way of your own, applying what you learn to solve some interesting problem.
You will participate in research in support of your final submission. In addition to a written submission, at the end of Capstone II, you will also be required to formally present your work.
Capstone II will be graded through assessment of a student’s final submission. In addition, students are also required to actively participate in advising activities and provide regular updates including the midterm submission.
What you might be expected to submit for Capstone II:
Midterm submission(s):
- Draft of the core theory
- A rough draft or outline of a thesis
End-of-term submission:
- A revised and professionally presented written thesis
- A finished applied project plus its documentation/report
1.7. IRB Approval
In rare cases, if your project requires working with human subjects through processes that include, but are not limited to, in-person or online interviews, direct or indirect observations, opinion surveys, etc., you will be responsible for obtaining approval from Fulbright University Vietnam’s Institutional Review Board (IRB). The IRB approval process involves taking an online module to learn about IRB procedures, as well as submitting an application detailing your research design and plan for data collection and protection. Please be advised that the IRB procedure applies to all forms of Applied Mathematics Capstones project, whether written thesis, applied or creative project.
Students must obtain IRB approval prior to the period of their Fulbright-affiliated research. Failure to do so would result in delays to the project and/or its suspension. For this reason, Applied Mathematics students are advised to begin their IRB application as soon as their Capstone application is accepted, or during Capstone I at the latest.
More information on the IRB approval process can be found at https://fulbright.edu.vn/irb/
1.8. Academic Integrity
The capstone is subject to the regulations described in Fulbright University Vietnam’s Code of Academic Integrity.
1.9. Grading process
As in Appendix 1, there are two graders for each capstone project: primary advisor and a second reader (which will be the secondary advisor, if there is one).
Research Process will be graded by the primary advisor.
The Thesis and Presentation will be graded by both the primary advisor and the second reader.
2. Capstone by Thesis Guidelines
2.1. Word Count Regulations
There is no minimum word count. However, typically, undergraduate theses are often less than 40 pages, including full bibliography and images with captions. Your thesis must be written in LaTeX.
2.2. Style and Formatting
LaTeX helps you not worry about styling. You may adopt the following template with Fulbright University Vietnam logo:
https://github.com/fuvmath/FUV-Thesis-Template/
Sequence of Thesis Materials:
Preliminary pages, in the following order:
Title Page. The title page should include the title of the thesis, your name, the date of submission, and your advisor’s name. Include this statement on the lower third of the page:
1
A thesis submitted to partially fulfill the requirements for the degree of Bachelor of Science in Applied Mathematics
- Table of Contents. A consecutive listing of chapters or major headings with page numbers; also include the page number for the additional sections (illustrations, the appendix (if included), and the bibliography. Double space between these elements.
- Abstract page. Double-spaced.
- Acknowledgment(s) page. Optional.
- List of Tables (as necessary), with titles and page references.
- List of Illustrations, with titles and page references.
Note: The preliminary pages should be paginated using small Roman numerals (i, ii, iii, iv, v, and so on). These may be placed at the bottom of the page. The title page counts as page i, but do not print a page number on this page. Begin the pagination with the next page (acknowledgments page, if you have one, or the table of contents).
Bibliography. Follow standard practice set by LaTeX. Discuss with your advisor(s) about this if you encounter technical issues.
2.3. Formal Presentation Requirement
While this presentation is not assessed as part of the final submission, in order for your final submission to be evaluated at the end of Capstone II you must present your work as a formal 15-minute paper at the Capstone Symposium. You are expected to attend the entire symposium and to engage with the presentations of your classmates.
2.4. Evaluation Criteria: Capstone by Thesis
We will follow the grading rubric in Appendix 1.
Total score: 18
Score breakdown:
- Honors: 15 and above
- Pass: 6 and above
- Fail: Below 6
3. Capstone Presentation
3.1 Timeline of the Capstone Presentation:
At the end of Capstone II, students are required to present their findings to the larger Fulbright community.
3.2. Format of the Capstone Presentation:
The format of the capstone presentation should be decided between the student and his/her advisors. Possible formats include, but are not limited to, a powerpoint presentations, a board presentation, combination of board presentations and other media presentations.
APPENDIX 1: Capstone grading rubric
The following is the grading rubric for Capstone project in Applied Mathematics major during academic year 2023-2024.
There are two graders for each capstone project: primary advisor and a second reader (which will be the secondary advisor, if there is one).
Research Process
This part is evaluated by the thesis advisor only.
Personal Development and attitude
| Insufficient 0 point | Satisfactory 1 point | Good 2 points | Excellent 3 points | |
|---|---|---|---|---|
| Understanding the material | Fails, despite guidance from the supervisor | studies literature with guidance from the supervisor | independently studies literature | independently finds and studies literature |
| Critical arguments about the results, literature or specialists | Fails to understand | Understands those of supervisor | Joins the supervisor in discussing | Comes up with their own |
| Taking responsibility for the project and working independently; handling data (if applicable) | Takes no responsibility, shows no independence, unreliable handling. | Takes responsibility, works semi-independently, clearly needing supervision, handles data quite reliably | Takes responsibility, works independently with some need of supervision, handles data in a reliable manner | Takes responsibility for the project and works independently, and if applicable, handles data in a reliable manner |
| Communication with supervisor, planning meetings, leading discussions | Communicates badly, plans inconsistently, no participation. | Communicates well, plans consistently, lets the supervisor lead the discussion | Communicates well, plans consistently and actively participates | Communicates well plans consistently and takes initiative |
Mathematical development
| Insufficient 0 point | Satisfactory 1 point | Good 2 points | Excellent 3 points | |
|---|---|---|---|---|
| Comprehensive understanding of the subject, given its difficulty | Failed to develop this | Developed this | Developed this, in its broader context | Developed this, in its broader context |
| Understanding and reproduce the mathematical theories used | Failed | Did this with while closely supervised | Did this, with some guidance | Did this with relatively little guidance |
| Development of practical (experimental/computer) skills (if applicable) | Insufficient | Know the basics and take time to implement | Developed good skills for the project | Developed good skills for the project |
Below evaluations will be filled by the thesis advisor and the second reader.
Thesis
Research Context
| Insufficient 0 point | Satisfactory 1 point | Good 2 points | Excellent 3 points | |
|---|---|---|---|---|
| Formulation and motivation of main mathematical questions | Inappropriate or lacking | Appropriate and well-motivated | Appropriate and well-motivated | Clearly stated, properly motivated and importance in the field is made clear |
| New concepts, theorems and techniques are put in context | Poorly, without understanding of own results; no consequences, open questions or future potential mentioned | Student demonstrates understanding of the results | Student demonstrates understanding of the results | Student demonstrates understanding of the results, discussed consequences, open questions or future potential |
| The approach is | Unclear and illogical | Clear but minor illogical points | Clearly outlined and appropriate | Clear and innovative |
| Relevant literature review | Missing | Included but may not be well-chosen | Well-chosen | Well-chosen |
Mathematical content
| Insufficient 0 point | Satisfactory 1 point | Good 2 points | Excellent 3 points | |
|---|---|---|---|---|
| Overview of background | Inadequate, missing crucial elements | Given, but some elements are missing | Given with relevant literature | Given with relevant literature and interesting insights |
| Proofs and discussions of the subject | Weak, missing crucial elements | Given, mostly complete but not in much depth | Given, complete but not too different from the references | Given, complete and in-depth; show a great level of mastery of the subject |
| Creativity | Lacking | Some | Some | Very original |
Writing style and mathematical exposition
| Insufficient 0 point | Satisfactory 1 point | Good 2 points | Excellent 3 points | |
|---|---|---|---|---|
| Style | The thesis contains a large number of spelling or grammatical errors; focus often drifts from the subject | Suitable, but sometimes inconsistent, but creates a decent flow; contains only few spelling or grammatical errors | Suitable and has a good flow; contains only few spelling or grammatical errors | Almost perfect, engaging to read |
| Layout and organization | Poor | Clear to read | Clear to read | Clear to read |
| Proofs | Poor | Minor errors | Error-free | Error-free and pleasant to read |
| Theorems, propositions and lemmas | Poorly chosen and not connected | Chosen with some shortcomings | Well-chosen | Well-chosen |
| Examples and/or figures | Absent or irrelevant | Reasonably chosen but could be better | Well-chosen | Well-chosen, interesting, and judiciously placed to aid readers |
Presentation
Content
| Insufficient 0 point | Satisfactory 0.5 point | Good 1 points | Excellent 1.5 points | |
|---|---|---|---|---|
| The selection of topics and examples | Weak; the presentation was missing parts or did not match the audience level | Reasonable; however, sometimes the choices did not match the audience level | Reasonable, taking into account the audience level | Good, taking into account the audience level |
| Organization and coherence of the presentation | Could have been better; there were many shortcomings | Well enough, have a nice flow, but there were some shortcomings | Well enough, nice flow in general | Almost perfect, giving a good flow and a sense of direction |
Presentation skills
| Insufficient 0 point | Satisfactory 0.5 point | Good 1 points | Excellent 1.5 points | |
|---|---|---|---|---|
| Interaction with the audience | Not good | Well enough, could be better | Good | Excellent |
| Understandability | Poor | Reasonable | Good | Good |
| Time management | Not knowing time | Within 10 minutes of assigned time | Within 5 minutes of assigned time | Within 2 minutes of assigned time |