MAT 4040: Mathematics Capstone (1 c.h.)

Instructor: Dr. Sarah J Greenwald
Office: Walker 326

In this course you will gain a fresh perspective about how the mathematics that you learned fits in with the broader mathematical fields, other academic fields of study, humanistic perspectives, and society in general. Oral and written communication skills are emphasized. This course will culminate in a project that investigates some aspect of mathematics - for many people this may be research on and putting together in a new way material from other courses or research or internship experiences. This course is open to majors with senior standing, or (with permission) those who have taken a broad range of courses in the mathematical sciences. This course will fulfill the capstone requirement for all of the concentrations in the BS degree in mathematics (260*/27.0101) and the BA degree (261A/27.0101). Gen Ed: Capstone Experience

Required Resources

  • LaTeX: A Document Preparation System - User's Guide and Reference Manual, by Leslie Lamport, Second Edition
  • The i-clicker - the official university clicker, available in the bookstore under the course resources. Bring the i-clicker with you to class every day.
  • Printed copies of your work
  • access to LaTeX on the campus file server, the online browser version and/or at your own computer (on-campus access is sufficient as long as you have the time to work on campus while the labs are open)


    Participation 30%. You are expected to contribute to discussions in a meaningful way. You are responsible for all materials presented and discussed during class, including any changes to assignments, deadlines, or requirements. Attendance is required at ALL classes, and will form a portion of your grade.*

    Homework 30%. Check the webpage frequently for homework. Late work will obtain at most half credit. Must be turned in by our assigned day during finals. *

    Course Project 40%. The course project will investigate some aspect of mathematics in significant depth through an exploration of recent research. This project will build upon previous research experiences, independent studies on advanced mathematics, foreign exchange program experiences, or advanced mathematical topics from 3000 or 4000 level classes in which the student has developed an interest. Our assigned meeting time during finals week includes part of the course project - no make-ups allowed * and participation in the final project is mandatory to pass the class.

    * Work may occur during the last week of classes. Accommodations in the determination of your final grade will be made for extenuating circumstances that are documented to prevent you from completing work early/on time. Also see the University-wide syllabus and policy statements which we adhere to. The grading scale is: A ≥93; 90≤ A- < 93; 87 ≤ B+ <90...

    Other Policies

    I am always happy to help you---make use of the resources available to you, including my office hours, online forums and the writing center!

    As per the University-wide Statement on Student Engagement with Courses you can expect to spend (on average) 2-3 hours outside of class for each hour in class. Homework during some weeks may take less than this time---your other time outside of class should be spent on the course project. You are responsible for all material covered and all announcements and assignments made at each class, whether you are present or not, and on the web pages.

    When writing up work, be sure to give acknowledgment where it is due. Submitting someone else's work as your own (PLAGIARISM) is a serious violation of the University's Academic Integrity Code, which defines:

    Plagiarism includes, but is not limited to, borrowing, downloading, cutting and pasting, and paraphrasing without acknowledgement, including from online sources, or allowing an individual's academic work to be submitted as another's work.

    Use of interactive technology is allowed only when it is related to our class. Put cell phones away and set them to vibrate. Photos or video or audio recordings may not be taken in class without prior permission. Food and beverages are allowed as long as they aren't distracting, but e-cigs, chewing tobacco/spit cups and other products are not allowed.

    Tentative Weekly Calendar

    Date     WORK DUE at the beginning of class unless otherwise noted!
    8 May-Fri
  • Our assigned meeting time during finals week is Fri May 8 beginning at 9AM and includes the last presentations, and the final draft of the paper for the course project. We'll also do some reflective activities. Any outstanding assignments are also due.
  • 27 Apr
  • Course project beamer presentations continue
  • 20 Apr
  • Course project beamer presentations continue
  • 13 Apr
  • Course project beamer presentations begin
  • 30 Mar
  • Appalachian General Education
  • 23 Mar
  • Mathematical Writing and Course Project Paper Draft
  • 16 Mar
  • Mathematics in a General Education
  • 2 Mar
  • Proof, Certainty, Success and Discoveries in Mathematics
  • 23 Feb
  • Part 2 of the Course Project
  • 16 Feb
  • Professional Associations and Ethics and Responsibilities of Community Membership
  • 9 Feb
  • Part 1 of the Course Project
  • 2 Feb
  • Careers
  • 26 Jan
  • Introduction to LaTeX
  • 12 Jan
  • The art of equations activities which includes a discussion of the syllabus and Cantor's diagonalization argument.
  • Course Objectives

    To investigate mathematical knowledge from different levels and areas
    To professionally express mathematical results in both written and oral form
    To relate mathematics to other disciplines and society
    To understand something of the breadth of mathematical study
    To reflect on mathematical ideas from the past and from abroad

    We will also reflect on the achievement of general education goals and connect to previous and current coursework as well as:
    I. Thinking critically and creatively
    A. Recognize, differentiate, and effectively employ appropriate and increasingly sophisticated strategies to collect and interpret information;
    B. Successfully integrate disparate concepts and information when interpreting, solving problems, evaluating, creating, and making decisions;
    E. Apply theories from a variety of disciplines and advance convincing reasons to connect as well as differentiate theories from different domains of knowledge.
    These are satisfied by the work on the project.

    II. Communicating effectively
    A. Articulate and comprehend effectively, using verbal or non-verbal communication suitable to topic, purpose, and audience;
    E. Read actively and analytically at the college level and synthesize and apply information and ideas from their reading across disciplines;
    F. Know, apply, and communicate college-level quantitative concepts and methods;
    G. Select and use hardware, software applications, databases, and other technologies effectively for both inquiry and communication.
    These outcomes are achieved through the write-up and presentation of the project and through class activities and reflections.

    IV. Understanding responsibilities of community membership
    C. Collaborate effectively with others in shared processes of inquiry and problem-solving;
    This outcome will be met through class discussions and group activities.

    Class sessions include the following topics:
    LaTeX typesetting and standard mathematical publishing formats
    Bibliographies and recognition of support and prior results
    Mathematics and society and stereotypes in mathematics
    Mathematical thought processes
    Discussion on success and career opportunities in mathematics
    Professional societies and their role in mathematics
    Mathematics and the general education
    Oral presentation styles, tools, and strategies
    Mathematics in other cultures and the culture of mathematics
    Special topics in different areas of mathematics, including "pure" and "applied"
    Special topics in the history of mathematics and mathematicians

    Instructor Bio

    I am a Professor of Mathematics and a Women's Studies core faculty member at Appalachian State University. I received my PhD from the University of Pennsylvania. My scholarship areas include Riemannian geometry of orbifolds, popular culture as it pertains to mathematics, and women and minorities in mathematics. Recognition for my teaching includes a 2005 Mathematical Association of America Alder Award winner for distinguished teaching and the winner of the 2010 Appalachian State University Wayne D. Duncan Award for Excellence in Teaching in General Education. In 2010 I was also inducted into the Appalachian State University College of Arts and Sciences Academy of Outstanding Teachers and in 2011 I was named the College of Arts and Sciences Outstanding Teacher of the Year. I am the associate editor of the Association for Women in Mathematics Newsletter and a member of the editorial board of PRIMUS. Andrew Nestler and I co-created the educational website My interactive mathematics lecture has been distributed on approximately one million DVDs worldwide as a 25-minute DVD extra for the 20th Century Fox Futurama movie Bender's Big Score and it is listed as "Mind-bending." Jill Thomley and I co-edited the 3-volume Encyclopedia of Mathematics & Society, which was named a "Best Reference 2011" by Library Journal. I've spoken about the impacts of scientific popular culture representations on NPR's Science Friday and all over the country.

    I am married to the bassist Joel Landsberg. We both happen to be on IMDb: Joel and me. My Erdos Bacon number is 6-7 or infinity, depending on what/how you count. In my spare time I like to travel, hike and conduct genealogy research (I also enjoy popular culture, as you can probably tell from some of my scholarly interests). In addition to my own personal genealogy, I like to give back to the broader community. I am the project coordinator for sites like the Bialobrzegi ShtetLink and the Book of Remembrance of the Community of Bialobrzeg. These projects strive to research and preserve information about communities that were destroyed in World War II. My great-grandparents lived there (it was the Russian empire back then!) in the late 1800s. Some of what I really like about mathematics is also what I enjoy about genealogy - the sense of exploration, discovery and aha moments that come with lots of patience and effort.