Math 3510 - Junior Honors Seminar
Applications of Geometry
Dr. Sarah J. Greenwald

Where to Get Help

Office Hours 326 Walker Hall, 262-2363. I am always happy to help you in office hours. An open door means that I am on the floor somewhere, so come look for me. Check this often.

Dr. Sarah's MAT 3510 WebCT The Bulletin Board is the easiest way to ask a math question outside of class and office hours. You are responsible for reading all posts - you should check the bulletin board about once a week. I prefer that you use office hours since it is easier to discuss material in person, but if you can not make them, then the newsgroup is a great alternative. I usually check the newsgroup numerous times every day including the weekends.

Required Resources

Geometry at Work by Cathy Gorini
handouts given out
loose-leaf notebook to organize handouts, notes and your work
printouts of your work - see for information about ASU charging for print services.

Course Syllabus and Goals

While geometry means measuring the earth, too often it is presented in an axiomatic way, divorced from reality and experiences. But in this course, we will use intuition from your experiences with hands on models and data to understand real-world applications of geometry such as the geometry of the universe and applications of geometry to art, mapping the brain, robotics, graphics, space shuttle navigation and more!

We will begin by studying the geometry of the earth and universe and a historical overview of geometry. The rest of the topics will be chosen by student interest (see for possible topics). In the process, we'll see the interplay between geometry and numerous other subdisciplines such as (depending on the topics chosen by the students) linear algebra, modern algebra, analysis, differential equations, probability and statistics. In addition, we will see the connections between geometry and numerous other fields such as (depending on the topics chosen by the students) history, physics, astronomy, philosophy, art, computer science, architechture, medicine, biology and chemistry.

Secondary goals of this class include devloping the skills to read and write mathematics, how to handle notation, how to use library resources effectively, and how to present mathematical information in a clear and concise way. Students will write about mathematics from both technical and expository viewpoints, and will research their chosen topics using the resources in our library and those available over the internet. In this manner, we will work to improve research, writing and typesetting skills.

Math 3510 has been designated as a writing intensive, and numerical data course.


  • Participation in Classroom Activities 20% There will be days when the activities are designed to be completed during class. Thus, attendance is required at ALL classes. Missing more than 4 classes (official and/or unofficial absences) will result in a lower participation grade. Missing more than 9 classes will result in a grade of F. An incomplete will be granted only in university justified cases. Save your absences for emergencies. You are expected to contribute to discussions.
  • Assignments and Projects 60% There will be a variety of assignments and projects given at regular intervals; these will be traditional "homework" style assignments mixed with writing assignments (where you will have a chance to revise your work) and library research. Course grades will be based on all of these assignments. Work must be turned in on or before the due date. If there is some reason you must miss a class, then obtain the assignment from the web pages. May occur the last week of classes and during the educational experience that replaces the final exam.
  • WebCT Tests 20% Each test will have up to 5 tries to achieve a perfect score, and the highest of this score will count as the WebCT grade for that test. You should view these tests primarily as a chance to reinforce learning, as reflected in the generous grading policy. This means that these tests are not only an opportunity for you to demonstrate your mastery of the material, but are also an opportunity for you to be challenged with new material in order for you to make new connections. May occur the last week of classes.
  • May 14 - Tues Educational experience will occur from 12-2pm
  • Extra credit There will extra credit opportunities during the semester for which points will accumulate. When final grades are given, extra credit points are taken into account in the determination of -, nothing, or + attached to a letter grade.
  • Other Policies

    Plan to spend 4-6 hours per week, out of class, on average, on this course. Attendance and participation are expected and required. Please try to be punctual in attending, as I try to start each class on time. If you must be late to a class, or must leave early, then do still attend, although you can expect that the portion of the class that you miss will be deducted from your attendance allowance. You are responsible for all material covered and all announcements and assignments made at each class, whether you are present or not. You are also responsible for announcements made on the web pages, so check them often.

    Sometimes revisions will be allowed in response to comments I have made. Respond to the comments-use them as invitations to clarify your understanding of the problem or my understanding of your solution. You cannot turn in revisions unless you have turned in work when it was originally due and you must resubmit the original along with the revision. Typically, you will have one week to revise your work.

    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.


    Asking questions, and explaining things to others, in or out of class, is one of the best ways to improve your understanding of the material. This course is to be an environment in which everyone feels comfortable asking questions, making mistakes, offering good guesses and ideas, and is respectful to one another.

    You should explore each problem and write out your thinking in a way that can be shared with others. Focus on your own ideas. Turn in projects or prepare to present problems even if it they are not complete, even if only to say, "I do not understand such and such" or "I am stuck here." Be as specific as possible. Conjecture.

    In this course, you will be challenged with problems that you have never seen before. I do not expect you to be able to solve all the issues immediately. Instead, I want to see what you can do on your own. Out in the real world, this is important, since no matter what job you have, you will be expected to seek out information and answers to new topics you have not seen before. This may feel uncomfortable and frustrating. I understand this and want to help you through the process. It helps to remember that there are no mathematical dead-ends! Each time we get stuck, it teaches us something about the problem we are working on, and leads us to a deeper understanding of the mathematics.

    In the real world though, you are not expected to face your work alone. You will be allowed to talk to other people and you may even be expected to work with other people. In this class, you are also not expected to face your work alone. I encourage you to talk to me often in class, office hours, and the bulletin board.

    I am always happy to help you in class, during office hours (or by appointment), or on the WebCT bulletin board, and will try to give you hints and direction. At times though, to encourage the exploration process, I may direct you to rethink a problem and to come back to discuss it with me again afterwards. This occurs when I believe that the struggle to understand is imperative for your deep understanding of the material.