Mathematics 380:  Topics in Mathematics: Symmetry
Spring 2019

Professor:        Jeff Johannes                                    Section 1    MF    2:30-3:45p    Sturges 105
Office:            South 326A                    
Telephone:      245-5403
Office Hours:   Monday 12:00N-1:20p, Tuesday 8:00 - 9:00p, Wednesday 11:30a - 12:30p, Thursday 4:30 - 5:30p, Friday 10:00 - 11:00a, or by appointment or visit.
Email Address:

    The Symmetries of Things by John Conway, Heidi Brugiel, and Chaim Goodman-Strauss, AK Peters, 2008

    Almost all beauty is because of symmetry.  There are amazing patterns all around us in art and nature.  In this course we will classify and analyse many diverse symmetries  from kaleidoscopes and wallpaper patterns to more exotic patterns on spheres and beyond. 

Learning Outcomes
Upon successful completion of Math 380:  Symmetry a student will be able to:

Upon successful completion of Math 381:  Algebraic Symmetry a student will also be able to:

    Your grade in this course will be based upon your performance on participation (on-line and in person), problem sets, take home exams, and a final experience.  The weight assigned to each is designated below:
        In-class Participation          1/4
        Project Presentation            1/4
        Field Trip Report                1/6
        Discovered examples          1/6
        Created examples                1/6
In-class Participation
    If you are present and engaged in class you will receive one participation point that day.  If you also participate to the class as a whole (answer a question, present a solution, ask an insightful question or offer important relevant commentary) you will receive two participation points for that day.  Working each day and never speaking in class will earn 80%.  Speaking every other day on which there is an opportunity to speak will earn 95%.  Scores between will be scaled linearly.

Field Trip Report
    One week after we take a field trip out of town, please write a report about what you saw and learned and how you felt about it.

Created Examples
    Create examples of symmetry as discussed in class.  Examples will be valued based on mathematical sophistication and something perhaps about artistic effort (not necessarily artistic success). 

Discovered Examples
    Find examples of symmetry in "real life" and analyse them as discussed in class.  By "real life" we mean anything that does not have a reference to mathematics.  More appreciation will be shown toward examples encountered in your actual physical life.  More appreciation will also be shown toward more sophisticated examples.  These two are likely to be at odds. 

Final Project
    You will give a 11-13 minute presentation on a symmetry topic not covered in class.   A topic proposal will be worth 5%, each of two rehearsals will be worth 20%, critiques of other students' presentations will be worth 10%, the 11-13 minute presentation will be worth 35%, and a reflective essay will be worth 10%.

    Occasionally you will be given anonymous feedback forms.  Please use them to share any thoughts or concerns for how the course is running.  Remember, the sooner you tell me your concerns, the more I can do about them.  I have also created a web-site which accepts anonymous comments.  If we have not yet discussed this in class, please encourage me to create a class code.  This site may also be accessed via our course page on a link entitled anonymous feedback.  Of course, you are always welcome to approach me outside of class to discuss these issues as well.  

Disability Accommodations
     SUNY Geneseo will make reasonable accommodations for persons with documented physical, emotional, or cognitive disabilities.  Accommodations will be made for medical conditions related to pregnancy or parenting. Requests for accommodations including letters or review of existing accommodations should be directed to Ms. Heather Packer in the Office of Disability Services in Erwin Hall 22 or or 585-245-5112.  Students with letters of accommodations should submit a letter to each faculty member at the beginning of the semester and discuss specific arrangements. Additional information on the Office of Disability Services is available at

Religious Holidays
    It is my policy to give students who miss class because of observance of religious holidays the opportunity to make up missed work.  You are responsible for notifying me no later than February 8 of plans to observe the holiday.  

Tentative Schedule subject to significant changes as we go forward.  This schedule and details are a work in progress actively negotiated with students.

Date              Topic                                                      
January 25     Introduction 

         28        1 and through p. 18 of 2
February 1      Kaleidoscope field trip                                             

        4            Complete 2
        8            Read 3, Select topic for presentation.  Field trip report

        11         Discuss exercises and start 4
        15         Complete 4, 5       

        18          6, found symmetries due.        
        22          7
        25          8
March 1         9 (includes part II preview)
        4          17 Final title & abstract due
        8          18 Deadline for GREAT Day proposals and for student talks at Seaway         
        11        Rehearsal #1
        15        Rehearsal #1 
        25        Part II prelude + 10
        29        Memorial Art Gallery

April 1       Seaway Rehearsals   
        5         Seaway meeting - Field trip report due
        6         MAA Seaway Meeting at St. John Fisher College, Rochester.         

        8        GREAT Rehearsals    
        12       11?   3 Found hyperbolic symmetries due

        15      11
        17        GREAT Day        
        19      12    

        22      13  Presentation reflections due  
        26      14   

        29      15    
May 3        Created examples of colourings due

Thursday, May 16 final experience 3:30 - 6:00p Show and tell of discovered and created examples.