This semester the seminar will be dedicated to the study of groups and their relation to other branches of mathematics, in particular to graph theory.

Our textbook will be Groups and Their Graphs by Israel Grossman and Wilhelm Magnus (The Mathematical Association of America, New Mathematics Library). The book is unfortunately out of print, but some used copies are available on-line, and bound photocopies can be obtained as 640:196 text for $18 from Pequod (119 Somerset Street, New Brunswick, 732-214-8787).

The chapters assigned as reading below are chapters of this book. Don't be dismayed at being assigned two or even three chapters in one week: most chapters in this book are very short, in some cases under three pages.

We will also rely on seminar notes. Some of these are already posted at this site; further notes will be added by professors and students as we go along, so do check this site frequently. The names of the student speakers, more lecture titles, and other details will be added to the list of talks as they become known.

There are some useful notes posted by students of this seminar. As inspiring examples from earlier semesters, look at two student webpages about Non-Euclidean Geometries: Cindy Nezames's (Spring '02) and Aron Samkoff's (Fall '03).

For bibliographical data, go to the excellent Scottish website of the University of St Andrews. You may want to start at the history page and browse, or go directly to the index of biographies.

January 20 and 27 (Profs):   Introduction to groups: basic definitions, examples familiar and unfamiliar, generators of groups, subgroups, the importance of groups in math and science.
Reading:  Chapters 1, 2, and 3;   seminar notes on basic algebraic structures,   exercises.

February 3 (Amrita Aranake and Laura Asmuth):   More group examples: modular arithmetic, cyclic groups.
Reading:  Chapters 4 and 5;   seminar notes on cyclic groups.

February 10 (Amrita Aranake and Laura Asmuth):   The graph of a group, more on cyclic groups and the dihedral groups (finite and infinite), product of cycles.
Reading:  Chapters 5 and 6.

February 17 (Leo Barinov):   Introduction to the symmetric and alternating groups.
Reading:  Chapters 10, 13, and the short summary.

February 24 (Jonathan Word):   The group of symmetries of each Platonic solid.
Reading:  The Appendix, and the website Symmetry groups of Platonic solids.

March 3 (Kevin Troyanos):   The Euler-Descartes Formula for polyhedra and for plane graphs and two of its consequences: (1) there are only five Platonic solids, (2) all plane maps can be colored with at most five colors.
Reading:  Seventeen proofs;  Platonic graphs;  Planar graphs and plane graphs; Mathworld on the Four-Color Theorem; coloring maps on other surfaces.

March 10 (Javier Sanchez):   Subgroups, conjugacy, cosets, Lagrange's Theorem.
Reading:  Chapter 8;   seminar notes.

March 24 (Robert Emanuele):   Isometries in Rⁿ.
Reading:  Seminar notes on isometries.

March 31 (Volodymyr Khlystov):   The game SET.
Reading:  Seminar notes on vector spaces and bases.

April 7 (Rohan Mathew):   Finite groups of symmetry in R² and R³.
Reading:  Topics in Geometry by John O'Connor, especially lectures 11, 10, 2, and 4. (Notice the St. Andrews website again!)

April 14 (Matt Connors and Karl Suabedissen):   Groups and wallpaper designs.
Reading:  Chapter 15;   The 17 plane symmetry groups.

April 21 (Craig Dana and Joe Paras):   Spatial symmetry (with applications in crystallography).

April 28 (John Bryk, graduate student in mathematics): The Geometry of the p-adic Numbers.