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Full-Text Articles in Algebra
Mckay Graphs And Modular Representation Theory, Polina Aleksandrovna Vulakh
Mckay Graphs And Modular Representation Theory, Polina Aleksandrovna Vulakh
Senior Projects Spring 2016
Ordinary representation theory has been widely researched to the extent that there is a well-understood method for constructing the ordinary irreducible characters of a finite group. In parallel, John McKay showed how to associate to a finite group a graph constructed from the group's irreducible representations. In this project, we prove a structure theorem for the McKay graphs of products of groups as well as develop formulas for the graphs of two infinite families of groups. We then study the modular representations of these families and give conjectures for a modular version of the McKay graphs.
Lose Big, Win Big, Sum Big: An Exploration Of Ranked Voting Systems, Erin Else Stuckenbruck
Lose Big, Win Big, Sum Big: An Exploration Of Ranked Voting Systems, Erin Else Stuckenbruck
Senior Projects Spring 2016
Senior Project submitted to The Division of Science, Mathematics and Computing of Bard College.
Associativity Of Binary Operations On The Real Numbers, Samuel Joseph Audino
Associativity Of Binary Operations On The Real Numbers, Samuel Joseph Audino
Senior Projects Spring 2016
It is known that there is an agreed upon convention of how to go about evaluating expressions in the real numbers. We colloquially call this PEMDAS, which is short for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It is also called the Order of Operations, since it is the order in which we execute the operators of a given expression. When we remove this convention and begin to execute the operators in every possible order, we begin to see that this allows for many different values based on the order in which the operations are executed. We will investigate this question …