# Themes of MATH4900 Seminar

### Themes and brief description of MATH4900, First term 2015-16

#### MATH 4900A Continued Fractions

In this section, possible topics are continued fractions representations, convergences as best

approximations, measure theory of continued fractions.

#### MATH 4900B Mathematics related to Rubik’s Cube

In this section, topics are to examine how group theory is used to model Rubik’s cube and similar puzzles.

Concrete and fun examples in finite group theory as well as ideas to solve the puzzles will be discussed.

#### MATH 4900C Some Geometry, some Topology, a little Analysis

In this section, topics are on the interface of geometry and topology with perhaps analysis involved.

Topics may include discussion of area and congruence, various meanings of dimensions, some

interesting theorems in geometry or topology.

#### MATH 4900D Computational Differential Geometry in Real World Applications

In this section, topics are surrounding the study and applications of digital geometric images through

differential geometry theories. Applications may include medical imaging, computer graphics, and

computer visions.

#### MATH 4900E All about Inequalities

In this section, the starting point is inequalities; then the focus leads to topics such as Fourier Analysis,

geometry, combinatorics, and number theory. The unity across different fields of mathematics will be

emphasized, as material will often be drawn from more than one area of mathematics.

#### MATH 4900F Studies in Operations Research

In this section, small projects and problems in the area of OR will be explored. The aim is to lead

students to a thorough understanding of the art and science of practical applications in OR. Students

may realize the successful way of undertaking projects and what obstacles are present to thwart success.

#### MATH 4900G Mathematics formulation of Classical Mechanics

In this section, topics about modern formulations of Hamiltonian and Lagrangian mechanical systems in

mathematics will be discussed. It may involve the algebraic presentation or analysis.

#### MATH 4900H Study of Partial Differential Equations

In this section, some analytic methods for PDEs arising in physics or geometry will be studied. Possible

topics may include Poisson problem, heat equation, and fractional Laplacian.

#### MATH 4900I Convex Sets and Functions

In this section, discussion topics are given in algebraic theory and separation theorems of convex sets on

a linear space, and analytical properties of convex functions.