# Mathematics

## Two planes are heading for the same destination 8000 miles away.

Plane A leaves at 1:00 pm, averaging 450 mph. Plane B leaves at 6:00 pm, averaging 400 mph. Which plane gets there first?

You’ve heard a problem like this before, but never outside a classroom. Because in the real world, it’s much less black and white.

That’s because life has invisible variables. For instance, it will depend on the accuracy of weather pattern predictions to account for delays. It will depend on assessments about the plane’s material parts and fuel efficiency. It will depend on the air traffic controllers issuing course corrections in real time. All these factors will contribute to when the planes will arrive.

**So what’s the answer?** The truth is that the answer is too small for the real question. The world depends on more than just calculations — it requires people who have the foresight and perspective necessary to keep the planes arriving on time.

The College of Science mathematics degree prepares students not only to solve for (x), but to see the whole equation.

**Algebra:** A vibrant, multi-faceted, and wide-ranging branch, having ties with almost every field of mathematics and computer science.

**Analysis:** Generally sharing a basis in calculus, analysis has played a crucial role in solving problems in physics and engineering.

**Partial Differential Equations & Dynamical Systems**

**Mathematical Physics**

**Geometric Analysis**

**Ergodic Theory**

**Combinatorics and Discrete Math:** Perhaps the fastest growing area of modern mathematics. It has a wealth of real-world applications, especially in computer science, which have greatly contributed to its rapid growth.

**The research of several other department members includes work on topics closely related to combinatorics:**

- Maxim Braverman (polytopes and toric varieties)
- Anthony Iarrobino (combinatorial aspects of Hilbert schemes)
- Venkatraman Lakshmibai (Coxeter groups and the geometry of Schubert varieties)
- David Massey (hyperplane arrangements and singularities)
- Alexandru Suciu (combinatorics and topology of hyperplane arrangements)
- Jonathan Weitsman (problems involving analysis and combinatorics of convex polytopes)

**Geometry:** Concerned with the shape, size, and orientation of objects in space, and indeed such properties of space itself. The particular objects studied and the tools used in investigating their properties create subfields of geometry, such as algebraic geometry and differential geometry.

**Algebraic Geometry**

**Differential Geometry**

**Singularities in Analytic Geometry**

**Discrete/Combinatorial Geometry**

**Symplectic Geometry**

**Probability and Statistics:** Encompasses a broad array of topics in pure and applied mathematics, and has applications in almost every field of scientific research. By its nature, the field is driven by real-world applications.

**Topology & Singularities:** The study of those properties that are preserved through continuous deformations of objects. It can be used to abstract the inherent connectivity of objects while ignoring their detailed form.

Develops problem-solving skills while simultaneously teaching mathematics concepts. Each unit centers on a particular applied problem, which serves to introduce the relevant mathematical topics.

Presents mathematical connections and foundations for art. Topics vary and may include aspects of linear perspective and vanishing points, symmetry and patterns, tilings and polygons, Platonic solids and polyhedra, golden ratio, non-Euclidean geometry, hyperbolic geometry, fractals, and other topics.

Traces the development of mathematics from its earliest beginning to the present. Emphasis is on the contributions of various cultures including the Babylonians, Egyptians, Mayans, Greeks, Indians, and Arabs.

## Co-Op Stories

Many math students choose to participate in the university’s signature co-operative education program because it offers excellent preparation and exposure to exciting careers. Here’s what our students are saying: