The mathematics department course outlines describe our courses, but sometimes with technical jargon and unfamiliar terminology. So here we give informal descriptions of our amazing mathematics courses!

Math 304, 404

Vector analysis continues the study of multivariable calculus from Calculus IV. Main results in the course, which have important physical interpretations, generalize of the fundamental theorem of calculus to higher dimensions. Differential Geometry is a continuation of vector analysis and focuses more on the theory of curves and surfaces in space.

Math 306, 406

Linear algebra deals with linear functions between abstract vector spaces and how these functions can be represented with matrices. Linear algebra is an extremely useful subject that finds applications in computer science, economics, statistics, physics and business, and more! Students should be ready for an abstract, proof heavy course.

Math 334

Combinatorics is the mathematics of counting. The techniques and ideas in combinatorics can be accessible to those with a modest math background. Combinatorial ideas are used regularly in many other areas of mathematics.

Math 335

Graph Theory is the study of sets of objects (vertices) and the relations (edges) that exist between them. Graph theory finds applications in many disciplines, especially computer science.

Math 341

Number Theory considers the mathematics of the integers, giving a precise foundation to some of these properties that we have known ("believed'' is a better word here) since elementary school. Prime numbers are studied. This course provides the theoretical underpinnings for most modern applications of cryptography.

Math 344

Linear Analysis is an applied course on solving differential equations with new tools such as the Laplace transform, series, and Fourier series. Many of these topics are especially relevant to applications of mathematics to engineering.

Math 350

Mathematical Software introduces how to implement advanced mathematics on the computer using a high level programming language, usually in Mathematica. The ability to use software to investigate mathematical ideas is an indispensable tool to many modern mathematicians. This course does not count towards the mathematics minor.

Math 410, 411

Complex Analysis explores the calculus of complex valued functions. It turns out that a complex valued function being differentiable implies a host of elegant geometric and computational properties. These are good courses for students who like calculus, geometry, and visualization.

Math 412, 413, 414

Real Analysis rigorously proves theorems first introduced in Calculus, including theorems about limits, sequences, series, and derivatives. Courses usually begin start with a detailed study of the real numbers from first principles. As Calculus is fundamental to many subjects, so is Real Analysis. This is one of the core courses in all of mathematics.

Math 416, 418

Differential Equations and Partial Differential Equations are advanced courses on solving differential equations in one and many variables. These are essential courses for those going into a career involving mathematical modeling. There is usually less emphasis on proofs in this course than other advanced mathematics courses, but that does not mean they are to be taken lightly!

Math 419

History of Mathematics follows the evolution mathematical thought from early to modern times. The contributions of great mathematicians are introduced. This course does not count towards the mathematics minor.

Math 435

Discrete Mathematics is an advanced course on enumeration that continues where combinatorics left off. Students who enjoy thinking about finite sets and structures will be at home in this challenging but interesting course.

Math 437

Game Theory is the mathematical modeling of conflict and cooperation. Always a popular course, Game theory uses linear optimization techniques to make optimal decisions in a broad range of contexts. This topic is especially useful in economics.

Math 440

Topology considers properties of spaces that are invariant under continuous deformations. For example, a square can be deformed into a circle without breaking it, but a figure 8 cannot. This is a rigorous and interesting course on spatial geometry and its deformation.

Math 451, 452, 453

Numerical Analysis introduces computational algorithms for doing mathematics on the computer. When does the computer give accurate and efficient solutions to mathematical problems? These courses are an excellent choice for students interested in numerical simulation and analysis or algorithm development.

Math 442, 443

Euclidean Geometry rigorously develops the axioms and theorems of Euclidean geometry first introduced in high school. Non-Euclidean Geometry reexamines and changes the traditional Euclidean axioms, producing new and strange geometries.

Math 481, 482, 483

Abstract algebra is a branch of mathematics that deals with how to combine mathematical objects. The algebra sequence consists of three main subject areas: Group theory (the study of symmetries), ring theory (the study of polynomials), and field theory (the study of sets where we can add, subtract, multiply and divide). This is an absolutely central subject in pure mathematics.