  # Courses

## Courses for Applied Math Majors

The Applied Math major requires the following math courses in addition to the common core courses (Calculus II, Linear Algebra, Vector Calculus, and Intro to Upper Level Math)).

### Math 333 - Differential Equations

Differential equations play an important role in the mathematical modeling of physical, technical or biological processes, from celestial motion, to bridge design, to interactions between neurons.  Any time-dependent phenomenon can be modeled by an equation describing the rate at which it changes (i.e. a differential equation), which can then be solved to obtain a predictive model.  This course studies the differential equations used in mathematical modeling, as well as various analytical, numerical and graphical methods of solving them.

### Math 364 - Mathematical Modeling

This applied course teaches how mathematics are used in the natural and social sciences.  The main topics include the modeling process, i.e. using and interpreting raw experimental and field data to build a model, and translating a observed phenomenon into a mathematical framework to be studied quantitatively.  The types of models studied include dynamical systems (predictive, time-dependent models), optimization models, stochastic models, and models based on graph theory and game theory.  Analytical methods (difference equations, Markov chains), numerical methods and computer simulations are used to study models in different fields: biology, ecology, economics, engineering, epidemiology, meteorology, pharmacology, sociology, and supply chain logistics.

### Math 385 - Topics in Applied Math

Topics in Applied Math (MATH 385) is a course with a special focus that changes every time the course is offered (so it is possible to take this course multiple times).  Each focus area is an area outside of mathematics in which important mathematical theory and methods are used.  Examples of past topics include:

• Community-Based Operations Research (CBOR)
• Numerical Analysis for solving differential equations
• Computational Epidemiology
• Agricultural Modeling
• Cryptography
• Structural Mechanics applied to Earthquake-Resistant Structures
• Chaos Theory in Dynamical Systems
• Digital Signal Processing / Digital Shortwave Radio

### Math 363 - Probability and Statistics I

This introduction focuses primarily on building a strong foundation in the basics probability theory, which in turn provides the knowledge needed for the statistical analysis methods taught in Math 463 (Probability and Statistics II).  The course covers basic probabilities using counting techniques and then moves on to random variables and distribution theory.

### Math 463 - Probability and Statistics II

The second course covers the most widely used statistical methods, including estimation with confidence intervals and analysis of variance.  There is also a modeling component via regression analysis, a unit on nonparametric techniques and a brief introduction to Bayesian methods.  Students in this course learn and use the R software package, which is one of the most commonly used statistical programming languages.

### Math 302 and 494-2 - Applied Project and Senior Capstone

The Applied Math major requires every student to be involved in a research project mentored by faculty.  Visit the Applied Project webpage for more information.

### Core and pure math courses

Visit the Math Courses webpage for more information on the core and pure math courses.