# Courses

The Applied Math major requires the following core math courses in addition to the Calculus sequence (Calculus I, Calculus II, Vector Calculus).

## MATH 245 - Linear Algebra

Linear algebra is central to both pure and applied mathematics.  It studies the algebraic properties of linear equations in multiple variables.  Applications are found in nearly every branch of science, especially in engineering, physics, the natural sciences computer science and the social sciences (particularly in economics).  Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations.  Nonlinear mathematical models are often approximated by linear ones in order to use the well-developed techniques of linear algebra.  This course studies the structure of vector spaces, operations with vectors and matrices, linear transformations, and the concepts of eigenvalues, eigenvectors and orthogonality.  The topics and techniques studied can be further generalized and extended to abstract algebra, and are foundational to topics encountered in differential equations and mathematical modeling.

## 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

Mathematical Modeling (MATH 364) focuses on various techniques used to translate a real life phenomenon into a mathematical framework (model).  This course covers a wide variety of models: spatial and time-dependent, discrete and continuous, deterministic and stochastic, and various the mathematical tools (difference equations, differential equations, Markov chains).  These modeling techniques are illustrated through several examples taken from different fields of application (engineering, economics, ecology, pharmacology, and biology).

## 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 courses include:

• Numerical Analysis: the study of algorithms that use numerical approximation to solve mathematical problems that cannot be solved algebraically.  These algorithms are at the core of any method involving a computer such as rootfinding, interpolation, numerical differentiation, integration and methods for solving differential equations.
• Study and analysis of the CWS model, a compartment dynamical system model using a nonlinear system of ODEs to model the distribution of Amyloid-beta proteins in the brain.  This model is used for the prevention and treatment of Alzheimer's disease.
• Digital Signal Processing / Digital Shortwave Radio
• Computational Epidemiology
• Agricultural Modeling
• Cryptography
• Structural Mechanics applied to Earthquake-Resistant Structures
• Chaos Theory in Dynamical Systems
• Partial Differential Equations

## 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 the second course.  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.

## MATH341 - Modern Algebra OR MATH 351 - Analysis

See the description in the course catalog.

## MATH 245 - Linear Algebra

Linear algebra is central to both pure and applied mathematics.  It studies the algebraic properties of linear equations in multiple variables.  Applications are found in nearly every branch of science, especially in engineering, physics, the natural sciences computer science and the social sciences (particularly in economics).  Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations.  Nonlinear mathematical models are often approximated by linear ones in order to use the well-developed techniques of linear algebra.  This course studies the structure of vector spaces, operations with vectors and matrices, linear transformations, and the concepts of eigenvalues, eigenvectors and orthogonality.  The topics and techniques studied can be further generalized and extended to abstract algebra, and are foundational to topics encountered in differential equations and mathematical modeling.

## 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

Mathematical Modeling (MATH 364) focuses on various techniques used to translate a real life phenomenon into a mathematical framework (model).  This course covers a wide variety of models: spatial and time-dependent, discrete and continuous, deterministic and stochastic, and various the mathematical tools (difference equations, differential equations, Markov chains).  These modeling techniques are illustrated through several examples taken from different fields of application (engineering, economics, ecology, pharmacology, and biology).

## 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 courses include:

• Numerical Analysis: the study of algorithms that use numerical approximation to solve mathematical problems that cannot be solved algebraically.  These algorithms are at the core of any method involving a computer such as rootfinding, interpolation, numerical differentiation, integration and methods for solving differential equations.
• Study and analysis of the CWS model, a compartment dynamical system model using a nonlinear system of ODEs to model the distribution of Amyloid-beta proteins in the brain.  This model is used for the prevention and treatment of Alzheimer's disease.
• Digital Signal Processing / Digital Shortwave Radio
• Computational Epidemiology
• Agricultural Modeling
• Cryptography
• Structural Mechanics applied to Earthquake-Resistant Structures
• Chaos Theory in Dynamical Systems
• Partial Differential Equations

## 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 the second course.  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.

## MATH341 - Modern Algebra OR MATH 351 - Analysis

See the description in the course catalog.