Courses Taught

Models are applied on a daily basis to provide insight into any number of current world problems. From diseases to government policy, modeling techniques are being used to predict outcomes and manage populations. With the advent of more computational power and data collection, novel model types and techniques for analysis are being derived. We will explore current models and techniques which are used across multiple disciplines. We will consider agent-based (or individual-based) modeling, and ordinary differential equation models with parameter estimation, along with additional topics. Students will have a chance to investigate using analytical and computational skills, that can be applied across a diversity of fields.

MATH 183 - Modeling and Simulation

This course is an introduction to mathematical models with deterministic and stochastic dynamics and with discrete and continuous time. Students will learn the mathematical analysis and numerical simulations for these models, and then present their results in both written and verbal forms. The models will be applied to various applications.

MATH 102- Differential Equations and Modeling

In this course, we will introduce some basic models including Lotka-Volterra (Predator-Prey) models, as well as some standard modeling techniques. The emphasis in the course will be placed on qualitative methods and the use of software to understand solutions. Eigenvalues and eigenvectors will be introduced to fully solve linear systems in the plane. Linear and non-linear systems of differential equations will be analyzed by classifying orbits near fixed-point solutions. Students may not receive credit for both MATH 102 and MATH 111.

MATH 060 - Linear Algebra

This course emphasizes vector spaces and linear transformations. Topics include linear independence, bases, nullity and rank of a linear transformation, The Dimension Theorem, the representation of linear transformations as matrices, eigenvalues and eigenvectors, and determinants. Additional topics may include inner product spaces and Gram-Schmidt orthogonalization.

MATH 052 - Introduction to Statistics

This course is meant to give a liberal arts student a sense of statistical theory and practice. It will emphasize the use and interpretation of statistics, with applications to both the natural and social sciences. Topics will include: collection and summarizing of data; measures of central tendency and dispersion; probability; binomial and normal distributions; confidence intervals and hypothesis testing; linear regression; ANOVA methods; topics in non-parametric statistics; and discussion and interpretation of statistical fallacies and misuses.

MATH 032 - Calculus III

This is the third course of a standard three-course sequence in calculus. The course covers calculus of multivariable and vector-valued functions. Topics include partial derivatives, the gradient, Lagrange multipliers, multiple integrals, change of variables, parameterized curves and surfaces, vector fields, line integrals, flux integrals, Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem.

MATH 030 - Calculus I

MATH 030 is the first course of a standard three course sequence in calculus. The topics covered include differentiation, integration, mean value theorem, transcendental functions, and trigonometric functions.

MATH 022 - Great Ideas in Modern Mathematics

Advances in mathematics have had far reaching influence across academia and society. A mathematical approach to problem solving is critical in the ever increasingly technological world in which we live. In this class we will study some of the most important results and ideas in modern mathematics. Topics will include the infinite and countability; knot theory and topology; dynamics, fractals, and chaos; symmetries; four-dimensional geometry. Additional topics may include cryptography; irrational and transcendental numbers; tilings of the plane; probability, expected value, and coincidence; and fair division. This course will satisfy the Scripps Math general education requirement. The course cannot be used to satisfy requirements in the math major or math minor.

CORE III - Histories of the Present - Living in a World of Numbers

In an age when we are bombarded with numbers, it is important to explore what stories are being told and how the numbers we observe are being formulated. We will investigate the interdisciplinary nature of dealing with numbers, considering a variety of disciplines and applications to life. Topics we will explore include social justice, journalism, disease outbreaks, politics, and more. Students will be encouraged to choose a field which interests them, then explore the field's use of numbers to communicate findings. Together we will examine various uses of numbers, looking for similarities and differences. Students will learn some basic analysis tools used across many disciplines, allowing students to understand presented results. Additionally, students will learn about different basic methods to create their own numbers, models, and analyses. With these skills students will then formulate their own findings, creating their own interdisciplinary work.

Courses at the University of Tennessee, Knoxville

MATH 411 - Mathematical Modeling

Construction and analysis of mathematical models used in science and industry. Projects emphasized. Writing-emphasis course.

MATH 151- Mathematics for the Life Sciences I

For students majoring in the life sciences. Does not serve as a prerequisite for 231 or 241. Topics include descriptive statistics, linear regression, discrete probability, matrix algebra, difference equations, calculus, and differential equations. Emphasis on applications in the life sciences. Includes computer projects.

MATH 241 - Calculus III

Calculus of functions in two or more dimensions. Includes solid analytic geometry, partial differentiation, multiple integration, and selected topics in vector calculus.

Courses at the University of Nebraska-Lincoln

MATH 208 - Calculus III

Vectors and surfaces, parametric equations and motion, functions of several variables, partial differentiation, maximum-minimum, Lagrange multipliers, multiple integration, vector fields, path integrals, Green's Theorem, and applications.

MATH 203- Contemporary Mathematics

Applications of quantitative reasoning and methods to problems and decision making in the areas of management, statistics, and social choice. Includes networks, critical paths, linear programming, sampling, central tendency, inference, voting methods, power index, game theory, and fair division problems.

MATH 103 - College Algebra and Trigonometry

First and second degree equations and inequalities, absolute value, functions, polynomial and rational functions, exponential and logarithmic functions, trigonometric functions and identities, laws of sines and cosines, applications, polar coordinates, systems of equations, graphing, conic sections.

MATH 101 - College Algebra

Real numbers, exponents, factoring, linear and quadratic equations, absolute value, inequalities, functions, graphing, polynomial and rational functions, exponential and logarithmic functions, system of equations.

MATH 107 - Calculus II - Teaching Assistant

Integration theory; techniques of integration; applications of definite integrals; series, Taylor series, vectors, cross and dot products, lines and planes, space curves.

NebraskaMath - Teaching Assistant

MATH 809: Math for High School Teachers II, Using Math to Understand Our World

This course is designed around a series of projects in which students examine the mathematics underlying several socially-relevant questions which arise in a variety of academic disciplines (i.e. real-world problems, such as how to use mathematics to understand the spread of a disease). Students learn to extract the mathematics out of the problem in order to construct models to describe them. The models are then analyzed using skills developed in this or previous mathematics courses. Note: this course is a high school version of Math 807T: Using Math to Understand our World, and is not appropriate for those who have already taken Math 807T.

MATH 802P: Geometry, Measurement and Algebraic Thinking for K-3 Math Specialists

This course builds on the mathematics studied in MATH 800P and 801P and extends teachers’ mathematical knowledge by considering how concepts studied in the K-3 curriculum lay a foundation for abstract thinking in grades 4 and beyond. The first week focuses on a study of fractions, and the second week emphasizes geometry topics. This is typically the fifth course in the Primarily Math sequence.

MATH 801P: Geometry, Measurement and Algebraic Thinking for K-3 Math Specialists

This course promotes a deep understanding of geometry, measurement and algebraic thinking and its role in the K-3 mathematics curriculum. Emphasis is placed on mathematical argument related to geometric relationships, measurement, spatial reasoning, patterns, relations and functions. This is typically the second course in the Primarily Math sequence.

MATH 800P: Number and Operation for K-3 Math Specialist

This course strengthens teachers’ conceptual knowledge of number and operation in the K-3 mathematics curriculum and connects the intuitive mathematical understandings that children bring to school with an understanding of place value in the K-3 curriculum. The significance of base 10 in our place value system, along with its role in arithmetic operations and their properties, is a major emphasis of the course. This is typically the first course in the Primarily Math sequence.