# Courses

## Graduate:

### Optimization

**Intro to Optimization (FIT)**

An applied treatment of modeling, analysis and solution of deterministic (e.g., nonprobabilistic) problems. Topics include model formulation, linear programming, network flow, discrete optimization and dynamic programming.

**Optimization Theory (UCF)**

Lagrangian function and duality, Kuhn-Tucker’ theorem, quadratic programming and Wolfe’s theorem, Griffith and Stewart’s method, search methods for unconstrained optimization.

### Mathematics

**Mathematical Statistics 1 (FIT)**

Covers discrete and continuous random variables, generating and moment generating functions, multivariate distributions, covariance and correlation, sums of independent random variables, conditional expectation, Central Limit Theorem, Markov and Chebyshev inequalities and the Law of Large Numbers.

### Financial Mathematics

**Financial Mathematics I (UCF)**

Single-period market, arbitrage, risk-neutral probability measure, market completeness, mean-variance portfolio analysis, multi-period market, binomial tree, contingent claim pricing.

### Business

**Small Business Consulting (UCF)**

This is a highly experiential course where students are assigned to teams that complete consulting projects for local small businesses.

## Undergraduate:

### Mathematics

**Calculus 1 (EFSC)**

Functions and graphs, limits and continuity, derivatives of algebraic and trigonometric functions, chain rule; applications to maxima and minima, and to related rates. Exponential logarithmic, circular and hyperbolic functions: their inverses, derivatives and integrals.

**Calculus 2 (EFSC)**

Integration and applications of integration, further techniques of integration, improper integrals, limits, l’Hospital’s rule, sequences and series, numerical methods, polar coordinates and introductory differential equations.

**Calculus 3 (EFSC)**

Cylindrical and spherical coordinates, vectors, functions of several variables, partial derivatives and extrema, multiple integral, vector integral calculus.

**Differential Equations/Linear Algebra (FIT)**

First-order differential equations, linear differential equations with constant coefficients, first-order systems of differential equations with constant coefficients, numerical methods, Laplace transforms, series solutions, algebraic systems of equations, matrices, determinants, vector spaces, eigenvalues and eigenvectors.

**Discrete Mathematics (FIT)**

Formulation of precise definitions and their negations using propositional and predicate logic; argument analysis and proof techniques including induction; number theory; and sets, relations, functions, directed graphs and elementary counting arguments.

**Introduction to Linear Algebra (FIT)**

Includes vectors and matrices, linear equations, vector spaces and subspaces, orthogonality, determinants, eigenvalues and eigenvectors, and linear transformations. Introduces students to solution and manipulation of matrix equations using a standard package of mathematical software.

**Introduction to Partial Differential Equations and Applications (FIT)**

Includes heat, wave and Laplace equations, initial and boundary value problems of mathematical physics and Fourier series. Also covers Dirichlet problem and potential theory, Dalambert’s solutions for wave equation, Fourier and Laplace transforms, and Poisson integral formula. Also includes PDEs in higher dimensions and special functions of mathematical physics.

**Introductory Analysis (FIT)**

Rigorous treatment of calculus. Includes sequences and series of real numbers, limits of functions, topology of the real line, continuous functions, uniform continuity, differentiation, Riemann integration, sequences and series of functions, Taylor’s theorem; uniform convergence and Fourier series.

**Models in Applied Mathematics (FIT)**

Allows students to formulate and construct mathematical models that are useful in engineering, physical sciences, biological sciences, environmental studies and social sciences.

**Numerical Analysis (FIT)**

Introduces numerical methods for solving equations in one variable, polynomial approximation, interpolation, numerical differentiation and integration, initial-value problems for ODE and direct methods for solving linear systems.

**Probability and Statistics (FIT)**

Random variables, expectations, sampling and estimation of parameters, normal and other distributions and central-limit theorem, tests of hypothesis, linear regression and design experiments.

### Software Development

**Introduction to Software Development With C++ (FIT)**

Focuses on the stages of software development and practice in using C++. Includes requirement analysis, design and implementation methods, testing procedures and an introduction to certifying program correctness.

**Introduction to Software Development With FORTRAN (FIT)**

Focuses on the stages of software development and practice in using Fortran. Includes requirement analysis, design and implementation methods, testing procedures and an introduction to certifying program correctness.

### Economics

**Principles of Economics 2 (Microeconomics) (EFSC)**

Microeconomics: introduction covering theory and practical applications. Topics include economic growth, resource allocation, economics of the firm and international economics.

### Physics

**Physics 1 (EFSC)**

Includes vectors; mechanics of particles; Newton’s laws of motion; work, energy and power; impulse and momentum; conservation laws; mechanics of rigid bodies, rotation, equilibrium; fluids, heat and thermodynamics; and periodic motion.

**Physics 1 Laboratory (EFSC)**

Experiments to elucidate concepts and relationships presented in Physics 1, to develop understanding of the inductive approach and the significance of a physical measurement, and to provide some practice in experimental techniques and methods.

**Physics 2 (EFSC)**

Includes electricity and magnetism, Coulomb’s law, electric fields, potential capacitance, resistance, DC circuits, magnetic fields, fields due to currents, induction, magnetic properties; and wave motion, vibration and sound, interference and diffraction.

**Physics 2 Laboratory (EFSC)**

Experiments to elucidate concepts and relationships presented in Physics 1, to develop understanding of the inductive approach and the significance of a physical measurement, and to provide some practice in experimental techniques and methods.

**Physical Mechanics (FIT)**

Fundamental principles of mechanics and applications in physics. Includes Newton’s Laws, equations of motion, types of forces, conservation laws, potential functions, Euler and Lagrange equations and Hamilton’s Principle.

**Modern Physics (FIT)**

Includes quantum mechanics of atoms, molecules, nuclei, solids and fundamental particles. Planck and de Broglie’s laws, the Bohr model of hydrogen, elementary examples of Schroedinger’s equation, relativity, elementary particles and symmetry, quantum electrodynamics and chromodynamics.

### STEM Education

**Apprenticeship in Secondary Mathematics and Science Teaching (FIT)**

Serves as the capstone course for students seeking teaching certification. Includes exposure and fieldwork in secondary school classrooms. Requires oversight by a school-based teach and intensive interaction with course instructor. Includes teaching responsibilities for three hours per day over term, using plan developed with teacher/mentor.

**Content Area Reading (FIT)**

Provides maximum interaction and strategies needed by teachers of grades 6-12 to teach their students how to succeed across the curriculum with reading.

**Educational Strategies for ESOL (FIT)**

Provides the requisite information and background needed to identify limited-English proficient (LEP) K-12 learners and equips them with appropriate instructional strategies to meet all student learning needs.

**Project-Based Instruction in Mathematics and Science Education (FIT)**

Covers project-based instruction (PBI) as a mathematics and science teaching method. Requires teams to develop and teach a project-based unit of instruction in a secondary school setting. Focuses on the tenets, planning and implementation of PBI, national and state curriculum and instruction standards, and how children learn mathematics and science.

**Research Methods (FIT)**

Provides the tools needed to solve scientific problems and the opportunity to use them in a laboratory setting. Covers how scientists communicate with each other through peer-reviewed literature. Includes how scientists develop new knowledge and insights such as those eventually used in textbooks and taught in conventional classes.

**Disclaimer: the text on this page does not belong to me nor was it written by me. The course descriptions were taken from EFSC’s, FIT’s, and UCF’s course catalogs.**