Introduction to complex algebra. Systems of linear equations, Gaussian elimination. Vector spaces and their extension to complex case, linear dependence/independence, bases. Matrix algebra, determinant, inverse, factorization. Eigenvalue problem, diagonalization, quadratic forms. Linear approximation, curve fitting. Linear constant coefficient difference equations and the z-transform. Linear constant coefficient differential equations and the Laplace transform. System of linear differential equations. Credit units: 4 ECTS Credit units: 6.5, Prerequisite: MATH 102 or MATH 112 or MATH 114.

Differential equations of first order, separable equations. Linear differential equations of higher order, homogeneous and nonhomogeneous equations. Numerical solutions of differential equations. Runge-Kutta method, boundary-value problems. Differential calculus of functions of several variables, Taylor series approximation. Jacobians, maxima and minima of a function, Method of Lagrange multipliers. Functions of a complex variable, differential complex calculus. Complex integration, Cauchy's theorem. Complex series, Taylor and Laurent series. Residue theorem. Credit units: 4 ECTS Credit units: 6.5, Prerequisite: MATH 241.

Fundamental principles of counting, including rules of sums and product, permutations and combinations. Fundamentals of logic and integers, including mathematical induction, recursive definitions, prime numbers, greatest common divisor, Cartesian products and relations, pigeonhole principle, partial orders, equivalence relations and partitions. The principle of inclusion and exclusion. Sums and recurrence relations: first and second order linear recurrence relations, finite and infinite calculus, infinite sums. Integer functions including floor and ceiling applications and recurrences, and the modulo operation. Generating functions including the method of generating functions for solving recurrences and exponential generating functions. Introduction to graph theory including graph isomorphism, Euler tours, Hamiltonian paths and cycles, planar graphs, and graph coloring. Credit units: 3 ECTS Credit units: 5, Prerequisite: MATH 101 or MATH 111 or MATH 113.

Introduction to methods of proof, sets and functions, metric spaces, functions on metric spaces, differential and integral equations, fundamentals of linear algebra. Credit units: 3 ECTS Credit units: 5.

A minimum of four weeks summer practice in a manufacturing organization; observation of organization in its original settings; written report. Credit units: None ECTS Credit units: 7, Prerequisite: IE 271 or IE 272.

Introduction to matrices. Fields and vector spaces, linear transformations, change of basis. Linear equations, existence and classification of solutions, Gaussian elimination and LU decomposition. Characteristic equation of a matrix: eigenvalues, eigenvectors and the Jordan form. Numerical techniques for computing eigenvalues and eigenvectors. Inner product spaces, quadratic forms. Credit units: 3 ECTS Credit units: 5.

Systems of linear equations, Elimination methods, matrices and matrix operations. Invertible matrices, determinants. Vector spaces, basis and dimension. Inner product spaces, orthogonality, orthogonal basis, rank and nullity. Eigenvalues and eigenvectors, systems of differential equations, matrix-valued functions. First and second order linear differential equations. n-th order linear differential equations, method of undetermined coefficient, variation of parameters. Credit units: 4 ECTS Credit units: 6.5, Prerequisite: MATH 102 or MATH 106.

Functions. Limits and Continuity. Tangent lines and derivatives. Chain rule. Implicit differentiation. Inverse functions. Related rates. Linear approximations. Extreme values. Mean Value Theorem and its applications. Sketching graphs. Indeterminate forms and L Hospital s rules. Definite integral. Fundamental Theorem of Calculus. Substitution. Areas between curves. Formal definition of natural logarithm function. Techniques of integration. Improper integrals. Arc length. Volumes and surface areas of solids of revolution. Parametric plane curves. Polar coordinates. Arc length in polar coordinates.

First order equations and various applications. Higher order linear differential equations. Power series solutions: The Laplace transform: solution of initial value problems. Systems of linear differential equations: Introduction Partial Differential Equations.