IStudies the development of differential calculus, starting with limits, continuity, and the definition of derivative. Emphasizes differentiation techniques and their applications.
IIIntegration theory and techniques with applications in science and engineering.
IIIStudies sequences and series, including convergence tests and Taylor polynomials and series, as well as the calculus of curves in the plane and space described in polar, parametric, or vector-valued form.
[IV]Introduction to the concepts and computation techniques of multivariable calculus, including partial derivative, the chain rule, double and triple integrals, vector fields, line integrals, surface integrals, Green's Theorem, Stokes' Theorem, and the Divergence Theorem.
Introduces linear algebra, including systems of linear equations, Gaussian elimination, matrices and matrix algebra, vector spaces, subspaces of Euclidean space, linear independence, bases and dimension, orthogonality, eigenvectors, and eigenvalues. Applications include data fitting and the method of least squares.
Introduces students to mathematical argument and to reading and writing proofs. Develops elementary set theory, examples of relations, functions and operations on functions, the principle of induction, counting techniques, elementary number theory, and combinatorics. Places strong emphasis on methods and practice of problem solving.
Covers concepts of probability and statistics; conditional probability, independence, random variable, and distribution functions; descriptive statistics, transformations, sampling errors, confidence intervals, least squares, and maximum likelihood; and exploratory data analysis and interactive computing.
This course focuses on developing career awareness and readiness as well as fostering community in the major. Topics include: mathematical writing and typesetting; mathematics and career presentations; diversity, equity, and inclusion challenges in the mathematical sciences; ethics in the mathematical sciences; introduction to mathematical software; career exploration and development of portfolios.
Introduction to methods of discrete mathematics, including topics from graph theory, network flows, and combinatorics. Emphasis on these tools to formulate models and solve problems arising in variety of applications, such as computer science, biology, and management science.
IIntroduction to group theory. Emphasizes examples, including cyclic, dihedral, and symmetric groups. Theoretical concepts include: Cosets and Lagrange's theorem; direct products; homomorphisms, normal subgroups, quotient groups, and the fundamental isomorphism theorems; orders and Cauchy's theorem; and the structure of finitely-generated abelian groups.
Introduces ordinary differential equations. Includes first-and second-order equations and Laplace transform.
IMethods and theory for numerically solving systems of equations, both linear and nonlinear. Topics include numerical error, stability and conditioning, root finding, direct and iterative methods for linear systems, linear least squares, eigenvalue problems, and nonlinear systems.
Maximize and minimize linear functions subject to constraints consisting of linear equations and inequalities. Define linear optimization models from problem description. Solve linear programming problems using the simplex method. Conduct duality and sensitivity analysis for linear programming.
IIntroduces real analysis, with a focus on the theoretical development of single-variable calculus, including topics from the following: Countable and uncountable sets, field axioms and completeness, topology of the real numbers, sequences and convergence, Cauchy sequences, monotone sequences, subsequences, limits of functions, continuity and uniform continuity, the derivative, Mean Value Theorem, L'Hospital's Rule, and Taylor's Theorem.
All course descriptions found on MyPlan