# SUMMARY

Below is just a small sample of courses you’ll take as a Mathematics major at Jessup. This list is not a guide for course selection. It was created to give you a peek at the program’s academic offerings. For official program requirements, please see the current course catalog.

### Major Courses (9 units)

Fundamentals of calculus including functions, limits and continuity, differentiation, and integration.

In this calculus-based physics course, students are introduced to foundational concepts of physics using trigonometric and differentiation techniques. Topics include Newtonian mechanics, conservation of energy and momentum, and introductory thermodynamics. Laboratory exercises provide students with hands-on application of principles discussed in lecture. Topics include Newtonian mechanics, conservation of energy and momentum, and introductory thermodynamics.

### Core Courses (41 units)

Continues in topics of calculus including integrals and transcendental functions, techniques of integration, first order differential equations, infinite sequence and series, and parametric equations.

Linear systems, matrices, vectors and vector spaces, linear transformations, inner products, norms, eigenvalues and eigenvectors, orthogonality and applications. Provides a foundation for many areas of study in mathematics, computer science, engineering, and science.

An introduction into the theory, methods of solution, and selected applications of ordinary differential equations. Topics include first order equations, second order linear equations with constant coefficients, numerical analysis of ordinary differential equations, Laplace Transforms, series solutions, and systems of differential equations.

The differential and integral calculus of Euclidean 2- and 3-space are developed in this course. The treatment of real-valued functions of two or more real variables and their partial derivatives are also included. Functions that associate vectors with real numbers are studied. Applications to geometry, physics, and engineering are covered. The course provides a brief study of both double and triple integrals for functions of two or three variables. A laboratory approach is used in graphing two- and three-space group activities and projects.

Designed to acquaint the student with the widely known theorem, conjectures, unsolved problems and proofs of number theory. Topics may include divisibility, primes, congruencies, Diophantine equations and arithmetic functions. In addition, the history of mathematics, from the beginning of recorded civilization to the present, will be covered.

A practical introduction to formal mathematical proof emphasizing preparation for advanced study in mathematics. Special attention is paid to reading and building proofs using standard forms and models within the context of specific examples.

Discrete and continuous probability including conditional probability; independence and Bayes’ Theorem; expected value, variance, and moments of a random variable; distributions, methods for identifying distributions, and the Central Limit Theorem; and statistical hypothesis testing, errors, correlation, regression equations, and analysis of variance.

An introduction to the theory of groups, rings, and fields. Topics in group theory include Lagrange’s theorem, quotient groups, applications to geometry, public key cryptography, and finitely generated abelian groups. Topics in ring theory include ideals, quotient rings, and polynomial rings. Topics in field theory include field extensions, Euclidean construction problems, cubic and quartic equations.

An advanced study of the real-number system, functions, sequences, series, continuity, differentiation, integrality, and convergence by use of the limit concept and basic axioms of the real number field.

A capstone seminar in which faculty members, some guests, and the students give lectures on topics of general interest in mathematics. Students compile their senior portfolio, which encapsulates their learning experience in the mathematics program.

Computing has profoundly changed the world. However, just using a computer is only a small part of the picture. Real empowerment comes when one learns how to program computers, to translate ideas into code. This course teaches basic Python programming — control structures, simple data types, and data structures. We use Turtle Graphics to build fun programs that illustrate fundamental ideas in programming.

**MATH305 | Discrete Mathematics **Covers a collection of topics useful to mathematics and computer science majors. The unifying factor is that the topics deal mainly with finite collections of mathematical objects (graphs, trees, finite state machines, etc.). Also includes examination of sets, logic, Boolean algebras, proof techniques, algorithm analysis, and recursion.

**MATH350 | Modern Geometry **Presents the foundation of Euclidean geometry and the development of non-Euclidean geometry from its Euclidean roots. The main structure is Hilbert’s axiomatic approach.

**MATH460 | Complex Analysis **An introduction to complex analysis. Topics to be covered may include complex numbers, analytic functions, elementary functions, integrals, Laurent series, residues, poles, and applications of residues.

**MATH462 | Numerical Analysis **Numerical methods for solving systems of linear equations, finding roots and fixed points, approximating data and functions, numerical integration, finding solutions to differential equations.

**MATH499 | Topics in Mathematics**

No course description available.