Advanced Courses

MATH 374 Modal Logic An introduction to the structure and techniques of the logic of necessity and possibility from an axiomatic standpoint. Topics include sentential modal logic and the systems T, S4, and kS5; validity; decision procedures and completeness; and quantified modal logic. Prerequisite: MATH 373 or permission of the instructor.

MATH 375 Mathematical Logic Development of the principal topics of mathematical logic. Through an axiomatic approach, the course treats the foundations of mathematics and illustrates the power as well as the limitations of mathematical reasoning. Topics include propositional and quantificational logic from an axiomatic standpoint; formal number theory; recursive functions, Gödel’s theorem, and recursive undecidability; and an introduction to axiomatic set theory. Prerequisite: MATH 373 or permission of the instructor.

MATH 401 Real Analysis This course is a rigorous introduction to the fundamental theorems of the introductory calculus courses. It aims to develop in the student a sense of the unity of mathematics and further expose him to the importance of rigorous proof in mathematics. Topics include: the real number system, sequences and limits, continuity of functions, the derivative, and the Riemann integral. Required of all majors. (4 credit hrs).

MATH 402 Abstract Algebra This course is an introduction to the ideas of modern algebra which enables one to reinterpret the results of classical algebra, giving them a greater unity and generality. Topics include: equivalence relations, functions, properties of the integers, groups, rings, integral domains, ideals, and fields. Required of all majors.

MATH 409 Number Theory An algebraic and historical approach to the theory of numbers. Topics include: the natural numbers and their properties, the Euclidean Division Algorithm, unique prime factorization, modular arithmetic, RSA Encryption, the Gaussian integers and other quadratic integer rings, and the Law of Quadratic Reciprocity. Prerequisite: MATH 351. Counts toward the mathematics major. (3 credits)

MATH 490-99 Special Topics or Directed Studies in Mathematics A topic chosen according to the interests of the students and the instructor, such as: applied mathematics, game theory, discrete mathematics, number theory, philosophy of mathematics, history of mathematics.

MATH 509 Senior Seminar A seminar on topics in mathematics to be determined by the instructor in consultation with the students. The student gains experience in learning the development of a topic, research methods, organizing and writing a mathematical paper. (1 credit hr)

Math 512 Senior Thesis Direction of the students with his senior thesis, a major scholarly paper on a mathematical topic of his interest. The student receives instruction and individual assistance in development of a topic, research methods, organizing and writing a mathematical paper.

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Natural Science Courses

Philosophy [i.e. natural philosophy] is written in this grand book — I mean the Universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics…

– Galileo Galilei, Il Saggiatore

It is plain then that nature is a cause, a cause that operates for a purpose.

– Aristotle, Physics Book II

In his Physics Aristotle laid the foundations for a philosophical knowledge of the natural, changeable world, but he was unable to fully develop what scientists, beginning with Galileo and Newton, have been able to exploit—the potential of Mathematics to describe and systematize our knowledge of the natural world.

Natural Science Core

To fulfill the core requirement in Natural Science students must take one science course, usually in the freshman year. Through the broader context of a Thomistic frame of reference, the core science courses show the student how modern science fits into the hierarchy of human knowledge and highlight the valid insights of both the Aristotelian and modern traditions. The College offers one introductory course dealing with the historical and philosophical principles of science, and another concentrating on the first quantified knowledge of the natural world, Descriptive Astronomy. Other core courses are offered as available. The more advanced science courses deepen the student’s understanding of the nature of physical reality and address some philosophical questions pertaining to the study of the natural sciences. Any of the science courses satisfies the core requirement in science.

Requirements for the Physics Minor

Five courses in Physics (18 semester hours) are required of minors – three designated and two electives 300 level or above. The designated courses are: SCIE 204 – 204L General Physics I & Lab SCIE 205 – 205L General Physics II & Lab SCIE 306 - 306L General Physics III & Lab

A mathematics major may complete the physics minor by taking a further 10 credits of physics beyond the requirements for the math major. A course grade of at least C- is necessary for a course to fulfill the department’s requirements for a minor.

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