Omnia in mensura et numero et pondere disposuisti.

Thou hast ordered all things in measure, and number, and weight.

—Wisdom 11:21

But when we begin to look above ourselves again, we find that numbers transcend our minds and remain fixed in the truth itself.

—St. Augustine, On Free Choice of the Will

The Mathematics Major and Minor are great ways to enhance your education, increase your set of skills, learn interesting mathematics, and see how it’s used in your field. From a professional standpoint a Mathematics Major or Minor can help your degree stand out to prospective employers. It will allow you to work in many computer-related jobs. Anyone considering entering the teaching profession will find their employment prospects are proportional to the number of mathematics courses taken.

Math Major Sample Course Plan |

The Mathematics & Natural Science Department offers a major that is in accord with the standards of the profession. A graduate will be able to enter into graduate programs throughout the country or pursue any of the innumerable careers available to graduates with undergraduate degrees in Mathematics.

The Department adheres to a realist philosophy of mathematics, that originated with Aristotle and has been develop by such scholars as Aquinas, Maritan, Apostle, and Franklin. Our graduates have a unique ability to carefully define the concepts used in Mathematics by means of a “non-arbitrary reference to real quantity” (to use a phrase from Benedict Ashley’s book *The Way toward Wisdom*). Moreover our very strong core curriculum gives our majors intellectual cross-training in the humanities (to use a phrase from Thomas Cech’s article *Science at Liberal Arts College: A Better Education*) which hones their ability to study Mathematics.

Mathematics has always been considered to be an essential part of a liberal education: the unique simplicity of its subject matter allows its students to practice logical thought in a realm in which truth is readily apparent; and its instrumental use opens insights into the nature of physical reality that are not apparent by other means. Christendom offers a variety of core courses that cover a broad range of mathematics. Any of the courses in mathematics fulfills the one course requirement of the core curriculum. In all courses the student is helped to understand the place of mathematics in man’s understanding of the world around him.

**Requirements for the Mathematics Major**

Ten upper-level courses in Mathematics (34 semester hours) are required of majors – eight designated and two electives. The designated courses are:

MATH 201 Calculus I (4 cr.)

MATH 302 Calculus II (4 cr.)

MATH 303 Calculus III

MATH 304 Differential Equations

MATH 351 Fundamentals of Advanced Mathematics

MATH 353 Linear Algebra (4 cr.)

MATH 401 Real Analysis (4 cr.)

MATH 402 Abstract Algebra

MATH 509 Senior Seminar (1 cr.) (Fall)

MATH 512 Senior Thesis (3 cr.) (Spring)SCIE 204 & SCIE 204L General Physics I & Lab (4 cr.)

SCIE 205 & SCIE 205L General Physics II & Lab (4 cr.)

To complete the mathematics major, students must take at least **two** additional mathematics elective courses numbered 300 or above.

Note: MATH 201 satisfies the core requirement for mathematics and SCIE 204 satisfies the core

requirement for natural science. A course grade of at least C- is necessary in a math course to

fulfill the department’s requirements for a major or minor, and students must demonstrate competency in physics by receiving a passing grade (D or above) in SCIE 204 and SCIE 205, along with their lab components.

A **minor in mathematics** may be obtained by completing the calculus sequence (MATH

201, MATH 302, MATH 303) and three additional math courses numbered 300 or above. (A General Physics course with lab may be substituted for one of the latter if a grade of at least C- is earned and it is not used to satisfy the core science requirement. MATH 201 satisfies the core requirement for mathematics).

## Foundational Curriculum

**MATH 101 Introduction to Mathematical Thought** This course focuses on our changing conception of the notion of extension leading to the rise of the various branches of mathematics and the application of mathematics to describing the universe.

**MATH 102 The Integers** Explores the fundamental properties of the integers. Topics include: natural numbers, integers, rational numbers, irrational numbers, prime numbers, the division algorithm, prime factorization, modular arithmetic, and RSA encryption. *This course has no prerequisites and satisfies the College core requirement in mathematics.* (3 credits)

**MATH 103 Euclidean Geometry** A study of selected books from Euclid’s *Elements*. Topics covered include plane geometry, theory of proportions, and classical arithmetic. Students will also investigate the relation between mathematics and more comprehensive philosophical issues.

**MATH 150 Introduction to Statistics** The purpose of the course is to introduce the student to the ideas and concepts of statistics and the statistical models used for the decision making in different areas of life. Topics covered include description of sets of data, elementary probability, discrete and continuous random variables, the binomial and normal random variables, confidence intervals and hypothesis testing.

**MATH 153 Computer Programming** An introduction to problem solving methods and algorithm development. Programming in a high-level language including how to design, code, debug, and document programs using techniques of good programming style.

**MATH 201 Calculus I** Basic course in differential calculus with an introduction to integration. Topics covered include limits and continuity, the notion of the derivative, techniques of differentiation, the definite and indefinite integral, and the fundamental theorem of calculus. *Prerequisite: Precalculus or permission of the instructor.* (4 credit hrs)

**MATH 294 Principles of Computer Science **Introduction to basic concepts in computer science, including computing theory, programming languages, algorithms, operating systems, artificial intelligence, and robotics. Incorporates student projects and presentations. *There are no prerequisites for this course, and no programming experience is necessary. The course fulfills the College core requirement in mathematics. * (3 credits)

**Advanced Courses**

**MATH 302 Calculus II** Continuation of MATH 201. Topics include inverse functions, techniques of integration, sequences and series, the conic sections, and the polar coordinate system. *Prerequisite: At least a C- in MATH 201 or equivalent*. **Required of all majors** (4 credit hrs)

**MATH 303 Calculus III** Continuation of MATH 302. Topics include limits and continuity in three dimensions, vectors, vector functions, partial derivatives, multiple integrals, the notions of gradient, divergence, and curl, and the basic theorems of vector calculus. **Required of all majors.**

**MATH 304 Differential Equations** This course covers the basic techniques for solution of ordinary differential equations. Topics include first and second order linear equations, non-linear equations, systems of linear equations, the fundamental matrix, series solutions of differential equations, numerical methods and introduction to stability theory. **Required of all majors**.

**MATH 332 Probability and Statistics** Introduction to the basic notions of probability and statistics. Topics covered include combinatorial probability, distribution functions, discrete and continuous random variables and distributions, conditional probability, the central limit theorem, and typical applications in reliability, sampling, and estimation theory including Bayesian Inference.

**MATH 351 Fundamentals of Advanced Mathematics** This course introduces the student to modern mathematical structures that are not present in introductory mathematics courses and aims to develop a student’s skill in composing and writing proofs. Topics include elementary logic, methods of proof, philosophies of mathematics, set theory, functions and relations, cardinality, and elementary number theory. **Required of all majors**.

**MATH 353 Linear Algebra** Introduction to the concepts and theory of linear algebra. Topics include vector spaces, bases, matrices, linear mappings, scalar products and orthogonality, determinants, bilinear forms, eigenvalues and eigenvectors, diagonalization, the spectral theorem and the SVD decomposition. **Required of all majors** (4 credit hrs)

**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 403 Foundations of Geometry** Exploration of axiomatic systems of geometry, beginning with the neutral geometry of Euclid’s *Elements*, in contrast to that of spherical and taxicab geometries, which motivates Hilbert’s axiomatization of Euclidean geometry. Further topics include independence, consistency, and completeness of axiomatic systems of geometry, Euclid’s geometry with the parallel postulate, and hyperbolic geometry. *Prerequisite: Calculus II and MATH 351.*

**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. *

**MATH 462 Combinatorics **Study of questions concerning enumeration and arrangements of objects. Topics include the Pigeonhole Principle, the Principle of Inclusion/Exclusion, recurrence relations, generating functions, graph theory, and other algebraic counting techniques.* Prerequisite: MATH 351*

**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.

## Natural Science

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.

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.

## Foundational Curriculum

**SCIE 102 Introduction to Scientific Thought** This course focuses on our changing conception of the universe, the rise of the various physical sciences, and the development of the scientific method.

**SCIE 104 Descriptive Astronomy** A study of astronomy beginning with its historical roots and leading to our current understanding of the universe. Major developments are placed in their historical and philosophic context by appropriate study of original works. Students also study the night sky and methods used by astronomers, by means of activities outside the classroom.

**SCIE 192 Introduction to Biology** Introduction to fundamental characteristics of living matter from the molecular level to the ecological community, with emphasis on general biological principles. Introduces basic chemistry of life, along with the diversity, structure, and function of living organisms. *This course has no prerequisites and satisfies the College core requirement in science. There is no lab component. This course is not intended as a prerequisite for further study in the health sciences*. (3 credits)

## Advanced Courses

**SCIE 204 General Physics I **Introduction to mechanics and thermodynamics. Topics in mechanics include Newton’s laws of motion; physical concepts of mass, velocity, acceleration, motion, energy, and work; conservation laws, oscillatory motion and application of mechanics to simple problems. *Co-requisite: MATH 201 or permission of the instructor.*

**SCIE 205 General Physics II **Continuation of SCIE 204. Topics include fluids, thermodynamics, geometric optics, electricity and magnetism. *Prerequisite: SCIE 204 or permission of the instructor.*

**SCIE 306 General Physics III Continuation of SCIE 205.** Topics include wave motion, the nature of light and optical phenomena, special relativity, atomic and nuclear physics. *Prerequisite: SCIE 205 or permission of the instructor*.

**SCIE 204L-205L, 306 L Laboratory for General Physics I, II & III** Students conduct experiments illustrating the physics discussed in the classroom and learn and practice principles of data acquisition and data analysis. (Required with SCIE 204-205, 306) (1 credit hour per

semester)

**SCIE 391 and SCIE 391L Anatomy and Physiology I.** This course is for those students intending to pursue further study in the health sciences. It is the first course in a two-semester sequence that satisfies an Anatomy and Physiology prerequisite for many health science programs and medical schools. Students should be prepared to commit to both semesters*. Lab component is required. Prerequisites: High school biology. * (4 credits)

**SCIE 392 and SCIE 392L Anatomy and Physiology II.** This course is for those students intending to pursue further study in the health sciences. It is the second course in a two-semester sequence that satisfies an Anatomy and Physiology prerequisite for many health science programs and medical schools. *Lab component is required. Prerequisites: SCIE 391 and SCIE 391L. *(4 credits)

**SCIE/PHIL 420 Philosophical Issues in Modern Science** The aim of the course is to familiarize students with the basic scientific discoveries of the 20th century regarding the origin of the universe, the existence of a creator, and the immaterial nature of man and how they relate to the Thomistic understanding of the same issues. Topics include “Big Bang” cosmology, anthropic coincidences, human mind and the computer, quantum mechanics and reality, and philosophical issues in contemporary evolutionary biology.

**SCIE 490-99 Special Topics or Directed Studies in Physics** A topic chosen according to the interests of the students and the instructor, such as Mechanics, Continuum Mechanics Thermodynamics, Electromagnetism and Quantum Theory.