# Mathematics & Natural Science

Dr. Greg Townsend explains the vital role which Mathematics and Natural Science play in Christendom's core curriculum.

Omnia in mensura et numero et pondere disposuisti.

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

—Wisdom 11:21

Take away number in all things and all things perish.

Take calculation from the world and all is enveloped in dark ignorance, nor can he who does not know the way to reckon be distinguished from the rest of the animals.

—St. Isidore of Seville

The Mathematics Minor is a great way 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 Minor can help your degree stand out to prospective employers. It will allow you to work in many computer-related jobs. It is also good preparation if you plan to take the *Engineer in Training* exam.
Anyone considering entering the teaching profession will find their employment prospects are proportional to the number of mathematics courses taken.

Math Minor Credit Worksheet | Math Minor Schedule |

The tradition of Aristotle and St. Thomas sees that mathematics is the science of abstract quantity, a science which arises directly or by analogy from a consideration of quantity as found in the physical world, which has the fundamental property of “having part outside of part.” The two branches of mathematics, Geometry and Algebra, arise out of the observation that the parts can have common boundaries (continuous quantity) or no common boundary (discrete quantity).

This discipline, delightful to know in itself, is also 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.

Christendom offers one elementary course in Euclidean Geometry and another in the historical development and philosophical aspects of mathematics. Both courses help the student understand the place of mathematics in man’s understanding of the world around him. College Algebra and several more advanced courses deepen a student’s mathematical knowledge, as well as preparing him for programs in business, engineering, mathematics, or science. Any of the courses in mathematics fulfills the one course requirement of the core curriculum.

**Requirements for
the Mathematics Minor**

A student may obtain a minor in mathematics by completing 18 credit hours of 200 or above level mathematics courses (General Physics can also be used to complete the mathematics minor). The minor generally corresponds to the first two years of an undergraduate degree in mathematics. Courses are for 3 credit hours unless otherwise noted. A course grade of at least C-minus is necessary for a course to fulfill the department’s requirements for a minor.

**Mathematics**

**
MATH 101 Introduction to Mathematical Though**t 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 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 105 College
Algebra and Trigonometry** Topics include theory of equations, inequalities,
trigonometry, logarithms, exponentials, and analytic geometry.

**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. Prerequisite: MATH 105 or equivalent.

**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: MATH 105 or equivalent
or permission of the instructor. (4 credit hours)

**MATH 202 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: MATH 201 or equivalent. (4 credit hours)

**MATH 203 Calculus
III **Continuation of MATH 202. 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. Prerequisite: MATH 201 or equivalent. (4
credit hours)

**MATH 204 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, and the spectral theorem. Prerequisite:
MATH 203 or equivalent. (4 credit hours)

**MATH 232 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, sums of random variables, the central limit theorem,
and typical applications in reliability, sampling, and estimation theory.
Prerequisite: MATH 202 or equivalent.

**MATH/PHIL 353 Symbolic Logic**Introduction to symbolic logic and the theory of formal systems. Topics include the traditional logic of categorical sentences, truth functional logic, the first order predicate calculus, higher order systems, the notions of decidability and completeness, and some typical applications, among them a brief look at the design of digital computing machinery. Prerequisite: PHIL 102 or equivalent. (Cross-listed in Philosophy)

**MATH/PHIL 354 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 353 or permission of the instructor. (Cross-listed in Philosophy)

**MATH 355 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 353 or permission of the instructor.

**MATH 361 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. Prerequisite: MATH 202 or
equivalent. (4 credit hours)

**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 nonparametric
statistics, linear programming, set theory, numerical analysis, and complex
variables.

**Natural
Science**

In his *Physics* Aristotle laid the foundations for a philosophical knowledge of the natural, changeable world, but he failed to fully develop what modern scientists, beginning with Galileo and Newton, have exploited, the potential of mathematics to describe and systematize our knowledge of the natural world. Yet the latter approach also has its limits; because it relies so heavily on mathematics, which deals entirely in abstract quantity, it fails to account for form and purpose in physical objects. Christendom=s approach to natural science integrates the best of both traditions.

The College offers one introductory course dealing with the historical and philosophical principles of science, and another concentrating on the first quantified natural knowledge, Descriptive Astronomy. The more advanced courses, the two semester sequence in General Physics, deepen the student=s understanding of the nature of physical reality while not neglecting philosophical questions. Any of the science courses satisfies the core requirement in science.

**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 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, and
application of mechanics to simple problems. Topics in thermodynamics
include the four laws, the concepts of temperature and entropy, and the
kinetic theory of gases. Prerequisite: MATH 201 or permission of the instructor.

SC**IE 205 General
Physics II** Continuation of SCIE 204. Topics include oscillatory motion
and wave motion, the nature of light and optical phenomena, geometric
optics, electricity and magnetism, and an introduction to special relativity
and quantum physics.

**SCIE 204L-205L Laboratory for General Physics I & II**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) (1 credit hour per semester)