Christendom College Bulletin

Table of Contents Page

Mathematics and Science

• Mathematics
• Science
  

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

Mathematics is the study of the relationships and attributes of quantities and forms by the use of numbers and symbols. Physics is the systematized study of the material universe by the use of observation, experimentation, and sound reasoning. Study in mathematics and physics is an excellent means to develop logical thought, skills of precise analysis, and universal conceptions about the natural order.

Because quantity is the most basic accident in physical things, and mathematics studies things as quantified and the relations that follow on quantity, mathematics has been applied to the study of the physical world with tremendous success. For this reason, and also because of the impact mathematics has had on our understanding of knowledge and truth throughout history, an understanding of the development of mathematics that aims to understand how it relates to reality and to the human mind is part of a liberal education.

Two courses dealing with a historical and philosophical understanding of the natures of science and mathematics are offered at the introductory level: Introduction to Scientific Thought and Introduction to Mathematical Thought. In addition, the College offers a one-semester course in astronomy, a two-semester course in General Physics, and several courses in mathematics at both the introductory and more advanced levels to provide a range of choices for the student's fulfillment of the College's core requirement in mathematics and natural science, and to provide a good preparation for programs in business, engineering, mathematics, or science.

All students at Christendom College must take at least 3 credits each of mathematics and science to fulfill the requirements of the core curriculum. Courses carry 3 semester hours credit unless otherwise indicated. All math courses listed satisfy the core requirement in mathematics.

Requirements for the Mathematics Minor

A minor in Mathematics requires a minimum 18 hours of mathematics at the 200-level or above. The General Physics courses may be applied to the Mathematics minor. A course grade of at least C-minus is necessary for a course to fulfill the department's requirements for a minor.

All math courses listed satisfy the core requirement in mathematics.

Mathematics

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 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 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

Aristotle's Physics is the study of being as changeable. Insofar as the modern physical sciences have developed out of and separated themselves from Aristotle's physical works, they still study material things insofar as they are changeable. What is primarily different about the modern physical sciences is the application of mathematics to the study of changeable material things. Also different about such modern sciences, except in biology, is a disinclination to seek for purposes or final causes of the changes things undergo. Of lesser importance is the increasing emphasis on experimentation to test physical theories and the development of a great variety of instruments to extend our observations of the changeable material world.
All science courses listed satisfy 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.

SCIE 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)

top of page