# Mathematics & Natural Science

Chairman of the Math and Natural Science Department, and vice president of academic affairs, 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 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. 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 Major Credit Worksheet | Physics Minor Credit Worksheet |

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 one elementary course in Euclidean Geometry and another in the historical development and philosophical aspects of mathematics. College Algebra and several more advanced courses deepen a student’s mathematical knowledge, as well as prepare him for programs in business, engineering, mathematics, or science. 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 302 Calculus II (4 credits)
- MATH 303 Calculus III
- MATH 304 Differential Equations
- MATH 351 Fundamentals of Advanced Mathematics
- MATH 353 Linear Algebra (4 credits)
- MATH 401 Real Analysis (4 credits)
- MATH 402 Abstract Algebra
- MATH 512 Senior Seminar and Thesis (4 credits)

In addition, the department requires students to have a competency in basic physics, demonstrated by passing SCIE 205 General Physics II and its lab course.

A student may obtain **a minor in mathematics **by completing 18 credit hours of 300 level or above mathematics courses. These must include MATH 302 and MATH 303; no more than two General Physics courses can be used to complete the mathematics minor. The minor generally corresponds to the first two years of an undergraduate degree in mathematics.

Courses listed below are for 3 credit hours unless otherwise noted. A course grade of at least “C-“ is necessary for a course to fulfill the department’s requirements for a major or minor.

## 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 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 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. *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)

**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 hours)

**MATH 303 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. **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, sums of random variables, the central limit theorem, and typical applications in reliability, sampling, and estimation theory.

**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, elementary number theory, rings and domains. **Required of all majors .**

**MATH 355 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 hours)

**MATH 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 101 or equivalent.*

**MATH 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.*

**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 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 & limits, continuity of functions , the derivative and , the Riemannian integral. **Required of all majors***. *(4 credit hours).

**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 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 512 Senior Seminar and 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. Includes a one hour per week seminar. (4 credit hours)

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. In the context of the broad Thomistic vision, the student is shown how the modern discipline is placed in the hierarchy of human knowledge and taught the valid insights 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 knowledge of the natural world: Descriptive Astronomy. The more advanced courses: the three semester sequence in General Physics and the special topics courses, 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.

**Requirements for the Physics Minor**

Five upper-level courses in Physics (18 semester hours) are required of minors – three designated and two electives. 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.

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.

## 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/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.