PATRICK HEADLEY, Chairperson
FACULTY: Associate Professors: Michael Caulfield, Monica Pierri-Galvao,
Edward A. Rogers. Assistant Professors: Christine Cedzo, Geoffrey Dietz,
Patrick Headley, JoAnne E. Revelt.
Aims and Objectives:
Mathematics majors at Gannon must satisfactorily complete a minimum of forty-seven upper-level credits ranging over such areas as discrete mathematics, calculus, abstract algebra, mathematical analysis, probability, statistics, linear algebra, differential equations, and mathematical modeling. In addition, mathematics majors will receive a significant career-enhancing experience through placement in an appropriate internship position or through a challenging undergraduate research project.
The Mathematics curriculum is designed to allow students to develop a strong secondary interest in allied fields such as business, computer science, economics, physics, biology, chemistry, engineering or education. There is ample opportunity to select the most beneficial combination of courses to achieve the student's goals. The content of a particular student's curriculum requires department approval to insure proper competency by graduation. Mathematics majors receive preparation for three or more Actuarial Exams administered by the Society of Actuaries.
This competency required of students in mathematics has resulted in careers in research, in education at all levels, and in advanced positions in industry and government. Among employers of Gannon mathematics graduates are IBM, GE, General Motors, International Paper and GTE. Mathematicians are increasingly in demand in today's employment market. Mathematics majors, by satisfying additional requirements of the School of Education, can earn Teacher Certification in Secondary Education for the State of Pennsylvania.
MATH 055: Algebra Refresher
Exponents, polynomial and rational expressions, factoring, linear equations and
inequalities, rational equations, graphing, functions, and applications. This
course will meet 4 hours per week during a regular semester, but will count as 3
credits of load for student financial aid and quality point average
considerations. It may not be used to satisfy any graduation requirements in any
degree program.
Prerequisites: One year of high-school algebra.
3 credits (see description)
MATH 105: Fundamentals of Mathematics I
This course investigates the nature of mathematical relationships through
problem solving. Topics include set theory, logic, systems of numeration, number
theory and the real number system, and voting theory.
Prerequisite: Two years of high school algebra.
3 credits
MATH 106: Fundamentals of Mathematics II
This course is a continuation of MATH 105, and like MATH 105, it continues to investigate mathematical relationships through problem solving. Topics include algebra, graphs, functions, measurement systems, geometry, probability, and statistics.
Prerequisite: Two years of high school algebra.
3 credits
MATH 110: Mathematics in Human Progress
Most of the mathematics discussed has been developed in this century. Topics
covered are based on down-to-earth, real-life problems and will include:
Mathematics of social choice including group decision making and democratic
voting methods; Management science including methods for solving problems
involving organization and management of complex activities; Growth and symmetry
including population growth, geometrical patterns of biological growth and
fractals.
Prerequisites: Two years of high-school algebra, or MATH 055.
3 credits, Spring
MATH 111: College Algebra
Polynomial, rational, radical, exponential, and logarithmic functions and
equations; systems of equations; matrices and determinants; sequences and
series; binomial theorem.
Prerequisite: Two years of high school algebra or MATH 055.
3 credits, Fall, Spring
MATH 112: Trigonometry
Trigonometric functions, radian measure, trigonometric identities and equations,
solution of triangles, DeMoivre's theorem, vectors, polar coordinates.
Prerequisite: MATH 111, or concurrently with MATH 111 or equivalent competency.
3 credits, Fall, Spring
MATH 114: Algebra for Business Students
Linear and quadratic equations, inequalities and systems of equations. Algebraic,
exponential and logarithmic functions and their graphs. Mathematics of finance.
Matrix algebra. Emphasis on business applications.
Prerequisite: High school algebra.
3 credits, Fall, Spring
MATH 115: Calculus for Business Students
Limits and continuity. Derivatives and partial derivatives with applied maxima and
minima problems. Integration with applications.
Prerequisite: MATH 114 or department recommendation.
3 credits
MATH 125: Great Ideas of Mathematics
A history of the great ideas of mathematics including the Pythagorean Theorem,
the works of Euclid, various discoveries of Archimedes, Cardano's
solution of the cubic equation, various investigations of Bernoulli, Euler, and
Gauss, and Cantor's study of infinite sets. The emphasis of the course is to be
entirely on the beauty, originality, and creativity of the ideas involved.
Prerequisite: Two years of high school algebra and one of geometry
3 credits, Fall
MATH 140: Calculus I
Limits; derivatives of algebraic and trigonometric functions; graphing; related
rates; optimization problems.
Prerequisites: Trigonometry.
3 credits, Fall, Spring
MATH 141: Calculus II
The definite and indefinite integrals; applications of integration; techniques of
integration; calculus of the exponential, logarithmic, and other transcendental functions.
Prerequisite: MATH 140
3 credits, Fall, Spring
MATH 213: Applied Statistics
Designed for students majoring in the natural or social sciences. Topics include
measures of central tendency and dispersion, combinations and permutations,
sampling distributions, testing hypotheses, Chi-Square applications, linear regression
and correlation.
Prerequisite: High school algebra
3 credits, Fall, Spring
MATH 222: Discrete Mathematics 1
Logic, sets, functions, mathematical induction, algorithms, counting methods, recurrence
relations, graphs.
Prerequisites: MATH 111, MATH 114 or MATH 140.
3 credits, Fall
MATH 223: Discrete Mathematics 2
Relations, topics in graph theory, tree traversal, spanning trees, Boolean algebra, logic
gates, circuits, automata, Turing machines.
Prerequisite: MATH 222.
3 credits, Spring
MATH 226: Geometry
Metric and synthetic approaches to two and three-dimensional Euclidean geometry. Incidence,
separation, distance, congruence, similarity, angle, measurement. Geometric transformations
of the Euclidean plane: isometries, symmetry groups, similarity and affine transformations.
Axiomatic systems and finite geometries, finite projective planes, application to error-correcting
codes, Desargues' and Pappus' configurations. Models of non-Euclidean geometries. The axiomatic
system and duality of projective geometry.
Prerequisite: MATH 140, or concurrently with MATH 140.
3 credits, Fall, even years
MATH 242: Calculus III
Infinite sequences and series; power series; conic sections; polar coordinates; vectors in the
plane and in space.
Prerequisite: MATH 141
3 credits, Fall, Spring
MATH 243: Calculus IV
Vector-valued functions; partial differentiation; multiple integration; integration in vector fields.
Prerequisite: MATH 242
3 credits, Fall, Spring
MATH 252: Linear Algebra
Systems of linear equations; matrix algebra; special matrices; determinants; vector spaces;
linear transformations; characteristic values and vectors.
Prerequisite: MATH 242
3 credits, Spring
MATH 260: History of Mathematics
Survey of the development of mathematics from the earliest historic times to the
present. A true appreciation of mathematics is developed through the knowledge
of the history of mathematics. The cultural and historical significance of
mathematics will be discussed.
Prerequisite: MATH 140
3 credits, Spring, odd years
MATH 296: Cooperative Education Seminar
Seminar focusing on the development of employment and professional competencies, required of students planning a co-op placement in MATH 375.
1 credit
MATH 301: Mathematical Analysis I
Elementary Logic and Set Theory: Properties of the Real Numbers; Topological
Concepts; Sequences of Functions; Limit of a Function; Continuous Functions;
Uniform Continuity.
Prerequisite: MATH 243
3 credits, Fall, odd years
MATH 302: Mathematical Analysis II
The Derivative of a Real-Valued Function; Mean Value Theorem; Riemann-Stieltjes
Integration; Infinite Series; Differentiation of Vector-Valued Functions;
Integration of Vector-Valued Functions.
Prerequisite: MATH 301
3 credits, Spring, even years
MATH 304: Differential Equations I
Ordinary differential equations with applications to biology, engineering,
physics and social sciences. Techniques include power series solutions and
Laplace transforms.
Prerequisite: MATH 242
3 credits, Fall, Spring
MATH 305: Differential Equations II
Bessel functions, Sturm-Liouville Problems, Fourier series and integral, partial
differential equations, Laplace’s equation.
Prerequisites: MATH 304 or MATH 307
3 credits
MATH 308: Applied Complex Variables
A study of complex algebra, analytic functions, integration in the complex
plane. Taylor and Laurent expansions, singularities, calculus of residues and
meromorphic functions.
Prerequisites: MATH 304
3 credits
MATH 309: Abstract Algebra I
Groups; subgroups; homomorphisms; normal subgroups; Cayley’s Theorem; Sylow
Theorem; Rings; Quotient Rings; Euclidean Rings; Polynomial Rings.
Prerequisite: MATH 123 and MATH 243.
3 credits, Fall, even years
MATH 310: Abstract Algebra II
Fields; Prime Fields and Characteristics; Extension Fields; Simple Algebraic
Extensions; Minimal Polynomial Finite Extensions; Galois Theory.
Prerequisite: MATH 309
3 credits
MATH 312: Probability and Statistics I
Enumeration, probability, independence, probability distributions, Bayes’
theorem, random variables, expectation, mean, variance, moment generating
function, special probability distributions, joint distributions, covariance and
correlation, Central Limit Theorem, sampling distributions, and selected topics
in statistical inference.
Prerequisite: MATH 141
3 credits, Fall
MATH 313: Probability and Statistics II
Point and interval estimations, hypothesis testing, Neyman-Pearson lemma,
likelihood ratio tests, tests concerning means, proportions and variances,
Chi-square tests, analysis of variance, regression, correlation analysis,
nonparametric methods.
Prerequisite: MATH 312
3 credits
MATH 314: Numerical Analysis
Taylor polynomials, machine representation of numbers, computational error,
interpolation, root finding, systems of linear equations, curve fitting,
numerical differentiation and integration.
Prerequisites: MATH 141 and CIS 214
3 credits, Fall
MATH 315: Numerical Analysis II
An extension in breadth and depth of MATH 314, including topics in the solution of
equations and approximation theory.
Prerequisite: MATH 314
3 credits
MATH 320: Mathematical Modeling
Construction and analysis of mathematical models for the solution of
‘real-world’ problems. Topics discussed may include genetics, predator-prey
problems, population growth, spread of disease, finance, etc.
Prerequisite: MATH 304
3 credits, Fall
MATH 341: Methods of Teaching Secondary Mathematics
This course is designed to prepare students to teach mathematics in secondary
schools. It includes an examination of theories, research, and methods related to
student learning and achievement in mathematics. Students will teach a variety of
mathematics lessons as well as analyze the strategies of others. Students will also
gain experience with graphing calculators and Geometer's Sketchpad.
Prerequisite: MATH 243
3 credits, Fall, odd years
MATH 375: Internship
Student obtains professional work experience in a position involving substantial
use of mathematics.
Prerequisite: MATH 296
3 credits
MATH 380: Undergraduate Mathematics Research
Student obtains an introduction to the nature and methods of modern mathematics
research after selection of an appropriate project under the guidance of a
faculty mentor.
3 credits
MATH 391-394: Directed Study in Mathematics
Supervised reading in selected subjects approved by a three-person department
committee. May be taken more than once for a total of at most four credits.
Prerequisite: Approval of faculty supervisor.
1-3 credits
MATH 395-399: Special Topics in Mathematics
Topics which are not covered by regularly scheduled courses but have the
approval of a three-person department committee. At most six credits of Special
Topics may be used toward meeting departmental requirements for mathematics
electives.
Prerequisite: Consent of the department chair.
3 credits
Mathematics Curriculum (128-129 credits)
(Numerals in front of courses indicate credits)
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| *1 | Students can choose either Physics IV & Lab or Physics V & Lab (PHYS 212 & 213 or 214 & 215). |
| *2 | Required Mathematics: MATH 301 (Fall odd years) and MATH 309 (Fall even years). |
| *3 | Required Mathematics: MATH 302 (Spring even years). |
| *4 | All mathematics and cognate electives must be approved by the Mathematics advisor and chosen to suit student interests. |
| *5 | Students are required to take either MATH 375 or MATH 380. MATH 296 is required of students planning a co-op placement in MATH 375. MATH 375 may be taken prior to the senior year. |
Mathematics Curriculum with Secondary Education (137 credits)
Students majoring in Mathematics qualify for Teacher Certification in Mathematics/Secondary Education.
Aima and Objectives
The objectives of the program are: (1) to give the students an opportunity to become broadly educated
in the areas of Mathematics, and (2) to provide a program of teacher education which promotes growth,
development, professionalism and expertise for successful teaching.
Students who wish to prepare themselves as secondary Mathematics teachers must make
formal application to the teacher education program through the School of Education. For a
detailed explanation of all requirements refer to the catalog portion under Education.
(Numerals in front of courses indicate credits)
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| *1 | Students can choose either Physics IV & Lab or Physics V & Lab (PHYS 212 & 213 or 214 & 215) |
| *2 | Required Mathematics: MATH 226 and MATH 341 |
| *3 | Required Mathematics: MATH 301 and MATH 309 |
| *4 | Required Mathematics: MATH 302 and MATH 260 |
MATHEMATICS MINOR
A total of 24 credits is required for a minor in mathematics, including MATH 140, 141, 242, and 243; and 12 credits chosen from among any MATH courses at the 200 level or higher.
A total of 24 credits in mathematics is required for a minor in statistics, including MATH 140, 141, 242, 243, 252, 213, 312, and 313.