PATRICK HEADLEY, Chairperson
FACULTY: Associate Professors: Michael Caulfield, Patrick Headley, Edward A. Rogers.
Assistant Professors: Christine Cedzo, Geoffrey Dietz, Jennifer Gorman, JoAnne E. Revelt.
Aims and Objectives:
Mathematics majors at Gannon must satisfactorily complete a minimum of forty-eight 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 signifcant 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 the first Actuarial Exam 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.
COURSE DESCRIPTIONS:
MATH 055: Algebra Refresher
3 credits (see description)
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.
Prerequisite: One year of high-school algebra
MATH 105: Fundamentals of Mathematics 1
3 credits
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.
MATH 106: Fundamentals of Mathematics 2
3 credits
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.
MATH 110: Mathematics in Human Progress
3 credits, Spring
Most of the mathematics discussed has been developed in the last 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.
Prerequisite: Two years of high-school algebra or MATH 055
MATH 111: College Algebra
3 credits, Fall, Spring
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
MATH 112: Trigonometry
3 credits, Fall, Spring
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.
MATH 114: Algebra for Business Students
3 credits, Fall, Spring
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.
MATH 115: Calculus for Business Students
3 credits
Limits and continuity. Derivatives and partial derivatives with applied maxima and minima
problems. Integration with applications.
Prerequisite: MATH 114 or department recommendation.
MATH 125: Great Ideas of Mathematics
3 credits, Fall
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
MATH 135: Precalculus
3 credits
The course addresses concepts in algebra and trigonometry through the use of functions. The
relationship between functions and their graphs is examined in detail. The course also covers
topics in the mathematics of functions such as composition and inverses. Rates of change are
studied with a view toward calculus.
Prerequisite: Two years of high school algebra.
MATH 140: Calculus 1
3 credits, Fall, Spring
Limits; derivatives of algebraic and trigonometric functions; graphing; related rates;
optimization problems.
Prerequisite: Trigonometry.
MATH 141: Calculus 2
3 credits, Fall, Spring
The definite and indefinite integrals; applications of integration; techniques of integration;
calculus of the exponential, logarithmic, and other transcendental functions.
Prerequisite: MATH 140
MATH 213: Applied Statistics
3 credits, Fall, Spring
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
MATH 222: Discrete Mathematics 1
3 credits, Fall
Logic, sets, functions, mathematical induction, algorithms, counting methods, recurrence
relations, graphs.
Prerequisite: MATH 111, MATH 114 or MATH 140
MATH 223: Discrete Mathematics 2
3 credits, Spring
Relations, topics in graph theory, tree traversal, spanning trees, Boolean algebra, logic gates,
circuits, automata, Turing machines.
Prerequisite: MATH 222
MATH 226: Geometry
3 credits, Fall, even years
Metric and synthetic approaches to Euclidean geometry. Incidence, separation, distance,
congruence, similarity, angle, measurement. Geometric transformations of the Euclidean
plane: isometries, symmetry groups, similarity, and affine transformations. Axiomatic systems
for Euclidean and non-Euclidean geometries. Models of hyperbolic, projective, and finite
geometries.
Prerequisite: MATH 222
MATH 242: Calculus 3
3 credits, Fall, Spring
Infinite sequences and series; power series; Taylor series and polynomials; parametric
equations; polar coordinates; vectors in the plane and space; vector-valued functions.
Prerequisite: MATH 141
MATH 243: Calculus 4
3 credits, Fall, Spring
Partial differentiation; multiple integration; vector calculus.
Prerequisite: MATH 242
MATH 252: Linear Algebra
3 credits, Spring
Systems of linear equations; matrix algebra; determinants; vector spaces; linear
transformations; eigenvalues and eigenvectors; inner products.
Prerequisite: MATH 242
MATH 260: History of Mathematics
3 credits, Spring, odd years
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
MATH 296: Cooperative Education Seminar
1 credit
Seminar focusing on the development of employment and professional competencies,
required of students planning a co-op placement in MATH 375.
MATH 301: Mathematical Analysis 1
3 credits
Elementary set theory; properties of the real numbers; topology of the real line; sequences of
functions; limits of functions; continuity; uniform continuity; differentiation of real-valued
functions; integration.
Prerequisite: MATH 243
MATH 302: Mathematical Analysis 2
3 credits
Additional topics in real analysis: integration; infinite series; differentiation of vector-valued
functions; integration of vector-valued functions.
Prerequisite: MATH 301
MATH 304: Differential Equations 1
3 credits, Fall, Spring
Ordinary differential equations with applications to science and engineering. Solution methods
for first-order equations, linear equations, and systems of equations, including Laplace
transforms. Other topics may include power series methods, numerical methods, or nonlinear
phenomena.
Prerequisite: MATH 242
MATH 305: Differential Equations 2
3 credits
Bessel functions, Sturm-Liouville Problems, Fourier series and integral, partial differential
equations, Laplace's equation.
Prerequisites: MATH 304
MATH 308: Applied Complex Variables
3 credits
A study of complex algebra, analytic functions, integration in the complex plane. Taylor and
Laurent expansions, singularities, calculus of residues and meromorphic functions.
Prerequisite: MATH 243
MATH 309: Abstract Algebra 1
3 credits
Fundamentals of groups, rings, fields, and homomorphisms.
Prerequisite: MATH 222 and MATH 243
MATH 310: Abstract Algebra 2
3 credits
Additional topics in algebra that may include: prime fields, extension fields, Galois Theory,
Sylow Theorems, number theory, advanced linear algebra and canonical forms, or
computational algebraic geometry.
Prerequisite: MATH 309
MATH 312: Probability and Statistics 1
3 credits, Fall
Enumeration, probability, independence, probability distributions, random variables,
expectation, mean, variance, moment generating functions, Central Limit Theorem, sampling
distributions, and other selected topics.
Prerequisite: MATH 141
MATH 313: Probability and Statistics 2
3 credits
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
MATH 314: Numerical Analysis
3 credits, Fall
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
MATH 315: Numerical Analysis 2
3 credits
An extension in breadth and depth of MATH 314, including topics in the solution of
equations and approximation theory.
Prerequisite: MATH 314
MATH 320: Mathematical Modeling
3 credits, Fall
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
MATH 341: Methods of Teaching Secondary Mathematics
3 credits, Fall, Odd years
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
MATH 375: Internship
3 credits, Fall
Student obtains professional work experience in a position involving substantial use of mathematics.
Prerequisite: MATH 296
MATH 380: Undergraduate Mathematics Research
3 credits
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.
MATH 391-394: Directed Study in Mathematics
1-3 credits
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.
MATH 395-399: Special Topics in Mathematics
3 credits
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.
Mathematics Curriculum (128 - 129 credits)
(Numerals in front of courses indicate credits)
FRESHMAN
First Semester
3 College Composition/LENG 111
3 Hist of West & World/LHST 111
3 Sacred Scripture/LTHE 121
3 Calculus I/MATH 140
3 Principles of Computing/CIS 190
3 Intro to Philosophy/LPHI 131
18
Second Semester
3 Critical Analysis & Composition/ LENG 112
3 Applied Statistics/MATH 213
3 Calculus II/MATH 141
3 Intro to Programming & Lab/ CIS 214 & 215
4 Gen Phys III & Lab/PHYS 111&112
1 Co-op Ed Seminar/MATH 296 *4
17
SOPHOMORE
First Semester
3 Theology II Series/LTHE
3 Calculus III/MATH 242
3 Discrete Mathematics 1/MATH 222
4 General Physics & Lab *1
3 Prob Solve with Obj Orient Prog/CIS 216
16
Second Semester
3 Philosophy II Series/LPHI
3 LBST Approved Core Elective
3 Linear Algebra/MATH 252
3 Calculus IV/MATH 243
3 Cognate Elective *3
15
JUNIOR
First Semester
3 Literature Series/LENG
3 Social Science
3 Fine Art Series/LFIN
3 Probability & Statistics I/MATH 312
3 MATH 301 or MATH 309 *2
3 General Elective
18
Second Semester
3 Philo/Theo III Series/LTHE or LPHI
3 Differential Equations 1/MATH 304
3 Mathematics Elective *3
3 Department approved 300 level MATH elective
3 Cognate Electives *3
15
SENIOR
First Semester
3 Senior Seminar/LBST 383
3 MATH 301 or MATH 309 *2
3 Mathematical Modeling/MATH 320
3 Cognate Electives *3
3 General Electives
15
Second Semester
3 Department approved 300 level MATH elective
3 Internship/Research/MATH 375 or 380 *4
3 Mathematics Elective *3
3 Cognate Electives *3
3 General Electives
15
* 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 All mathematics and cognate electives must be approved by the Mathematics advisor and
chosen to suit student interests.
* 4 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 (131 credits)
Students majoring in Mathematics qualify for Teacher Certification in Mathematics/
Secondary Education.
Aims 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)
FRESHMAN
First Semester
3 College Composition/LENG 111
3 Hist of West & World/LHST 111
3 Sacred Scripture/LTHE 121
3 Calculus I/MATH 140
3 Principles of Computing/CIS 190
3 Intro to Philosophy/LPHI 131
18
Second Semester
3 Critical Analysis & Comp/LENG 112
3 Applied Statistics/MATH 213
3 Calculus II/MATH 141
3 Intro to Prog & Lab/CIS 214 & 215
3 Found of Teach/EDCR 103
1 Practicum 1/EDFL 101
16
SOPHOMORE
First Semester
3 Philosophy II Series/LPHI
3 Calculus III/MATH 242
3 Discrete Mathematics/MATH 222
3 Prob Solve with Obj Orient Prog/CIS 216
3 Literature Series/LENG
3 Psych of Learning/EDCR 101
18
Second Semester
3 Theology II Series/LTHE
3 Linear Algebra/MATH 252
1 Practicum 2/EDFL 102
4 Gen Phys III & Lab/PHYS 111&112
3 Calculus IV/MATH 243
3 MATH 260 or Fine Arts Series/LFIN
17
JUNIOR
First Semester
3 Meeting the Needs of Students with Exceptionalities/SPED 340
1 Practicum 3/EDFL 103
4 General Physics & Lab *1
3 Probability & Statistics I/MATH 312
3 MATH 226 or MATH 341 *2
3 MATH 301 or MATH 309 *3
17
Second Semester
3 Phil/Theo III Series/LTHE or LPHI
3 Fine Art Series/LFIN or MATH 260 *4
3 Reading & Literacy across the Secondary Curriculum/EDCR 326
3 Department approved 300 level MATH elective
3 Differential Equations I/MATH 304
15
SENIOR
First Semester
3 Approved Soc Sci, Humanities or other elective course
3 Assessment/EDCR 330
3 MATH 226 or MATH 341 *2
3 MATH 301 or MATH 309 *3
3 Mathematical Modeling/MATH 320
15
Second Semester
12 Student Teaching/EDFL 410
3 Professional Seminar/EDCR 401
15
* 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 260
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.
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