Mathematics

Gorguis (chair), Ankney, McGill, Mirza

The overall goal of the department of mathematics is to equip its students for a lifetime of
learning and service via God’s gift of mathematical thought and practice. Some specific objectives
include developing in each student: (1) the ability to think rigorously; (2) an understanding
of the fundamental principles and techniques of mathematics; (3) an appreciation of mathematics
as the primary language of science and an important part of our cultural heritage; (4)
the ability to learn independently and to utilize technology effectively for learning and problem
solving: (5) the ability to communicate mathematics well in both oral and written form.

Major requirements for the B.A. degree in Mathematics

Required semester hours

36 sh

Prerequisites and supporting courses

(4 sh) CSIS 1210

Required core courses

(32 sh) MATH 1510, 1520, 3050, 3060, 3100, 3110, 3150, 4010, 4020

Electives

4 additional hours in Mathematics, numbered 2000 or higher

Notes and restrictions

A comprehensive examination is required for graduation.
An oral presentation of a paper outside the classroom (the paper and venue to be previously
approved by the department) is required for graduation.
For students in secondary education: The B.A. in Math requires 36 sh in MATH, namely
MATH 1510, 1520, 3010, 3050, 3060, 3100, 3110, 3150, 3210, 4010, and 4020 as well
as CSIS 1210 (4 sh) as a supporting course.

Honors

For Departmental Honors in Mathematics, 4 sh of MATH 4000 are required in addition
to the 36 sh for a B.A. Application for admission should be made the second semester of
the third year. For general Departmental Honors requirements and MATH 4000 course
description, see appropriate sections of this catalog.

Major requirements for the B.S. degree in Mathematics

Required semester hours

40 sh

Prerequisites and supporting courses

(4 sh) CSIS 1210

Required core courses

(36 sh) MATH 1510, 1520, 3050, 3060, 3100, 3110, 3150, 3620, 4010, 4020

Electives

4 additional hours in Mathematics, numbered 2000 or higher

Notes and restrictions

A comprehensive examination is required for graduation. An oral presentation of a paper
outside the classroom (the paper andvenue to be previously approved by the department)
is required forgraduation.

Honors

4 sh of MATH 4000 are required in addition to the 40 sh for a B.S. Application for admission
should be made the second semester of the third year. For general departmental
honors requirements and a MATH 4000 course description, see appropriate sections of
this catalog.

Minor requirements in Mathematics

Required semester hours

20 sh

Required core courses

20 sh in the Mathematics department in courses numbered 1510 or higher, including
MATH 1510 and 1520

Designates a course that fulfills all or part of a General Education (G.E.) requirement; see
the General Education Program section of the catalog for more information.

1000 Fundamentals of Algebra (4 sh)
Topics in basic algebra with a focus on linear equations, graphs, inequalities, and
systems, and other topics such as numbers and polynomials. Designed for students who
need additional preparation for Math 1010: Intermediate Algebra. Prerequisite: math
placement.

1010 Intermediate Algebra (4 sh)
Topics in beginning and intermediate algebra such as: equations and inequalities,
systems, polynomials, factoring, graphing, roots and radicals, rational functions, and
quadratic equations. Designed for students who need additional preparation for math
classes numbered 1020 or higher. Prerequisite: MATH 1000 or math placement.

1020 Modern Mathematics for Elementary Teachers (4 sh)
Content and trends in the mathematics usually taught at the elementary school level.
Emphasis is on philosophy and concepts of mathematics. Includes computer applications.

1030 Concepts and Structures (4 sh)
Acquaints students with some of the diversity of mathematics and mathematical thinking
through the study of topics such as symbolic logic, set theory, probability, graph
theory, linear programming, game theory and coding theory. Oral and written presentations
required. Prerequisite: Grade of C or higher in MATH 1010 or designated score on
NPU Math Placement examination.

1150 First-Year Mathematics (4 sh)
Analysis of polynomial, rational, algebraic, trigonometric, exponential, and logarithmic
functions. Prerequisite: MATH 1010 or designated mathematics sub-score on the ACT
or SAT.

1300 Finite Mathematics and an Introduction to Calculus (4 sh)
Survey of mathematical concepts and techniques applied to problems in life, social
and managerial sciences. Topics include linear models, matrices, linear programming,
and an introduction to calculus. Prerequisite: MATH 1010 or designated mathematics
subscore on the ACT or SAT.

1410 Discrete Mathematics I (4 sh)
Introduction to discrete mathematics as applied to computer science, providing a solid
theoretic foundation for further work that is illustrated by computing applications. Topics
include functions, relations, sets, simple proof techniques, Boolean algebra, propositional
logic, digital logic, elementary number theory, and the foundations of counting
such as combinations and permutations. Prerequisite: MATH 1150 or four years of high
school mathematics.

1420 Discrete Mathematics II (4 sh)
Continuation of the discrete mathematics introduced in MATH 1410. Topics include
predicate logic, recurrence relations, graphs, trees, matrices, computational complexity,
elementary computability, and discrete probability. Prerequisite: Math 1410.

1490 Statistics for Social Science (4 sh)
Introduction to applied statistical analysis. Descriptive, correlational, and inferential statistics;
concepts of population, sample, sampling distribution; elements of probability;
parameters of discrete distributions; hypothesis testing: analysis of proportions, means,
and variance; linear regression. Prerequisite: Grade of C or higher in MATH 1010 or
designated score on NPU Math Placement examination. Cross-listed with STAT 1490.

1510 Calculus I (4 sh)
Beginning calculus, limits and continuity, derivatives, mean value theorem, appli-cations
of derivatives, antiderivatives, Riemann Sums, introduction to the definite integrals.
Uses computers. Lab included. Prerequisite: MATH 1150 or 4 years of high school
mathematics.

1520 Calculus II (4 sh)
Continuation of MATH 1510. Fundamental theorem of calculus, evaluation of definite
integrals, applications of definite integrals, introduction to differential equations, infinite
sequences and series. Uses computers. Lab included. Prerequisite: MATH 1510.

2030 Differential Equations (4 sh)
Study of ordinary differential equations, especially first and second order, with applications
to geometry and the physical life sciences. Uses computers. Prerequisite: MATH
1520.

3010 Introduction to Geometry (2 sh)
A study of Euclidean and non-Euclidean geometries by synthetic, analytic, and transformation
methods. Prerequisite: MATH 1520.

3050 Vector Calculus (4 sh)
A detailed study of functions of several variables including differentiation, line and
surface integrals, and Green and Stokes’ theorems. Uses computers. Prerequisite:
MATH 1520.

3060 Real Analysis (4 sh)
Introduction to the fundamentals of real analysis including real numbers, limits, derivatives,
and the Riemann integral. Prerequisite: MATH 1520.

3100 Linear Algebra (4 sh)
A study of matrices, vector spaces, linear transformations, orthogonality, eigenvalues,
and eigenvectors. Uses computers. Lab included. Prerequisite: MATH 1520.

3110 Modern Abstract Algebra (4 sh)
Study of groups, rings, ideals, integral domains, fields and their applications. Prerequisite:
MATH 1520.

3150 Statistical Theory (4 sh)
Probability, probability distributions, random variables, numerical and descriptive
statistics, and statistical inference. Prerequisite: MATH 1520.

3210 History of Mathematics (2 sh)
Study of primary sources in mathematics. Focuses on the changing nature of mathematics.
Prerequisite: MATH 1520

3310 Complex Analysis (4 sh)
Complex numbers, elementary complex functions, the Cauchy theory, infinite series, the
calculus of residues, and introduction to conformal representation. Prerequisite: MATH
3060 or consent of instructor.

3620 Numerical Methods (4 sh)
An introduction to numerical methods with computer implementation. Solution of
linear, non-linear, and differential equations; interpolation and approximation; numerical
integration and differentiation; and error analysis. Prerequisite: MATH 1520. Crosslisted
with CMPT 3620.

3910 Topics in Mathematics (2 or 4 sh)
In-depth treatment of selected topics. Possible topics include point set topology, philosophy
of mathematics, and Dynamical Systems. Prerequisite: Math 1520 plus consent of
instructor.

4000 Departmental Honors in Mathematics (4 sh)
Honors independent study in Mathematics.

4010 Fourth-Year Seminar (2 sh)
Capstone course for mathematics major. Students learn to read, analyze, and learn mathematics
not contained in standard undergraduate textbooks. Written and oral presentations
required. Prerequisite: fourth-year standing mathematics major.

4020 North Park Distinctives in Mathematics (2 or 4 sh)
In consultation with the mathematics faculty, students will select one of the three North
Park Distinctives to relate to mathematics. Students will choose a service learning
project modeling mathematics in an urban setting, an international experience studying
or applying mathematics in a foreign country, or a historical/theological study relating
mathematics to their faith. Written and oral presentations required. Prerequisite: fourth
year standing mathematics major.

4910 Independent Study in Mathematics (1-4 sh)
Prerequisite: Consent of instructor and chairperson of division.

4970 Internship in Mathematics (1-4 sh)
Please refer to the Internship section for requirements and guidelines.