# 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.