Bachelor of Science in Mathematics

The purpose of the Mathematics program is to offer a broad based curriculum in science and mathematics that leads to a Bachelor of Science degree in Mathematics.

In keeping with the institution’s Statement of Purpose, this program seeks to enable students to integrate academic discipline, Christian lifestyle, and an enriched cultural experience by offering course work that prepares students to pursue advanced studies, enter the teaching profession or enter into mathematics-related employment. The program will provide a basic foundation for beginning graduate studies in mathematics, teaching mathematics at the secondary level and seeking mathematics-related employment. Students will have a thorough understanding of mathematical concepts at the undergraduate level and will possess comprehension, application and critical thinking skills applicable to a wide range of opportunities in education and business.

The Department of Mathematics will guide students through the development of mathematical thinking and communication skills by helping them: (1) progress from a procedural/computational understanding of mathematics to a broad understanding encompassing logical reasoning, generalization, abstraction and formal proof, (2) gain experience in careful analysis of data and (3) become skilled at conveying mathematical knowledge in a variety of settings, both orally and in writing. In addition, the department will assist students in developing skills in a variety of technologies by giving them experience with technological tools such as computer algebra systems, visualization software, statistical packages and computer programming languages. Finally, the department will help students develop a broad view of the mathematical sciences by working with ideas representing the breadth of the mathematical sciences including: continuous and discrete, algebraic and geometric, theoretical and applied.

The Mathematics Department focuses on in-depth knowledge by requiring students to study at least one area in-depth, drawing on ideas and tools from previous coursework and making connections by completing two related courses or a year-long sequence at the upper level. Students are also asked to complete a senior-level project that requires them to analyze and create mathematical arguments and leads to a written and an oral report.

The Mathematics Department encourages and nurtures mathematical sciences majors by:

• Putting a high priority on effective and engaging teaching in introductory courses,
• Seeking out prospective majors and encouraging them to consider majoring in the mathematical sciences and
• Informing students about the careers open to mathematical sciences majors and assigning every major a mathematics faculty advisor.

The fact that mathematics is a cornerstone of modern society implies that the study of mathematical sciences is important for all students. It is also important that some leaders in all areas have the broader and deeper knowledge of mathematics conveyed by a degree in the mathematical sciences. Business, law, medicine and other professional schools seek mathematical sciences majors and would welcome more.

Bachelor of Science in Mathematics

General Education Requirements

COLL 1100 or HNRS 1210    1(2) hours
ENGL 1310, 1320    6 hours
ENGLISH LITERATURE ( ENGL 2000 level)    3 hours
ARTS 1300, MUSC 1300 or 1310, or THTR 1300    3 hours
HIST 1350 or 1360    3 hours
MATH 1330    3 hours
BIOL 1410/1411    4 hours
PHSC 1420 or PHYS 1450    4 hours
PHED 1200    2 hours
PSYC, SOCY, or PLSC    3 hours
CHST 1310, 1320 or 2335    6 hours
COMM 2300    3 hours
CSCI 1305    3 hours
Total    44-45 hours

Mathematics Requirements

MATH 1410  Calculus I    4 hours
MATH 2410  Calculus II    4  hours
MATH 2420  Calculus III    4 hours
MATH 2310  Foundations of  Mathematics    3 hours
MATH 3345  Probability and Statistics II    3 hours
MATH 3310   Linear Algebra    3 hours
MATH 3320   Abstract Algebra    3 hours
MATH 3330   Differential Equations    3 hours
MATH 3360   Numerical Analysis    3 hours
MATH 4310  Foundations of Geometry    3 hours
MATH 4320   Real Analysis    3 hours
MATH 4390  Senior Seminar    3 hours
Total    39 hours

Supporting Courses

CSCI 2325 Structured Computer Programming    3 hours
PHYS 1410, 1420    8 hours
Total Supporting Courses    11 hours

Total General Education Requirements    44-45 hours
Mathematics Requirements    39 hours
Total Supporting Courses    11 hours
Minor Courses Chosen from any minors offered by NGU    18-24 hours
Electives    10-16 hours
Total Hours    128-129 hours

Course Descriptions

MATH 0310. Introduction to Mathematics
Recommended for students who have not met the level of proficiency in basic math skills. Course includes development of proficiency in areas involving fractions, decimals, and percents. Students who pass this course must take MATH 0320 as their next course, or be exempted by a proficiency test administered by the Mathematics Department.Three class hours per week. No credit.

MATH 0320. Basic Algebra
Recommended for students who did not successfully master the level of proficiency of basic algebra. This course involves a study of basic concepts in algebra in order to prepare the student for success in intermediate and college level algebra courses. Topics include: operations with exponents, monomials and polynomials and solutions of elementary linear equations. Three class hours per week. No credit.

MATH 1310. College Algebra
Prerequisite: MATH 0320 or satisfactory score on SAT or passing score on the placement test. A college level course covering operations of real and complex numbers: First and second degree equations; inequalities; linear functions; systems of equations; operations on polynomials; rational expressions and exponents; ratio and proportion; radicals and quadratic equations; exponential and logarithmic functions. Three class hours per week. Three semester hours credit.

MATH 1315. Comtemporary Mathematics
Prerequisite: MATH 0320 or satisfactory score on the SAT or passing score on the placement test An introduction to mathematical concepts that are used in our contemporary world. This course covers mathematical concept development and problem solving in the topics of Problem Solving, Consumer Mathematics, Geometry, Probability and Statistics. Three class hours per week. Three semester hours credit.

MATH 1330. Probability and Statistics
Prerequisite: MATH 0320 or satisfactory score on the SAT or passing score on the placement test A study of measures of central tendency and variability as well as binomial and normal probability distributions. Additionally, calculations involving linear relationships and correlation of variables are covered. Three class hours per week. Three semester hours credit.

MATH 1335. Advanced Algebra and Trigonometry
Prerequisite: High School Algebra II or MATH 1310. A study of algebraic, exponential, logarithmic, and trigonometric functions as a foundation for calculus. This course may not be taken if AP Calculus credit has been earned. Three class hours per week. Three semester hours credit

MATH 1410. Calculus One
Prerequisite: MATH 1335 or permission of instructor. A study of differentiation and integration of elementary algebraic and transcendental functions with applications. Four class hours per week. Four semester hours credit.

MATH 2310. Foundations of Mathematics
Prerequisite: MATH 1410 This course provides the knowledge needed to move into advanced mathematical work. There are introductions to logic and set theory, discussions of proof writing and proof discovery and introductions to number systems. A part of the course will involve an introduction to the history and professional culture of mathematics. Three class hours per week. Three semester hours credit.

MATH 2410. Calculus Two
Prerequisite: MATH 1410 A continuation of MATH 1410 involving the study of definite integrals and techniques of integration. Four class hours per week. Four semester hours credit.

MATH 2420. Calculus Three
Prerequisite: MATH 2410 A study of vector calculus, partial differentiation, multiple integration and calculus of variations. Four class hours per week. Four semester hours credit.

MATH 2430. Statistics for Science Majors
Prerequisite: MATH 0320 or satisfactory score on the SAT or passing score on the placement test The topics covered in the course will include: descriptive statistics, the role of probability in hypothesis testing, the normal distribution and central limit theorem. Hypothesis tests involving: 1 sample t-test, independent t-test and related means t-test, analysis of variance, proportions and the Chi-square statistic, Confidence intervals and estimation, correlation and regression. Three class hours per week. Two lab hours per week. Four semester hours credit.

MATH 3310. Linear Algebra
Prerequisite: MATH 2410 The theory and applications of matrices and vector spaces leading to matrix solutions of systems of equations, linear transformations and eigenvalues and eigenvectors. Three class hours per week. Three semester hours credit.

MATH 3320. Abstract Algebra
Prerequisite: MATH 2420, MATH 2310 An introductory course on the principles and concepts of modern abstract algebra. Included is a study of groups, rings and fields. Many concepts will require both application and proof. Three class hours per week. Three semester hours credit.

MATH 3330. Differential Equations
Prerequisite: MATH 2420 A study of ordinary and partial differential equations, their solutions and their use in mathematical modeling. Three class hours per week. Three semester hours credit.

MATH 3345. Probability and Statistics II
Prerequisite: MATH 2430 A study of discrete and continuous distributions, expectation, special probability distributions, moment generating functions, central limit theorem, maximum likelihood estimators, tests of hypotheses.Three class hours per week. Three semester hours credit.

MATH 3360. Numerical Analysis
Prerequisite: MATH 2420 and CSCI 2335 or equivalent A study of the algorithms and numerical methods utilized for solving mathematical problems using computers. Three class hours per week. Three semester hours credit.

MATH 3480. Discrete Modeling
Prerequisite: MATH 2420 The topics covered in the course include: logic, set theory, functions and their growth, Boolean functions, the integers, algorithms, relations and digraphs, inductive and recursive definitions and arguments, fundamentals of counting and discrete probability, recurrence relations, elementary graph theory, and finite difference approaches. Numerical techniques used in modeling the behavior of a discrete variable will be employed to research a number of mathematical models used in approximating diverse discrete structures. Topics involving the heat equation, elastic media, graphing of non-Euclidean objects and optimization will be explored using various technological and optimization tools. Three class hours per week. Two laboratory hours per week. Four semester hours credit.

MATH 4310. Foundations of Geometry
Prerequisite: MATH 2410 and MATH 2310 This is a course in college geometry for students who may teach the subject or who need to take a fresh look at the subject. The topics covered are Line and Angle Relationships, Parallel Lines, Triangles, Quadrilaterals, Similar Triangles, Circles, Areas of Polygons and Circles, and selected topics from Non-Euclidean Geometry. Three class hours per week. Three semester hours credit.

MATH 4320. Real Analysis
Prerequisite: MATH 2420, MATH 2310 This course is an advanced study of the fundamental concepts of analysis, including properties of the real number system, sequences, limits, continuity, the derivative, and the Riemann integral. Three class hours per week. Three semester hours credit.

MATH 4380. Special Topics in Mathematics
Prerequisite: Instructor’s Permission A senior level course in an advanced topic, such as abstract algebra II, algebraic topoloty, coding theory, complex analysis, measure theory, non-Euclidean geometry, number theory, partial differential equations, and real analysis II. Offered with sufficient demand. For each different topic offered, this course may be repeated. Three class hours per week. Three semester hours credit.

MATH 4390. Senior Seminar in Mathematics
Prerequisite: Senior status and eight mathematic courses successfully completed or approval of departmental head. This course is a capstone for seniors majoring in mathematics with emphasis on a study of recent developments in pure and applied mathematics. The student prepares a senior project which leads to written and oral presentations. Three class hours per week. Three semester hours credit.