Bachelor of Science Mathematics

Lead Faculty: Dr. Igor Y. Subbotin

The Bachelor of Science in Mathematics provides a strong foundation in mathematics and its applications. Designed to help address our nation's increasing need for mathematical scientists, technicians and especially teachers, the program emphasizes reflective and conceptual understanding and technique.

First, it provides the fundamental mathematical knowledge to formulate and solve problems in industry and research (concentration in mathematics and applications). Computer science courses are encouraged, since the use of computers has been instrumental in the expansion of these opportunities. Students who want a basic mathematics degree can culminate their program with the project courses.

Second, the program trains mathematics teachers who want to provide quality mathematical instruction to students in primary or secondary schools. The single-subject teaching concentration was created for this purpose.

The Department of Mathematics and Natural Sciences is committed to the complete academic development of its students. Consequently, where practical, all mathematics and science courses are writing-intensive and incorporate a diversity component. Students are advised that all mathematics courses encourage critical thinking by their very nature. Moreover, all mathematics courses require that the student purchase and use a scientific calculator for the operations of the subject matter. Some courses require a more advanced graphing calculator and computer software.

The program includes two concentrations.

• The concentration in mathematics and applications provides students with the fundamental mathematical knowledge to formulate and solve problems in industry and research.
• The single-subject teaching concentration was created to train mathematics teachers who want to provide quality mathematical instruction to students in secondary schools.

Single-Subject Mathematics Preparation Program
The Single-Subject Mathematics Preparation Program is approved by the Commission on Teacher Credentialing. Students who complete the program with the Concentration in Single Subject Teaching will not be required to take the California Subject Examination for Teachers (CSET) in mathematics in order to receive their teaching credential. The program emphasizes a strong foundation in mathematical content together with activities designed to help future teachers assume leadership roles in an increasingly complex educational world.

Interested students should complete the following application process:

• Send a letter to the Department Chair requesting admission to the program and copies of transcripts to the Lead Mathematics Faculty for evaluation.
• Upon enrollment, submit two essays for the Mathematics Portfolio (Instructions for the development and completion of a Mathematics Portfolio are sent upon receipt of the request letter. The portfolio is completed for review by the Department Chair or Lead Faculty two months before the last class.)
• After completing the major program requirements, students must complete all required courses from the single-subject teaching concentration (MTH 304, MTH 410, MTH 460, MTH 461, MTH 450A).

The study of mathematics must encompass the discipline in its broadest sense. The future mathematician should develop in an academic environment that stresses scholarship, diversity, and growth through a rigorous and focused curriculum of advance mathematics that incorporates: problem solving, mathematics as communication, reasoning, and mathematical connections. The Bachelor of Science in Mathematics program is dedicated to providing such sound preparation and training to a diverse population of nontraditional learners whose goal is to work professionally in mathematics or teach Mathematics in California public schools.

Program Outcomes
Upon completion of this program, students will be able to:

• Experience, master, and apply skills and knowledge in problem solving. Using appropriate mathematical models students will be able to examine given situations, extract quantitative information, formulate and solve mathematical problems described these situations.
• Use language and mathematical symbols to communicate mathematical ideas. They will be able to communicate mathematical concepts clearly and effectively using graphs, formulas, tables, computer technology, and graphing calculators, using appropriate mathematical symbols and notions.
• Demonstrate a variety of reasoning skills. They will develop their ability to reason inductively and deductively, test conjectures, construct counter-examples, make valid arguments, and judge the validity of mathematical arguments, apply a variety of reasoning processes such as spatial, probabilistic, and proportional process, evaluate the reasonableness of solutions to problems.
• Investigate the connections and interplay among various mathematical topics and their applications that cover range of phenomena across appropriate disciplines.
• Use current technology tools, such as computers, calculators, graphing utilities, video, and interactive programs, that is appropriate for the research and study in mathematics.
• Be able to have an understanding of the classic and modern algebra as a fundamental language through which mathematics is communicated. They will have deep knowledge in abstract, linear, and matrix algebra.
• Have a fundamental knowledge of geometry. They will translate between synthetic and coordinate representations, understand axiomatic systems, master in Euclidian and non-Euclidean geometries, apply geometry to the real world problems.
• Be able to model real world problems with a variety of algebraic and transcendental functions, to translate between the tabular, symbolic, and graphical representation of functions, master in the main concepts of calculus, including the derivative, integral, differential equations, their interconnections, and their use in analyzing and solving real-world problems.
• Understand the beauty of pure number theory, including such advanced topics as diophantine equations, number-theoretic functions, quadratic reciprocity, primitive roots, and continued fractions. They will be able to discuss errors in numerical computation, use function approximation, polynomial interpolation, cubic spline interpolations, quadratures, numerical differentiation, and so on.
• Use advanced statistics and probability concepts and methods to analyze and study different real-world problems.

Requirements

To receive a Bachelor of Science in mathematics degree, students must complete at least 180 quarter units as articulated below, 45 of which must be completed in residence at National University and 76.5 of which must be completed at the upper-division level. In the absence of transfer credit, students may need to take additional general electives to satisfy total units for the degree. Refer to the section on undergraduate admission procedures for specific information regarding admission and evaluation.

Preparation for the Major (7 courses; 31.5 quarter units):
MTH 210 - Introduction to Probability and Statistics*
  (Prerequisites: Placement Evaluation)
CSC 242 - Introduction to Programming Concepts and Methods
  (Prerequisites: CSC 200 and CSC 208)
SCI 102 - Survey of Physical Sciences* 
MTH 220 - Calculus I*  (Prerequisite: MTH 215, or placement evaluation)
or
CSC 208 - Calculus for Computer Science I* (Prerequisite: Math 215)
MTH 221 - Calculus II  (Prerequisite: MTH 220)
MTH 222 - Calculus III  (Prerequisite: MTH 221)
MTH 223 - Calculus IV (Prerequisite: MTH 222)

*May be used to satisfy general education requirements.

Requirements for the Major (12 courses; 54 quarter units):
MTH 311 - Topics from Geometry
  (Prerequisites: MTH 215 or placement evaluation)
MTH 317 - Mathematical Modeling
  (Prerequisites: MTH 215 or MTH 216A/B and MTH 210)
MTH 325 - Discrete Structures and Logic Design
  (Prerequisites: MTH 215 or MTH 216A/B or placement evaluation)
or
CSC 331 - Discrete Structures and Logic (Prerequisites: CSC 252, CSC 310)
MTH 435 - Linear Algebra (Prerequisites: MTH 325 and MTH 220)
MTH 433 - Differential Equations (Prerequisite: MTH 223 and MTH 435)
MTH 411 - Number Theory
  (Prerequisite: MTH 215 or MTH 216A/B or MTH 301 or placement evaluation)
MTH 416 - Algebraic Structures (Prerequisites: MTH 325 and MTH 435)
MTH 417 - Foundation of Geometry
  (Prerequisites: MTH 215 or MTH 216 A/B and MTH 311)
MTH 418 - Statistical Analysis (Prerequisites: MTH 210 and MTH 220)
MTH 432 - Advanced Calculus (Prerequisites: MTH 223)
MTH 412 - History of Mathematics (Prerequisites: MTH 215, MTH 216A/B, or MTH 301)
MTH 438 - Applied Mathematical Modeling (core capstone course)
  (Prerequisites: MTH 433, MTH 416, and MTH 432)

Additional Requirement for Single Subject Teaching Concentration (1 course; 4.5 quarter units):
MTH 304 - Mathematics Practicum and Portfolio Project
  (Prerequisites: MTH 215 or MTH 216 A/ B or placement evaluation, which should be taken as early in the program as possible.)

Upper-Division Concentration Requirements (4 courses; 18 quarter units):

Concentration in Mathematics and Applications (172)
Students must successfully complete the following courses for a concentration in mathematics and applications. It is recommended that students take these classes at or near the end of their program after completing the upper-division major requirements.

MTH 440 - Numerical Analysis (Prerequisite: MTH 220)
MTH 441 - Abstract Algebra with Applications (Prerequisite: MTH 416)
MTH 442 - Functions of Complex Variables and its Applications
  (Prerequisite: MTH 223)
MTH 450A - Mathematics Project Course I
  (Prerequisites: All core requirements for mathematics major)

Concentration in Single-Subject Teaching (173)
Students must successfully complete the following courses for a concentration in single-subject teaching. It is recommended that students take these classes at or near the end of their program after completing the upper-division major requirements.

MTH 410 - Computer Technology in the Mathematics Classroom
  (Prerequisite: MTH 215 or MTH 216A/B or MTH 301)
MTH 460 - Problem Solving Strategy
  (Prerequisites: MTH 416 and MTH 417)
MTH 461 - Methods of Teaching of Mathematics
  (Prerequisites: MTH 311, MTH 325, MTH 412, MTH 460)
MTH 450A - Mathematics Project Course I
  (Prerequisites: All core requirements for mathematics major)

Students must complete the major for a BS in Mathematics and complete an interview with the department chair before taking a project course. Students can select additional electives from any other upper-division courses.

Program Information

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Program Locations

• Costa Mesa Campus
• La Mesa Campus
• South Bay Campus
• Spectrum Business Park Campus
• Technology and Health Sciences Center

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