
Graduate Catalog  20192020 Previous Edition
Mathematics, M.S.


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The Master of Science in Mathematics degree is organized into five concentrations.
The Concentration in General Mathematics is a robust but flexible program that allows a student to develop a broad background in Mathematics ranging over a variety of courses chosen from both pure and applied areas, or to tailor a program toward a particular focus that may not be as closely covered by the department’s other degree concentrations (e.g., one that is interdisciplinary in nature).
The Concentration in Applied Mathematics develops analytical and computational skills focused toward applications of mathematics in the physical sciences as encountered in industry, government, and academia.
The Concentration in Mathematics Education is designed primarily for secondary school mathematics teachers interested in professional growth in mathematics teaching. Emphasis in this program is given to developing depth and breadth in mathematics teaching and learning, appropriate to the role of the secondary school teacher.
The Concentration in Actuarial Statistics provides advanced skills and knowledge to individuals seeking actuarial careers in insurance and financial institutions.
The Concentration in Applied Statistics provides theoretical understanding of, and training in, statistical analysis and methods applicable to particular areas of business, industry, government, and academia.

Admission Requirements
For requirements for admission to The Graduate School, see The Graduate School section of this Catalog. Each concentration within the M.S. in Mathematics has its own additional admission requirements listed below.
Early Entry Program
Exceptional undergraduate students at UNC Charlotte may apply for the Early Entry Program and begin work toward the graduate degree before completion of the baccalaureate degree. See the Undergraduate Catalog for details and requirements. Also see the Degree Requirements and Academic Policies section of the Graduate Catalog for more information about Early Entry Programs.
Degree Requirements
All candidates, regardless of which concentration is chosen, are required to take two courses in mathematical or statistical analysis and a comprehensive exam. Students in all concentrations except for the Mathematics Education concentration may also choose a thesis option for 36 credit hours towards the required credit hour total.
Concentration in General Mathematics
The Master of Science in Mathematics with Concentration in General Mathematics program is designed both to provide advanced skills and knowledge for persons seeking positions in industry, government, or teaching at the community college level, and to provide professional development to persons currently in such positions. Qualified graduates are also prepared to enter directly into at least the second year of a Ph.D. program in mathematics, applied mathematics, or statistics, depending on the particular course of study.
Additional Admission Requirements
In addition to the general requirements for admission to the Graduate School, the following are required for the concentration in General Mathematics:
 Applicants must present evidence of the satisfactory completion of at least 27 credit hours of mathematics approved by the department Graduate Committee.
 A satisfactory score is required on at least the Quantitative portion of the general Graduate Record Examination (GRE).
 It is recommended that the student have a basic knowledge of at least two of the areas of algebra, real analysis, and topology.
Concentration Requirements
The M.S. in Mathematics with Concentration in General Mathematics degree requires successful completion of at least 30 credit hours of graduate work approved by the department Graduate Committee, including: MATH 5143 and MATH 5144 or their equivalents; at least one course each from two of the groups I, II, III, V, and VI below; and at least 15 credit hours in 7000level courses. No credit shall be given for 6000level math courses other than mathematical finance courses in group V. With the approval of the department Graduate Committee, a 3 credit hour 6000level course in another department of a theoretical nature or a 3 credit hour 6000level mathematical finance course may be applied toward the 15 credit hours in the 7000level courses. Candidates for the degree concentration must demonstrate, to the satisfaction of the department Graduate Committee, competence on general knowledge in at least three of six groups of courses listed below. This may be accomplished by (a) successful performance on a written or oral comprehensive examination or (b) successful completion of courses in these areas.
Group I  Applied Mathematics
Group II  ProbabilityStatistics
Group III  AlgebraTopology
Group V  Mathematical Finance
Group VI  Computer Science
All 5000 and 6000level ITCS courses
Assistantships
A number of graduate assistantships are available each year (with nationallycompetitive stipends) for qualified applicants. A limited number of fellowship awards can be applied to supplement these stipends for especially qualified students.
Thesis
Completion of a thesis is optional. With the approval of the department Graduate Committee, a candidate may receive up to six of the 15 hours required at the 7000 level for the writing of a master’s thesis on an approved topic. This thesis may be original work, work of an expository nature, or the mathematical formulation and solution of a particular industrial or business problem suggested by the career interests of the student. A candidate may receive no more than six of the hours required at the 7000 level for course and thesis work in another department. If the thesis option is selected, the candidate will be required to defend his/her thesis in an oral examination.
Comprehensive Examination
A candidate must perform satisfactorily on a written or oral comprehensive examination over his/her program of study. The thesis defense is the comprehensive examination for those students who select the thesis option.
Degree Total = 30 Credit Hours
Concentration in Applied Mathematics
The Master of Science in Mathematics with Concentration in Applied Mathematics program is designed to develop critical thinking, intuition, and advanced experience in the techniques of mathematical analysis and their application to the problems of industry and technology. Skills are developed to deal with technical problems encountered in industry, business, and government and to hold leadership positions therein; to teach Applied Mathematics at the undergraduate or community college level; and to potentially study Applied Mathematics leading to the Ph.D. degree.
Concentration Requirements
A candidate for the M.S. in Mathematics with Concentration in Applied Mathematics degree must complete at least 30 credit hours of graduate work approved by the department Graduate Committee to include:
Core Courses (21 credit hours)
Numerical Analysis Courses
Select one of the following:
Advanced Analysis Courses
Select one of the following:
Advanced Applied Mathematics Courses
Select two of the following:
Elective Courses (6 credit hours)
Advanced Elective Courses
Select one of the following:
Mathematics or Application Elective Courses
Select one Mathematics or suitable area of application course with the approval of the student’s advisor. Suggested electives include:
Research Seminar (3 credit hours)
All candidates for the degree concentration must complete three hours of a Research Seminar course in which they carry out an independent project under the supervision of a member of the graduate faculty. The project could involve a specific application to a concrete problem of techniques identified in the literature or studied in other courses. All projects are subject to prior approval of the department Graduate Committee and must be successfully defended before a committee of three graduate faculty members appointed by the department Graduate Committee.
Assistantships
A number of graduate assistantships are available each year (with nationallycompetitive stipends) for qualified applicants. A limited number of fellowship awards can be applied to supplement these stipends for especially qualified students.
Thesis
A student may choose to expand the work begun in MATH 7691 into a master’s thesis by registering for 3 credit hours of MATH 7893 to fulfill the advanced elective course requirement described above. This thesis option affords the student the opportunity to do professional/scholarly work demonstrating proficiency in the area of Applied Mathematics.
Comprehensive Examination
Each candidate for the degree concentration in Applied Mathematics must perform satisfactorily on a final comprehensive examination. This examination will be set and administered by a committee appointed by the department Graduate Committee. It may be in either written or oral form, and it will cover those areas of study and/or research deemed appropriate by the committee. The thesis defense is the comprehensive examination for those students who select the thesis option.
Degree Total = 33 Credit Hours
Concentration in Mathematics Education
The Master of Science in Mathematics with Concentration in Mathematics Education degree program is designed primarily for secondary school mathematics teachers interested in professional growth in mathematics teaching. Emphasis in this program is given to developing depth and breadth in mathematics teaching and learning, appropriate to the role of the secondary school teacher.
By the end of his/her first semester in the program, each student will select a member of the Mathematics Education faculty to serve as his/her Graduate Advisor throughout the program. Approval of the program of each student and provision of advice regarding progress toward the degree are the responsibility of the Graduate Advisor.
Additional Admission Requirements
In addition to the general requirements for admission to the Graduate School, the following are required for graduate study in Mathematics Education:
 Twentyseven hours of undergraduate coursework in Mathematics beyond the freshman level, or evidence of equivalent academic preparation.
 Possession of a North Carolina “A” teacher’s license or the equivalent from another state. An applicant may be admitted on the condition that he/she satisfies the Class “A” requirements early in his/her course of study. Work applied to the Class “A” deficiency may not be applied toward the degree.
 Two years of fulltime experience teaching mathematics in a secondary school or other acceptable teaching experience.
 A satisfactory score is required on the general Graduate Record Examination.
Concentration Requirements
Candidates for the M.S. in Mathematics with Concentration in Mathematics Education degree must complete a minimum of 33 credit hours of graduate coursework or the equivalent. Of these, 18 credit hours must be in courses numbered 6000 or above. Programs of study beyond these 33 credit hours may be required to remove deficiencies in undergraduate programs or to develop areas of need, interest, or desired experience.
Core Courses (15 credit hours)
Mathematical Foundations and Algebra Courses (6 credit hours)
Select two of the following:
Mathematics Education Courses (9 credit hours)
Students take graduatelevel courses covering mathematics education learning theory, research, and contemporary topics in secondary mathematics teaching.
Professional Education Course (3 credit hours)
Basic Portfolio
Each student must complete a Basic Portfolio consisting of documents and artifacts that provides evidence of the student’s professional growth during the program.
Substitutions to satisfy any of the Concentration Requirements must be approved by the Graduate Advisor and the Mathematics Education Coordinator.
Comprehensive Examination
Upon successful completion of all coursework, each candidate for the M.S. in Mathematics with Concentration in Mathematics Education degree must pass a comprehensive final exam consisting of two parts. The student must pass an oral exam on the mathematics content courses. The second part of the exam involves the student presenting documentation that demonstrates his/her professional growth as teachers and educational researchers. The student has the option of presenting either a researchbased project or a comprehensive portfolio. The Graduate Advisor will advise and assist the student in planning his/her Comprehensive Portfolio or Final Research Report.
Degree Total = 33 Credit Hours
Concentration in Actuarial Statistics
The M.S. in Mathematics with Concentration in Actuarial Statistics provides advanced skills and knowledge to individuals seeking actuarial careers in insurance and financial institutions. In addition to acquiring statistical and computational skills, the required courses for this concentration are designed to prepare students to pass a series of examinations needed to earn an Actuarial Designation with the Society of Actuaries or the Casualty Actuarial Society.
Admission Requirements
In addition to the general requirements for admission to the Graduate School, the following are required for the Concentration in Actuarial Statistics:
 9 credit hours of calculus at the level of MATH 1241, MATH 1242, and MATH 2241
 3 credit hours of linear algebra at the level of MATH 2164
 Applicants must present evidence of undergraduate preparation in basic actuarial science including:
 6 credit hours of probability courses at the level of MATH 3122 or STAT 3122 and MATH 3123 or STAT 3123 with a grade of B or above, or passing the SOA Exam P
 6 credit hours of financial mathematics courses at the level of MATH 2228 and MATH 3228 with a grade of B or above, or passing the SOA Exam FM
 6 credit hours of statistics courses at the level of STAT 3110 and STAT 3150 with a grade of B or above
Concentration Requirements
Core Courses (18 credit hours)
The following required courses prepare students for Actuarial Exams IFM (Investment and Financial Markets), LTAM (LongTerm Actaurial Mathematics), STAM (ShortTerm Actuarial Mathematics), and SRM (Statistics for Risk Modeling). Note that Actuarial Exam P (Probability) and FM (Financial Mathematics) are taught at the undergraduate level.
Elective Courses (12 credit hours)
Select from the following with at least 6 credit hours in MATH or STAT courses:
Note:
Other courses may be considered with permission of the department.
Capstone Requirement
Students in the M.S. in Mathematics with Concentration in Actuarial Statistics may select one of the following options as their Capstone Requirement:
Research Seminar
Students who select this option complete 3 credit hours of MATH 7691 in which they carry out an independent project under the supervision of a member of the graduate faculty. If the project option is selected, the candidate is required to defend his/her project before a committee of three graduate faculty members appointed by the department Graduate Committee.
Comprehensive Examination
Each candidate for the Concentration in Actuarial Statistics must perform satisfactorily on a final comprehensive examination. This examination is set and administered by a committee appointed by the department Graduate Committee. It may be in either written or oral form, and it covers those areas of study on the LongTerm and ShortTerm Actuarial Mathematics, including MATH 5229 and STAT 6228 . The research seminar project defense is the comprehensive examination for those students who select the research seminar option.
Grade Requirements
Students must receive a grade of B or above for this concentration.
Degree Total = 30 Credit Hours
Concentration in Applied Statistics
The Master of Science in Mathematics with Concentration in Applied Statistics program is designed to provide advanced skills and knowledge in the planning, design, testing, and implementation of statistical methods. Skills are developed to deal with problems encountered in statistical applications in business, industry, and government; to hold administrative positions requiring planning and implementation of statistical analysis; to teach statistics at the undergraduate or community college level; and to potentially study statistics leading to the Ph.D. degree.
Additional Admission Requirements
In addition to the general requirements for admission to the Graduate School, the following are required for the concentration in Applied Statistics:
 An overall GPA of at least 3.0 on all previous college work including a GPA of at least 3.0 in courses prerequisite to the area of applied statistics.
 Evidence of undergraduate preparation in mathematics and computer science including: 12 credit hours of calculus at the level of MATH 1241, MATH 1242, MATH 2241, and MATH 2242; 3 credit hours of linear algebra at the level of MATH 2164; 3 credit hours of differential equations at the level of MATH 2171; 6 credit hours of probability and statistics at the level of MATH 3122 and MATH 3123; and 3 credit hours of computer programming at the level of ITCS 1214.
Concentration Requirements
A candidate for the M.S. in Mathematics with Concentration in Applied Statistics degree must complete a minimum of 33 credit hours of graduate work approved by the department Graduate Committee, including:
Core Courses (21 credit hours)
Note:
Students who, because of their undergraduate work or other experience, can demonstrate sufficient knowledge of the material in one or more of the core courses may be exempted from taking a course or courses. Exemption from a course carries no credit towards the degree concentration.
Elective Courses (9 credit hours)
MATH/STAT or Applied Elective Courses
Select two courses from an approved list. Examples include:
MATH or STAT Elective Course
Select any MATH or STAT course at the 7000level.
Research Seminar (3 credit hours)
All candidates for the M.S. in Mathematics with Concentration in Applied Statistics degree are required to complete 3 credit hours of a Research Seminar in which they carry out an independent project under the supervision of a member of the graduate faculty. The project could involve a specific application of techniques identified in the literature or studied in other courses. All projects are subject to the prior approval of the department Graduate Committee and must be successfully defended before a committee of three graduate faculty members appointed by the department Graduate Committee.
Assistantships
A number of graduate assistantships are available each year (with nationallycompetitive stipends) for qualified applicants. A limited number of fellowship awards can be applied to supplement these stipends for especially qualified students.
Thesis
A student may choose to expand the work begun in MATH 7691 into a master’s thesis by registering for 3 credit hours of MATH 7893 to fulfill the MATH/STAT 7000level elective course requirement above. This thesis option affords the student the opportunity to do professional and scholarly work demonstrating proficiency in the area of applied statistics.
Comprehensive Examination
Each candidate for the M.S. in Mathematics with Concentration in Applied Statistics degree must perform satisfactorily on an oral comprehensive examination over the candidate’s program of study. The thesis defense is the oral comprehensive examination for those students who select the thesis option.
Degree Total = 30 Credit Hours

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