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CPO #2350 One University Heights Asheville, NC 28804-8511 Office: (828) 251-6556 Fax: (828) 251-6438 |
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A Student Handbook for UNCA Math Majors
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Contents |
Robinson Hall, the science building at UNCA |
FALL 2006
Welcome
To the Prospective Mathematics Student:
Today more than ever mathematics is taking a leading role in shaping our rapidly changing, highly technological world. Mathematicians are joining hands with scientists from other disciplines to solve many pressing problems in medicine, ecology, economics, business, and social sciences.
Mathematics can help you become one of these problem solvers.
Many students have not yet formed specific career goals and want a broad-based education that will provide flexibility in their future choices. For such a student a major or minor in mathematics at a liberal arts school like UNCA is an excellent option. Mathematics is fundamental to many
disciplines and an important part of a liberal arts education. It is highly respected for developing skills which are increasingly vital to modern professions – skills such as analytical thinking, data analysis, mathematical modeling, pattern recognition, and problem solving. Choosing mathematics will keep many career possibilities open. It will give you an invaluable education for whichever profession you eventually choose. In this modern ever-changing world the ability to think in quantitative terms, to reason analytically, and to understand and communicate mathematical ideas will be essential for your success.
The Mathematics Department at UNCA prides itself in the diversity of its curriculum. We offer four concentrations: pure mathematics, applied mathematics, teaching of mathematics, and statistics. Students are encouraged to pursue a broad educational experience while participating in our program. Our classes are small and are taught by professional instructors. In our program you can expect personalized attention. The professors have an open-door policy, and students are free to meet with a professor whenever he/she is available. We hope to foster the type of atmosphere that will make your educational experience most rewarding.
Our department is located on the third floor of the science building, Robinson Hall. The Mathematics Assistance Center (Math Lab) has large windows overlooking the campus quadrangle. This is arguably one of the most pleasant places to work on this campus. All faculty are equipped with computers which are connected to the internet. Students have access to the internet and mathematics software through the machines located in our computer classroom in Robinson 105, and through other computer laboratories on campus.
I hope that this handbook will provide you with the necessary information concerning your program of study in mathematics. Additional information about the Mathematics Department and the university are provided in the university's catalog and on the internet. The Mathematics Department Web address is http://www.unca.edu/math/. If you have any questions concerning mathematics at UNCA, please feel free to contact me at my office phone number 232-5187 or my e-mail address at dpeifer@unca.edu. The department phone number is (828) 251-6556.
David Peifer, Chair
Mathematics Department
FACILITIES
D. H. Ramsey Library
The university's library maintains subscriptions of several dozen mathematical journals suitable for an undergraduate institution. The library's holdings also include a wide variety of resource materials for mathematics such as video tapes, reference works and indices, and instructional materials. These materials are catalogued on a computer system that allows a person to search for a title from any terminal on campus. This system also allows students to check materials from neighboring libraries. A special agreement between our university, Appalachian State University, and Western Carolina University makes it possible for the books of any of the three libraries to be available to all three colleges.
University Computing Center
Throughout campus the Computer Center maintains computer labs and computer classrooms. Many additional classrooms have been upgraded with data projectors and Internet access so that instructors can enhance their instructions with multimedia technology. The Department has two computer classrooms that allow instructors to assign in-class hands-on mathematical investigations using computers. Students wishing to write a paper with a word processor, surf the Internet, or use a specific application should have little trouble finding the necessary computer for their work.
Mathematics Assistance Center (Math Lab)
The Mathematics Department maintains a professionally staffed learning resource center better known as The Math Lab. The Math Lab is designed for students who require additional help for lower-level mathematics courses. Students are invited to drop in at any time to study, to obtain help, and to work in groups. Computers with mathematical software are also available.
In addition to staff members, the Math Lab employs mathematics majors to help tutor students. The Lab is open Monday - Thursday from 8:00 a.m. to 9:30 p.m, Friday from 8:00 a.m. to 4:30 p.m., and Sunday from 4:30 p.m. to 9:30 p.m.
FACULTY PROFILE
ATKINSON, Leigh L. – Asst. Professor; B.A., 1982, University of Mississippi; M.A., 1985,Dartmouth College; Ph.D., 1989, Dartmouth College.
Interests: real analysis and dynamical systems.
BAHLS, Patrick – Asst. Professor; B.S., 1998, University of Denver; M.S., 2000 and Ph.D., 2002, Vanderbilt University.
Interests: algebra (group theory), math and the environment, and number theory.
Additional Responsibilities: Project NExT
BOUDREAUX, Gregory – Asst. Professor; B.S., 1987, Loyola University; M.S., 1996, University of Southwestern Louisiana; Ph.D., 2001, University of Louisiana at Lafayette.
Interests: abstract algebra and topology.
DOHSE, Lothar A. – Professor; B.S., 1975, University of New Orleans; M.S., 1978,and Ph.D., 1982, both from North Carolina State University.
Interests: mathematical modeling, dynamical systems and probability.
Additional Responsibilities: coordinator of the North Carolina's State Mathematics Contest and consultant for Vision of Asheville.
HARTSFIELD, Jane – Asst. Professor; B.S., 1979, Columbus College; M.A., 1982 & M.A.M.S., 1983, University of Georgia; M.A., 2004, Rice University; Ph.D., 2006, Rice University.
Interests: computational neuroscience, mathematical modeling, dynamical systems.
JOHNSON, Ed – Lecturer; M.S., 1998, University of South Carolina.
Interests: topology; Java GUI; evolution.
KAPLAN, Samuel – Assoc. Professor; B.S., 1990, University of North Carolina; M.A., 1992, Boston University; Ph.D., 1996, Boston University.
Interests: differential equations, chaos, math and music
Additional Responsibilities: Member Midwest Dynamical Systems group;
KENDRICK, Peter –Director of the Mathematics Assistance Center; B.S.,1969, State University of New York at Stony Brook; M.A., 1972, SUNY at Stony Brook.
Interests: factors influencing optimal learning, math puzzles and interesting applications of math to daily life.
McCLURE, Mark C. – Assoc. Professor; B.S., 1988, and Ph.D., 1994, Ohio State University.
Interests: fractal geometry and measure theory.
PARSONS, Joe – Professor Emeritus
PATCH, Steve C. – Professor; B.A., 1975, University of Connecticut; M.S., 1982, and Ph.D., 1984, Clemson University.
Interests: applied statistics and data analysis, water quality.
Additional Responsibilities: Director of the Environmental Quality Institute.
PEIFER, David E.– Assoc. Professor; B.A., 1986, Northeastern Illinois University; Ph.D.,1992, University of Illinois.
Interests: modern algebra and geometric group theory.
Additional Responsibilities: Chair of the Mathematics Department and teaches in the Humanities Program.
SPICUZZA, Robert – Lecturer; B.S. Physics, 1969, Worcester Polytechnic Institute; M.S. Physics, 1972, University of Connecticut; Ph.D. Physics, 1976, University of Connecticut.
Interests: experimental Atomic Physics
STEELE, David – Assoc. Professor; B.A. 1971, Clearwater Christian College; M.A., University of South Florida; Ph.D., 1983, U.S.F.
Interests: probability theory and discrete mathematics.
SULOCK, Dorothy R.– Lecturer; B.S., 1970, Glassboro State University; M.A., 1972, University of Virginia; Certificate of Advanced Studies, 1973, U.V.
Interests: applied mathematics, mathematics education, mathematics as a liberal art, nuclear studies.
Additional Responsibilities: teaches: The Nuclear Dilemma, The Ancient World, and the Individual in the Contemporary World.
WHITLOCK, Cathy – Lecturer; B.S., 1989, Salem College, Winston-Salem, NC; M.S., 1995, North Carolina State University.
Interests: applied mathematics and mathematics education.
Additional Responsibilities: Science Olympiad, Math Counts and Math Club.
THE CURRICULUM
Declaration of Major
Declaring a major in mathematics requires a student to first complete Lang 120. Once that is established the student needs to complete and submit a Declaration of Major form to the departmental Chair.
The mathematics major is designed to provide the student with a foundation in mathematics or statistics. There are four concentrations to choose from: Pure (theoretical) Mathematics, Mathematics with Teacher Licensure, Applied Mathematics, and Statistics
You can go here for sample programs.
Course Requirements
All students, in addition to the General Education Requirements, must complete the following course work. For specific courses, see individual programs. It is assumed that a student's mathematics background is sufficient to start with calculus. If this is not the case, he or she will be asked to take MATH 167 (Precalculus).
I. Required courses in the major - 38-39 hours, including:
MATH 191, 192, and 291 (Calculus I, II, and III)
MATH 280 (Math Foundations)
MATH 365 (Linear Algebra I)
MATH 381 (Math Problems)
and MATH 480 (Senior Seminar)
18-19 additional hours of courses in Mathematics or Statistics. See specific concentrations for exact course requirements.
II. Required courses outside major - 9-31 hours including: 3 hours in CSCI 201 (Algorithm
Design). See specific concentrations for possible options.
III. Other departmental requirements - A passing score on a comprehensive Mathematics exam.
The comprehensive exam consists of a standardized two-hour exam, usually given at the end of the problem solving course. If a student fails to attain a passing score on the exam, he or she may be asked to do additional work in mathematics in order to fulfill this requirement. Students are expected to take this exam during the semester prior to their last.
Concentration in Pure Mathematics
This program stresses the concept of mathematics as a liberal art. The courses are designed to give students a general understanding of mathematical theory and the background needed to pursue mathematics in graduate school. Students who enjoy mathematics for mathematics sake are encouraged to choose this program.
The 18 additional hours in Mathematics must include:
MATH 461 (Abstract Algebra I)
MATH 491 (Analysis I)
one of the following:
MATH 366 (Linear Algebra II)
MATH 462 (Abstract Algebra II)
MATH 492 (Analysis II) or
STAT 425-426 (Probability and Mathematical Statistics)
and 9 hours chosen from STAT 225 (Introduction to Calculus-Based Statistics) or
300-400 level MATH and STAT courses.
Other requirements: 6-8 hours in one of the following two-course sequences:
CHEM 111,132 and 144, ECON 101-102, or PHYS 221-222.
Concentration in Mathematics with Teacher Licensure
If a student is interested in teaching mathematics at the high school level, he/she must fulfill two sets of requirements: one to obtain a B.A. in Mathematics, and the other to get a teaching certificate. Thus any student in this program will have two advisors, one in the Mathematics Department and the other in the Education Department.
More information on the requirements of teacher licensure can be found HERE.
The 19 additional hours in Mathematics must include:
MATH 332 (Geometry)
MATH 461 (Abstract Algebra I)
STAT 225 (Introduction to Calculus-Based Statistics)
and 9 hours chosen from MATH 251(Discrete Math) and 300-400 level MATH and STAT courses.
Other requirements: 28 hours, consisting of PSYC 101, 318; and EDUC 310, 311, 314,
383, 396, 455 496. Please see the Education curriculum for more detail.
(Also EDUC 320 for 6-9 licensure.)
Concentration in Statistics
The statistics program is suited for students who are interested in pursuing careers in actuarial science, quality control, or data analysis. This program is also suited for students wishing to enter graduate school in disciplines for which data analysis plays an important roll.
The 19 additional hours in Mathematics must include:
STAT 225 (Introduction to Calculus-Based Statistics) or STAT 185 (Intro Stats)
STAT 325 and 326 (Linear Regression and Analysis of Variance Models)
STAT 425 and 426 (Probability and Mathematical Statistics)
and 3 hours chosen from 300-400 level MATH and STAT courses.
Other requirements: 6 hours in a pre-approved two course sequence. Possible options include: MGMT 220 and 380, ECON 101-301, or ECON 102-302.
Students thinking of pursuing graduate study are strongly advised to take MATH 491 (Analysis I).
Concentration in Applied Mathematics
The Applied Mathematics program is designed for students who are interested in combining two disciplines. This is suited for those who are interested in pursuing careers or graduate studies that are related to mathematics. Although obtaining a minor in a second discipline is not required it is strongly recommended.
The 19 additional hours in Mathematics must include:
MATH 352 (Mathematical Models)
MATH 394 (Differential Equations)
MATH 461(Abstract Algebra I) or
MATH 491 (Analysis I)
STAT 225 (Introduction to Calculus-Based Statistics) or
STAT 425 (Introduction to Probability Theory)
and one of the following:
MATH 366 (Linear Algebra II)
MATH 395 (Partial Differential Equations) or
STAT 425-426 (Probability and Mathematical Statistics).
and 3 hours chosen from 300-400 level MATH and STAT courses.
Other requirements: 15-17 hours in an area of specialization. This area of concentration may be any discipline to which mathematics can be applied. At least 9 hours must be numbered 300 or higher. Course used for area of specialization must be approved by the department chair.
Examples of courses taken for a chosen area of specialization:
Accounting: ACCT 215/216 Principles of Accounting 1 & 2
ACCT 301/302 Intermediate Accounting 1 & 2
ACCT 317 Cost Accounting
Computer Science: CSCI 201/202 Intro to Algorithms & Data Structure
CSCI 255 Computer Organization
CSCI 320 Computer Architecture
CSCI 331 Operating Systems
CSCI 346 Computer Graphics
Environ. Science: CHEM 111/144 Intro Chemistry (lab-science elective)
ENVR 130 Intro to Environmental Science
ENVR 241 Principles to Air Pollution
ENVR 321 Limnology
ENVR 338 Principles to Hydrology and Water Pollution
ENVR 362 Principles of Water Pollution Control
Mathematics Minor
21 hours in mathematics or statistics: Calculus I, II, and III (MATH 191, 192, and 291), and at least nine semester hours of mathematics or statistics courses numbered above 300 with no more than one credit in MATH 381 or one credit in MATH 480. MATH 280 may be substituted for a 300-level course.
Preparation for Graduate School
Students who wish to continue their studies of mathematics in graduate school should consider completing MATH 461, MATH 462, MATH 491 and MATH 492. They should also elect additional upper-level mathematics courses in fields of their interest to broaden their understanding. The requirements for graduation listed in the catalog reflect minimum standards. A student who wishes to have a sound education in mathematics should use the opportunities provided by this university and its Mathematics Department to broaden his or her knowledge base. The best preparation for advanced studies in mathematics is to have some understanding of the different branches of mathematics.
Undergraduate Research
Undergraduate research is not required in the Mathematics major. However, it is a great opportunity for students planning to go on to graduate studies or who enjoy doing research. If you are interested, you should talk with a mathematics professor to discuss possible topics. Most research students work one or two semesters and typically begin in the second semester of their junior year. Below is a list of a few of the past student research projects and the faculty advisors:
Analysis of Taxicab Geometry (Atkinson)
Dynamics of Frisbee Flight (Kaplan)
The Maney Force and Satellite Motion (Kaplan)
Aperiodic Fractal Tilling (McClure)
An Examination of Factors Influencing Lead Leaching in New York City Drinking Water (Patch)
Rewriting Systems for Knot Groups (Peifer)
Classifying Cylindrical Braids (Peifer).
The department secretary has a more thorough handout on Undergraduate Research in the Mathematics Department.
LIST OF COURSE OFFERINGS IN MATHEMATICS
The following is a list of courses that are offered by the department on a regular basis over a two- year period. (Special topics courses are also periodically taught.). Courses included in every concentration are in bold. For a more complete description check your catalogue. For a list of sample programs go here.
MATH 155 Nature of Mathematics (All)
MATH 167 Precalculus (All)
MATH 191 Calculus I (All)
MATH 192 Calculus II (All)
MATH 211 Structure of Math I (F)
MATH 212 Structure of Math I: Lab & Field Experience (F)
MATH 215 Structure of Math II (S)
MATH 216 Structure of Math II: Lab & Field Experience (S)
MATH 251 Discrete Mathematics (S)
MATH 280 Foundations of Mathematics (F & S)
MATH 291 Calculus III (F & S)
MATH 303 History of Math (S-even)
MATH 332 Geometry e (F-odd)
MATH 341 Numerical Analysis (S-even)
MATH 352 Mathematical Models a (S-odd)
MATH 365 Linear Algebra I (F & S)
MATH 366 Linear Algebra II (S-even)
MATH 368 Number Theory (S-odd)
MATH 381 Problems in Mathematics (F)
MATH 391 Advanced Calculus (S-even)
MATH 394 Ordinary Differential Equations (F & S)
MATH 395 Partial Differential Equations (S-odd)
MATH 398 Complex Variables (F-even)
MATH 431 Topology (S-even)
MATH 461 Abstract Algebra I (F)
MATH 462 Abstract Algebra II (S-odd)
MATH 480 Senior Seminar (S)
MATH 491 Analysis I (F)
MATH 492 Analysis II (S-even)
STAT 185 Introductory Statistics (All)
STAT 225 Calculus Based Statistics (F & S)
STAT 321 Exploratory Data Analysis and Nonparametric Statistics (F-even)
STAT 325 Intro to Regression Models (F-odd)
STAT 326 Intro to Anal of Variance Models (S-even)
STAT 327 Applied Multivariate Analysis (S-odd)
STAT 425 Intro to Probability (F-even)
STAT 426 Intro to Mathematical Statistics (S-odd)
CAREERS IN MATHEMATICS AND STATISTICS
The University of North Carolina at Asheville is a school that strives toward giving the student the best possible liberal arts education. Mathematics is one of the traditional liberal arts. Mathematics graduates are not trained for particular jobs or professions, but rather they are equipped with the problem solving and analytical thinking skills necessary for a wide range of careers. The opportunities for a mathematics major are boundless when the undergraduate combines his/her background in mathematics with a specialty in an applied field and with more advanced graduate-level training.
Each year about one-third of the UNCA mathematics graduates become teachers, about one-third go on to graduate school, and about one-third seek employment in industry and government. The following list gives examples of the types of professions some of our graduates have pursued.
Non-Teaching Professions
of Former UNCA Mathematics Majors
| Assistant Principal Biomedical Technician / Statistician Business Systems Manager Clinical Psychologist Computer Analyst Computer Systems Manager Corporate Manager Furniture Manufacturer Instructor at a Community College Kennel Owner Mainframe Systems Manager Market Analyst |
Medical Doctor NASA Technician Personnel Manager Product Planner Production Technician Quality Processor Real Estate Appraiser Senior Vice President of a Bank State IRS Agent (Currently in Law School) Systems Analyst U.S. Navy Budget Analyst U.S. Navy Specialist |
In the past, mathematics majors have found employment in banks, computer companies, and telephone or power companies; in government; in medicine; and in the military. In today's highly technological and ever-changing world there is no specific training which will guarantee you a job. Many companies are looking for a work force with diverse expertise and are interested in persons whose expertise is mathematics.