# Undergraduate Course Catalog 2010-2011

# College of Engineering and Physical Sciences

### » http://www.ceps.unh.edu

## Mathematics and Statistics (MATH)

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*Professor: * Liming Ge, Karen J. Graham, Eric L. Grinberg, Donald W. Hadwin, Rita A. Hibschweiler, A. Robb Jacoby, Ernst Linder, Dmitri A. Nikshych, Samuel D. Shore, Kevin M. Short, Marianna A. Shubov*Associate Professor: * Maria Basterra, David V. Feldman, Edward K. Hinson, Linyuan Li, Sharon M. McCrone, Junhao Shen*Assistant Professor: * Timothy P. Fukawa-Connelly, John F. Gibson, Mark Lyon*Instructor: * Philip J. Ramsey*Lecturer: * Adam Boucher, Samuel L. Cook, Mehmet Orhon, Neil Portnoy, Yitang Zhang

The Department of Mathematics and Statistics offers a variety of programs. These programs provide flexibility through elective choices and are designed to maximize educational and employment opportunities. Each student must enroll in one specific program; however, changes between programs usually can be accommodated.

The first two years of all programs are similar. In the first year, students are expected to take Calculus I (MATH 425) and Calculus II (MATH 426) as well as an introductory scientific programming course (CS 410). A sophomore typically takes follow-up calculus courses in differential equations (MATH 527) and multidimensional calculus (MATH 528), an introductory statistics course (MATH 539), and a course in mathematical proof (MATH 531). The Senior Capstone Experience is fulfilled by a designated course in each of the degree programs; specific details are given in each program's course listing below.

In addition to its degree programs, the department has an active interest in the actuarial profession and is an examination center for the Society of Actuaries. Those interested in actuarial science should seek the advice of the coordinator of the actuarial program in the department.

For more information about the department’s undergraduate programs, visit www.math.unh.edu.

*Standards for Graduation
*To be certified for graduation with a degree from the Department of Mathematics and Statistics, a student must complete

1. University Academic Requirements

2. All courses used to satisfy the requirements for the major program with a grade of C- or better and have an overall grade-point average of at least 2.0 in these courses.

Note that some Discovery Program requirements will be satisfied by required courses for the major program. In particular MATH 425 satisfies the Discovery Quantitative Reasoning requirement; PHYS 406 (required for the Math Education Elementary Option) and 407 (required for the Mathematics BS) each satisfy the Discovery Physical Sciences requirement.

**Bachelor of Arts, Mathematics Major**

This program may offer a broader liberal arts program than the bachelor of science degree programs. By a careful selection of electives, students can shape this major into a preparation for graduate school, business, or industry.

**Required MATH courses**

MATH 425, Calculus I

MATH 426, Calculus II

MATH 527*, Differential Equations with Linear Algebra

MATH 528*, Multidimensional Calculus

MATH 531, Mathematical Proof, or MATH 545, Introduction to Linear Algebra and Mathematical Proof

MATH 539, Introduction to Statistical Analysis

MATH 761, Abstract Algebra

MATH 762, Linear Algebra

MATH 767, One-Dimensional Real Analysis

Two approved MATH courses chosen in consultation with the academic adviser, one of which must be MATH 797**, Senior Seminar, or MATH 799, Senior Thesis**

*These requirements can be satisfied by MATH 525-526, Linearity I-II.

** Each of these courses satisfies the Capstone Experience requirement for this program.

**Other required courses**

CS 410, Introduction to Scientific Programming

**Foreign language requirement**

Foreign language requirement as defined by the University for the B.A. degree

**Bachelor of Science in Mathematics**

This program offers the strongest concentration in mathematics, requiring courses that are intended to prepare the student for graduate work in mathematics. Through a judicious choice of electives, students may design stronger pre-graduate programs, a program in applied mathematics, or slant the program toward a career in business or industry.

**Required MATH courses**

MATH 425, Calculus I

MATH 426, Calculus II

MATH 527*, Differential Equations with Linear Algebra

MATH 528*, Multidimensional Calculus

MATH 531, Mathematical Proof, or MATH 545, Introduction to Linear Algebra and Mathematical Proof

MATH 539, Introduction to Statistical Analysis

MATH 761, Abstract Algebra

MATH 762, Linear Algebra

MATH 767, One-Dimensional Real Analysis

MATH 784, Topology

MATH 788, Complex Analysis

Two approved MATH courses chosen in consultation with the academic adviser, one of which must be MATH 797**, Senior Seminar, or MATH 799**, Senior Thesis

*These requirements can be satisfied by MATH 525-526, Linearity I-II.

** Each of these courses satisfies the Capstone Experience requirement for this program.

**Other required courses**

CS 410, Introduction to Scientific Programming

PHYS 407-408, General Physics I and II

**Bachelor of Science: Interdisciplinary Programs in Mathematics and Its Applications**

The programs in interdisciplinary mathematics prepare students for employment in areas of applied mathematics and statistics. Some of them can lead to graduate work in appropriate fields (e.g., physics, computer science, or economics). The major may consist of mathematics combined with:

- Computer science,
- Economics,
- Statistics,
- Electrical science, or
- Physics

Each program requires at least 10 mathematics courses along with at least six courses in the discipline of the option. Specific requirements for each option are given in the following listing.

**Computer Science Option**

**Required MATH courses**

MATH 425, Calculus I

MATH 426, Calculus II

MATH 527,* Differential Equations with Linear Algebra

MATH 528,* Multidimensional Calculus

MATH 531, Mathematical Proof

MATH 532, Discrete Mathematics

MATH 539, Introduction to Statistical Analysis

MATH 645,* Linear Algebra for Applications

MATH 753, Introduction to Numerical Methods I

Two approved MATH courses chosen in consultation with the academic adviser, one of which must be either MATH 797**, Senior Seminar, or MATH 798**, Senior Project, or MATH 799**, Senior Thesis

*These requirements can be satisfied by MATH 525-526, Linearity I-II.

** Each of these courses satisfies the Capstone Experience requirement for this program.

**Other required CS courses**

CS 415, Introduction to Computer Science I

CS 416, Introduction to Computer Science II

CS 515, Data Structures

CS 516, Introduction to Software Design and Development

CS 658, Analysis of Algorithms

CS 758, Algorithms

One approved CS elective chosen in consultation with the academic adviser

**Economics Option**

**Required MATH courses**

MATH 425, Calculus I

MATH 426, Calculus II

MATH 527,* Differential Equations with Linear Algebra

MATH 528,* Multidimensional Calculus

MATH 531, Mathematical Proof

MATH 539, Introduction to Statistical Analysis

MATH 645,* Linear Algebra for Applications

MATH 739, Applied Regression Analysis

MATH 753, Introduction to Numerical Methods I

MATH 755, Probability and Stochastic Processes with Applications

Two approved MATH courses at the 700-level chosen in consultation with the academic adviser, of which one must be either MATH 797**, Senior Seminar, or MATH 798**, Senior Project, or MATH 799**, Senior Thesis

*These requirements can be satisfied by MATH 525-526, Linearity I-II.

** Each of these courses satisfies the Capstone Experience requirement for this program.

**Other required courses**

CS 410, Introduction to Scientific Programming

ECON 401, Principles of Economics (Macro)

ECON 402, Principles of Economics (Micro)

ECON 605, Intermediate Microeconomic Analysis

ECON 611, Intermediate Macroeconomic Analysis

ECON 726, Introduction to Econometrics

One approved ECON or DS course chosen in consultation with the academic adviser

**Electrical Science Option**

**Required MATH courses**

MATH 425, Calculus I

MATH 426, Calculus II

MATH 527,* Differential Equations with Linear Algebra

MATH 528,* Multidimensional Calculus

MATH 531, Mathematical Proof

MATH 539, Introduction to Statistical Analysis

MATH 645,* Linear Algebra for Applications

MATH 646, Introduction to Partial Differential Equations

MATH 647, Complex Analysis for Applications

MATH 753, Introduction to Numerical Methods I

One course chosen in consultation with the academic adviser from MATH 797**, Senior Seminar, MATH 798**, Senior Project, and MATH 799**, Senior Thesis

*These requirements can be satisfied by MATH 525-526, Linearity I-II.

** Each of these courses satisfies the Capstone Experience requirement for this program.

**Other required courses**

CS 410, Introduction to Scientific Programming

ECE 541, Electrical Circuits

ECE 548, Electronics Design I

ECE 603, Electromagnetic Fields and Waves I

ECE 633, Signals and Systems I

ECE 634, Signals and Systems II

ECE 757, Fundamentals of Communication Systems

**Physics Option**

**Required MATH courses**

MATH 425, Calculus I

MATH 426, Calculus II

MATH 527,* Differential Equations with Linear Algebra

MATH 528,* Multidimensional Calculus

MATH 531, Mathematical Proof

MATH 539, Introduction to Statistical Analysis

MATH 645,* Linear Algebra for Applications

MATH 646, Introduction to Partial Differential Equations

MATH 647, Complex Analysis for Applications

MATH 753, Introduction to Numerical Methods I

Two approved MATH courses at the 700-level chosen in consultation with the academic adviser, one of which must be either MATH 797**, Senior Seminar, MATH 798**, Senior Project, or MATH 799**, Senior Thesis

*These requirements can be satisfied by MATH 525-526, Linearity I-II.

** Each of these courses satisfies the Capstone Experience requirement for this program.

**Other required courses**

CS 410, Introduction to Scientific Programming

PHYS 407, General Physics I

PHYS 408, General Physics II

PHYS 505-506, General Physics III

PHYS 615, Classical Mechanics and Mathematical Physics I

PHYS 616, Classical Mechanics and Mathematical Physics II

PHYS 701, Introduction to Quantum Mechanics I

PHYS 703, Electricity and Magnetism I

**Statistics Option**

**Required MATH courses**

MATH 425, Calculus I

MATH 426, Calculus II

MATH 527,* Differential Equations with Linear Algebra

MATH 528,* Multidimensional Calculus

MATH 531, Mathematical Proof

MATH 539, Introduction to Statistical Analysis

MATH 645,* Linear Algebra for Applications

MATH 739, Applied Regression Analysis

MATH 755, Probability and Stochastic Processes with Applications

MATH 756, Principles of Statistical Inference

*These requirements can be satisfied by MATH 525-526, Linearity I-II.

**Other required courses**

CS 410, Introduction to Scientific Programming

Three MATH courses chosen in consultation with the academic adviser from the following:

MATH 736, Statistical Methods for Research:

MTH 737, Statistical Methods for Quality Improvement

MATH 740, Design of Experiments I

MATH 741, Survival Analysis

MATH 743, Time Series Analysis

MATH 744, Design of Experiments II

Three approved MATH electives, at least two of which are at the 700-level, chosen in consultation with the academic adviser, one of which must be either MATH 797**, Senior Seminar, or MATH 798**, Senior Project, or MATH 799**, Senior Thesis

** Each of these courses satisfies the Capstone Experience requirement for this program.

**Bachelor of Science in Mathematics Education**

This professional degree program prepares students for mathematics teaching at the elementary, middle/junior high, or secondary level. The program is coordinated with the education department’s teacher certification programs. For the elementary option, full certification requires the five-year program. Students may complete the degree requirements for middle/junior high or secondary option with full teacher certification in either four or five years. Students electing the four-year option must plan for one semester of student teaching (EDUC 694) in their senior year and must consult with the departmental adviser in order to accommodate the scheduling of required MATH courses. The five-year program requires a year-long teaching internship in the fifth year that can be coupled with other graduate work leading to a master’s degree. See education, College of Liberal Arts.

**Elementary School Option**

**Required MATH courses**

MATH 425, Calculus I

MATH 426, Calculus II

MATH 531, Mathematical Proof

MATH 539, Introduction to Statistical Analysis

MATH 545, Introduction to Linear Algebra and Mathematical Proof

MATH 619, Historical Foundations of Mathematics

MATH 621, Number Systems for Teachers

MATH 622, Geometry for Teachers

MATH 623, Topics in Mathematics for Teachers

MATH 657, Geometry

MATH 700, Introduction to Mathematics Education

MATH 703, The Teaching of Mathematics, K-6

MATH 797**, Senior Seminar

** This course satisfies the Capstone Experience requirement in this program.

**Other required courses**

CS 410, Introduction to Scientific Programming

PHYS 406, Introduction to Modern Astronomy, EDUC 500, Exploring Teaching

EDUC 700, Educational Structure and Change

EDUC 701, Human Development and Learning: Educational Psychology

EDUC 705, Alternative Perspectives on the Nature of Education

EDUC 706, Introduction to Reading Instruction in the Elementary Schools

*Note*: EDUC 703F, EDUC 703M and EDUC 751 are requirements for certification that may be taken as an undergraduate.

**Middle/Junior High School Option**

**Required MATH courses**

MATH 425, Calculus I

MATH 426, Calculus II

MATH 531, Mathematical Proof

MATH 539, Introduction to Statistical Analysis

MATH 545, Introduction to Linear Algebra and Mathematical Proof

MATH 619, Historical Foundations of Mathematics

MATH 621, Number Systems for Teachers

MATH 622, Geometry for Teachers

MATH 623, Topics in Mathematics for Teachers

MATH 657, Geometry

MATH 700, Introduction to Mathematics Education

MATH 70878Teaching of Mathematics, 5-8

MATH 797**, Senior Seminar

One approved MATH course chosen in consultation with the academic adviser

** This course satisfies the Capstone Experience requirement in this program.

**Other required courses**

CS 410, Introduction to Scientific Programming

EDUC 500, Exploring Teaching

EDUC 700, Educational Structure and Change

EDUC 701, Human Development and Learning: Educational Psychology

EDUC 705, Alternative Perspectives on the Nature of Education

*Note*: EDUC 751A or EDUC 751B is a requirement for certification that may be taken as an undergraduate.

**Secondary School Option**

**Required MATH courses**

MATH 425, Calculus I

MATH 426, Calculus II

MATH 527, Differential Equations with Linear Algebra

MATH 528, Multidimensional Calculus

MATH 531, Mathematical Proof

MATH 539, Introduction to Statistical Analysis

MATH 545, Introduction to Linear Algebra and Mathematical Proof

MATH 619, Historical Foundations of Mathematics

MATH 624, Analysis for Secondary School Teachers

MATH 657, Geometry

MATH 700, Introduction to Mathematics Education

MATH 709, Teaching of Mathematics, 7-12

MATH 761, Abstract Algebra

MATH 797**, Senior Seminar

** This course satisfies the Capstone Experience requirement in this program.

**Other required courses**

CS 410, Introduction to Scientific Programming

EDUC 500, Exploring Teaching

EDUC 700, Educational Structure and Change

EDUC 701, Human Development and Learning: Educational Psychology

EDUC 705, Alternative Perspectives on the Nature of Education

*Note*: EDUC 751A or EDUC 751B is a requirement for certification that may be taken as an undergraduate.

**Minoring in Mathematics**

The Department of Mathematics and Statistics offers three minor programs: mathematics, applied mathematics, and statistics. These programs, which are open to all students enrolled at the University, require a minimum of five MATH courses as detailed below. Students whose major program requires more than two courses required by the minor program must substitute additional courses from the list of optional courses to meet the five-course minimum.

**Mathematics Minor**

Required (3): MATH 528*, MATH 531 ( and either MATH 761 or MATH 767)

Options (2): Two courses chosen from: MATH 527*, 656, 657, 658, 761, 762, 764, 767, 776, 783, 784, 788

*These requirements can be satisfied by MATH 525-526, Linearity I-II.

**Applied Mathematics Minor**

Required (4): MATH 527*, 528*, 645* (or 545), and 753

Options (1): One course chosen from: MATH 539, 644, 646, 647, 745, 746, 747, or 754

*These requirements can be satisfied by MATH 525-526, Linearity I-II.

* Statistics Minor
*Required (2): MATH 539 (or 644) and MATH 645 (or 545)

Options (3): Three courses chosen from: MATH 737, 740, 741, 742, 744, 755, 756