# Undergraduate Course Catalog 2015-2016

# College of Engineering and Physical Sciences

### » http://www.ceps.unh.edu

## Mathematics and Statistics (MATH)

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

The Department of Mathematics and Statistics offers a variety of programs leading to five different degrees: B.A. degree: mathematics major; B.S. in mathematics degree; B.S. in applied mathematics degree; B.S. in mathematics education degree; and B.S. in statistics degree. 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 programming course (either MATH 445 or 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 variety of designated courses in each of the degree programs; specific details are given in each program's course listing below.

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

**Standards for Graduation**

In all courses used to satisfy the requirements for its major programs, the Department of Mathematics & Statistics requires that a student earn a grade of C- or better and have an overall grade-point average of at least 2.00 in these courses.

**Bachelor of Arts, Mathematics Major**

The bachelor of arts degree with the mathematics major 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,

*which satisfies the QR* *requirement for the Discovery Program,*

MATH 426, Calculus II

MATH 445, Mathematics and Applications with MATLAB

or CS 410, Introduction to Scientific Programming

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

or MATH 645*, Linear Algebra for Applications

MATH 761, Abstract Algebra

MATH 767, One-Dimensional Real Analysis

THREE approved MATH course chosen in consultation with the major adviser

MATH 797**, Senior Seminar,

or MATH 799**, Senior Thesis

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

** This course satisfies the capstone experience requirement for the Discovery Program.

*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

*which satisfies the QR* *requirement for the Discovery Program,*

MATH 426, Calculus II

MATH 445, Mathematics and Applications with MATLAB,

or CS 410, Introduction to Scientific Programming

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;

or MATH 645*, Linear Algebra for Applications

MATH 761, Abstract Algebra

MATH 762, Linear Algebra

MATH 767, One-Dimensional Real Analysis

MATH 784, Topology

MATH 788, Complex Analysis

THREE approved MATH courses chosen in consultation with the major adviser, two of which are chosen from the following:

MATH 765, Algebraic Geometry;

MATH 768, Real Analysis II;

MATH 769, Introduction to Differential Geometry;

MATH 770, Foundations of Number Theory;

MATH 772, Combinatorics

MATH 797**, Senior Seminar;

or MATH 799**, Senior Thesis

** This course satisfies the Capstone Experience requirement for the Discovery Program.

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

*Other Required Courses*

PHYS 407, General Physics I,

*which satisfies the PS and Lab* *requirement for the Discovery Program,*

PHYS 408, General Physics II

**Bachelor of Science in Applied Mathematics**

This degree program prepares students for employment and/or graduate study in a variety of fields and research specializations in which mathematics plays a critical role in the solution of important scientific and technological problems. Students pursuing this degree must choose one of the following options:

Computation, Dynamics and Control, Economics, Fluid Dynamics, or Solid Mechanics and ibrations.

*Required Courses for All Options*

MATH 425, Calculus I,

*which satisfies the QR* *requirement for the Discovery Program,
*MATH 426, Calculus II

MATH 445, Mathematics and Applications with MATLAB

*which satisfies the ETS*

*requirement for the Discovery Program,*

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 753, Introduction to Numerical Methods I

MATH 797**, Senior Seminar;

MATH 798**, Senior Project:

or MATH 799**, Senior Thesis

PHYS 407, General Physics I

*which satisfies the PS and lab*

*requirement for the Discovery Program*

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

** This course satisfies the capstone experience for the Discovery Program.

*Additional Option-specific Course Requirements**Computation Option
*PHYS 408, General Physics II

MATH 647, Complex Analysis for Applications

MATH 745, Fundamentals of Applied Mathematics

CS 415, Introduction to Computer Science I

CS 416, Introduction to Computer Science II

CS 515, Data Structures

CS 659, Introduction to Theory of Computation

CS 758, Algorithms

IAM 751, Introduction to High-Performance Computing

*Dynamics and Control Option
*PHYS 408, General Physics II

MATH 647, Complex Analysis for Applications

MATH 747, Introduction to Nonlinear Dynamics and Chaos

ME 525, Statics

or CIE 525, Statics for Civil Engineers

ME 627, Dynamics

ME 629, Kinematics and Dynamics of Machines

ECE 633, Signals and Systems I

ECE 634, Signals and Systems II

ECE 772, Control Systems

*Economics Option
*MATH 739, Applied Regression Analysis

MATH 755, Probability with Applications

ONE approved MATH elective at the 700-level, chosen in consultation with the major adviser

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 elective

*Fluid Dynamics Option
*PHYS 408, General Physics II

MATH 647, Complex Analysis for Applications

MATH 745, Fundamentals of Applied Mathematics I

ME 503, Thermodynamics

ME 525, Statics

or CIE 525, Statics for Civil Engineers

ME 608, Fluid Dynamics

ME 627, Dynamics

TWO of the following:

ME 707, Analytic Fluid Dynamics

ME 709, Computational Fluid Dynamics

ME 712, Waves in Fluids

*Solid Mechanics and Vibrations Option
*PHYS 408, General Physics II

MATH 647, Complex Analysis for Applications

MATH 745, Fundamentals of Applied Mathematics I

ME 525, Statics

or CIE 525, Statics for Civil Engineers

ME 526, Mechanics of Materials

or CIE 526, Strength of Materials

ME 561, Introduction to Materials Science

ME 627, Dynamics

TWO of the following:

ME 724, Vibration Theory and Applications

ME 727, Advanced Mechanics of Solids

ME 730, Mechanical Behavior of Materials

ME 731, Fracture and Fatigue Engineering Materials

**Bachelor of Science in Statistics**

This program prepares students for employment and/or graduate study in a variety of fields and research specializations in which statistical analysis and its applications play a critical role. In addition to its degree programs, the department has an active interest in the actuarial profession. Those interested in actuarial science should seek the advice of Professor Linyuan Li.

*Required MATH Courses*

MATH 425, Calculus I

*which satisfies the QR* *requirement for the Discovery Program*

MATH 426, Calculus II

MATH 445, Mathematics and Application with MATLAB,

or CS 410, Introduction to Scientific Programming

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 with Applications

MATH 756, Principles of Statistical Inference

THREE MATH courses chosen from:

MATH 736, Statistical Methods for Research

MATH 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

TWO approved MATH electives at least one of which is at the 700-level, chosen in consultation with the major adviser

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.

** This course satisfies the capstone experience requirement for the Discovery 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,

*which satisfies the QR* *requirement for the Discovery Program*

MATH 426, Calculus II

MATH 445, Mathematics and Applications with MATLAB,

or CS 410, Introduction to Scientific Programming

MATH 531, Mathematical Proof

MATH 539, Introduction to Statistical Analysis

MATH 545, Introduction to Linear Algebra;

or MATH 645, Linear Algebra for Applications

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;

or MATH 799**, Senior Thesis

** This course satisfies the capstone experience requirement for the Discovery Program.

*Other Required Courses*

PHYS 406, Introduction to Modern Astronomy,

*which satisfies the PS and Lab* *requirement for the Discovery Program,
*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 751A are requirements for certification that may be taken as an undergraduate.

**Middle/Junior High School Option**

*Required MATH Courses*

MATH 425, Calculus I,

*which satisfies the QR* *requirement for the Discovery Program*

MATH 426, Calculus II

MATH 445, Mathematics and Applications with MATLAB,

or CS 410, Introduction to Scientific Programming

MATH 531, Mathematical Proof

MATH 539, Introduction to Statistical Analysis

MATH 545, Introduction to Linear Algebra

or MATH 645, Linear Algebra for Applications

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 708, Teaching Middle School Mathematics

ONE approved MATH course chosen in consultation with the academic adviser

MATH 797**, Senior Seminar;

or MATH 799**, Senior Thesis

** This course satisfies the Capstone Experience requirement for the Discovery Program.

*Other Required Courses*

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 751B is a requirement for certification that may be taken as an undergraduate.

*Secondary School Option*

*Required MATH Courses*

MATH 425, Calculus I

*which satisfies the QR* *requirement for the Discovery Program*

MATH 426, Calculus II

MATH 445, Mathematics and Applications with MATLAB,

or CS 410, Introduction to Scientific Programming

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

or MATH 645, Linear Algebra for Applications

MATH 619, Historical Foundations of Mathematics

MATH 624, Analysis of Secondary School Mathematics

MATH 657, Geometry

MATH 700, Introduction to Mathematics Education

MATH 709, Teaching of Mathematics, 7-12

MATH 761, Abstract Algebra

MATH 797**, Senior Seminar,

or MATH 799**, Senior Thesis

** This course satisfies the Capstone Experience requirement for the Discovery Program.

*Other Required Courses*

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 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 elective courses to meet the five-course minimum.

**Mathematics Minor**

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

Electives (2): Two courses chosen from: MATH 657, 658, 761, 762, 765, 767, 768, 769, 770, 772, 776, 783, 784, 788

* This requirement can be satisfied by MATH 526, Linearity II.

**Applied Mathematics Minor**

Required (4): MATH 528*, 645*, 745 and 753

Elective (1): One course chosen from: MATH 647, 746, 747, or 755 .

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

**Statistics Minor**

Required (2): MATH 539 (or 644) and MATH 645

Electives (3): Three courses chosen from: MATH 736, 737, 739, 740, 741, 743, 744, 755, 756