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Undergraduate Course Catalog 2016-2017

College of Engineering and Physical Sciences

» http://www.ceps.unh.edu


Mathematics and Statistics (MATH)

» http://www.math.unh.edu

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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 and 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 courses 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

* These requirements can be satisfied by MATH 525-526, Linearity I-II.
**  This course satisfies the capstone experience requirement for the Discovery Program.

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 Vibrations.

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


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