# UWM Undergraduate Catalog 2013-2014

## College of Letters and Science

## Mathematical Sciences

- Web Home Pages:

- Actuarial Science Major
- Atmospheric Science Major
- Mathematics Major
- Actuarial Science Minor
- Atmospheric Science Minor
- Mathematics Minor
- Applied Mathematics and Computer Science
- Courses: Atmospheric Sciences (ATM SCI)
- Courses: Mathematics (MATH)
- Courses: Mathematical Statistics (MTHSTAT)
- Faculty

Mathematics is the international language of science and technology. Much of the subject matter in engineering and the natural sciences, as well as some social sciences such as economics, is presented in mathematical terms. Mathematical and statistical techniques are vital in fields that usually are not considered mathematical, such as biology, psychology, and political science.

Some students come to mathematical sciences with the intention of teaching in high school or college or pursuing research in mathematics. Some are attracted to mathematics for its own sake, for the beauty, discipline, logic, and problem-solving challenges. Other students pursue mathematics in order to achieve deeper understanding in their own areas of study.

**Actuarial science** is the mathematical analysis of problems in economics,
finance, and insurance. It requires knowledge of statistics, probability, and
interest theory and how they relate to financial issues.

**Applied mathematics** is a discipline using mathematical analysis to solve
problems coming from outside the field of mathematics.

**Atmospheric science** is the study of short-term weather and long-term
climate, involving activities such as weather forecasting and analysis and air
pollution meteorology. It uses advanced methods in statistics and numerical
modeling.

**Computational mathematics** is closely related to applied mathematics.
It emphasizes techniques of scientific computing and other computational analysis.

**Pure mathematics** emphasizes the theory and structure underlying all
areas of mathematics.

**Statistics** is a field of mathematics that provides strategies and tools
for using data to gain insight into real world and experimental problems.

A major in **mathematical sciences** allows students to design, in conjunction
with an advisor, a personalized program to fit individual interests and talents.
Students may major in *actuarial science*, *atmospheric science,* or *mathematics*.

The **basic mathematics major** has been designed for students who are completing
a double major. For this reason, flexibility is offered; students should find
it relatively easy to combine the requirements of the mathematics major with
the mathematical requirements or electives of other programs.

**Students may specialize** in any of four particularly significant areas– applied mathematics, computational mathematics, pure mathematics, and
statistics. Completing a specialization gives a student expertise that is indicated
on the transcript and that will be helpful in seeking employment or gaining
admission to graduate school.

Students of the sciences, engineering, computer science, economics, and business often complete a significant number of mathematical sciences credits. These students are encouraged to take a mathematics major or minor, which adds an official recognition of important analytical skills valued by employers and graduate schools.

Students interested in teaching mathematics at the K-12 level should consult the School of Education section of this catalog.

Please visit the departmental Web page at **http://www.math.uwm.edu** and
follow the links to the undergraduate program.

**Curricular Areas in Mathematical Sciences **

Students should note that there are three curricular areas and corresponding abbreviations in the Department of Mathematical Sciences: Atmospheric Science (Atm Sci), Mathematics (Math), and Mathematical Statistics (MthStat).

**Course of Study: Majors**

Students considering a major in the Department of Mathematical Sciences need to come to the department to declare their major and be assigned an advisor. All courses selected for the major must be approved by the advisor, and students should check regularly with their advisors to plan their courses of study in a coherent and timely fashion.

**Preparatory Curriculum.** Students in all majors in the Department of Mathematical Sciences must complete Math 231, 232, and 233 (or equivalent). Math 225 and 226 are equivalent to Math 231; Math 221 and 222 are equivalent to Math 231, 232, and 233. Students majoring in actuarial science or mathematics must have a GPA of at least 2.5 in these courses. All majors must take either Math 234 or 240, as well as a course in computer programming in a modern, high-level language. The department also recommends strongly one year of calculus-based physics. Actuarial science and atmospheric science majors must complete additional preparatory curricula, as indicated below.

**Capstone Experience.** Students in all majors and major options in the Department of Mathematical Sciences must complete either Atm Sci 599 or Math 599, "Capstone Experience." The aim of the department’s capstone experience is to encourage independent learning. Students complete a research paper in the context of this course, which satisfies the L&S research requirement. Students must obtain consent of a professor to enroll in Atm Sci 599 or Math 599.

The actuarial science major is an interdisciplinary program intended to prepare students for professional examinations and employment as actuaries. Students must complete the courses listed below, including at least 15 upper-division (numbered 300 and above) credits in the major in residence at UWM. The College requires that students attain at least a 2.5 GPA on all credits in the major attempted at UWM. In addition, students must attain a 2.5 GPA on all major credits attempted, including any transfer work.

**Additional Preparatory Curriculum **

Bus Adm 201 | Understanding and Using Financial Statements | 3 |

Econ 103 | Principles of Microeconomics | 3 |

Econ 104 | Principles of Macroeconomics | 3 |

Math 234 | Linear Algebra and Differential Equations | 4 |

At least 6 credits to be completed from among: |

Bus Adm 230 | Introduction to Information Systems | 3 |

CompSci 151 | Introduction to Scientific Programming in Fortran | 3 |

CompSci 201 | Introductory Computer Programming | 4 |

One of the following three courses: |

MthStat 215 | Elementary Statistical Analysis | 3 |

Econ 210 | Economic Statistics | 3 |

Bus Adm 210 | Introduction to Management Statistics | 3 |

**Core Curriculum **

*The following coursework is required:*

Econ 301 |
Intermediate Microeconomics | 3 |

Econ 302 |
Intermediate Macroeconomics |
3 |

Math 311 | Theory of Interest | 3 |

Math 571 |
Introduction to Probability Models | 3 |

Math 599 |
Capstone Experience |
1 |

MthStat 361 |
Introduction to Mathematical Statistics I | 3 |

MthStat 362 |
Introduction to Mathematical Statistics II | 3 |

MthStat 563 |
Regression Analysis | 3 |

MthStat 564 |
Time Series Analysis | 3 |

MthStat 591 | Foundations in Professional Practice in Actuarial Science | 1 |

MthStat 592 | Actuarial Science Laboratory I: Probability | 1 |

MthStat 593 | Actuarial Science Laboratory II: Interest Theory, Finance, Economics | 1 |

One of the following: |

Bus Adm 350 |
Principles of Finance | 3 |

Bus Adm 450 |
Intermediate Finance | 3 |

**Recommendations for Actuarial Science Students**. To achieve the best preparation for the actuarial examinations, students should take more than the minimum number of credits from the above list. Students are encouraged strongly to take two courses in communication to prepare for an actuarial career. Commun 103, 262, and/or 264 are recommended. Some of the required and recommended course work will satisfy portions of the Letters and Science distribution requirements. Econ 103 and 104 satisfy 6 credits of the social science requirement; Econ 248 (Economics of Discrimination) satisfies the cultural diversity requirement; the recommended communication courses count toward the humanities requirement. Students also are advised to enroll in an internship (MthStat 489) as part of their elective credits.

Students may find information regarding the actuarial profession by checking the web pages of the Department of Mathematical Sciences or those of the Society of Actuaries (www.soa.org).

The atmospheric science division of the department offers courses designed to prepare students for professional work in meteorology in both government and private service and for graduate study in atmospheric sciences. Students must complete at least 15 upper-division (numbered 300 and above) credits in the major in residence at UWM. The College requires that students attain at least a 2.5 GPA on all credits in the major attempted at UWM. In addition, students must attain a 2.5 GPA on all major credits attempted, including any transfer work. The following courses are required for the atmospheric science major.

**Additional Preparatory Curriculum.** In addition to the preparatory curriculum
required of all mathematical sciences majors, the following courses are required. These courses do not count in calculating the major GPA.

Math 234 |
Linear Algebra and Differential Equations |

Chem 102 |
General Chemistry |

Physics 209/214 |
Physics I (Calculus Treatment) |

Physics 210/215 |
Physics II (Calculus Treatment) |

CompSci 151 |
Introduction to Scientific Programming in Fortran |

**Required Courses (Core) **

Atm Sci 240 |
Introduction to Meteorology |

Atm Sci 330 |
Air-Pollution Meteorology |

Atm Sci 350 |
Atmospheric Thermodynamics |

Atm Sci 351 |
Dynamic Meteorology I |

Atm Sci 352 |
Dynamic Meteorology II |

Atm Sci 360 |
Synoptic Meteorology I |

Atm Sci 361 |
Synoptic Meteorology II |

Atm Sci 464 |
Cloud Physics |

Atm Sci 511 | Seminar in Atmospheric Radiation and Remote Sensing |

Atm Sci 599 |
Capstone Experience |

Math 320 |
Introduction to Differential Equations |

**Electives - at least 9 credits from the following
courses: **

Atm Sci 320 | Atmospheric Chemistry |

Atm Sci 460 |
Mesoscale Circulations |

Atm Sci 465 |
Meteorological Instrumentation |

Atm Sci 470 | Tropical Meteorology |

Atm Sci 480 |
The General Circulation and Climate Dynamics |

Atm Sci 497 | Study Abroad: (Subtitle) |

Atm Sci 505 |
Micrometeorology |

Atm Sci 531 |
Numerical Weather Prediction |

Atm Sci 690 |
Topics in Atmospheric Sciences: (Subtitle) |

Math 313 |
Linear Programming and Optimization |

Math 314 |
Mathematical Programming and Optimization |

Math 321 |
Vector Analysis |

Math 322 | Introduction to Partial Differential Equations |

Math 405 | Mathematical Models and Applications |

Math 413 |
Introduction to Numerical Analysis |

Math 414 |
Numerical Analysis |

Math 416 |
Computational Linear Algebra |

Math 471 |
Introduction to the Theory of Probability |

Math 521 |
Advanced Calculus |

Math 522 |
Advanced Calculus |

Math 535 |
Linear Algebra |

Math 571 |
Introduction to Probability Models |

Math 581 |
Introduction to the Theory of Chaotic Dynamical Systems |

Math 601 |
Advanced Engineering Mathematics I |

Math 602 |
Advanced Engineering Mathematics II |

MthStat 361 |
Introduction to Mathematical Statistics I |

MthStat 362 |
Introduction to Mathematical Statistics |

MthStat 467 |
Introductory Statistics for Physical Sciences and Engineering Students |

MthStat 563 |
Regression Analysis |

MthStat 564 |
Time Series Analysis |

Upper-division math refers to any Math or MthStat course at the 300 level or above. Sequence refers to any of the following pairs of courses: 313/314, 320/322, 361/362, 413/414. 521/522, 531/535, 621/622, 631/632.

Many courses fall naturally into groups:

**Applied mathematics group**: Math 307, 320, 321, 322, 371, 405, 431, 520, 525, 581, 623.

**Computational mathematics group**: Math 313, 314, 413, 414, 416.

**Probability and statistics group**: Math 471, 571; MthStat 361, 362, 561, 562, 563, 564, 565, 567, 568, 569.

**Pure mathematics group**:

I. Math 521, 531, 535, 551, 621, 631;

II. Math 451, 453, 511, 522, 529, 537, 553, 555, 622, 632

**Basic Mathematics Major**. Students electing the basic mathematics major must complete Math 341 and 24 additional upper-division math credits, including at least 3 each from the applied math, computational math, probability and statistics, and pure math I groups. At least one sequence is required among these 24 upper-division math credits. Students must complete at least 15 upper-division (numbered 300 and above) credits in the major in residence at UWM. The College requires that students attain at least a 2.5 GPA on all credits in the major attempted at UWM. In addition, students must attain a 2.5 GPA on all major credits attempted, including transfer work.

**Specialization Options**

The following four options add a specialty to the basic math major. Students must complete the requirements of the basic math major as stated above as well as the appropriate course requirements for the specialties, as listed below. Completion of any of the specialty options requires at least 30 upper-division math credits, in addition to Math 341.

**Applied Mathematics Option.** At least 9 credits from the applied math
group, 9 from the computational math group, and 6 from the probability and statistics
group; two courses from CompSci 151 or 153, 201, and 251.

**Computational Mathematics Option.** At least 6 credits from the applied
math group, 12 from the computational math group, and 6 from the probability
and statistics group; all of CompSci 151 or 153, 201, 251, 317, 351, and 535.

**Pure Mathematics Option.** At least 18 credits from the pure math group,
with at least 9 from the pure math I group; CompSci 151 or 153 or 201.

**Statistics Option**. Students must complete the following:

**Additional Preparatory Curriculum**

MthStat 215 | Elementary Statistical Analysis | 3 |

At least one selection from: |

CompSci 151 | Introduction to Scientific Programming in Fortran | 3 |

CompSci 153 | Introduction to Scientific Programming in C++ | 3 |

or both |
||

CompSci 201 | Introductory Computer Programming | 3 |

and |

CompSci 251 | Intermediate Computer Programming | 4 |

**Core Curriculum**

At least one of the following two sequences: |

Math 521 and 522 | Advanced Calculus | 6 |

Math 621 and 622 | Introduction to Analysis | 6 |

All of the following three courses: |

MthStat 361 | Introduction to Mathematical Statistics I | 3 |

MthStat 362 | Introduction to Mathematical Statistics II | 3 |

MthStat 563 | Regression Analysis | 3 |

At least three of the following: |

MthStat 562 | Design of Experiments | 3 |

MthStat 564 | Time Series Analysis | 3 |

MthStat 565 | Nonparametric Statistics | 3 |

MthStat 568 | Multivariate Statistical Analysis | 3 |

Math 571 | Introduction to Probability Models | 3 |

**Preparation for Graduate Work in Mathematical Sciences. **It is recommended
that students who plan to do graduate work in mathematical sciences complete
as many as possible of the following courses: Math 521, 522, 531 and 535 (or
631 and 632), 551, and 623. Many graduate programs require reading knowledge
of French, German, or Russian.

**Course of Study: Minors**

**Actuarial Science Minor**. Admission to this minor requires a minimum grade point average of 2.5 in Math 231, 232, and 233. Students who have completed these courses with the required grade point average may complete a formal declaration of minor at the department office. These three courses do not count in the minor GPA. The following courses are required:

Math 234 | Linear Algebra and Differential Equations | 4 |

Math 311 | Theory of Interest | 3 |

MthStat 361 | Introduction to Mathematical Statistics I | 3 |

MthStat 362 | Introduction to Mathematical Statistics II | 3 |

*One of the following, with a grade of B- or better in each course taken:*

Bus Adm 450 | Intermediate Finance | 3 |

or both |
||

Econ 301 | Intermediate Microeconomics | 3 |

and |
||

Econ 302 | Intermediate Macroeconomics | 3 |

Students must complete at least 9 upper-division (numbered 300 and above) credits for the minor in residence at UWM. The College requires that students attain at least a 2.5 GPA on all credits in the minor attempted at UWM. In addition, students must attain a 2.5 GPA on all minor credits attempted, including any transfer work.

**Atmospheric Science Minor. **The minor consists
of a minimum of 18 credits in atmospheric science. Six of these credits must
include Atm Sci 240 and 360. The remaining 12 Atm Sci credits must be at the
300 level or above. Students must complete at least 9 upper-division (numbered 300 and above) credits in the minor in residence at UWM. The College requires that students attain at least a 2.5 GPA on all credits in the minor attempted at UWM. In addition, students must attain a 2.5 GPA on all minor credits attempted, including any transfer work.

**Mathematics Minor. **Students
minoring in mathematics must complete Math 231, 232, and 233 or an equivalent
math sequence with a GPA of at least 2.5. They must take 12 credits in mathematical
sciences (curricular areas Math and MthStat) courses numbered 300 and above,
at least 9 of them in residence at UWM. Math 234 may substitute for 3 of these
12 credits. All courses chosen to complete the 12-credit requirement must be
approved by the associate chair of the Department of Mathematical Sciences. Students must complete at least 9 upper-division (numbered 300 and above) credits in the minor in residence at UWM. The College requires that students attain at least a 2.5 GPA on all credits in the minor attempted at UWM. In addition, students must attain a 2.5 GPA on all minor credits attempted, including any transfer work.

**Applied Mathematics and Computer Science**

A related degree program is Applied Mathematics and Computer Science (AMCS), offered and awarded jointly by the College of Letters and Science Department of Mathematical Sciences and the College of Engineering and Applied Science Department of Computer Science. This program allows students to study a mixture of mathematics and computer science suited to their natural interests and ambitions. It highlights the unity of the fields of mathematical sciences and computer science, while still providing a firm foundation for all areas of applied and computational mathematics and computer science. For further information, please refer to the Inter-School/College Programs section of this catalog, and visit the program's
web page at http**://**www4.uwm.edu/letsci/math/undergraduate/majors/cs.cfm.

**Courses**

**Atmospheric Sciences (ATM SCI)**

**Mathematics (MATH)**

**Mathematical Statistics (MTHSTAT)**

**Fredric D. Ancel, Prof., Ph.D.
**University
of Wisconsin-Madison

James E. Arnold, Jr., Assoc. Prof. Emeritus, Ph.D.

**Jay H. Beder, Prof., Ph.D., Asst. Chair
**George Washington University

**Allen D. Bell, Assoc. Prof., Ph.D.**

University of Washington

**Vytaras Brazauskas, Prof., Ph.D.**

University of Texas at Dallas

**Suzanne L. Body, Asst. Prof., Ph.D.**

**Cornell University**

**Karen M. Brucks, Assoc. Prof., Ph.D.**

University of North Texas

Associate Dean, College of Letters and Science

**Clark Evans, Asst. Prof., Ph.D.**

**Florida State University**

**Dashan Fan, Prof., Ph.D.**

Washington University

**Daniel Gervini, Assoc. Prof., Ph.D.**

Universidad de Buenos Aires

**Jugal K. Ghorai, Prof., Ph.D.**

Purdue University

**Craig R. Guilbault, Prof., Ph.D., Graduate Dir.**

University of Tennessee

Robert L. Hall, Assoc. Prof. Emeritus, Ph.D.

**Peter Hinow, Asst. Prof., Ph.D.**

Vanderbilt University

Ingrid Holzner, Sr. Lect. Emerita, M.S.

**G. Christopher Hruska, Assoc. Prof., Ph.D.**

**Cornell University**

**Jonathan Kahl, Prof., Ph.D.**

University of Michigan

**Eric S. Key, Prof., Ph.D.**

Cornell University

**Kelly Kaiser Kohlmetz, Sr. Lect., Ph.D.**

**University of Wisconsin-Milwaukee**

**Sergey Kravtsov, Assoc. Prof., Ph.D.**

**Florida State University**

**Vincent Larson, Prof., Ph.D.**

Massachusetts Institute of Technology

**Istvan G. Lauko, Assoc. Prof., Ph.D.**

Texas Tech University

Cheng-Ming Lee, Prof. Emeritus, Ph.D.

**Tzu-Chu Lin, Assoc. Prof., Ph.D.**

University of Iowa

**Wiliam Mandella, Sr. Lect., M.S.**

University of New Orleans

**Kevin B. McLeod, Assoc. Prof., Ph.D.**

University of Minnesota

Genevieve T. Meyer, Instr. Emerita

Richard J. Mihalek, Assoc. Prof. Emeritus, Ph.D.

Albert J. Milani, Prof. Emeritus, Ph.D.

Robert H. Moore, Assoc. Prof. Emeritus, Ph.D.

**Ian M. Musson, Prof., Ph.D.**

University of Warwick, U.K.

Thomas O’Bryan, Assoc. Prof. Emeritus, Ph.D.

Richard J. O’Malley, Prof. Emeritus, Ph.D.

**Boris L. Okun, Assoc. Prof., Ph.D.**

State University of New York at Binghamton

Dattatraya J. Patil, Assoc. Prof. Emeritus, Ph.D.

**Gabriella Pinter, Assoc. Prof., Ph.D.**

Texas Tech University

**Paul Roebber, Distinguished Prof., Ph.D.**

McGill University

David H. Schultz, Prof. Emeritus, Ph.D.

**Steven Schwengels, Sr. Lect., M.S.**

University of Wisconsin-Milwaukee

Lindsay A. Skinner, Prof. Emeritus, Ph.D.

Donald W. Solomon, Assoc. Prof. Emeritus

**Richard Stockbridge, Prof., Ph.D., Chair**

University of Wisconsin-Madison

**Lijing Sun, Asst. Prof., Ph.D.**

Wayne State University

**Kyle Swanson, Prof., Ph.D., Atmos. Sci. Coord.**

University of Chicago

**Anastasios Tsonis, Distinguished Prof., Ph.D.**

McGill University

**Hans W. Volkmer, Prof., Ph.D.**

University of Konstanz

**Bruce A. Wade, Prof., Ph.D.**

University of Wisconsin-Madison

Gilbert G. Walter, Prof. Emeritus, Ph.D

**.**

**Jeb Willenbring, Assoc. Prof., Ph.D.**

**University of California, San Diego**

**Dexuan Xie, Prof., Ph.D.**

University of Houston

**Chao Zhu, Assoc. Prof., Ph.D.**

Wayne State University

**Yi Ming Zou, Prof., Ph.D., Assoc. Chair**

Indiana University

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University of Wisconsin-Milwaukee Undergraduate Catalog 2013-2014:

**Mathematical Sciences**

[ College of Letters and Science ]

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