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UWM Undergraduate Catalog 2014-2015

College of Letters & Science

Mathematical Sciences

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 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.

Actuarial Science Major

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 work is required:

 

MATH 311

Theory of Interest

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 two courses:

 

     

BUS ADM 350

Principles of Finance

3

BUS ADM 450

Intermediate Finance

3

One of the following two courses:

 

ECON 301

Intermediate Microeconomics

3

ECON 302

Intermediate Macroeconomics

3

One of the following three pairs:

 

     

A1. MATH 571

Introduction to Probability Models

3

A2. MTHSTAT 691

Actuarial Models I: Life Contingencies

3

B1. MATH 571

Introduction to Probability Models

3

B2. MTHSTAT 692

Actuarial Models II: Financial Economics

3

C1. MTHSTAT 596

Actuarial Statistics I: Fitting of Loss Models

3

C2. MTHSTAT 597

Actuarial Statistics II: Risk Measures, Credibility, and Related Topics

3

Recommended Electives. To achieve the best preparation for the actuarial examinations and for an actuarial career, students should enroll in an internship (MTHSTAT 489), take courses in communication (COMMUN 103, 264), and expand their knowledge in economics (ECON 221, 248). Note that ECON 248 satisfies the cultural diversity requirement.

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).

Atmospheric Science Major

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)

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 415

Introduction to Scientific Computing

MATH 417

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

MATH 615

Numerical Solution of Partial Differential Equations for Scientific Computing

MATH 617

Optimization

MTHSTAT 361

Introduction to Mathematical Statistics I

MTHSTAT 362

Introduction to Mathematical Statistics II

MTHSTAT 467

Introductory Statistics for Physical Sciences and Engineering Students

MTHSTAT 563

Regression Analysis

MTHSTAT 564

Time Series Analysis

Mathematics Major

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, 413/415. 413/417, 415/417, 413/615, 413/617, 415/615, 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, 415, 417, 615, 617.

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 & 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 www4.uwm.edu/letsci/math/undergraduate/majors/cs.cfm.

Courses

Atmospheric Sciences (ATM SCI)

Mathematics (MATH)

Mathematical Statistics (MTHSTAT)


Faculty

Fredric D. Ancel, Prof., PhD
University of Wisconsin-Madison

James E. Arnold, Jr., Assoc. Prof. Emeritus, PhD

Jay H. Beder, Prof., PhD, Asst. Chair
George Washington University

Allen D. Bell, Assoc. Prof., PhD
University of Washington

Vytaras Brazauskas, Prof., PhD
University of Texas at Dallas

Suzanne L. Boyd, Assoc. Prof., PhD
Cornell University

Karen M. Brucks, Assoc. Prof., PhD
University of North Texas
Associate Dean, College of Letters & Science

Clark Evans, Asst. Prof., PhD
Florida State University

Dashan Fan, Prof., PhD
Washington University

Daniel Gervini, Assoc. Prof., PhD
Universidad de Buenos Aires

Jugal K. Ghorai, Prof., PhD
Purdue University

Craig R. Guilbault, Prof., PhD, Graduate Dir.
University of Tennessee

Robert L. Hall, Assoc. Prof. Emeritus, PhD

Peter Hinow, Asst. Prof., PhD
Vanderbilt University

Ingrid Holzner, Sr. Lect. Emerita, MS

G. Christopher Hruska, Assoc. Prof., PhD
Cornell University

Jonathan Kahl, Prof., PhD, Atmos. Sci. Coord.
University of Michigan

Eric S. Key, Prof., PhD
Cornell University

Kelly Kaiser Kohlmetz, Sr. Lect., PhD
University of Wisconsin-Milwaukee

Sergey Kravtsov, Assoc. Prof., PhD
Florida State University

Vincent Larson, Prof., PhD
Massachusetts Institute of Technology

Istvan G. Lauko, Assoc. Prof., PhD
Texas Tech University

Cheng-Ming Lee, Prof. Emeritus, PhD

Tzu-Chu Lin, Assoc. Prof., PhD
University of Iowa

Wiliam Mandella, Sr. Lect., MS
University of New Orleans

Kevin B. McLeod, Assoc. Prof., PhD
University of Minnesota

Genevieve T. Meyer, Instr. Emerita

Richard J. Mihalek, Assoc. Prof. Emeritus, PhD

Albert J. Milani, Prof. Emeritus, PhD

Robert H. Moore, Assoc. Prof. Emeritus, PhD

Ian M. Musson, Prof., PhD
University of Warwick, U.K.

Thomas O’Bryan, Assoc. Prof. Emeritus, PhD

Richard J. O’Malley, Prof. Emeritus, PhD

Boris L. Okun, Prof., PhD
State University of New York at Binghamton

Dattatraya J. Patil, Assoc. Prof. Emeritus, PhD

Gabriella Pinter, Assoc. Prof., PhD
Texas Tech University

Paul Roebber, Distinguished Prof., PhD
McGill University

David H. Schultz, Prof. Emeritus, PhD

Steven Schwengels, Sr. Lect., MS
University of Wisconsin-Milwaukee

Lindsay A. Skinner, Prof. Emeritus, PhD

Donald W. Solomon, Assoc. Prof. Emeritus

Richard Stockbridge, Prof., PhD
University of Wisconsin-Madison

Lijing Sun, Asst. Prof., PhD
Wayne State University

Kyle Swanson, Prof., PhD, Chair
University of Chicago

Anastasios Tsonis, Distinguished Prof., PhD
McGill University

Hans W. Volkmer, Prof., PhD
University of Konstanz

Bruce A. Wade, Prof., PhD
University of Wisconsin-Madison

Lei Wang, Asst. Prof., PhD
University of Michigan

Gilbert G. Walter, Prof. Emeritus, PhD

Wei Wei, Asst. Prof., PhD
University of Waterloo

Jeb Willenbring, Assoc. Prof., PhD
University of California, San Diego

Dexuan Xie, Prof., PhD
University of Houston

Chao Zhu, Assoc. Prof., PhD
Wayne State University

Yi Ming Zou, Prof., PhD, Assoc. Chair
Indiana University



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