UWM Undergraduate Catalog 20172018
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 problemsolving challenges. Other students pursue mathematics in order to achieve deeper understanding in their own areas of study.
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.
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.
Atmospheric science is the study of shortterm weather and longterm climate, involving both applied activities such as weather forecasting and analysis and fundamental research. It uses advanced methods in statistics and numerical modeling.
The mathematics major has been designed to be flexible so that students could complete their major requirements via courses that match their interests and goals. Many tudents should find it relatively easy to complete double majors in mathematics and another subject.
Most mathematics courses belong in one of the following four groups: applied mathematics, computational mathematics, pure mathematics, and statistics.
Applied Mathematics is a discipline using mathematical analysis to solve problems coming from outside the field of mathematics.
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 realworld and experimental problems.
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 K12 level should consult the School of Education section of this catalog.
Please visit the departmental web page at http://uwm.edu/math/ 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 a faculty 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 (or 213), 232, and 233 (or equivalent). 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 2.500 in these courses. All majors must take either Math 234 or 240, as well as a course in computer programming in a modern, highlevel language (e.g., CompSci 151, 153, 250, or 251). The department also recommends strongly one year of calculusbased 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 a "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. For Actuarial Science majors, the capstone is Math 599. For Atmospheric Science majors, the capstone is Atm Sci 599. Mathematics majors may choose either Math 599 or Math 575. 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. This major is available as a BA degree from the College of Letters and Science, or as a second major for students completing another UWM degree. Students must complete the courses listed below, including at least 15 upperdivision (numbered 300 and above) credits in the major in residence at UWM. The College requires that students attain at least a 2.500 GPA on all credits in the major attempted at UWM. In addition, students must attain a 2.500 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 250 
Introductory Computer Programming 
3 
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 
4 
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 an actuarial career, students actively should pursue internship opportunities with insurance companies, consulting firms, and other organizations that require actuarial science knowledge. Once such an opportunity is secured, the student should enroll in MthStat 489. Students also should take courses in communication (Commun 103, 264) and expand their knowledge in economics (Econ 248, 450). Note that Econ 248 satisfies the cultural diversity requirement.
Honors in the Major
Students in Actuarial Science who meet all of the following criteria can be awarded honors in the major upon graduation:
 A 3.000 cumulative GPA in all UWM graded credits;
 A 3.500 GPA over all UWM courses counting toward the Actuarial Science major;
 A 3.500 GPA over all upperdivision UWM courses counting toward the Actuarial Science major; and
 The passing of at least three professional actuarial exams.
Students who believe they may qualify for honors in Actuarial Science should apply to the Mathematical Sciences Department during their last semester of study.
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. The atmospheric science major is available as a BS degree from the College of Letters and Science, or as a second major for students completing another UWM degree. Students must complete at least 15 upperdivision (numbered 300 and above) credits in the major in residence at UWM. The College requires that students attain at least a 2.500 GPA on all credits in the major attempted at UWM. In addition, students must attain a 2.500 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.
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 
AirPollution 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 
Physical Meteorology: 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 460 
Mesoscale Circulations 
Atm Sci 470 
Tropical Meteorology 
Atm Sci 480 
The General Circulation and Climate Dynamics 
Atm Sci 497 
Study Abroad: (subtitle) 
Atm Sci 500 
Statistical Methods in the Atmospheric Sciences I 
Atm Sci 505 
Micrometeorology 
Atm Sci 690 
Topics in Atmospheric Sciences: (subtitle) 
Math 313 
Linear Programming and Optimization 
Math 315 
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 521 
Advanced Calculus I 
Math 522 
Advanced Calculus II 
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 
Honors in the Major
Students in Atmospheric Sciences who meet all of the following criteria can be awarded honors in the major upon graduation:
 A 3.000 cumulative GPA in all UWM graded credits;
 A 3.500 GPA over all UWM courses counting toward the Atmospheric Sciences major;
 A 3.500 GPA over all upperdivision UWM courses counting toward the Atmospheric Sciences major; and
 Successful completion of at least two semesters of research and/or internship experiences. The research and internship experiences can include one or more of the Capstone Experience (Atm Sci 599), a directed independent study for credit (Atm Sci 699), an internship for credit (Atm Sci 695), the Atmospheric Sciences Study Abroad course (Atm Sci 297/497), undergraduate research for compensation, and participation in the Innovative Weather program at the staff level. The staff level of Innovative Weather is the third level of participation, coming after a preinternship (several weeks in one semester) and an internship (one semester at 510 hours per week). Staff positions are paid, and staff members typically work around 10 hours per week during the fall or spring semesters, more in the summer session.
Students who believe they may qualify for honors in Atmospheric Sciences should apply to the Mathematical Sciences Department during their last semester of study.
The mathematics major is available as either a BA or a BS degree from the College of Letters and Science, or as a second major for students completing another UWM degree.
Students electing the mathematics major must complete Math 341 and 24 additional credits in upperdivision math courses (those numbered 300 and above, and in curricular areas Math or MthStat). Required among these 24 upperdivision math credits are at least six credits in math courses numbered 500 and above, excluding Math or MthStat 591,599, 699.
Note that Math 381 and MthStat 465 and 467 are not open for credit in the Mathematics major. Students must complete at least 15 upperdivision (numbered 300 and above) credits in the major in residence at UWM. The College requires that students attain at least a 2.500 GPA on all credits in the major attempted at UWM. In addition, students must attain a 2.500 GPA on all major credits attempted, including transfer work.
Recommendations
Mathematics courses fall naturally into the following groups:
Applied mathematics group: Math 305, 320, 321, 322, 371, 405, 431, 581, 601, 602
Computational mathematics group: Math 313, 315, 413, 415, 417, 615, 617
Probability and statistics group: Math 571; MthStat 361, 362, 562, 563, 564, 565, 566, 568
Pure mathematics group:
 Math 521, 522, 531, 535, 551, 621, 622, 631, 632
 Math 423, 451, 453, 511, 537, 553
For students planning to pursue graduate studies in mathematics, we recommend students take at least 36 cr upper division mathematics courses, with as many courses as possible from Pure Mathematics, Group 1. Many PhD programs require reading knowledge of French, German, or Russian.
For students planning to pursue graduate studies in statistics or economics, we recommend Math 521, 522, and as many as possible of MthStat 361, 362, and 562568.
For students seeking employment in statistics after the bachelor's degree, we recommend MthStat 361, 362, and as many as possible of MthStat 562568, as well as courses in computer programming (Comp Sci 250, 251, etc.).
For students seeking general nonacademic employment after the bachelor’s degree, we recommend courses from the Probability and Statistics group (including MthStat 362), the Applied Mathematics group (including both modeling and differential equations), the Computational Mathematics group, Linear Algebra (Math 535), and courses in computer programming (Comp Sci 240, 250, 251, etc.).
For students intending to become high school mathematics teachers, we recommend courses in algebra (Math 431, 531), geometry (451, 453), linear algebra (535), numerical methods (413), advanced calculus (521, 522), the math education capstone (575), and probability and statistics (MthStat 361&362).
For students pursuing a major in mathematics as a liberal art, for general logical and critical thinking skills, we recommend the Pure Mathematics courses.
Honors in the Major
Students in Mathematics who meet all of the following criteria can be awarded honors in the major upon graduation:
 A 3.000 cumulative GPA in all UWM graded credits;
 A 3.500 GPA over all UWM courses counting toward the Mathematics major;
 A 3.500 GPA over all upperdivision UWM courses counting toward the Mathematics major; and
 At least one of the following:
 Successful completion of at least two semesters of research and/or internship experiences. These may include one or more of the Capstone Experience (Math 599), a directed independent study for credit (Math 699), an internship for credit (Math 489), and undergraduate research for compensation.
 Successful completion of at least 6 credits in Mathematical Sciences (curricular areas Math or MthStat) courses numbered 600 or above.
 A score of at least the 50th percentile on the Math Subject GRE.
Students who believe they may qualify for honors in Mathematics should apply to the Mathematical Sciences Department during their last semester of study.
Course of Study: Minors
Actuarial Science Minor. Admission to this minor requires a minimum GPA of 2.500 in Math 231, 232, and 233 (or equivalent course sequence). Students who have completed these courses with the required GPA 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 and 311, and MthStat 361 and 362. In addition, one of the following, with a grade of B or better in each course taken also is required: Bus Adm 450 or both Econ 301 and 302.
Students must complete at least 9 upperdivision (numbered 300 and above) credits for the minor in residence at UWM. The College requires that students attain at least a 2.500 GPA on all credits in the minor attempted at UWM. In addition, students must attain a 2.500 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 upperdivision (numbered 300 and above) credits in the minor in residence at UWM. The College requires that students attain at least a 2.500 GPA on all credits in the minor attempted at UWM. In addition, students must attain a 2.500 GPA on all minor credits attempted, including any transfer work.
Mathematics Minor. Students minoring in mathematics must complete 18 credits in mathematical sciences (curricular areas Math and MthStat) courses numbered 200 and above, of which 9 credits must be upperdivision (numbered 300 and above) courses taken in residence at UWM. The College requires that students attain at least a 2.500 GPA on all credits in the minor attempted at UWM. In addition, student must attain a 2.500 GPA on all minor credits attempted, inlcuding any transfer work. The minor is available as a postbaccalaureate option for students who have graduated.
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 InterSchool/College Programs section
of this catalog, and visit the program's web page at uwm.edu/math/undergraduate/majors/appliedmathematicscomputerscience/.
Courses
Atmospheric Sciences (ATM SCI)
Mathematics (MATH)
Mathematical Statistics (MTHSTAT)
Fredric D. Ancel, Prof. Emeritus, PhD
James E. Arnold, Jr., Assoc. Prof. Emeritus, PhD
Jay H. Beder, Prof., PhD, Asst. Chair for Undergraduate Studies
George Washington University
Allen D. Bell, Assoc. Prof., PhD
University of Washington
Rebecca Bourn, Asst. Fac. Assoc., PhD
University of Virginia
Suzanne L. Boyd, Assoc. Prof., PhD, Assoc. Chair for Undergraduate Studies
Cornell University
Vytaras Brazauskas, Prof., PhD
University of Texas at Dallas
Codirector of Actuarial Science (Graduate)
Karen M. Brucks, Assoc. Prof. Emerita, PhD
A. Clark Evans, Assoc. Prof., PhD
Florida State University
Atmospheric Science Coordinator
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
University of Tennessee
Robert L. Hall, Assoc. Prof. Emeritus, PhD
Peter Hinow, Assoc. Prof., PhD
Vanderbilt University
Yang Ho, Clinical Professor, PhD
Indiana University
Codirector
of Actuarial Science (Undergraduate)
Ingrid Holzner, Sr. Lect. Emerita, MS
G. Christopher Hruska, Assoc. Prof., PhD
Cornell University
Jonathan Kahl, Prof., PhD
University of Michigan
Eric S. Key, Prof. Emeritus, PhD
Kelly Kohlmetz, Sr. Lect., PhD
University of WisconsinMilwaukee
Sergey Kravtsov, Prof., PhD
Florida State University
Vincent Larson, Prof., PhD
Massachusetts Institute of Technology
Istvan G. Lauko, Assoc. Prof., PhD
Texas Tech University
ChengMing Lee, Prof. Emeritus, PhD
TzuChu Lin, Assoc. Prof., PhD
University of Iowa
Kevin B. McLeod, Assoc. Prof., PhD
University of Minnesota
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
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 WisconsinMilwaukee
Lindsay A. Skinner, Prof. Emeritus, PhD
Donald W. Solomon, Assoc. Prof. Emeritus, PhD
Richard Stockbridge, Prof., PhD
University of WisconsinMadison
Lijing Sun, Assoc. Prof., PhD
Wayne State University
Kyle Swanson, Prof., PhD, Chair
University of Chicago
Anastasios Tsonis, Distinguished Prof., PhD
McGill University
Xianwei Van Harpen, Fac. Assoc., PhD
Illinois State University
Hans W. Volkmer, Prof., PhD
University of Konstanz
Bruce A. Wade, Prof., PhD
University of WisconsinMadison
Applied Mathematics & Computer Science Program Coordinator
Lei Wang, Asst. Prof., PhD
University of Michigan
Gilbert G. Walter, Prof. Emeritus, PhD
Wei Wei, Asst. Prof., PhD
University of Waterloo
Jeb Willenbring, 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, Graduate Program
Indiana University
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