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.

Many students assume that most math majors become teachers. While many do, there are many other opportunities for math majors. The United States National Security Agency is the largest employer of math majors in the country. Math majors will also be found at NASA; in engineering firms; at insurance and risk management firms; in robotics and computer science companies; at large and small corporations working in market research, data management and web management; at social media start ups and established firms like YouTube; and any place that needs to make decisions based on numerical facts.

At UWM, the Math major has been designed to be flexible so that students could complete their major requirements via courses that match their interests and goals. Many students 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 real-world 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 K-12 level should examine the School of Education programs.

Some students with an interest in computer science choose to enroll in the Applied Math and Computer Science program. This program is ideal for the student who might have considered double majoring in both math and computer science; it combines applied math courses with computer science classes for you into one program.

## Requirements

**Course of Study – Bachelor of Arts Degree**

Complete 120 credits including 90 credits in the College of Letters & Science and with 36 of the 90 credits in L&S upper-level (numbered above 300) courses. The College requires that students must complete in residence at UWM at least 15 credits in upper-division (numbered 300 or above) courses in their major. Students are also required to complete University-wide General Education Requirements and the specific L&S requirements listed below.

To complete a major, students must satisfy all the requirements of the major as stated in this catalog. Students who declare their majors within five years of entering the UW System as a degree candidate may satisfy the requirements outlined in any catalog issued since the time they entered. Credits used to satisfy the major also may be used to satisfy other degree requirements.

### University General Education Requirements (GER)

Code | Title | Credits |
---|---|---|

Oral and Written Communication | ||

Part A | ||

Achieve a grade of C or better in the following course: | ||

ENGLISH 102 | College Writing and Research (or equivalent) | |

Part B | ||

Course designated as OWC-B; may be completed through a major-specific course requirement | ||

Quantitative Literacy | ||

Part A | ||

Earn at least 3 credits with a grade of C or higher in one of the following courses or an equivalent course, or achieve a placement code of at least 30 on the mathematics placement test (or other appropriate test, as determined by the Mathematical Sciences Department) | ||

Mathematical Literacy for College Students II | ||

Contemporary Applications of Mathematics | ||

Introduction to College Algebra | ||

Algebraic Literacy II | ||

Introduction to Logic - Critical Reasoning ^{1} | ||

or PHILOS 111 | Introduction to Logic - Critical Reasoning | |

College Algebra | ||

Or equivalent course | ||

Part B | ||

Course designated as QL-B; may be completed through a major-specific course requirement | ||

Arts | ||

Select 3 credits | 3 | |

Humanities | ||

Select 6 credits | 6 | |

Social Sciences | ||

Select 6 credits | 6 | |

Natural Sciences | ||

Select 6 credits (at least two courses including one lab) | 6 | |

UWM Foreign Language Requirement | ||

Complete Foreign Language Requirement through: | ||

Two years (high school) of a single foreign language | ||

Two semesters (college) of a single foreign language | ||

Or equivalent | ||

UWM Cultural Diversity Requirement | ||

One course from the Arts, Humanities, or Social Sciences must also satisfy UWM's Cultural Diversity requirement |

^{1} | Math 111 and Philosophy 111 are jointly offered and count as repeats of one another. Students cannot receive credit for both courses. |

### College of Letters & Science Requirements

#### I. English Composition Requirement

Students must satisfy the English Composition Requirement with one of the following options:

1) Completing ENGLISH 102 with a grade of C or higher; or

2) by placing beyond ENGLISH 102 on the English Placement Test (EPT) (or other assessment as determined by the English Department); or

3) transferring a course of at least 2.5 equivalent credits from another institution that is equivalent to English 102, or a UWM higher-level expository writing course, with a grade of C or higher.

**Note:** This requirement is the same as the University General Education Requirement for Oral and Written Communication Part A. The College of Letters & Science does not have a specific requirement for a writing course beyond English 102, but students must complete the university-wide requirement for Oral and Written Communication Part B listed above.

#### II. Mathematics and Formal Reasoning

To satisfy the Mathematics and Formal Reasoning Requirement, students must satisfy the following two requirements:

1. Achieve a placement code of at least 30 on the mathematics placement test (or other appropriate test, as determined by the Mathematical Sciences Department) or earn at least 3 credits with a grade of C or higher in one of the following courses or an equivalent course:

Code | Title | Credits |
---|---|---|

MATH 102 | Mathematical Literacy for College Students II | 3 |

MATH 103 | Contemporary Applications of Mathematics | 3 |

MATH 105 | Introduction to College Algebra | 3 |

MATH 108 | Algebraic Literacy II | 3 |

MATH 111 | Introduction to Logic - Critical Reasoning ^{1} | 3 |

or PHILOS 111 | Introduction to Logic - Critical Reasoning | |

MATH 116 | College Algebra | 3 |

MATH 175 | Mathematical Explorations for Elementary Teachers I | 3 |

^{1} | Math 111 and Philosophy 111 are jointly offered and count as repeats of one another. Students cannot receive credit for both courses. |

**Note:** This requirement is the same as the University General Education Requirement for Quantitative Literacy Part A, listed above.

2. Complete one course (at least 3 credits) at the 200 level or above chosen from courses in Mathematics, PHILOS 211, or Letters and Science statistics courses:

Code | Title | Credits |
---|---|---|

Complete one of the following: | ||

3 or more credits in any 200-level or above Math course | ||

Introduction to Statistics in African and African Diaspora Studies | ||

Introduction to Anthropological Statistics | ||

Statistical Methods in Atmospheric Sciences | ||

Biostatistics | ||

Economic Statistics | ||

Quantitative Analysis in Geography | ||

The Quantitative Analysis of Historical Data | ||

Elementary Statistical Analysis | ||

Elementary Logic | ||

Political Data Analysis | ||

Survey Research | ||

Psychological Statistics | ||

Introduction to Statistical Thinking in Sociology |

**Note: **This requirement is __NOT__ the same as the University General Education Requirement for Quantitative Literacy Part B. To complete the BA, students must take one of the L&S approved courses. **Not all of the courses listed here will satisfy the QL-B requirement**.

#### III. Foreign Language Requirement

Placement testing may be used to satisfy all or part of this requirement. Language courses (including American Sign Language) other than English taken in high school may be used to satisfy all or part of this requirement. One year of high school language equates to one semester of college work.

Completion of the L&S Language Requirement also satisfies the university-wide Foreign Language GER, but not vice versa.

Code | Title | Credits |
---|---|---|

Completed in one of the following ways: | 0-18 | |

Successful completion of the 4th semester of college work or equivalent in one language other than English (including American Sign Language) | ||

Successful completion of the 3rd semester of college work or equivalent in one language other than English (including American Sign Language) PLUS the 2nd semester of college work or equivalent in another language other than English (including American Sign Language) |

#### IV. International Requirement

See Approved Courses for the L&S International Requirement for course options.

Code | Title | Credits |
---|---|---|

Completed in one of the following ways: | 9 | |

Complete 3 courses (min. 9 cr) in a single foreign language (not including literature-in-translation or American Sign Language) at the 3rd semester level and above | ||

Complete 3 non-language courses (min. 9 credits) with an international content chosen from at least 2 curricular areas. | ||

Complete 9 credits in combination of the two options above. |

#### V. Breadth Requirement

Along with completing the University General Education Requirements of 3 credits in the Arts (A); 6 credits in the Humanities (HU), Social Sciences (SS), and Natural Sciences (NS/NS+); and a course with the Cultural Diversity (CD/+) designation, L&S students must complete the Breadth requirement.

Code | Title | Credits |
---|---|---|

Arts | ||

Select 3 credits | 3 | |

Humanities | ||

Complete 12 credits of L&S courses with Humanities Breadth designation; no more than 6 credits from a single subject area. ^{*} | 12 | |

Social Sciences | ||

Complete 12 credits of L&S Courses with Social Science Breadth designation; no more than 6 credits from a single curricular area. ^{*} | 12 | |

Natural Sciences | ||

Complete 12 credits of L&S Courses with Natural Sciences Breadth designation, including at least one laboratory or field course; no more than 6 credits from a single curricular area. ^{*} | 12 | |

Cultural Diversity | ||

Complete 3 credits in a course with Cultural Diversity (CD) designation. ^{**} | 3 |

* | Students should check their course selections carefully with the list of approved L&S Breadth Courses. Students are advised to select at least 6 credits worth of courses in each of the Humanities, Social Science, and Natural Sciences areas that can satisfy both the campus-wide General Education Requirements and the L&S Breadth requirement. |

** | Students are advised to select a course that satisfies the Cultural Diversity requirement as well as a Humanities or Social Science breadth/GER requirement. |

#### VI. The Major

The College of Letters and Science requires that students attain at least a 2.0 GPA in all credits in the major attempted at UWM. In addition, students must attain a 2.0 GPA on all major credits attempted, including any transfer work. Individual departments or programs may require higher GPAs for graduation. Some departmental majors require courses from other departments. Contact your major department for information on whether those credits will count as part of the major GPA. The College requires that students must complete in residence at UWM at least 15 credits in upper-division (numbered 300 or above) courses in their major.

##### Research Requirement

Within their majors, students must complete a research experience approved by the L&S faculty. A list of courses satisfying the research requirement in each major can be found here.

#### VII. The Minor

The College of Letters and Science requires that students attain at least a 2.0 GPA in all credits in the minor attempted at UWM. In addition, students must attain a 2.0 GPA on all minor credits attempted, including any transfer work.

## Mathematics **Major Requirements**

**Preparatory Curriculum**

Students in all majors in the Department of Mathematical Sciences must complete MATH 231 (or MATH 213), MATH 232, and MATH 233 (or equivalent). MATH 221 and MATH 222 are equivalent to MATH 231, MATH 232, and MATH 233. Students majoring in mathematics must have an average GPA of at least 2.500 in these courses. All majors must take either MATH 234 or MATH 240, as well as a course in computer programming in a modern, high-level language (e.g., COMPSCI 151, COMPSCI 202, COMPSCI 240, COMPSCI 250, or COMPSCI 251). The department also recommends strongly one year of calculus-based physics.

#### 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. Mathematics majors may choose either MATH 599 or MATH 575. Students must obtain consent of a professor to enroll in MATH 599.

#### Requirements

The following courses are required for the Mathematics major:

Code | Title | Credits |
---|---|---|

MATH 341 | Seminar: Introduction to the Language and Practice of Mathematics | 3 |

Select 24 credits in upper-division math courses (those numbered 300 and above, and in curricular areas MATH or MTHSTAT or ACTSCI). Required among these 24 upper-division math credits are at least six credits in math courses numbered 500 and above, excluding MATH 591, MATH 599, MATH 699, ACTSCI 490, or ACTSCI 599. | 24 | |

Total Credits | 27 |

### Additional Requirements

- Note that MATH 381 and MTHSTAT 465 and MTHSTAT 467 are not open for credit in the Mathematics major.
- Actuarial Science majors wishing to complete Math as a second major must take 9 cr of upper div Math/MthStat courses beyond the major requirements of Actuarial Science.
- Students completing an AMCS degree who wish to add Mathematics as a second major must take 9 cr of additional upper division Math/MthStat/ActSci courses beyond those used to fulifill the AMCS degree Math/MthStat/ActSci requirements.
- 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 2.0 GPA on all credits in the major attempted at UWM. In addition, students must attain a 2.0 GPA on all major credits attempted, including transfer work.

### Recommendations

Mathematics courses fall naturally into the following groups (see below for individual courses):

- Applied Mathematics
- Computational Mathematics
- Probability and Statistics
- Pure Mathematics

*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, MATH 522, and as many as possible of MTHSTAT 361, MTHSTAT 362, and MTHSTAT 562-MTHSTAT 568.

*For students seeking employment in statistics after the bachelor's degree,* we recommend MTHSTAT 361, MTHSTAT 362, and as many as possible of MTHSTAT 562-MTHSTAT 568, as well as courses in computer programming (COMPSCI 250, COMPSCI 251, etc.).

*For students seeking general non-academic 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 (COMPSCI 240, COMPSCI 250, COMPSCI 251, etc.).

*For students intending to become high school mathematics teachers*, we recommend courses in algebra (MATH 431, MATH 531), geometry (MATH 451, MATH 453), linear algebra (MATH 535), numerical methods (MATH 413), advanced calculus (MATH 521, MATH 522), the math education capstone (MATH 575), and probability and statistics (MTHSTAT 361 & MTHSTAT 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.

### Mathematics Groups

#### Applied Mathematics

Code | Title | Credits |
---|---|---|

MATH 305 | Introduction to Mathematical and Computational Modeling | 3 |

MATH 320 | Introduction to Differential Equations | 3 |

MATH 321 | Vector Analysis | 3 |

MATH 322 | Introduction to Partial Differential Equations | 3 |

MATH 371 | Introduction to Stochastic Models in Finance | 3 |

MATH 405 | Mathematical Models and Applications | 3 |

MATH 431 | Modern Algebra with Applications | 3 |

MATH 581 | Introduction to the Theory of Chaotic Dynamical Systems | 3 |

MATH 601 | Advanced Engineering Mathematics I | 3 |

MATH 602 | Advanced Engineering Mathematics II | 3 |

#### Computational Mathematics

Code | Title | Credits |
---|---|---|

MATH 313 | Linear Programming and Optimization | 3 |

MATH 315 | Mathematical Programming and Optimization | 3 |

MATH 413 | Introduction to Numerical Analysis | 3 |

MATH 415 | Introduction to Scientific Computing | 3 |

MATH 417 | Computational Linear Algebra | 3 |

MATH 615 | Numerical Solution of Partial Differential Equations | 3 |

MATH 617 | Optimization | 3 |

#### Probability and Statistics

Code | Title | Credits |
---|---|---|

MATH 571 | Introduction to Probability Models | 3 |

MTHSTAT 361 | Introduction to Mathematical Statistics I | 3 |

MTHSTAT 362 | Introduction to Mathematical Statistics II | 3 |

MTHSTAT 562 | Design of Experiments | 3 |

MTHSTAT 563 | Regression Analysis | 3 |

MTHSTAT 564 | Time Series Analysis | 3 |

MTHSTAT 565 | Nonparametric Statistics | 3 |

MTHSTAT 566 | Computational Statistics | 3 |

MTHSTAT 568 | Multivariate Statistical Analysis | 3 |

#### Pure Mathematics

Code | Title | Credits |
---|---|---|

MATH 521 | Advanced Calculus I | 3 |

MATH 522 | Advanced Calculus II | 3 |

MATH 531 | Modern Algebra | 3 |

MATH 535 | Linear Algebra | 3 |

MATH 551 | Elementary Topology | 3 |

MATH 621 | Introduction to Analysis I | 3 |

MATH 622 | Introduction to Analysis II | 3 |

MATH 631 | Modern Algebra I | 3 |

MATH 632 | Modern Algebra II | 3 |

MATH 423 | Complex Analysis | 3 |

MATH 451 | Axiomatic Geometry | 3 |

MATH 453 | Transformations in Geometry | 3 |

MATH 511 | Symbolic Logic | 3 |

MATH 537 | Number Theory | 3 |

MATH 553 | Differential Geometry | 3 |

## Mathematics Advising

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.

**Letters & Science Advising**

The College of Letters and Science provides general academic advising for all students with a major in the College, particularly as it relates to campus' general education requirements and the College's degree requirements. We also provide specialized advising for pre-professional students (pre-med, pre-dental, pre-pharmacy, etc.) regardless if their major is in Letters and Science or not. Prospective students, including high school students and students seeking to transfer to a program in Letters and Science may also receive advising from our admissions counselors.

Upon admission, students are assigned an advisor in the College advising office. Academic advising is available Monday through Friday from 8:30 a.m. to 4:30 p.m. by appointment. Appointments outside of these times may be available and phone appointments are available for online students. The advising office is located on the first floor of Holton Hall. Current students should call (414) 229-4654 to schedule an appointment or use the Navigate website to make an appointment with your assigned advisor; online scheduling is only available if you already have a Letters & Science advisor assigned to you. Prospective students should call (414) 229-7711 or email let-sci@uwm.edu.

When students declare a major, they will receive an additional faculty advisor located within the major department who will assist with requirements for that major. Students should read the "Declaration of Major" information on the website of the major that they are interested in. In some cases, the student will need to choose a faculty advisor as part of the declaration process.

All students are cautioned to consult their Letters & Science academic advisor AND their major advisor prior to each registration period to ensure they understand all requirements. Do not rely on pre-printed sample plans, as they are intended to be samples only and may not be right for your particular situation.

**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 upper-division 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.

## Honors in the College of Letters and Science

### Dean's Honor List

GPA of 3.750 or above, earned on a full-time student's GPA on 12 or more graded credits in a given semester.

### Honors College Degree and Honors College Degree with Distinction

Granted to graduating seniors who complete Honors College requirements, as listed in the Honors College section of this site.

### Commencement Honors

Students with a cumulative GPA of 3.500 or above, based on a minimum of 40 graded UWM credits earned prior to the final semester, will receive all-university commencement honors and be awarded the traditional gold cord at the December or May Honors Convocation. Please note that for honors calculation, the GPA is **not** rounded and is truncated at the third decimal (e.g., 3.499).

### Final Honors

Earned on a minimum of 60 graded UWM credits: Cum Laude - 3.500 or above; Magna Cum Laude - 3.650 or above; Summa Cum Laude - 3.800 or above.