# Department of Mathematics

**(College of Humanities, Arts and Sciences)**

The Department of Mathematics offers the following undergraduate and graduate programs, and program certificate. Specific requirements for these programs are listed within this Department of Mathematics section in the following order:

**Undergraduate Majors (B.A.)**- Mathematics
- Mathematics-Statistics/Actuarial Science
- Mathematics-Teaching

**Minors**- Mathematics
- Mathematics-Teaching
- Mathematics (K-8)-Teaching
- Statistics and Actuarial Science

**Graduate Majors (M.A.)**- Mathematics:
- Mathematics
- Secondary Teaching
- Community College Teaching

- Mathematics for the Middle Grades (4-8)

- Mathematics:

**Graduate Majors (P.S.M.)**- Industrial Mathematics

**Program Certificate**- Continuous Quality Improvement Certificate

**Notes:**

- A student majoring or minoring in mathematics, who has a grade point average of less than 2.25 in all departmental courses used for that major or minor may not apply a departmental course in which a grade of less than C- is earned to her/his major or minor.
- Undergraduate students who have been admitted to the university provisionally because of non-satisfaction of the high school mathematics requirements may not enroll in any mathematics credit course before this requirement has been met.
- Students who complete the requirements for more than one program (major or minor) within mathematics may have that noted on their transcripts.

## Bachelor of Arts Degree Programs

### Mathematics Major

The Mathematics major requires a minimum of 120 total hours to graduate. This total includes Liberal Arts Core requirements and the following specified major requirements, plus electives to complete the minimum of 120 hours.

Required | ||

Mathematics: | ||

Common core: | 15 | |

Calculus I (required) ^{*} | ||

Calculus II | ||

Calculus III | ||

Linear Algebra for Applications | ||

Mathematics core: | 12 | |

Intermediate Mathematical Analysis I | ||

Intermediate Mathematical Analysis II | ||

Modern Algebra I | ||

Modern Algebra II | ||

Electives | 12-13 | |

Mathematics: | ||

Senior Mathematics Seminar ^{**} | ||

or | ||

Undergraduate Research in Mathematics ^{**} | ||

Group I: | ||

Modern Geometries | ||

Euclidean Geometry | ||

Differential Geometry | ||

Topology I | ||

Group II: | ||

Dynamical Systems: Chaos Theory and Fractals | ||

Differential Equations | ||

Numerical Analysis ^{*} | ||

Combinatorics | ||

Introduction to Probability | ||

Introduction to Complex Analysis | ||

Group III: | ||

History of Mathematics: To the Calculus | ||

Elementary Number Theory | ||

Total Hours | 39-40 |

* | These courses have additional prerequisites as follows: MATH 1420 (800:060) has prerequisite of MATH 1140 (800:046), or MATH 1110 (800:043) and MATH 1130 (800:044), or equivalent. MATH 3440/5440 (800:176g) has prerequisite of CS 1130 (810:030), CS 1160 (810:036), or CS 1510 (810:051). |

** | Either MATH 4900 (800:194) and four courses as described below, or MATH 4990 (800:195) and three courses as described below. One course must be from each of Groups I, II, III. If a fourth course is required, it may be either any other course from Groups I, II, III, or any course that has one of the courses from Groups I, II, and III as a prerequisite. |

### Mathematics Major-Statistics/Actuarial Science

The Mathematics-Statistics/Actuarial Science major requires a minimum of 120 total hours to graduate. This total includes Liberal Arts Core requirements and the following specified major requirements, plus electives to complete the minimum of 120 hours.

The major is available in two emphases, the Statistics emphasis and the Actuarial Science emphasis. Each emphasis requires completion of the common core, the seminar/research requirement, the core for the chosen emphasis (Statistics or Actuarial Science), and 6 hours of electives that do not duplicate course work chosen to meet the chosen emphasis (Statistics or Actuarial Science) core requirement.

Required | ||

Mathematics: | ||

Common core: | 15 | |

Calculus I ^{*} | ||

Calculus II | ||

Calculus III | ||

Linear Algebra for Applications | ||

Statistics/Actuarial Science core: | 9 | |

Introductory Statistics for Life Sciences | ||

Introduction to Statistical Methods | ||

Introduction to Mathematical Statistics | ||

Introduction to Probability | ||

Computer Science: | 3-4 | |

Select one of the following: | ||

Visual BASIC Programming | ||

C/C++ Programming | ||

Introduction to Computing | ||

Seminar/research: | 1-3 | |

Senior Mathematics Seminar | ||

Undergraduate Research in Mathematics | ||

Select and complete ONE of the following Emphasis Cores: | 9 | |

Statistics Emphasis Core: | ||

Select three from the following: | ||

Applied Statistical Methods for Research | ||

Regression Analysis | ||

Design and Analysis of Experiments | ||

Applied Multivariate Statistical Analysis | ||

Actuarial Science Emphasis Core: | ||

Select three from the following: | ||

Mathematics of Finance | ||

Actuarial Mathematics | ||

Loss Models | ||

Introduction to Financial Engineering | ||

Electives | 6 | |

Select two from the following: | ||

Applied Statistical Methods for Research | ||

Regression Analysis | ||

Spatial Data Analysis | ||

Statistical Computing | ||

Design and Analysis of Experiments | ||

Statistical Quality Assurance Methods | ||

Applied Multivariate Statistical Analysis | ||

Actuarial Examination Preparation ^{**} | ||

Actuarial Mathematics | ||

Topics in Actuarial Science | ||

Introduction to Financial Engineering | ||

Loss Models | ||

Numerical Analysis | ||

Mathematics of Finance | ||

Introduction to Stochastic Processes | ||

Total Hours | 43-46 |

* | MATH 1420 (800:060) has prerequisite of MATH 1140 (800:046), or MATH 1110 (800:043) and MATH 1130 (800:044), or equivalent. |

** | ACT SCI 3731 (800:146) may be repeated for credit for preparation for different exams, however only 3 hours will count toward the Statistics/Actuarial Science major. |

### Mathematics Major-Teaching

The Mathematics-Teaching major requires a minimum of 122-123 total hours to graduate.

This total includes Liberal Arts Core requirements, the Professional Education Requirements, and the following specified major requirements to complete the minimum of 122-123 hours.

Required | ||

Mathematics: | ||

Common core: | 15 | |

Calculus I (required) ^{*} | ||

Calculus II | ||

Calculus III | ||

Linear Algebra for Applications | ||

Teaching core: | 33 | |

Technology and Programming for Secondary Mathematics Teachers | ||

The Teaching of Middle School/Junior High Mathematics | ||

The Teaching of Secondary Mathematics | ||

Connections: University Mathematics and the Secondary Curriculum | ||

Combinatorics | ||

Modern Geometries | ||

Euclidean Geometry | ||

History of Mathematics: To the Calculus | ||

Probability and Statistics | ||

Modern Algebra I | ||

Select two of the following: | ||

Modern Algebra II | ||

Elementary Number Theory | ||

Geometric Transformations | ||

Computer Science: | 3-4 | |

Select one of the following: | ||

Media Computation | ||

Visual BASIC Programming | ||

Introduction to Programming Environments for Education | ||

C/C++ Programming | ||

Introduction to Computing | ||

Total Hours | 51-52 |

* | MATH 1420 (800:060) has a prerequisite of MATH 1140 (800:046), or MATH 1110 (800:043) and MATH 1130 (800:044), or equivalent. |

For departmental approval to student teach, a student on the program must satisfy the university requirements to student teach and the following departmental requirements:

- Must earn a C- or better in:
- Must complete all of the courses in the major with a major grade point average of 2.50 or higher.

Calculus I | ||

Calculus II | ||

Linear Algebra for Applications | ||

The Teaching of Middle School/Junior High Mathematics | ||

The Teaching of Secondary Mathematics | ||

Combinatorics | ||

Modern Geometries | ||

Euclidean Geometry | ||

Modern Algebra I | ||

Probability and Statistics |

### Minors

#### Mathematics Minor

Required | ||

Mathematics: | 11 | |

Calculus I (required) ^{*} | ||

Calculus II | ||

Linear Algebra for Applications | ||

Electives | 12 | |

Mathematics: | ||

Topics in Actuarial Science | ||

Calculus III | ||

Dynamical Systems: Chaos Theory and Fractals | ||

Combinatorics | ||

Differential Equations | ||

Numerical Analysis | ||

Partial Differential Equations | ||

Modern Geometries | ||

Euclidean Geometry | ||

Differential Geometry | ||

History of Mathematics: To the Calculus | ||

Probability and Statistics | ||

Introduction to Probability | ||

Intermediate Mathematical Analysis II | ||

Elementary Number Theory | ||

Introduction to Complex Analysis | ||

Intermediate Mathematical Analysis I | ||

Modern Algebra I | ||

Modern Algebra II | ||

Geometric Transformations | ||

Topology I | ||

Introduction to Stochastic Processes | ||

Introduction to Mathematical Statistics | ||

Regression Analysis | ||

Statistical Quality Assurance Methods | ||

Applied Multivariate Statistical Analysis | ||

Total Hours | 23 |

* | MATH 1420 (800:060) has prerequisite of MATH 1140 (800:046), or MATH 1110 (800:043) and MATH 1130 (800:044), or equivalent. |

#### Mathematics Minor-Teaching

Required | ||

Mathematics: | ||

MATH 1310 (800:096) | Technology and Programming for Secondary Mathematics Teachers | 3 |

MATH 1420 (800:060) | Calculus I (required) ^{*} | 4 |

MATH 1421 (800:061) | Calculus II | 4 |

Select one of the following: | 3 | |

Introductory Statistics for Life Sciences (required) | ||

Introduction to Statistical Methods (required) | ||

Probability and Statistics | ||

MATH 2500 (800:076) | Linear Algebra for Applications | 3 |

MATH 3530/5530 (800:143g) | Combinatorics | 3 |

MATH 4500/5500 (800:160g) | Modern Algebra I | 3 |

MATH 3610/5610 (800:165g) | Modern Geometries | 3 |

or MATH 3600/5600 (800:166g) | Euclidean Geometry | |

MATH 3303 (800:188) | The Teaching of Middle School/Junior High Mathematics | 3 |

MATH 3304 (800:190) | The Teaching of Secondary Mathematics | 3 |

Computer Science: | ||

Select one of the following: | 3-4 | |

Media Computation | ||

Visual BASIC Programming | ||

Introduction to Programming Environments for Education | ||

C/C++ Programming | ||

Introduction to Computing | ||

Total Hours | 35-36 |

* |

#### Mathematics Minor (K-8)-Teaching

Required | ||

Mathematics: | ||

MATH 1201 (800:031) | Mathematical Reasoning for Teaching I | 3 |

MATH 1210 (800:037) | Technology for Elementary School Mathematics Teachers | 3 |

MATH 3211 (800:111g) | Introduction to Algebraic Thinking for Elementary Teachers | 4 |

MATH 3212/5212 (800:112g) | Introduction to Geometry and Measurement for Elementary Teachers | 3 |

MATH 3213/5213 (800:113g) | Topics in Mathematics for Grades K-8 | 3 |

MATH 3214/5214 (800:114g) | Problem Solving in Mathematics for Elementary Teachers | 4 |

MATH 3202 (800:131) | Mathematical Reasoning for Teaching II | 3 |

MATH 3215 (800:192) | Mathematics for Elementary Students with Special Needs | 1 |

Total Hours | 24 |

#### Statistics and Actuarial Science Minor

Required | ||

Mathematics: | ||

MATH 1420 (800:060) | Calculus I (required) ^{*} | 4 |

MATH 1421 (800:061) | Calculus II | 4 |

STAT 1774 (800:064) | Introductory Statistics for Life Sciences (required) | 3 |

or STAT 1772 (800:072) | Introduction to Statistical Methods | |

MATH 3752/5752 (800:152g) | Introduction to Probability | 3 |

Electives | 9 | |

Mathematics: | ||

Select three of the following: | ||

Actuarial Examination Preparation | ||

Topics in Actuarial Science | ||

Introduction to Financial Engineering | ||

Calculus III | ||

Linear Algebra for Applications | ||

Mathematics of Finance | ||

Introduction to Stochastic Processes | ||

Applied Statistical Methods for Research | ||

Introduction to Mathematical Statistics | ||

Regression Analysis | ||

Spatial Data Analysis | ||

Statistical Computing | ||

Design and Analysis of Experiments | ||

Statistical Quality Assurance Methods | ||

Applied Multivariate Statistical Analysis | ||

Total Hours | 23 |

* | MATH 1420 (800:060) has a prerequisite of MATH 1140 (800:046), or MATH 1110 (800:043) and MATH 1130 (800:044), or equivalent. |

## Master of Arts Degree Programs

### Major in Mathematics

The major in Mathematics is available in three emphases: Mathematics, Secondary Teaching, and Community College Teaching.

**Only graduate courses (course numbers 5000 or above) will apply to a graduate degree, even if the undergraduate course number (4999 or less) is listed. No exceptions will be made.**

The Mathematics emphasis is available on the **thesis** and **non-thesis** options. A **minimum of 36 hours** is required for the **thesis** option, including 6 hours of MATH 6299 (800:299) and a **minimum of 15 additional hours of 200/6000-level course work.** A **minimum of 32 hours** is required for the **non-thesis** option, including a minimum of 2 hours of MATH 6299 (800:299) and a **minimum of 15 additional hours of 200/6000-level course work.**

The Secondary Teaching emphasis is offered on a **non-thesis** option only; a **minimum of 32 hours,** including a **minimum of 18 hours of 200/6000-level course work **is required.

The Community College Teaching emphasis is offered on a **non-thesis** option only; **a minimum of 33 hours**, including a minimum of 15 hours of 200/6000-level course work is required.

Students interested in this program must submit a completed Application for Admission to Graduate Study and should contact the Department of Mathematics for other admission requirements. Graduate information and application for graduate admission can be found at www.grad.uni.edu/admission.

The Graduate Record Examination (General Test) **is not** required for admission to the program.

Courses taken to satisfy B.A. requirements may not be repeated to count toward the graduate program.

Successful completion of a final written comprehensive examination is required for the **non-thesis option on the Mathematics emphasis only**.

#### Mathematics Emphasis

Required | ||

Mathematics: | ||

MATH 3630/5630 (800:155g) | Differential Geometry | 3 |

or MATH 4615/5615 (800:189g) | Geometric Transformations | |

MATH 6420 (800:201) | Mathematical Analysis I | 3 |

MATH 6460 (800:203) | Complex Analysis I | 3 |

MATH 6500 (800:240) | Abstract Algebra I | 3 |

Select at least two of the following: | 6 | |

Mathematical Analysis II | ||

Complex Analysis II | ||

Abstract Algebra II | ||

Research: | 2 or 6 | |

MATH 6299 (800:299) | Research ^{*} | |

Thesis option (6 hours) | ||

Non-thesis option (2 hours) | ||

Electives | 12 | |

Mathematics: | ||

Select 12 hours from any of the courses listed above that were not used for the requirements there or from among the following: | ||

Topics in Actuarial Science | ||

Differential Equations | ||

Partial Differential Equations | ||

Numerical Analysis | ||

Combinatorics | ||

History of Mathematics: To the Calculus | ||

Introduction to Probability | ||

Intermediate Mathematical Analysis II | ||

Introduction to Complex Analysis | ||

Modern Algebra II | ||

Topology I | ||

Introduction to Stochastic Processes | ||

Theory of Numbers | ||

Topics in the History of Mathematics | ||

Topics in Mathematical Logic and Set Theory | ||

Topics in Probability and Statistics | ||

Introduction to Mathematical Statistics | ||

Regression Analysis | ||

Statistical Quality Assurance Methods | ||

Applied Multivariate Statistical Analysis | ||

Total hours thesis option | 36 | |

Total hours non-thesis option | 32 |

#### Secondary Teaching Emphasis

The Secondary Teaching emphasis is designed for secondary school mathematics teachers interested in developing a deeper background in mathematics and pedagogy to enhance teaching and increase student learning.

Required | ||

Mathematics Education: | 20 | |

New Developments in Mathematics Education | ||

Contemporary Assessment in Mathematics Education I | ||

Contemporary Assessment in Mathematics Education II | ||

Algebraic Content and Pedagogy for Teachers | ||

Geometric Content and Pedagogy for Teachers | ||

Reflective Teaching-Cognitive Demand of Mathematical Tasks | ||

Reflective Teaching-Classroom Discourse | ||

Reflective Teaching: Meaningful Distributed Instruction | ||

Reflective Teaching: Leadership | ||

Reflective Teaching: Investigation of Classroom Practice | ||

Current Research in Mathematics Education | ||

Mathematics: | 6 | |

Applied Linear Statistical Methods for Secondary Mathematics Teachers | ||

Foundations of Calculus | ||

Select two courses from the following: | 6 | |

Modern Algebra II | ||

Abstract Algebra I | ||

Probability and Statistics for Secondary Mathematics Teachers | ||

Topics in Discrete Mathematics | ||

Non-Euclidean Geometry | ||

Total Hours | 32 |

#### Community College Teaching Emphasis

The Community College Teaching emphasis is designed to serve those seeking to prepare for a career in community college teaching or working professionals in the field who are seeking career advancement.

Required: | ||

Mathematics Education: | 12 | |

New Developments in Mathematics Education | ||

Contemporary Assessment in Mathematics Education II | ||

Reflective Teaching-Cognitive Demand of Mathematical Tasks | ||

Reflective Teaching-Classroom Discourse | ||

Reflective Teaching: Meaningful Distributed Instruction | ||

Reflective Teaching: Leadership | ||

Reflective Teaching: Investigation of Classroom Practice | ||

Current Research in Mathematics Education | ||

Mathematics: | 18 | |

Modern Algebra II | ||

Abstract Algebra I | ||

Applied Linear Statistical Methods for Secondary Mathematics Teachers | ||

Probability and Statistics for Secondary Mathematics Teachers | ||

Foundations of Calculus | ||

Topics in Discrete Mathematics | ||

Non-Euclidean Geometry | ||

Postsecondary Education: | ||

POSTSEC 6260 (170:260) | History and Philosophy of Higher Education | 3 |

Total Hours | 33 |

### Major in Mathematics for the Middle Grades (4-8)

This major is intended for teachers interested in mathematics for the middle grades (4-8) and for mathematics specialists and supervisors. Teacher licensure is a prerequisite for completing the program approval process for this major. Normally, candidates will have at least 2 years teaching experience.

Students interested in this program must submit a completed Application for Admission to Graduate Study and should contact the Department of Mathematics for other admission requirements. Graduate information and application for graduate admission can be found at www.grad.uni.edu/admission.

The Graduate Record Examination (General Test) **is not** required for admission to the program.

**Only graduate courses (course numbers 5000 or above) will apply to a graduate degree, even if the undergraduate course number (4999 or less) is listed. No exceptions will be made.**

This major is available on the **non-thesis** option only; a **minimum of 32 hours** is required. **A minimum of 15 hours of 200/6000-level course work is required.**

Required | ||

Mathematics: | ||

MATH 6201 (800:220) | New Developments in Mathematics Education | 3 |

MATH 6203 (800:222) | Contemporary Assessment in Mathematics Education I | 2 |

MATH 6204 (800:191g) | Contemporary Mathematics Curricula | 2 |

MATH 6205 (800:215) | Teaching Rational Numbers and Proportionality | 3 |

MATH 6208 | Contemporary Assessment in Mathematics Education II | 1 |

MATH 6210 (800:237) | Technology in Middle Grades Mathematics | 1 |

MATH 6212 (800:211) | Algebraic Content and Pedagogy for Teachers | 3 |

MATH 6215 | Geometric Content and Pedagogy for Teachers | 3 |

MATH 6224 (800:236) | Mathematics for the Middle Grades Teachers I | 3 |

MATH 6226 (800:238) | Mathematics for the Middle Grades Teacher II | 3 |

MATH 6230 | Reflective Teaching-Cognitive Demand of Mathematical Tasks | 1 |

MATH 6231 | Reflective Teaching-Classroom Discourse | 1 |

MATH 6232 | Reflective Teaching: Meaningful Distributed Instruction | 1 |

MATH 6234 | Reflective Teaching: Leadership | 1 |

MATH 6235 | Reflective Teaching: Investigation of Classroom Practice | 1 |

MATH 6381 (800:281) | Current Research in Mathematics Education | 3 |

Total Hours | 32 |

## Professional Science Master’s Degree Program

### Major in Industrial Mathematics

The Professional Science Master’s Degree in Industrial Mathematics is designed to prepare students for a career in industry. The curriculum combines a business and experiential component with advanced course work. Requirements for admission to the program include the completion of a bachelor’s degree with a GPA of 3.00 or higher and successful completion of the following university-level courses:

##### Prerequisite Courses:

MATH 1420 (800:060) | Calculus I | 4 |

MATH 1421 (800:061) | Calculus II | 4 |

MATH 2422 (800:062) | Calculus III | 4 |

MATH 2500 (800:076) | Linear Algebra for Applications | 3 |

STAT 1772 (800:072) | Introduction to Statistical Methods | 3 |

One course in computer programming (or equivalent): | ||

CS 1130 (810:030) | Visual BASIC Programming | 3 |

CS 1160 (810:036) | C/C++ Programming | 3 |

CS 1510 (810:051) | Introduction to Computing | 4 |

Graduate information and application for graduate admission can be found at www.grad.uni.edu/admission.

The Graduate Record Examination (General Test)** is not** required for admission to the program.

**Only graduate courses (course numbers 5000 or above) will apply to a graduate degree, even if the undergraduate course number (4999 or less) is listed. No exceptions will be made.**

This major is a **non-thesis** program. A **minimum of 34 hours** is required. **A minimum of 12 hours of 200/6000-level course work is required.**

No comprehensive examination is required for this **non-thesis** option.

This major requires completion of the business and experiential component, the seminar experience, the Mathematics core, the Actuarial Science core, and 9 hours of electives that do not duplicate course work chosen from the Actuarial Science core requirement.

Required | ||

Business and Experiential Component: | 9 | |

Mathematics: | ||

Industrial Internship/Project | ||

Science and Science Education: | ||

Business Management for Science Professionals | ||

Seminar experience: | 1-2 | |

Select one of the following: | ||

MATH 6289 (800:289) Seminar in Lean and Six Sigma Methods in Industry | ||

Professional Science Master's Seminar | ||

Mathematics core: | ||

MATH 6745 (800:250) | Deterministic Operations Research | 3 |

MATH 6747 (800:252) | Discrete-Event System Simulation | 3 |

Actuarial Science Core: | 9 | |

Select three courses from the following: | ||

Mathematics of Finance | ||

Actuarial Mathematics | ||

Topics in Actuarial Science | ||

Loss Models | ||

Introduction to Financial Engineering | ||

Electives | 9 | |

Marketing: | ||

Marketing Strategy | ||

Marketing Management | ||

Management: | ||

Strategic Planning and Organization Analysis | ||

Cross-Functional Operations | ||

Finance: | ||

Corporation Finance | ||

Principles of Investments | ||

Financial Management and Markets | ||

Technology: | ||

Advanced CAD and Modeling | ||

Mathematics: | ||

Applied Statistical Methods for Research | ||

Statistical Computing | ||

Design and Analysis of Experiments | ||

Geometric Modeling for CAD | ||

Combinatorics | ||

Mathematics of Finance | ||

Differential Equations | ||

Partial Differential Equations | ||

Introduction to Probability | ||

Actuarial Mathematics | ||

Introduction to Stochastic Processes | ||

Differential Geometry | ||

Introduction to Complex Analysis | ||

Statistical Quality Assurance Methods | ||

Topics in Actuarial Science | ||

Loss Models | ||

Spatial Data Analysis | ||

Introduction to Mathematical Statistics | ||

Regression Analysis | ||

Numerical Analysis | ||

Applied Multivariate Statistical Analysis | ||

Introduction to Financial Engineering | ||

Probabilistic Operations Research | ||

Modeling Industrial Systems Using Queueing Networks | ||

Advanced Statistical Methods | ||

Topics in Probability and Statistics | ||

Computer Science: | ||

Networking | ||

Computer Systems | ||

Physics: | ||

Modeling and Simulation of Physical Systems | ||

Total Hours | 34 |

## Program Certificate

The University of Northern Iowa makes available, in addition to traditional programs, the opportunity for students to earn program certificates. Program certificates provide an alternative to programs leading to a degree, a major, or a minor; they certify that an individual has completed a program approved by the university. For information on the following program certificate, contact the Department of Mathematics or the Office of the Registrar, which serves as the centralized registry.

### Certificate in Continuous Quality Improvement

The Continuous Quality Improvement certificate provides academic course work that covers all of the Body of Knowledge (BOK) on which the American Society for Control (ASQ) Six Sigma Black Belt certification examination is based, as well as the overwhelming majority of the BOK on which the ASQ Quality Engineer certification examination is based. The course work requirements are a subset of those required in the Continuous Quality Improvement emphasis of the Professional Science Master’s Degree in Industrial Mathematics. The certificate is awarded on successful completion of the following courses:

Required | ||

Mathematics: | ||

STAT 3771/5771 (800:121g) | Applied Statistical Methods for Research | 3 |

STAT 4773/5773 (800:123g) | Design and Analysis of Experiments | 3 |

STAT 4777/5777 (800:157g) | Statistical Quality Assurance Methods | 3 |

MATH 6745 (800:250) | Deterministic Operations Research | 3 |

STAT 6772 (800:272) | Advanced Statistical Methods | 3 |

MATH 6289 (800:289) Seminar in Lean and Six Sigma Methods in Industry | 2 | |

Total Hours | 17 |

**B.A. Degree - Mathematics Major (Major Code 80B)**

Freshman | |||
---|---|---|---|

Fall | Hours | Spring | Hours |

Social Science - Group A (1 Course) | 3 | Fine Arts | 3 |

University Electives | 6 | University Electives | 3 |

Writing And Reading | 3 | COMM 1000 (48C:001) | 3 |

MATH 1420 (800:060) | 4 | HUM 1021 (680:021) | 3 |

MATH 1421 (800:061) | 4 | ||

16 | 16 | ||

Sophomore | |||

Fall | Hours | Spring | Hours |

University Electives | 3 | Mathematics elective as specified | 3 |

Physical Sciences | 3-4 | Social Science - Group B (1 Course) | 3 |

HUM 1022 (680:022) | 3 | University Electives | 6 |

MATH 2422 (800:062) | 4 | Life Sciences | 3-4 |

MATH 2500 (800:076) | 3 | ||

16-17 | 15-16 | ||

Junior | |||

Fall | Hours | Spring | Hours |

Mathematics elective as specified | 3 | Mathematics elective as specified | 3 |

Non-Western Cultures | 3 | Social Science-Group C (1 Course In A,B, Or C | 3 |

Personal Wellness | 3 | University Electives | 6 |

University Electives | 3 | MATH 4501/5501 (800:162g) | 3 |

MATH 4500/5500 (800:160g) | 3 | ||

15 | 15 | ||

Senior | |||

Fall | Hours | Spring | Hours |

Mathematics elective as specified | 3 | senior seminar/research | 1-3 |

MATH 4420/5420 (800:140g) | 3 | Literature, Philosophy Or Religion | 3 |

University Electives | 9 | University Electives | 6-9 |

MATH 4421/5421 (800:141g) | 3 | ||

15 | 13-18 | ||

Total credit hours: 121-128 |

**B.A. Degree - Mathematics Teaching Major (Major Code 800)**

**B.A. Degree - Mathematics: Statistics/Actuarial Sciences Major (Major Code 80R)**

Freshman | |||
---|---|---|---|

Fall | Hours | Spring | Hours |

STAT 1772 OR STAT 1774 (Intro Stat for Life Sciences OR Intro to Stats) | 3 | University Electives | 3 |

ECON 1041 (920:053) | 3 | COMM 1000 (48C:001) | 3 |

ENGLISH 1005 (620:005) | 3 | MATH 3780/5780 (800:145g) | 3 |

MGMT 2080 (150:080) | 3 | ECON 1051 (920:054) | 3 |

MATH 1420 (800:060) | 4 | MATH 1421 (800:061) | 4 |

16 | 16 | ||

Sophomore | |||

Fall | Hours | Spring | Hours |

ECON 1011 (BusStat) or STAT 3771 (ApplStatMeth) | 3 | Humanities | 3 |

Humanities | 3 | Life Sciences | 3-4 |

ACCT 2120 (120:030) | 3 | Visual BASIC recommended | 3-4 |

MATH 2422 (800:062) | 4 | MATH 2500 (800:076) | 3 |

MATH 3752/5752 (800:152g) | 3 | STAT 3775/5775 (800:174g) | 3 |

16 | 15-17 | ||

Junior | |||

Fall | Hours | Spring | Hours |

Sociocultural And Historical Perspectives | 3 | Physical Sciences | 3-4 |

University Electives | 3 | ACT SCI 4739/5739 (800:158g) | 3 |

ACT SCI 4735/5735 (800:153g) | 3 | ACT SCI 4785/5785 (800:197g) | 3 |

FIN 3130/5130 (160:151g) | 3 | FIN 3160/5160 (160:152g) | 3 |

STAT 3776/5776 (800:175g) | 3 | MKTG 2110 (130:101) | 3 |

15 | 15-16 | ||

Senior | |||

Fall | Hours | Spring | Hours |

Capstone Experience | 2 | MATH 4900 Senior Mathematics Seminar (1 hr.) or Undergraduate Research in Mathematics (3 hrs.) | 1-3 |

Fine Arts | 3 | Literature, Philosophy Or Religion | 3 |

ACT SCI 4788/5788 (800:170g) | 3 | Non-Western Cultures | 3 |

FIN 3050 (160:162) | 3 | Social Science-Group C (1 Course In A,B, Or C | 3 |

HPELS 1010 (440:010) | 3 | MGMT 3153 (150:153) | 3 |

MGMT 3100 (150:100) | 3 | ||

17 | 13-15 | ||

Total credit hours: 123-128 |

### Actuarial Science Courses

**ACT SCI 3731 (800:146). Actuarial Examination Preparation — 1-3 hrs.**

Strengthening student skills solving computational problems similar to those included on actuarial examinations. Analyzing and practicing appropriate choice of problem solving techniques and strategies. May be repeated for credit for preparation for different examinations. (Fall, Spring)

**ACT SCI 3780/5780 (800:145g). Mathematics of Finance — 3 hrs.**

Measurement of interest, annuities, yield rates, amortization and sinking funds, bonds, term structure of interest rates, interest rate sensitivity, stocks and derivatives, elements of risk management. Prerequisite(s): MATH 1420 (800:060) (800:060); junior standing. (Same as MATH 3780/5780 (800:145g))(Fall, Spring)

**ACT SCI 4735/5735 (800:153g). Actuarial Mathematics — 3 hrs.**

Survival distributions and life tables, life insurance, life annuities, benefit premiums. Prerequisite(s): MATH 3752/5752 (800:152g); junior standing. (Even Falls)

**ACT SCI 4739/5739 (800:158g). Topics in Actuarial Science — 3 hrs.**

Topics from mathematics of life contingencies, risk theory, survival analysis, construction of actuarial tables, demography, gradation. May be repeated on different topic with consent of instructor. Prerequisite(s): MATH 3752/5752 (800:152g); junior standing; consent of instructor. (Spring)

**ACT SCI 4785/5785 (800:197g). Introduction to Financial Engineering — 3 hrs.**

Financial derivatives, option pricing, Binomial model, Black-Scholes formula, Greeks and hedging, introduction to stochastic calculus, financial model simulation, Monte-Carlo valuation. Prerequisite(s): MATH 3752/5752 (800:152g); junior standing. (Spring)

**ACT SCI 4788/5788 (800:170g). Loss Models — 3 hrs.**

Applied probability methods used in modeling loss. Loss distributions, aggregate loss models, credibility theory and long term models. Prerequisite(s): MATH 3752/5752 (800:152g); STAT 3775/5775 (800:174g); junior standing. (Odd Falls)

### Mathematics Courses

**MATH 0100 (800:004). Intermediate Algebra — 3 hrs.**

Fundamental mathematical concepts; functions and graphs; solutions of equations; systems of equations and inequalities; matrices and determinants. Successful completion will satisfy the university's high school mathematics requirement. Does not count toward minimum hours required for baccalaureate degree. (Fall)

**MATH 1100 (800:023). Mathematics in Decision Making — 3 hrs.**

Selection of mathematical topics and their applications with an emphasis on mathematical reasoning. Topics include probability and statistics. (Fall, Spring, Summer)

**MATH 1110 (800:043). Analysis for Business Students — 3 hrs.**

Analysis and interpretation of data using numerical, graphical, and functional viewpoints; linear and exponential functions; modeling data using functions. No credit for students with credit in MATH 1140 (800:046) or MATH 1120 (800:056). (Fall, Spring)

**MATH 1120 (800:056). Mathematics for Biological Sciences — 3 hrs.**

Proportional reasoning, linear functions and linear regression, exponential functions, and logarithmic functions with scientific applications. No credit for students with credit in MATH 1110 (800:043) or MATH 1140 (800:046). (Fall, Spring)

**MATH 1130 (800:044). Trigonometry — 2 hrs.**

Trigonometric functions, solution of triangles and applications of simple harmonic motions, polar coordinates, and vectors. No credit for students with credit in MATH 1140 (800:046). (Fall, Spring)

**MATH 1140 (800:046). Precalculus — 4 hrs.**

Pre-calculus mathematics; equations and inequalities; logarithms, exponential and circular functions; analytic trigonometry, analytic geometry, mathematical induction; applications. Credit reduced to 1 hour for students with credit in MATH 1110 (800:043) or MATH 1120 (800:056), and to 2 hours for students with credit in MATH 1130 (800:044). (Fall, Spring)

**MATH 1150 (800:048). Calculus for Technology — 4 hrs.**

Survey of analytic geometry and elementary calculus with emphasis on applications. May not be applied to Mathematics major or minor. Prerequisite(s): MATH 1140 (800:046) or consent of instructor. (Spring)

**MATH 1201 (800:031). Mathematical Reasoning for Teaching I — 3 hrs.**

Mathematics as problem solving, communication, connections, and reasoning. Includes rational numbers, data and statistical reasoning, probabilistic reasoning. Activities investigating these topics connect to elementary school mathematics. Primarily for education majors. (Fall, Spring)

**MATH 1210 (800:037). Technology for Elementary School Mathematics Teachers — 3 hrs.**

Survey of technologies used to develop mathematical thinking in elementary grades. Technologies addressed include calculators, LOGO, spreadsheets, Geometer's Sketchpad, other educational software, and the Internet. (Fall, Spring)

**MATH 1300 (800:095). Exploring Mathematics Teaching — 1 hr.**

Exploration of mathematics teaching with well-qualified teacher speakers, classroom discussions about innovative teaching, student learning and teaching as a profession. A brief field experience will be included. (Fall, Spring)

**MATH 1310 (800:096). Technology and Programming for Secondary Mathematics Teachers — 3 hrs.**

Introduction to technologies (calculators, spreadsheets, and dynamic geometric and statistical programs) used in mathematics classrooms (5-12). Activities to develop facility with the technologies and programming skills while addressing mathematics and pedagogical implications. Prerequisite(s) or corequisite(s): MATH 1420 (800:060). (Spring)

**MATH 1420 (800:060). Calculus I — 4 hrs.**

The derivatives and integrals of elementary functions and their applications. Prerequisite(s): MATH 1140 (800:046), or MATH 1110 (800:043) and MATH 1130 (800:044), or equivalent. (Fall, Spring)

**MATH 1421 (800:061). Calculus II — 4 hrs.**

Continuation of MATH 1420 (800:060). Prerequisite(s): C- or better in MATH 1420 (800:060). (Fall, Spring)

**MATH 1900 (800:090). Mathematical Problem Solving — 1 hr.**

Basic techniques used to solve challenging mathematics problems. Problems considered will come from a broad range of courses. Prepares students to take the William Lowell Putnam Examination and the Iowa Collegiate Mathematics Competition. May be repeated. (Fall, Spring)

**MATH 2422 (800:062). Calculus III — 4 hrs.**

Continuation of MATH 1421 (800:061). Prerequisite(s): C- or better in MATH 1421 (800:061). (Fall, Spring)

**MATH 2500 (800:076). Linear Algebra for Applications — 3 hrs.**

Gaussian elimination; matrix algebra; vector spaces, kernels, and other subspaces; orthogonal projection; eigenvalues and eigenvectors. Prerequisite(s): MATH 1420 (800:060). (Fall, Spring)

**MATH 3202 (800:131). Mathematical Reasoning for Teaching II — 3 hrs.**

Mathematics as problem solving, communication, connections, and reasoning. Includes geometry, measurement, proportional reasoning, percent. Activities connected to elementary school mathematics. Designed for elementary education majors. Prerequisite(s): MATH 1201 (800:031); UNI and cumulative GPA of 2.50 or better; junior standing or consent of department. (Fall, Spring)

**MATH 3203 (800:134). Teaching Mathematics in the Elementary School — 3 hrs.**

Effective instructional models and strategies for teaching elementary school mathematics; involves selecting and designing mathematical tasks, creating an environment, and orchestrating discourse. Using and supplementing mathematics materials within a sound psychological framework for making instructional decisions. Prerequisite(s): MATH 3202 (800:131); UNI and cumulative GPA of 2.50 or better; full admission to teacher education is required. (Fall, Spring, Summer)

**MATH 3211 (800:111g). Introduction to Algebraic Thinking for Elementary Teachers — 4 hrs.**

Investigation of problems involving patterns, variables, relations, functions, and their graphs. Exploration and representation of these problems using physical models and technology. Prerequisite(s): MATH 1201 (800:031). (Fall, Spring)

**MATH 3212/5212 (800:112g). Introduction to Geometry and Measurement for Elementary Teachers — 3 hrs.**

Van Hiele levels of thinking. Investigation of two- and three-dimensional concepts, rigid transformations, symmetry, and spatial sense. Prerequisite(s): MATH 1201 (800:031); MATH 1210 (800:037); MATH 3202 (800:131); junior standing. (Fall, Spring)

**MATH 3213/5213 (800:113g). Topics in Mathematics for Grades K-8 — 3 hrs.**

Investigation of number theory, extending ratio, proportion and probability with connections to rational numbers, algebra and geometry. Reasoning about topics in the context of the K-8 mathematics curriculum. Prerequisite(s): MATH 1201 (800:031); MATH 1210 (800:037); MATH 3202 (800:131); junior standing. (Fall, Spring)

**MATH 3214/5214 (800:114g). Problem Solving in Mathematics for Elementary Teachers — 4 hrs.**

Strategies for constructing and communicating a mathematics problem-solving process. Analysis of resources and strategies to generate mathematics tasks and to create an effective problem-solving environment. Problem solving as a means of constructing mathematics knowledge. Prerequisite(s): MATH 3203 (800:134); at least one of MATH 3211 (800:111g), MATH 3212/5212 (800:112g), MATH 3213/5213 (800:113g); junior standing. (Fall, Spring)

**MATH 3215 (800:192). Mathematics for Elementary Students with Special Needs — 1 hr.**

Assessing, designing, and providing appropriate mathematical tasks for students with special needs. Prerequisite(s): MATH 3203 (800:134) or MATH 3304 (800:190). (Fall, Spring)

**MATH 3303 (800:188). The Teaching of Middle School/Junior High Mathematics — 3 hrs.**

Teaching strategies for grades 5-8; roles of content and methods; participation in a middle school/junior high teaching situation. Prerequisite(s): EDPSYCH 3128 (200:128); EDPSYCH 3148 (200:148); 6 hours of 100/3000/4000-level courses in mathematics. (Spring)

**MATH 3304 (800:190). The Teaching of Secondary Mathematics — 3 hrs.**

Teaching strategies for grades 5-12; roles of content and methods; participation in a secondary teaching situation. Prerequisite(s): EDPSYCH 3128 (200:128); EDPSYCH 3148 (200:148); MEASRES 3150 (250:150); MATH 4500/5500 (800:160g); MATH 3610/5610 (800:165g) or MATH 3600/5600 (800:166g); MATH 3303 (800:188). (Fall)

**MATH 3305 (800:183). Connections: University Mathematics and the Secondary Curriculum — 3 hrs.**

Connections between the undergraduate mathematics major and the secondary mathematics curriculum. Consideration of modern algebra, modern geometry, probability and statistics, calculus and number theory in the context of the secondary mathematics curriculum. Prerequisite(s): 6 hours of 100/3000/4000-level courses in mathematics. Corequisite(s): EDPSYCH 3148 (200:148); MEASRES 3150 (250:150). Prerequisite(s) or corequisite(s): EDPSYCH 2017 (200:017); EDPSYCH 2030 (200:030); EDPSYCH 3128 (200:128); MATH 3303 (800:188). (Spring)

**MATH 3410/5410 (800:142g). Dynamical Systems: Chaos Theory and Fractals — 3 hrs.**

Historical background, including examples of dynamical systems; orbits, fixed points, and periodic points; one-dimensional and two-dimensional chaos; fractals: Julia sets, the Mandelbrot set, and fractal dimension; computer programs and dynamical systems. Prerequisite(s): MATH 1421 (800:061); MATH 2500 (800:076); junior standing. (Variable)

**MATH 3425/5425 (800:149g). Differential Equations — 3 hrs.**

Elementary theory and applications of first order differential equations; introduction to numerical techniques of solving differential equations; solutions of nth order linear differential equations with constant coefficients. Prerequisite(s): MATH 2422 (800:062); MATH 2500 (800:076); junior standing. (Fall)

**MATH 3430/5430 (800:150g). Partial Differential Equations — 3 hrs.**

Study of applied partial differential equations using heat, wave, and potential equations as basis; Fourier series and integrals; Laplace transformations. Prerequisite(s): MATH 3425/5425 (800:149g); junior standing. (Even Springs)

**MATH 3440/5440 (800:176g). Numerical Analysis — 3 hrs.**

Theory and application of standard numerical techniques dealing with nonlinear equations, systems of linear equations, interpolation and approximation, numerical differentiation and integration. Prerequisite(s): MATH 1421 (800:061); MATH 2500 (800:076); CS 1130 (810:030) or CS 1160 (810:036) or CS 1510 (810:051) or equivalent; junior standing. (Odd Falls)

**MATH 3530/5530 (800:143g). Combinatorics — 3 hrs.**

Various ways to enumerate elements of a set and graph theory. Appropriate for mathematics, mathematics education, computer science, and actuarial science students. Prerequisite(s): MATH 1420 (800:060) or CS 1800 (810:080); junior standing. (Fall, Spring)

**MATH 3600/5600 (800:166g). Euclidean Geometry — 3 hrs.**

Topics of plane geometry beyond a first course; compass and straightedge constructions, the nine-point circle, Ceva's and Menelaus' theorems, triangle centers, conics, and tessellations. Prerequisite(s): MATH 1420 (800:060) or equivalent; junior standing. (Fall)

**MATH 3610/5610 (800:165g). Modern Geometries — 3 hrs.**

Euclid's postulates serve as a model for studying various axiomatic systems defining incidence geometries. Geometries include finite geometries, plane geometry, neutral geometry, taxicab geometry, spherical geometry, and hyperbolic geometry. Prerequisite(s): MATH 1420 (800:060) or equivalent; junior standing. (Spring)

**MATH 3630/5630 (800:155g). Differential Geometry — 3 hrs.**

Analytic study of curves and surfaces in three-dimensional Euclidean space. Prerequisite(s): MATH 2422 (800:062); MATH 2500 (800:076); junior standing. (Odd Springs)

**MATH 3640/5640 (800:180g). History of Mathematics: To the Calculus — 3 hrs.**

Survey of mathematical activities of humankind in numeration and number systems, algebra, and number theory, from pre-history through the present day. Motives, influences, and methods affecting development of these mathematical topics in Mesopotamian, Egyptian, Greek, Islamic, Indian, Chinese, Native American, and Western civilizations. Ethnomathematics as related to these topics. Prerequisite(s): junior standing. (Fall)

**MATH 3751 (800:173). Probability and Statistics — 3 hrs.**

Descriptive statistics and graphical representations, basic concepts of probability and distributions, random variables, expectations, sampling theory, tests of statistical significance. Calculus is employed in developing and applying these ideas. Specific attention devoted to the use of technology in motivating and explaining concepts and techniques. Emphasis on applications appropriate for secondary school probability/statistics courses. No credit with credit in STAT 3770/5770 (800:172g). Prerequisite(s): MATH 1421 (800:061). (Same as STAT 3751)(Fall and Even Springs)

**MATH 3752/5752 (800:152g). Introduction to Probability — 3 hrs.**

Axioms of probability, sample spaces having equally likely outcomes, conditional probability and independence, random variables, expectation, moment generating functions, jointly distributed random variables, weak law of large numbers, central limit theorem. Prerequisite(s): MATH 1421 (800:061); junior standing. (Same as STAT 3752/5752 (800:152g))(Fall, Spring)

**MATH 3780/5780 (800:145g). Mathematics of Finance — 3 hrs.**

Measurement of interest, annuities, yield rates, amortization and sinking funds, bonds, term structure of interest rates, interest rate sensitivity, stocks and derivatives, elements of risk management. Prerequisite(s): MATH 1420 (800:060); junior standing. (Same as ACT SCI 3780/5780 (800:145g))(Fall, Spring)

**MATH 4198 (800:198). Independent Study.**

(Variable)

**MATH 4420/5420 (800:140g). Intermediate Mathematical Analysis I — 3 hrs.**

Algebraic and topological structure of the reals; limits and continuity; theory of differentiability of functions of a single real variable. Prerequisite(s): MATH 2422 (800:062); MATH 2500 (800:076); junior standing. (Even Falls)

**MATH 4421/5421 (800:141g). Intermediate Mathematical Analysis II — 3 hrs.**

Riemann integration; sequences and series of functions; introduction to Lebesgue integration. Prerequisite(s): MATH 4420/5420 (800:140g); junior standing. (Odd Springs)

**MATH 4460/5460 (800:156g). Introduction to Complex Analysis — 3 hrs.**

Differentiation and integration of functions of a single complex variable; Taylor and Laurent expansions; conformal mapping. Prerequisite(s): MATH 2422 (800:062); junior standing. (Even Springs)

**MATH 4500/5500 (800:160g). Modern Algebra I — 3 hrs.**

Introduction to study of algebraic systems. Groups, rings, fields, homomorphisms and isomorphisms. Prerequisite(s): MATH 1421 (800:061) or equivalent; MATH 2500 (800:076); junior standing. (Fall, Spring)

**MATH 4501/5501 (800:162g). Modern Algebra II — 3 hrs.**

Basic properties of rings, integral domains and fields. Polynomials over fields, field extensions, straightedge and compass constructions. Prerequisite(s): MATH 4500/5500 (800:160g); junior standing. (Spring)

**MATH 4510/5510 (800:144g). Elementary Number Theory — 3 hrs.**

Topics from properties of integers, prime numbers, congruences, cryptography, Pythagorean triples, Diophantine equations, Fermat's last theorem, Fibonacci numbers, and the golden rectangle. Also, number theoretic connections to abstract algebra. Prerequisite(s): MATH 4500/5500 (800:160g); junior standing. (Odd Falls and Spring)

**MATH 4615/5615 (800:189g). Geometric Transformations — 3 hrs.**

Isometries of the plane in context of Klein's definition of a geometry as a group acting on a set of points. Rotations, reflections, and translations are used to study congruence, similarity, and symmetry and to solve problems that would otherwise be difficult using analytic geometry and calculus. Prerequisite(s): MATH 2500 (800:076); MATH 3610/5610 (800:165g) or MATH 3600/5600 (800:166g); junior standing. (Fall)

**MATH 4641/5641 (800:167g). Topology I — 3 hrs.**

Introductory study of metric spaces, completeness, topological spaces, continuous functions, compactness, connectedness, separability, product, and quotient spaces. Prerequisite(s): MATH 2422 (800:062); MATH 2500 (800:076); junior standing. (Even Falls)

**MATH 4742/5742 (800:125g). Geometric Modeling for CAD — 3 hrs.**

B-spline curves and surfaces, Bezier curves and surfaces, NURBS, curve and surface design, multi-resolution methods, subdivision/refinement methods, scattered data fitting, mesh generation, solid representation, solid modeling. Prerequisite(s): MATH 2422 (800:062); MATH 2500 (800:076); junior standing. (Variable)

**MATH 4754/5754 (800:154g). Introduction to Stochastic Processes — 3 hrs.**

Markov chains, Poisson processes, continuous time Markov chains, renewal processes, Brownian motion and stationary processes. Prerequisite(s): MATH 3752/5752 (800:152g); junior standing. (Same as STAT 4754/5754 (800:154g))(Fall)

**MATH 4900 (800:194). Senior Mathematics Seminar — 1 hr.**

Researching and writing a paper exploring specific theme, topic, or problem in mathematics, culminating with oral presentation to the class. Prerequisite(s): senior mathematics major. (Fall, Spring)

**MATH 4990 (800:195). Undergraduate Research in Mathematics — 3 hrs.**

Research on selected topic in mathematics with faculty supervision. Presentation of written paper at departmental seminar. Prerequisite(s): completion of the major core with minimum GPA of 3.00. (Fall, Spring)

**MATH 6201 (800:220). New Developments in Mathematics Education — 3 hrs.**

Introduce current recommendations and policies regarding mathematics goals, content, frameworks, instructional strategies, and curricula. Investigate topics and documents with a focus on application and impact to classrooms. Prerequisite(s): consent of department. (Variable)

**MATH 6203 (800:222). Contemporary Assessment in Mathematics Education I — 2 hrs.**

Study of strategies and practices for assessing students' thinking and performance. Multiple forms of quality assessment with an emphasis on formative assessment, aligning assessment to instruction, and interpreting evidence. Prerequisite(s): MATH 6201 (800:220) or consent of department. (Variable)

**MATH 6204 (800:191g). Contemporary Mathematics Curricula — 2 hrs.**

Study and evaluation of innovative curriculum materials. Focus on application to classroom practice and planning for change for a selected topic. Prerequisite(s): MATH 6201 (800:220) or consent of department. (Variable)

**MATH 6205 (800:215). Teaching Rational Numbers and Proportionality — 3 hrs.**

Examination of literature, problems, and issues related to teaching fractions, decimals, ratios, proportion, and percent. Exploration of innovative strategies for developing concepts, skills, and proportional reasoning. Prerequisite(s): MATH 6201 (800:220) or consent of department. (Variable)

**MATH 6207 (800:221). Mathematics Literacy in an Information Age — 2 hrs.**

Examination of applications and contributions of mathematics to other disciplines, the workplace, personal lives, and society. Investigation of shifting conceptions of mathematics and mathematics literacy in today's world. Diverse uses of mathematics illustrated. Prerequisite(s): MATH 6201 (800:220); MATH 6224 (800:236); MATH 6226 (800:238). (Variable)

**MATH 6208. Contemporary Assessment in Mathematics Education II — 1 hr.**

Focus on assessment design for classroom use and development of an assessment scheme. Prerequisite(s): MATH 6201 (800:220) or consent of department. Prerequisite(s): MATH 6201 (800:220) or consent of department. (Variable)

**MATH 6210 (800:237). Technology in Middle Grades Mathematics — 1 hr.**

Uses of technology in teaching and learning mathematics. Examination of research related to incorporating technology in the teaching of mathematics. Prerequisite(s): MATH 6201 (800:220) or consent of department. (Variable)

**MATH 6212 (800:211). Algebraic Content and Pedagogy for Teachers — 3 hrs.**

Examine algebraic standards, content, instructional strategies and curricula. Focus on application and impact on classroom practice, planning, and assessment in algebra. Focus on change in one's teaching and curriculum. Prerequisite(s): consent of department. (Summer)

**MATH 6213 (800:213). Selected Topics in Mathematics for the Middle Grades — 2 hrs.**

Investigation of mathematical topic(s), such as geometry, data analysis, probability, or number sense. Examination of a major mathematical idea including implications of research literature, and examination of relevant curriculum materials. May be repeated once on a different topic with consent of department. Prerequisite(s): consent of department. (Variable)

**MATH 6214 (800:214). Mathematical Problem Solving in the Middle Grades — 1 hr.**

Solving problems from a variety of mathematical topics such as linear programming, geometry, and probability. Analyzing problem-solving techniques and teaching strategies. Investigating issues related to implementing a problem-solving approach in the classroom. (Variable)

**MATH 6215. Geometric Content and Pedagogy for Teachers — 3 hrs.**

Examine geometric standards, content, methods and curricula. Analyze student thinking, examine van Hiele levels and expand conceptions of proof. Focus on impact on one's own practice, planning and assessment. Prerequisite(s): MATH 6201 (800:220) or consent of department. (Variable)

**MATH 6224 (800:236). Mathematics for the Middle Grades Teachers I — 3 hrs.**

Integrated, historical, and cultural study of development and structure of quantity, data, and chance. Focus on mathematical ways of knowing and verification. (Variable)

**MATH 6226 (800:238). Mathematics for the Middle Grades Teacher II — 3 hrs.**

Integrated, historical, and cultural study of development and structure of patterns, functions, relationships, and shapes. Focus on ways of knowing and verification. Prerequisite(s): MATH 6224 (800:236). (Variable)

**MATH 6230. Reflective Teaching-Cognitive Demand of Mathematical Tasks — 1 hr.**

Students will critically reflect on classroom practice with the focus on cognitive demand of mathematical tasks. Prerequisite(s): MATH 6201 (800:220) or consent of department. (Variable)

**MATH 6231. Reflective Teaching-Classroom Discourse — 1 hr.**

Students will critically reflect on classroom practice with the focus on classroom discourse. Prerequisite(s): MATH 6201 (800:220) or consent of department. (Variable)

**MATH 6232. Reflective Teaching: Meaningful Distributed Instruction — 1 hr.**

Students will critically reflect on classroom practice with the focus on meaningful distributed instruction. Prerequisite(s): MATH 6201 (800:220) or consent of department. (Variable)

**MATH 6234. Reflective Teaching: Leadership — 1 hr.**

Students will critically reflect on classroom practice with the focus on leadership in mathematics education. Prerequisite(s): MATH 6201 (800:220) or consent of department. (Variable)

**MATH 6235. Reflective Teaching: Investigation of Classroom Practice — 1 hr.**

Students will critically reflect on classroom practice with the focus on instruction. Prerequisite(s): MATH 6201 (800:220) or consent of department. (Variable)

**MATH 6299 (800:299). Research.**

(Variable)

**MATH 6370 (800:270). Applied Linear Statistical Methods for Secondary Mathematics Teachers — 3 hrs.**

Elements of experimental design. Statistical inferential processes, confidence intervals and hypothesis tests, for comparing means, medians and proportions from multiple groups. Prerequisite(s): STAT 1772 (800:072), MATH 3751 (800:173) or consent of instructor. (Fall, Spring)

**MATH 6371 (800:271). Probability and Statistics for Secondary Mathematics Teachers — 3 hrs.**

Discrete and continuous random variables, central limit theorem, regression, correlation, analysis of covariance and categorical data analysis. Multiple regression, ANOVA and categorical data analysis will provide students with tools to analyze real data sets. Prerequisite(s): STAT 1772 (800:072) or MATH 3751 (800:173) or consent of instructor. (Variable)

**MATH 6380 (800:280). Mathematics at the Secondary Level — 1-3 hrs.**

History of secondary mathematics in the U.S. Overview of the most recent reform movement in mathematics education; its effect on the teaching and learning of high school mathematics. May be repeated on different topics for up to 3 hours of credit. Prerequisite(s): graduate standing in mathematics. (Variable)

**MATH 6381 (800:281). Current Research in Mathematics Education — 3 hrs.**

Understand purposes and methods of research in math education with a focus on action research. Review mathematics education research and its implications for instruction. Conduct a classroom-based action research project. Prerequisite(s): MATH 6201 (800:220) or consent of department. (Variable)

**MATH 6391 (800:291). Problems and Issues in Teaching High School Mathematics — 3 hrs.**

Course content decided by participants and instructor. Consideration of both mathematics content and methodology of the senior high school. Prerequisite(s): consent of department. (Variable)

**MATH 6393 (800:293). The Secondary School Mathematics Curriculum — 3 hrs.**

Comparison of current secondary curriculum with national standards, implementation, assessment, and the role of technology. (Variable)

**MATH 6410. Foundations of Calculus — 3 hrs.**

Fundamentals of Calculus from the viewpoint of exploring reasons for the details that support Differential and Integral Calculus. Emphases on examples and proving justifications for a variety of mathematical statements. (Variable)

**MATH 6420 (800:201). Mathematical Analysis I — 3 hrs.**

Set theory; the real number system; Lebesque measure; Lebesque integral. Prerequisite(s): MATH 4420/5420 (800:140g). Corequisite(s): MATH 4421/5421 (800:141g) or consent of instructor. (Odd Springs)

**MATH 6421 (800:202). Mathematical Analysis II — 3 hrs.**

Differentiation and integration; classical Banach spaces; metric spaces; general measure and integration theory. Prerequisite(s): MATH 6420 (800:201). (Spring)

**MATH 6460 (800:203). Complex Analysis I — 3 hrs.**

Analyticity; differentiation and integration of functions of one complex variable; power series, Laurent series; calculus of residues. Prerequisite(s): MATH 4420/5420 (800:140g); MATH 4460/5460 (800:156g); or consent of instructor. (Spring)

**MATH 6461 (800:204). Complex Analysis II — 3 hrs.**

Analytic continuation; harmonic functions; entire functions; conformal mapping; selected applications. Prerequisite(s): MATH 6460 (800:203). (Variable)

**MATH 6500 (800:240). Abstract Algebra I — 3 hrs.**

Groups: quotient groups, isomorphism theorems, products of groups, group actions, Sylow theorems, solvable and nilpotent groups. Rings and fields: quotient rings, rings of polynomials, integral domains, fields of fractions. Prerequisite(s): MATH 4500/5500 (800:160g). Corequisite(s): MATH 4501/5501 (800:162g) or consent of instructor. (Fall)

**MATH 6501 (800:241). Abstract Algebra II — 3 hrs.**

Rings: arithmetic properties, prime and maximal ideals, Noetherian rings. Modules and vector spaces: linear transformations, free modules, finitely generated modules over PIDs, canonical forms. Fields: field extensions, Galois theory, solvability by radicals. Prerequisite(s): MATH 6500 (800:240) (Spring)

**MATH 6510 (800:210). Theory of Numbers — 3 hrs.**

Mathematical study of integers: induction, divisibility, prime numbers, congruences, quadratic reciprocity, multiplicative functions. (Variable)

**MATH 6530 (800:243). Topics in Discrete Mathematics — 3 hrs.**

Topics from combinatorics, graph theory, analysis and application of algorithms, recurrence relations, difference equations, linear programming, and mathematical induction. Applications of these topics in the secondary curriculum. Prerequisite(s): MATH 3530/5530 (800:143g) or MATH 4500/5500 (800:160g). (Variable)

**MATH 6640 (800:246). Topics in the History of Mathematics — 3 hrs.**

Topics from history of algebra, analysis, arithmetic, geometry, number theory, probability, and topology as they appear in the development of Mesopotamian, Greek, Islamic, Indian, Chinese, and Western civilizations. May be repeated on different topic with consent of instructor. Prerequisite(s): MATH 3640/5640 (800:180g). (Variable)

**MATH 6650 (800:263). Topics in Mathematical Logic and Set Theory — 3 hrs.**

Topics from the predicate calculus and first-order mathematical theories; the Godel completeness and incompleteness theorems; algebraic and many-valued logic; Boolean algebras, lattices, representation theorems, and models in set theory and mathematical logic; independence of the axioms of set theory (including the axiom of choice and the continuum hypothesis). May be repeated on different topic with consent of instructor. (Variable)

**MATH 6670 (800:267). Non-Euclidean Geometry — 3 hrs.**

Historical development of geometry models that do not assume Euclid's fifth postulate. Emphasis on Poincare's disc and upper half-plane models, distance and area in the hyperbolic plane, and Mobius transformations. Prerequisite(s): MATH 2500 (800:076); MATH 4500/5500 (800:160g); MATH 3610/5610 (800:165g) or MATH 3600/5600 (800:166g). (Variable)

**MATH 6745 (800:250). Deterministic Operations Research — 3 hrs.**

Overview of optimization models, mathematical programming (linear, integer, goal), optimization software LINGO, transportation and assignment problems, network models (shortest-path, maximum-flow), multi-period planning problems. Prerequisite(s): MATH 2422 (800:062); MATH 2500 (800:076). (Fall, Spring)

**MATH 6746 (800:251). Probabilistic Operations Research — 3 hrs.**

Decision making under uncertainty, Markov chains, deterministic and probabilistic dynamic programming, inventory control, production scheduling, supply chain management, portfolio optimizations. Prerequisite(s): MATH 2422 (800:062); MATH 2500 (800:076), MATH 3752/5752 (800:152g). (Same as STAT 6746)(Fall, Spring)

**MATH 6747 (800:252). Discrete-Event System Simulation — 3 hrs.**

Discrete-event systems simulation theory including input analysis, output analysis; applications of simulation software ARENA to studying performances of systems such as bank services, call centers, material-handling systems, and computer networks. Prerequisite(s): MATH 2422 (800:062); STAT 1772 (800:072). (Same as STAT 6747)(Fall, Spring)

**MATH 6748 (800:253). Modeling Industrial Systems Using Queueing Networks — 3 hrs.**

Queueing networks, applications to modeling and evaluating industrial systems such as flexible manufacturing systems, pull-type production systems, polling systems in computer networks, handoff schemes in cellular mobile networks; computational package MATLAB. Prerequisite(s): MATH 2422 (800:062); MATH 2500 (800:076); MATH 3752/5752 (800:152g). (Same as STAT 6748)(Fall, Spring)

**MATH 6779 (800:273). Topics in Probability and Statistics — 3 hrs.**

Topics from correlation and regression analysis, analysis of variance and co-variance, non-parametric methods, order statistics. May be repeated on different topic with consent of instructor. Prerequisite(s): consent of instructor. (Same as STAT 6779)(Variable)

**MATH 6795 (800:275). Industrial Internship/Project — 6 hrs.**

Mathematical analysis of industrial problems. Features work on a project of interest to a cooperating company. Oral and written reports required on the project. Prerequisite(s): approval of graduate coordinator and admittance to the P.S.M. program. (Variable)

### Statistics Courses

**STAT 1772 (800:072). Introduction to Statistical Methods — 3 hrs.**

Descriptive statistics including correlation and curve fitting. Intuitive treatment of probability and inferential statistics including estimations and hypothesis testing. No credit for students with credit in STAT 1774 (800:064). Students with credit in STAT 3770/5770 (800:172g) should not enroll in STAT 1772 (800:072). (Fall, Spring, Summer)

**STAT 1774 (800:064). Introductory Statistics for Life Sciences — 3 hrs.**

Descriptive statistics, basic probability concepts, confidence intervals, hypothesis testing, correlation and regression, elementary concepts of survival analysis. No credit for students with credit in STAT 1772 (800:072). (Fall, Spring)

**STAT 3751. Probability and Statistics — 3 hrs.**

Descriptive statistics and graphical representations, basic concepts of probability and distributions, random variables, expectations, sampling theory, tests of statistical significance. Calculus is employed in developing and applying these ideas. Specific attention devoted to the use of technology in motivating and explaining concepts and techniques. Emphasis on applications appropriate for secondary school probability/statistics courses. No credit with credit in STAT 3770/5770 (800:172g)/5770 (800:172g). Prerequisite(s): MATH 1421 (800:061) (800:061). (Same as MATH 3751 (800:173))(Fall and Even Springs)

**STAT 3752/5752 (800:152g). Introduction to Probability — 3 hrs.**

Axioms of probability, sample spaces having equally likely outcomes, conditional probability and independence, random variables, expectation, moment generating functions, jointly distributed random variables, weak law of large numbers, central limit theorem. Prerequisite(s): MATH 1421 (800:061) (800:061); junior standing. (Same as MATH 3752/5752 (800:152g))(Fall, Spring)

**STAT 3770/5770 (800:172g). Statistical Methods — 3 hrs.**

Descriptive statistics; elementary probability; estimation and hypothesis testing from an intuitive approach; use of statistical packages. No credit for students who have credit in STAT 1774 (800:064), STAT 1772 (800:072), or STAT 3775/5775 (800:174g). Prerequisite(s): junior standing. (Variable)

**STAT 3771/5771 (800:121g). Applied Statistical Methods for Research — 3 hrs.**

Inference about two or more population variances, multiple comparisons, categorical data analysis, linear and logistic regression, design of experiments, analysis of variance and covariance, repeated measures and random effects. Prerequisite(s): STAT 1774 (800:064) or STAT 1772 (800:072); junior standing. (Fall, Spring)

**STAT 3775/5775 (800:174g). Introduction to Mathematical Statistics — 3 hrs.**

Sampling distribution theory, point and interval estimation, Bayesian estimation, statistical hypotheses including likelihood ratio tests and chi-square tests, selected nonparametric methods. Prerequisite(s): MATH 2422 (800:062); MATH 3752/5752 (800:152g); junior standing. (Spring)

**STAT 3776/5776 (800:175g). Regression Analysis — 3 hrs.**

Regression analysis, analysis of variance, time series methods. Prerequisite(s): STAT 3775/5775 (800:174g); junior standing. (Fall)

**STAT 3778/5778 (800:171g). Spatial Data Analysis — 3 hrs.**

Analysis and interpretation of spatial point processes, area, geostatistical and spatial interaction data. Applications to geographic data in real estate, biology, environmental, and agricultural sciences using S-Plus software. Prerequisite(s): STAT 1774 (800:064) or STAT 1772 (800:072) or SOC 2020 (980:080); junior standing. (Same as GEOG 4340/5340 (970:160g))(Odd Springs)

**STAT 4754/5754 (800:154g). Introduction to Stochastic Processes — 3 hrs.**

Markov chains, Poisson processes, continuous time Markov chains, renewal processes, Brownian motion and stationary processes. Prerequisite(s): MATH 3752/5752 (800:152g)/5752 (800:152g); junior standing. (Same as MATH 4754/5754 (800:154g))(Fall)

**STAT 4772/5772 (800:122g). Statistical Computing — 3 hrs.**

Use of statistical software such as SAS, SPSS, S-Plus, Minitab. Data management, graphical techniques and data analysis, computer-intensive statistical methods. Prerequisite(s): STAT 1774 (800:064) or STAT 1772 (800:072); junior standing. (Variable)

**STAT 4773/5773 (800:123g). Design and Analysis of Experiments — 3 hrs.**

Planning and organizing experiments, one-factor experiments, randomized blocks, Latin squares and related designs, factorial designs and fractional factorial designs, response surface methodology, nested and split-plot designs. Prerequisite(s): STAT 3771/5771 (800:121g) or consent of instructor; junior standing. (Variable)

**STAT 4777/5777 (800:157g). Statistical Quality Assurance Methods — 3 hrs.**

Exploratory data analysis, Shewhart control charts and their variations, process capability analysis, CUSUM charts, EWMA charts, sampling inspection by attributes and by variables, continuous sampling plans, application of design of experiments in quality engineering. Prerequisite(s): MATH 3752/5752 (800:152g) or consent of instructor; junior standing. (Variable)

**STAT 4779/5779 (800:196g). Applied Multivariate Statistical Analysis — 3 hrs.**

Multivariate normal distribution, tests of significance with multivariate data, discrimination and classification, clustering, principal components, canonical correlations, use of statistical computer packages. Prerequisite(s): MATH 2500 (800:076); STAT 3775/5775 (800:174g); junior standing. (Variable)

**STAT 6746. Probabilistic Operations Research — 3 hrs.**

Decision making under uncertainty, Markov chains, deterministic and probabilistic dynamic programming, inventory control, production scheduling, supply chain management, portfolio optimizations. Prerequisite(s): MATH 2422 (800:062) (800:062); MATH 2500 (800:076) (800:076), MATH 3752/5752 (800:152g)/5752 (800:152g). (Same as MATH 6746 (800:251))(Fall, Spring)

**STAT 6747. Discrete-Event System Simulation — 3 hrs.**

Discrete-event systems simulation theory including input analysis, output analysis; applications of simulation software ARENA to studying performances of systems such as bank services, call centers, material-handling systems, and computer networks. Prerequisite(s): MATH 2422 (800:062) (800:062); STAT 1772 (800:072) (800:072). (Same as MATH 6747 (800:252))(Fall, Spring)

**STAT 6748. Modeling Industrial Systems Using Queueing Networks — 3 hrs.**

Queueing networks, applications to modeling and evaluating industrial systems such as flexible manufacturing systems, pull-type production systems, polling systems in computer networks, handoff schemes in cellular mobile networks; computational package MATLAB. Prerequisite(s): MATH 2422 (800:062) (800:062); MATH 2500 (800:076) (800:076); MATH 3752/5752 (800:152g)/5752 (800:152g). (Same as MATH 6748 (800:253))(Fall, Spring)

**STAT 6772 (800:272). Advanced Statistical Methods — 3 hrs.**

Categorical data analysis, logistic and Poisson regression, forecasting, repeated measures, classification and discriminant analysis, cluster analysis, data mining. Prerequisite(s): STAT 4773/5773 (800:123g). (Variable)

**STAT 6779. Topics in Probability and Statistics — 3 hrs.**

Topics from correlation and regression analysis, analysis of variance and co-variance, non-parametric methods, order statistics. May be repeated on different topic with consent of instructor. Prerequisite(s): consent of instructor. (Same as MATH 6779 (800:273))(Variable)