Department of Mathematics
(College of Humanities, Arts and Sciences)
The Department of Mathematics offers the following undergraduate and graduate programs. Specific requirements for these programs are listed within this Department of Mathematics section in the following order:
 Data Science (also listed in Department of Computer Science and Department of Physics)
 Mathematics
 MathematicsTeaching
 Mathematics (K8)Teaching
 Statistics and Actuarial Science
 Mathematics:
 Mathematics emphasis
 Secondary Teaching emphasis
 Community College Teaching emphasis
 Mathematics for the Elementary and Middle Grades (K8)
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 nonsatisfaction 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 UNIFI/General Education requirements and the following specified major requirements, plus electives to complete the minimum of 120 hours. Students are encouraged to discuss Undergraduate Research (MATH 4990) with their adviser.
Common core:  15  
Calculus I ^{*}  
Calculus II  
Calculus III  
Linear Algebra for Applications  
Mathematics core:  16  
Discrete and Argumentative Mathematics  
Advanced Calculus I  
Advanced Calculus II  
Modern Algebra I  
Modern Algebra II  
Senior Mathematics Seminar  
Probability/Statistics: select one of the following. MATH/STAT 3751 will not satisfy this requirement if a student has credit for STAT 1772.  36  
Probability and Statistics  
Introduction to Statistical Methods  
and  
Introduction to Probability  
Introduction to Statistical Methods and Applied Statistical Methods for Research  
Electives: Select two of the following. MATH/STAT 3752/5752 cannot be used if used for the Probability/Statistics requirement. Other junior/senior level mathematics courses may be substituted with approval of advisor and Department Head.  6  
Dynamical Systems: Chaos Theory and Fractals  
Differential Equations  
Numerical Analysis ^{*}  
Combinatorics  
Euclidean Geometry  
Modern Geometries  
Differential Geometry  
History of Mathematics  
Introduction to Probability  
Mathematics of Finance  
Introduction to Complex Analysis  
Elementary Number Theory  
Topology I  
Total Hours  4043 
 *
These courses have additional prerequisites as follows:
MATH 1420 has prerequisite of a satisfactory score on a mathematics placement exam, or subsequent remediation.
MATH 3440/5440 has prerequisite of CS 1130, CS 1160, or CS 1510.
Mathematics MajorStatistics/Actuarial Science
The MathematicsStatistics/Actuarial Science major requires a minimum of 120 total hours to graduate. This total includes UNIFI/General Education 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  
Introduction to Statistical Methods  
or STAT 1774  Introductory Statistics for Life Sciences  
Introduction to Mathematical Statistics  
Introduction to Probability  
Computer Programming:  34  
Select one of the following:  
Visual BASIC Programming  
C/C++ Programming  
Introduction to Computing  
Statistical Computing I  
Seminar/research:  13  
Senior Mathematics Seminar  
or MATH 4990  Undergraduate Research in Mathematics  
Select and complete ONE of the following Emphasis Core:  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  
Topics in Actuarial Science,Topics in Actuarial Science: LongTerm Actuarial Mathematics  
Loss Models  
Introduction to Financial Engineering  
Electives  6  
Select two electives from the following list. The same course cannot be used to satisfy both the emphasis core and elective requirement.  
Applied Statistical Methods for Research  
Regression Analysis  
Spatial Data Analysis  
Statistical Computing I  
Design and Analysis of Experiments  
Statistical Quality Assurance Methods  
Applied Multivariate Statistical Analysis  
Statistical Computing II  
Actuarial Examination Preparation ^{**}  
Actuarial Mathematics  
Topics in Actuarial Science,Topics in Actuarial Science: LongTerm Actuarial Mathematics  
Introduction to Financial Engineering  
Loss Models  
Numerical Analysis  
Mathematics of Finance  
Total Hours  4346 
 *
MATH 1420 has prerequisite of satisfactory score on mathematics placement exam or subsequent remediation.
 **
ACT SCI 3731 may be repeated for credit for preparation for different exams, however only 3 hours will count toward the Statistics/Actuarial Science major.
Mathematics MajorTeaching
The MathematicsTeaching major requires a minimum of 122123 total hours to graduate. This total includes UNIFI/General Education requirements, the Professional Education Requirements, and the following specified major requirements to complete the minimum of 122123 hours.
This major leads to endorsement #143: 512 Mathematics.
Required  
Mathematics:  
Common core:  
MATH 1420  Calculus I ^{*}  4 
MATH 1421  Calculus II  4 
MATH 2422  Calculus III  4 
MATH 2500  Linear Algebra for Applications  3 
Teaching core:  
MATH 1310  Technology for Secondary Mathematics Teachers  3 
MATH 2303  Introduction to Teaching Secondary Mathematics  3 
MATH 2313  Topics in Secondary Mathematics  3 
MATH 2900  Discrete and Argumentative Mathematics  3 
MATH 3302  Field Experience in Teaching Secondary Mathematics  1 
MATH 3304  The Teaching of Secondary Mathematics  3 
MATH 3305  Connections: University Mathematics and the Secondary Curriculum  3 
MATH 3600/5600  Euclidean Geometry  3 
MATH 4500/5500  Modern Algebra I  3 
Probability and Statistics:  36  
Probability and Statistics  
Introduction to Statistical Methods and Introduction to Probability  
Introduction to Statistical Methods and Applied Statistical Methods for Research  
Select two of the following:  6  
Combinatorics  
Modern Geometries  
Advanced Calculus I  
Modern Algebra II  
Elementary Number Theory  
Geometric Transformations  
Computer Science:  34  
Select one of the following:  
Media Computation  
Visual BASIC Programming  
C/C++ Programming  
Fundamentals of Programming  
Introduction to Computing  
Total Hours  5256 
 *
MATH 1420 has a prerequisite of satisfactory score on mathematics placement exam or subsequent remediation.
Notes: For departmental approval to student teach, a student in the program must satisfy the University requirements to student teach and the following specific departmental requirements:
1) Must earn a C– or better in: MATH 1420, MATH 1421, MATH 2500, MATH 2900, MATH 3302, MATH 3600/5600, MATH 4500/5500, and courses taken to satisfy the Probability and Statistics and Computer Science requirements.
2) MATH 3302 is offered credit/no credit only effective Fall 2019 and beyond, and student must pass this course.
3) Must earn a grade of C or higher in: MATH 2303 and MATH 3304.
4) Must complete all of the courses in the major with a major grade point average of 2.50 or higher.
Minors
Data Science Minor
The Data Science minor is an interdisciplinary program that integrates computer programming, machine learning, statistics, predictive modeling and visualization to provide students with broad based skills for extracting gainful information from data that originate from a variety of sources. A final project (ideally with corporate or nonprofit partnerships) will ensure that students employ their skills to solve a realworld problem.
Statistics:  
STAT 1772  Introduction to Statistical Methods  3 
STAT 4784/5784  Introduction to Machine Learning  3 
Computer Science:  
CS 1510  Introduction to Computing  4 
CS 2150  Computing for Data Science  37 
or  
Data Structures and Discrete Structures  
CS 3140/5140  Database Systems  3 
Physics:  
PHYSICS 4160/5160  Data Visualization, Modeling and Simulation  3 
Required Data Science Project  23  
Undergraduate Research in Computer Science  
or MATH 4990  Undergraduate Research in Mathematics  
or PHYSICS 3000  Undergraduate Research in Physics  
Total Hours  2126 
Mathematics Minor
Required  
Mathematics:  11  
Calculus I ^{*}  
Calculus II  
Linear Algebra for Applications  
Electives  12  
Mathematics:  
Topics in Actuarial Science,Topics in Actuarial Science: LongTerm Actuarial Mathematics  
Calculus III  
Discrete and Argumentative Mathematics  
Dynamical Systems: Chaos Theory and Fractals  
Differential Equations  
Partial Differential Equations  
Numerical Analysis  
Combinatorics  
Euclidean Geometry  
Modern Geometries  
Differential Geometry  
History of Mathematics  
Probability and Statistics  
Introduction to Probability  
Advanced Calculus I  
Advanced Calculus II  
Introduction to Complex Analysis  
Modern Algebra I  
Modern Algebra II  
Elementary Number Theory  
Geometric Transformations  
Topology I  
Introduction to Mathematical Statistics  
Regression Analysis  
Statistical Quality Assurance Methods  
Applied Multivariate Statistical Analysis  
Total Hours  23 
 *
MATH 1420 has prerequisite of satisfactory score on mathematics placement exam or subsequent remediation.
Mathematics MinorTeaching
This minor leads to endorsement #143: 512 Mathematics.
Required  
Mathematics:  
MATH 1420  Calculus I ^{*}  4 
MATH 1421  Calculus II  4 
Select one of the following:  3  
Introduction to Statistical Methods  
Introductory Statistics for Life Sciences  
Probability and Statistics  
MATH 2303  Introduction to Teaching Secondary Mathematics  3 
MATH 2500  Linear Algebra for Applications  3 
MATH 2900  Discrete and Argumentative Mathematics  3 
MATH 3600/5600  Euclidean Geometry  3 
MATH 4500/5500  Modern Algebra I  3 
MATH 3302  Field Experience in Teaching Secondary Mathematics  1 
MATH 3304  The Teaching of Secondary Mathematics  3 
Computer Science:  
Select one of the following:  34  
Media Computation  
Visual BASIC Programming  
C/C++ Programming  
Fundamentals of Programming  
Introduction to Computing  
Total Hours  3334 
 *
MATH 1420 has prerequisite of satisfactory score on mathematics placement exam or subsequent remediation.
Notes: For departmental approval to student teach, a student in the program must satisfy the University requirements to student teach and the following specific departmental requirements:
1) Must earn a C– or better in MATH 1420, MATH 1421, MATH 2500, MATH 2900, MATH 3302, MATH 3600, MATH 4500, and STAT 1772 or STAT 1774 or MATH 3751.
2) MATH 3302 is offered credit/no credit only effective Fall 2019 and beyond, and student must pass this course.
3) Must earn a grade of C or higher in MATH 2303 and MATH 3304.
4) Must complete all of the courses in the minor with a minor grade point average of 2.50 or higher
Mathematics Minor (K8)Teaching
This minor leads to endorsement #142: K8 Mathematics.
Required  
Mathematics:  
MATH 1204  Mathematical Reasoning  3 
MATH 2204  Mathematical Reasoning for Elementary Teachers II  3 
MATH 3204  Mathematical Reasoning for Elementary Teachers III  3 
MATH 3211  Algebra  3 
MATH 3212  Introduction to Geometry and Measurement for Elementary Teachers  3 
MATH 3213  Topics in Mathematics for Grades K8  3 
MATH 3214  Problem Solving in Mathematics for Elementary Teachers  3 
Computer Science:  
CS ED 1310  Programming Environments for Elementary Education  3 
Total Hours  24 
Statistics and Actuarial Science Minor
Complete one of the following emphases  
Actuarial Science emphasis:  14  
MATH 1420  Calculus I ^{*}  4 
MATH 1421  Calculus II  4 
ACT SCI/MATH 3780  Mathematics of Finance  3 
MATH/STAT 3752  Introduction to Probability  3 
Statistics emphasis  12  
STAT 1772  Introduction to Statistical Methods  3 
STAT 3771/5771  Applied Statistical Methods for Research  3 
STAT 4772/5772  Statistical Computing I  3 
STAT 4782/5782  Statistical Computing II  3 
Electives  9  
Select three courses from the following or from the emphasis not chosen:  
ACT SCI 3731  Actuarial Examination Preparation  3 
ACT SCI 4785/5785  Introduction to Financial Engineering  3 
ACT SCI 4735/5735  Actuarial Mathematics  3 
ACT SCI 4788/5788  Loss Models  3 
MATH 2422  Calculus III  4 
MATH 2500  Linear Algebra for Applications  3 
STAT 3775/5775  Introduction to Mathematical Statistics  3 
STAT 3776/5776  Regression Analysis  3 
STAT 3778/5778  Spatial Data Analysis  3 
STAT 4773/5773  Design and Analysis of Experiments  3 
STAT 4777/5777  Statistical Quality Assurance Methods  3 
STAT 4779/5779  Applied Multivariate Statistical Analysis  3 
Total hours  2124 
 *
MATH 1420 has a prerequisite of satisfactory score on mathematics placement exam or subsequent remediation.
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 nonthesis options. A minimum of 36 hours is required for the thesis option, including 6 hours of MATH 6299 and a minimum of 15 additional hours of 6000level course work. A minimum of 33 hours is required for the nonthesis option, including a minimum of 3 hours of MATH 6299 and a minimum of 15 additional hours of 6000level course work.
The Secondary Teaching emphasis is offered on a nonthesis option only; a minimum of 30 hours, including a minimum of 18 hours of 6000level course work is required.
The Community College Teaching emphasis is offered on a nonthesis option only; a minimum of 30 hours, including a minimum of 15 hours of 6000level course work is required.
Students interested in this program must submit a completed Application for Admission to Graduate Study and should refer to their MyUNIverse Student Center ToDo list or contact the Department of Mathematics for other application requirements. Graduate information and application for graduate admission can be found at https://admissions.uni.edu/application.
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 nonthesis option on the Mathematics emphasis only.
Mathematics Emphasis
Required  
Mathematics:  
MATH 3630/5630  Differential Geometry  3 
or MATH 4615/5615  Geometric Transformations  
MATH 6420  Mathematical Analysis I  3 
MATH 6460  Complex Analysis I  3 
MATH 6500  Abstract Algebra I  3 
Select at least two of the following:  6  
Mathematical Analysis II  
Complex Analysis II  
Abstract Algebra II  
Research:  3 or 6  
Research  
Thesis option (6 hours)  
Nonthesis option (3 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,Topics in Actuarial Science: LongTerm Actuarial Mathematics  
Differential Equations  
Partial Differential Equations  
Numerical Analysis  
Combinatorics  
History of Mathematics  
Introduction to Probability  
Advanced Calculus II  
Introduction to Complex Analysis  
Modern Algebra II  
Topology I  
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 nonthesis option  33 
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:  
MATH 6201  Foundations of Mathematics Education  3 
MATH 6381  Current Research in Mathematics Education  3 
MATH 6209  Mathematics Curriculum and Assessment  3 
MATH 6225  Teaching and Learning Mathematics  3 
MATH 6236  Equity and Mathematics Education  3 
Mathematics:  
MATH 6371  Probability and Statistical Inference  3 
MATH 6370  Applied Linear Statistical Methods  3 
Select one course from the following:  
MATH 6212  Foundations of Algebraic Reasoning  3 
or MATH 6504  Advanced Linear Algebra  
Select One Course from the Following:  
MATH 6215  Foundations of Geometric Reasoning  3 
or MATH 6670  NonEuclidean Geometry  
Select One Course from the Following:  
MATH 6410  Foundations of Calculus  3 
or MATH 6205  Teaching Rational Numbers and Proportionality  
Total Hours  30 
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:  
MATH 6201  Foundations of Mathematics Education  3 
MATH 6381  Current Research in Mathematics Education  3 
MATH 6225  Teaching and Learning Mathematics  3 
MATH 6236  Equity and Mathematics Education  3 
MATH 6209  Mathematics Curriculum and Assessment  3 
Mathematics:  
MATH 6504  Advanced Linear Algebra  3 
MATH 6370  Applied Linear Statistical Methods  3 
MATH 6371  Probability and Statistical Inference  3 
MATH 6410  Foundations of Calculus  3 
MATH 6670  NonEuclidean Geometry  3 
Total Hours  30 
Major in Mathematics for the Elementary and Middle Grades (K8)
This major is intended for teachers interested in mathematics for the elementary and middle grades (K8) 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 refer to their MyUNIverse Student Center ToDo list or contact the Department of Mathematics for other application requirements. Graduate information and application for graduate admission can be found at https://admissions.uni.edu/application.
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 nonthesis option only; a minimum of 30 hours is required. A minimum of 15 hours of 6000level course work is required.
Required  
Mathematics Education:  
MATH 6201  Foundations of Mathematics Education  3 
MATH 6205  Teaching Rational Numbers and Proportionality  3 
MATH 6212  Foundations of Algebraic Reasoning  3 
MATH 6215  Foundations of Geometric Reasoning  3 
MATH 6381  Current Research in Mathematics Education  3 
MATH 6227  Data Analysis, Probability, and Discrete Mathematical Reasoning  3 
MATH 6225  Teaching and Learning Mathematics  3 
MATH 6236  Equity and Mathematics Education  3 
MATH 6216  Number and Operations  3 
MATH 6209  Mathematics Curriculum and Assessment  3 
Total Hours  30 
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.
Students interested in this program must submit a completed Application for Admission to Graduate Study and should refer to their MyUNIverse Student Center ToDo list or contact the Department of Mathematics for any other application requirements. Graduate information and application for graduate admission can be found at https://admissions.uni.edu/application.
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 nonthesis program. A minimum of 30 hours is required. A minimum of 12 hours of 6000level course work is required.
No comprehensive examination is required for this nonthesis option.
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 universitylevel courses:
Prerequisite Courses:
MATH 1420  Calculus I  4 
MATH 1421  Calculus II  4 
MATH 2422  Calculus III  4 
MATH 2500  Linear Algebra for Applications  3 
STAT 1772  Introduction to Statistical Methods  3 
One course in computer programming (or equivalent):  
CS 1130  Visual BASIC Programming  3 
CS 1160  C/C++ Programming  3 
CS 1510  Introduction to Computing  4 
This major requires completion of 9 hours of the PSM Industrial Mathematics core, and 21 hours of electives.
Required Core:  
MATH 6745  Deterministic Operations Research  3 
MATH 6747  DiscreteEvent System Simulation  3 
MATH 6796  PSM Capstone Project  3 
Electives from the following:  21  
Marketing:  
Marketing Strategy  
or MKTG 6170  Marketing Management  
Management:  
Business Strategy  
CrossFunctional Operations  
Finance:  
Corporate Finance  
Principles of Investments  
Financial Management and Markets  
Technology:  
Solid Modeling and Additive Manufacturing for Design  
Computer Aided Manufacturing  
Mathematics:  
Mathematics of Finance  
Actuarial Mathematics  
Topics in Actuarial Science,Topics in Actuarial Science: LongTerm Actuarial Mathematics  
Introduction to Financial Engineering  
Loss Models  
Differential Equations  
Partial Differential Equations  
Numerical Analysis  
Combinatorics  
Differential Geometry  
Introduction to Probability  
Introduction to Complex Analysis  
Probabilistic Operations Research  
Modeling Industrial Systems Using Queueing Networks  
Topics in Probability and Statistics  
Applied Statistical Methods for Research  
Introduction to Mathematical Statistics  
Regression Analysis  
Spatial Data Analysis  
Statistical Computing I  
Design and Analysis of Experiments  
Statistical Quality Assurance Methods  
Applied Multivariate Statistical Analysis  
Statistical Computing II  
Advanced Statistical Methods  
Computer Science:  
Networking  
Computer Systems  
Physics:  
Modeling and Simulation of Physical Systems  
Total Hours  30 
Program Certificates
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 certificates, contact the Department of Mathematics or the Office of the Registrar, which serves as the centralized registry.
Statistical Computing Certificate
Required:  
STAT 3771/5771  Applied Statistical Methods for Research  3 
STAT 4772/5772  Statistical Computing I  3 
STAT 4782/5782  Statistical Computing II  3 
Electives: 6 hours from the following  6  
Regression Analysis  
Spatial Data Analysis  
Design and Analysis of Experiments  
Applied Multivariate Statistical Analysis  
Any other courses with the consent of the mathematics department  
Total Hours  15 
Mathematics, B.A.
Goal 1. Problem Solving Specification:
 Understanding: Students will understand or state problems and definitions correctly;
 Modification: Students will modify problems when necessary to make them tractable;
 Reaching a solution: Students will articulate assumptions and reason logically to conclusions;
 Communication and Interpretation: Students will communicate steps and interpret results intelligently when necessary.
Goal 2. Content Specification:
 Knowledge Foundation: Students will demonstrate an understanding of the core knowledge of mathematics.
 Advanced Content: Students will demonstrate comprehension of upperlevel content of mathematics, statistics and actuarial science.
 Communication and Interpretation: Students will communicate using correct content terms and interpret concepts when necessary.
Goal 3. Technology/Software:
 Software Proficiency: Students will demonstrate basic proficiency with mathematical and statistical software.
 Analytical Skills: Students will be able to make informed choices about when the use of technology or data analysis is viable and useful.
 Communication and Interpretation: Students will communicate using the right language and interpret results intelligently.
Goal 4. Professional Development:
 Proof and Argument Specification: Students will be able to compose and explain proofs in clear mathematical style, both orally and in writing, and to critically evaluate mathematical arguments made by others. Students will be able to use a variety of techniques of proof, including direct proof, proof by contradiction, and mathematical induction.
Mathematics: Statistics/Actuarial Science, B.A.
Goal 1. Problem Solving Specification:
 Understanding: Students will understand or state problems and definitions correctly;
 Modification: Students will modify problems when necessary to make them tractable;
 Reaching a solution: Students will articulate assumptions and reason logically to conclusions;
 Communication and Interpretation: Students will communicate steps and interpret results intelligently when necessary.
Goal 2. Content Specification:
 Knowledge Foundation: Students will demonstrate an understanding of the core knowledge of mathematics.
 Advanced Content: Students will demonstrate comprehension of upperlevel content of mathematics, statistics and actuarial science.
 Communication and Interpretation: Students will communicate using correct content terms and interpret concepts when necessary.
Goal 3. Technology/Software:
 Software Proficiency: Students will demonstrate basic proficiency with mathematical and statistical software.
 Analytical Skills: Students will be able to make informed choices about when the use of technology or data analysis is viable and useful.
 Communication and Interpretation: Students will communicate using the right language and interpret results intelligently.
Goal 4. Professional Development:
 Actuarial Science Development: Students with actuarial science emphasis will develop skills and acquire the content knowledge needed to pass actuarial exams offered by the professional organizations including Society of Actuaries and Casualty Actuarial Society.
Mathematics Teaching, B.A.
Goal 1: Social Contexts of Mathematics Teaching and Learning  Wellprepared beginning teachers of mathematics realize that the social, historical, and institutional contexts of mathematics affect teaching and learning and know about and are committed to their critical roles as advocates for each and every student.
Goal 2: Knowledge of Students as Learners of Mathematics  Wellprepared beginning teachers of mathematics have foundational understandings of students' mathematical knowledge, skills, and dispositions. They also know how these understandings can contribute to effective teaching and are committed to expanding and deepening their knowledge of students as learners of mathematics.
Goal 3: Pedagogical Knowledge and Practices for Teaching Mathematics  Wellprepared beginning teachers of mathematics have foundations of pedagogical knowledge, effective and equitable mathematics teaching practices to support students' sense making, understanding, and reasoning. Additionally, wellprepared beginning teachers can develop effective assessment plans.
Goal 4: Knowledge of Mathematics Wellprepared beginning teachers of mathematics possess robust knowledge of mathematical and statistical concepts that underlie what they encounter in teaching. They engage in appropriate mathematical and statistical practices and support their students in doing the same.
Mathematics, M.A.
Goal 1. Graduates will be able to undertake advanced mathematical reasoning:
a. Students will construct logically valid mathematical arguments;
b. Students will apply information learned in one setting to different situations;
c. Students will make connections between seemingly different concepts.
Goal 2. Graduates will be able to conduct independent work and develop new mathematical ideas:
a. Students will demonstrate that they can work independently;
b. Students will identify problems in their readings and to find ways to fix them;
c. Students will create original method(s) for solving known problem(s) or find solution(s) to new problem(s) in their theses or culminating papers.
Goal 3. Graduates will be able to solve problems at the level of graduate mathematics:
a. Students will use/apply researchlevel (advanced) methods used to solve problems in their theses or culminating papers;
b. Students will solve problems in graduate courses. Department faculty will identify 12 problems on the final examinations to assess this goal.
Goal 4. Graduates will be able to comprehend and communicate advanced mathematics both orally and in writing:
a. Students will clearly state the goal(s) of their theses or paper;
b. Students will place the questions/problems they addressed in their theses or papers in context (history, literature review, etc);
c. Students will describe in detail the method(s) they used to answer the questions/problems in their theses or papers;
d. Students will demonstrate mastery of the subject matter covered in their theses by answering questions from the theses committees about the theses.
Mathematics Emphasis in Secondary Teaching or Community College Teaching, M.A.
Goal 1: Use evidence from teaching to analyze current practices and work to improve future teaching through the Mathematical Teaching Practices
Goal 2: Demonstrate proficiency in mathematics oriented toward deepening mathematical knowledge
Goal 3: Incorporate mathematics education research and resources (e.g. curriculum, current and emerging technology, manipulatives) into teaching practices
Goal 4: Explore equitable teaching practices from theory through implementation
Goal 5: Analyze current assessment practices through the lens of current assessment research
Mathematics for the Elementary and Middle Grades (K8), M.A.
In working to develop a productive mathematical disposition for teaching, students will
a. Use evidence from teaching to analyze current practices and work to improve future teaching through the following Mathematical Teaching Practices:

Establish mathematics goals to focus learning

Implement takes that promote reasoning and problem solving

Use and connect mathematical representations

Facilitate meaningful mathematical discourse

Pose purposeful questions

Build procedural fluency from conceptual understanding

Support productive struggle in learning mathematics

Elicit and use evidence of student thinking.
b. Demonstrate proficiency in mathematics oriented toward deepening mathematical knowledge.
c. Incorporate mathematics education research and resources (e.g. curriculum, current and emerging technology, manipulatives) into teaching practices.
d. Explore equitable teaching practices from theory through implementation.
e. Analyze current assessment practices through the lens of current assessment research.
Industrial Mathematics, P.S.M.
1. Students will demonstrate an indepth understanding of a variety of mathematical models and techniques needed in business/industry.
2. Students will demonstrate the practical skills needed to apply mathematical models and techniques to problemsolving in business/industry.
3. Students will demonstrate communication skills appropriate for working in business/industry.
Mathematics, B.A.
This is a sample plan of study with a suggested sequencing of classes for the major. University electives may be applied to earn additional academic majors, minors, or certificates. Students should regularly meet with their academic advisor to plan their specific semester schedule to include UNIFI/General Education program and/or university elective hours required.
Freshman  

Fall  Hour  
ENGLISH 1005  College Writing and Research  3 
MATH 1420  Calculus I  4 
UNIFI/General Education or University Electives  9  
Hours  16  
Spring  
COMM 1000  Oral Communication  3 
MATH 2500  Linear Algebra for Applications  3 
MATH 1421  Calculus II  4 
UNIFI/General Education or University Electives  6  
Hours  16  
Sophomore  
Fall  
MATH 2422  Calculus III  4 
MATH 2900  Discrete and Argumentative Mathematics  3 
UNIFI/General Education or University Electives  9  
Hours  16  
Spring  
Mathematics elective as specified  3  
UNIFI/General Education or University Electives  13  
Hours  16  
Junior  
Fall  
Mathematics elective as specified  3  
MATH 4500 or MATH 4420  3  
UNIFI/General Education or University Electives  8  
Hours  14  
Spring  
MATH 3751/STAT 3751  3  
MATH 4501 or MATH 4421  3  
UNIFI/General Education or University Electives  9  
Hours  15  
Senior  
Fall  
MATH 4420 or MATH 4500  3  
UNIFI/General Education or University Electives  11  
Hours  14  
Spring  
MATH 4421 or MATH 4501  3  
MATH 4900  Senior Mathematics Seminar  1 
UNIFI/General Education or University Electives  9  
Hours  13  
Total Hours  120 
 *
Note: A student who has a grade point average of less than 2.25 in all departmental courses used for this major may not apply a departmental course in which a grade of less than C is earned.
Mathematics Teaching, B.A.
This is a sample plan of study with a suggested sequencing of classes for the major. University electives may be applied to earn additional academic majors, minors, or certificates. Students should regularly meet with their academic advisor to plan their specific semester schedule to include UNIFI/General Education program and/or university elective hours required.
Freshman  

Fall  Hour  
ENGLISH 1005  College Writing and Research  3 
MATH 1310  Technology for Secondary Mathematics Teachers  3 
MATH 1420  Calculus I  4 
UNIFI/General Education or University Electives  6  
Hours  16  
Spring  
EDPSYCH 2030  Dynamics of Human Development  3 
MATH 1421  Calculus II  4 
TEACHING 2017  Level 1 Field Experience: Exploring Teaching  1 
UNIFI/General Education or University Electives  6  
Hours  14  
Sophomore  
Fall  
COMM 1000  Oral Communication  3 
CS ED 1320  Fundamentals of Programming  3 
MATH 2500  Linear Algebra for Applications  3 
MATH 2900  Discrete and Argumentative Mathematics  3 
UNIFI/General Education or University Electives  4  
Hours  16  
Spring  
MATH 2303  Introduction to Teaching Secondary Mathematics  3 
MATH 2313  Topics in Secondary Mathematics  3 
MATH 2422  Calculus III  4 
TEACHING 3128  Level 2 Field Experience: Lesson Planning and Instruction  1 
EDPSYCH 3148  Learning and Motivation in Classroom Contexts  3 
MEASRES 3150  Classroom Assessment  2 
Hours  16  
Junior  
Fall  
MATH 3600/5600  Euclidean Geometry  3 
MATH 4500/5500  Modern Algebra I  3 
SPED 3150  Meeting the Needs of Diverse Learners in Classrooms  2 
UNIFI/General Education or University Electives  8  
Hours  16  
Spring  
MATH 3305  Connections: University Mathematics and the Secondary Curriculum  3 
MATH 3751 or STAT 3771 or MATH 3752  3  
MATH 4510/5510  Elementary Number Theory (or MATH 4501 Modern Algebra II)  3 
SOCFOUND 3119  Schools and American Society  3 
UNIFI/General Education or University Electives  3  
Hours  15  
Senior  
Fall  
MATH 3302  Field Experience in Teaching Secondary Mathematics  1 
MATH 3304  The Teaching of Secondary Mathematics  3 
MATH 4615/5615  Geometric Transformations (or MATH 3530 Combinatorics)  3 
TEACHING 4170/5170  Human Relations: Awareness and Application  3 
UNIFI/General Education or University Electives  5  
Hours  15  
Spring  
TEACHING 3138  Secondary School Teaching  12 
Hours  12  
Total Hours  120 
Mathematics: Statistics/Actuarial Science, B.A.
This is a sample plan of study with a suggested sequencing of classes for the major. University electives may be applied to earn additional academic majors, minors, or certificates. Students should regularly meet with their academic advisor to plan their specific semester schedule to include UNIFI/General Education program and/or university elective hours required.
Freshman  

Fall  Hour  
ECON 1041  Principles of Macroeconomics  3 
ENGLISH 1005  College Writing and Research  3 
MATH 1420  Calculus I  4 
MGMT 2080  Introduction to Information Systems  3 
STAT 1772  Introduction to Statistical Methods  3 
Hours  16  
Spring  
COMM 1000  Oral Communication  3 
ECON 1051  Principles of Microeconomics  3 
MATH 3780/5780  Mathematics of Finance  3 
MATH 1421  Calculus II  4 
UNIFI/General Education or University Electives  3  
Hours  16  
Sophomore  
Fall  
ACCT 2120  Principles of Financial Accounting  3 
ECON 1011  Statistics for Business Analytics ( or STAT 3771 Applied Statistical Methods for Research)  3 
MATH 2500  Linear Algebra for Applications  3 
MATH 3752/5752  Introduction to Probability  3 
UNIFI/General Education or University Electives  3  
Hours  15  
Spring  
MATH 2422  Calculus III  4 
STAT 3775/5775  Introduction to Mathematical Statistics  3 
UNIFI/General Education or University Electives  3  
Visual BASIC recommended  3  
Hours  13  
Junior  
Fall  
ACT SCI 4735/5735  Actuarial Mathematics  3 
FIN 3130/5130  Corporate Finance  3 
STAT 3776/5776  Regression Analysis  3 
UNIFI/General Education or University Electives  6  
Hours  15  
Spring  
ACT SCI 4739/5739  Topics in Actuarial Science,Topics in Actuarial Science: LongTerm Actuarial Mathematics  3 
ACT SCI 4785/5785  Introduction to Financial Engineering  3 
FIN 3160/5160  Principles of Investments  3 
MKTG 2110  Principles of Marketing  3 
UNIFI/General Education or University Electives  4  
Hours  16  
Senior  
Fall  
ACT SCI 4788/5788  Loss Models  3 
FIN 3050  Risk Management and Insurance  3 
MGMT 3100  Legal and Social Environment of Business  3 
UNIFI/General Education or University Electives  7  
Hours  16  
Spring  
MATH 4900  Senior Mathematics Seminar  1 
MGMT 3153  Organizational Management  3 
UNIFI/General Education or University Electives  9  
Hours  13  
Total Hours  120 
 *
Note: A student who has a grade point average of less that 2.25 in all departmental courses used for this major may not apply a departmental course in which a grade of less than C is earned.
Actuarial Science Courses
ACT SCI 3731. Actuarial Examination Preparation — 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 and Spring)
ACT SCI 3780/5780. 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; junior standing. (Same as MATH 3780/5780) (Spring)
ACT SCI 3790. Introduction to Actuarial Science — 1 hr.
Fundamental concepts of actuarial science; actuarial areas of practice; connections between coursework and actuarial practice; key competencies for actuaries, development of computing and communications skills in the context of actuarial science. Prerequisite(s): ACT SCI 3780/5780/MATH 3780/5780. (Variable)
ACT SCI 4735/5735. Actuarial Mathematics — 3 hrs.
Survival distributions and life tables, life insurance, life annuities, benefit premiums. Prerequisite(s): MATH 3752/5752; junior standing. (Even Falls)
ACT SCI 4739/5739. 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; junior standing. (Odd Springs)
ACT SCI 4785/5785. Introduction to Financial Engineering — 3 hrs.
Financial derivatives, option pricing, Binomial model, BlackScholes formula, Greeks and hedging, introduction to stochastic calculus, financial model simulation, MonteCarlo valuation. Prerequisite(s): MATH 3752/5752; junior standing. (Spring)
ACT SCI 4788/5788. 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; STAT 3775/5775; junior standing. (Odd Falls)
Mathematics Courses
MATH 100. Intermediate Algebra — 3 hrs.
Fundamental mathematical concepts; functions and graphs; solutions of equations; systems of equations and inequalities; matrices and determinants. Does not count toward minimum hours required for baccalaureate degree. (Fall)
MATH 1000. Exploring Social Justice Issues through Mathematics — 3 hrs.
Exploration of a number of social justice issues through the lens of mathematics. Students will explore, understand, and respond to local and global social justice issues using mathematical concepts and ideas including geometry, statistics, and algebra. (Spring)
MATH 1100. 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. 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 or MATH 1120. Prerequisite(s): Satisfactory score on ALEKS exam. (Fall and Spring)
MATH 1120. 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 or MATH 1140. Prerequisite(s): Satisfactory score on ALEKS exam. (Fall)
MATH 1130. Trigonometry — 2 hrs.
Trigonometric functions, solution of triangles and applications of simple harmonic motion, polar coordinates, and vectors. No credit for students with credit in MATH 1140. Prerequisite(s): Satisfactory score on ALEKS exam. (Spring)
MATH 1140. Precalculus — 4 hrs.
Precalculus 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 or MATH 1120, and to 2 hours for students with credit in MATH 1130. Prerequisite(s): Satisfactory score on ALEKS exam. (Fall and Spring)
MATH 1150. 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): Satisfactory score on ALEKS exam. (Spring)
MATH 1160. Calling Hogwash: Mathematics for Critical Thinking — 3 hrs.
This course will discuss how mathematics, statistics, and "mathematics" are used to persuade people, and to spread hogwash with a veneer of scientific credibility. Example topics include uses and abuses of data visualization, choices in measures of center and spread, selective use of percentages, truncating axes, the relationship between correlation and causation, forms of bias, and abuses of Big Data. There will be discussions, videos, readings, and examples from current traditional and social media. There will be at least one project where students will apply these techniques to attempt to persuade their classmates of something important to them. (Fall)
MATH 1204. Mathematical Reasoning — 3 hrs.
Mathematics as problem solving, communication, connections, and reasoning. Includes whole numbers, rational number concepts, operations, and connections to algebraic thinking. (Fall and Spring)
MATH 1310. Technology for Secondary Mathematics Teachers — 3 hrs.
Introduction to technologies (calculators, spreadsheets, and dynamic geometric and statistical programs) used in mathematics classrooms (512). Activities to develop facility with the technologies while addressing mathematics and pedagogical implications. Prerequisite(s) or corequisite(s): MATH 1420. (Fall)
MATH 1420. Calculus I — 4 hrs.
Limits, differentiation, introduction to integration including the fundamental theorem of calculus. Prerequisite(s): Satisfactory score on ALEKS exam. (Fall and Spring)
MATH 1421. Calculus II — 4 hrs.
Integration techniques, sequences and series, applications. Prerequisite(s): C or better in MATH 1420. (Fall and Spring)
MATH 1900. 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 and Spring)
MATH 2204. Mathematical Reasoning for Elementary Teachers II — 3 hrs.
Mathematics as problem solving, communication, connections, and reasoning. Includes data analysis, probability, and algebraic reasoning. Activities connected to elementary school mathematics. Designed for elementary education majors. Prerequisite(s): MATH 1204. (Fall and Spring)
MATH 2303. Introduction to Teaching Secondary Mathematics — 3 hrs.
Students will be introduced to National Council of Teachers of Mathematics Principles and Standards and researchbased methods of teaching secondary mathematics while learning ways to teach proportional reasoning and rational numbers. A grade of C or better is required for MATH 3304. Prerequisite(s): admitted to Teacher Education; sophomore standing. (Spring)
MATH 2313. Topics in Secondary Mathematics — 3 hrs.
Investigation of selected topics from algebra, geometry and data analysis. Reasoning about topics in the context of the secondary mathematics curriculum. Prerequisite(s): TEACHING 2017; EDPSYCH 2030. (Spring)
MATH 2422. Calculus III — 4 hrs.
The derivatives and integrals of multivariable functions and their applications; Gauss', Green's, and Stokes' theorems. Prerequisite(s): for Mathematics majors and minors: C or better in MATH 1421 and MATH 2500. Prerequisites for nonMathematics majors and minors: C or better in MATH 1421; MATH 2500 or consent of department. (Fall and Spring)
MATH 2500. 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. (Fall and Spring)
MATH 2900. Discrete and Argumentative Mathematics — 3 hrs.
Logical argument techniques. The writing process in a mathematical context. Theory of sets, functions, and relations. Elements of graph theory. Prerequisite(s): MATH 1420. (Fall)
MATH 3203. 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 3204; UNI and cumulative GPA of 2.50 or better; full admission to teacher education is required. (Fall, Spring, Summer)
MATH 3204. Mathematical Reasoning for Elementary Teachers III — 3 hrs.
Mathematics as problem solving, communication, connections, and reasoning. Includes geometry, measurement, and proportionality. Activities connected to elementary school mathematics. Designed for elementary education majors. Prerequisite(s): MATH 2204; UNI and cumulative GPA of 2.50 or better; junior standing or consent of department. (Fall and Spring)
MATH 3211. Algebra — 3 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 2204. (Fall and Spring)
MATH 3212. Introduction to Geometry and Measurement for Elementary Teachers — 3 hrs.
Van Hiele levels of thinking. Investigation of two and threedimensional concepts, rigid transformations, symmetry, and spatial sense. Prerequisite(s): MATH 3204; junior standing. (Fall and Spring)
MATH 3213. Topics in Mathematics for Grades K8 — 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 K8 mathematics curriculum. Prerequisite(s): CS ED 1310; MATH 3204; junior standing. (Fall and Spring)
MATH 3214. Problem Solving in Mathematics for Elementary Teachers — 3 hrs.
Strategies for constructing and communicating a mathematics problemsolving process. Analysis of resources and strategies to generate mathematics tasks and to create an effective problemsolving environment. Problem solving as a means of constructing mathematics knowledge. Prerequisite(s): at least one of MATH 3211, MATH 3212, MATH 3213; junior standing. Prerequisite(s) or corequisite(s): MATH 3203. (Fall and Spring)
MATH 3302. Field Experience in Teaching Secondary Mathematics — 1 hr.
Field experience in which students are actively involved in preparing and teaching lessons in 612 mathematics classrooms. Teacher candidates will spend a minimum of 30 hours in math classrooms. In preparing, teaching and reflecting on their lessons, teacher candidates will be expected to draw on theory and research related to teaching and learning processes, motivation, and classroom management and to discuss these theory/practice connections in required written assignments. Offered on credit/no credit basis only. Prerequisite(s): TEACHING 3128; EDPSYCH 3148; MEASRES 3150; MATH 3600/5600; MATH 4500/5500. Corequisite(s): MATH 3304. (Fall)
MATH 3304. The Teaching of Secondary Mathematics — 3 hrs.
Mathematics teaching strategies for grades 512; roles of content and methods; addressing the needs of diverse learners in secondary mathematics classes; assessing teaching and learning of secondary mathematics. A grade of C or better is required to be eligible for student teaching. Prerequisite(s): TEACHING 3128; EDPSYCH 3148; MEASRES 3150; MATH 3610/5610 or MATH 3600/5600; a grade of C or better in MATH 2303. (Fall)
MATH 3305. 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): MATH 2303; MATH 4500/5500. (Spring)
MATH 3410/5410. Dynamical Systems: Chaos Theory and Fractals — 3 hrs.
Historical background, including examples of dynamical systems; orbits, fixed points, and periodic points; onedimensional and twodimensional chaos; fractals: Julia sets, the Mandelbrot set, and fractal dimension; computer programs and dynamical systems. Prerequisite(s): MATH 1421; MATH 2500; junior standing. (Even Falls)
MATH 3425/5425. 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; MATH 2500; junior standing. (Odd Falls)
MATH 3430/5430. 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; junior standing. (Even Springs)
MATH 3440/5440. 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; MATH 2500; CS 1130 or CS 1160 or CS 1510 or equivalent; junior standing. (Odd Springs)
MATH 3530/5530. 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 or CS 1800; junior standing. (Fall and Spring)
MATH 3600/5600. Euclidean Geometry — 3 hrs.
Topics of plane geometry beyond a first course; compass and straightedge constructions, the ninepoint circle, Ceva's and Menelaus' theorems, triangle centers, conics, and tessellations. Prerequisite(s): MATH 1420 or equivalent; junior standing. (Fall and Spring)
MATH 3610/5610. 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 2900 or MATH 3600/5600; junior standing. (Even Springs)
MATH 3630/5630. Differential Geometry — 3 hrs.
Analytic study of curves and surfaces in threedimensional Euclidean space. Prerequisite(s): MATH 2422; MATH 2500; junior standing. (Odd Springs)
MATH 3640/5640. History of Mathematics — 3 hrs.
Survey of mathematical activities of humankind in numeration and number systems, algebra, number theory, and calculus from prehistory 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. (Variable)
MATH 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. No credit with credit in STAT 3770, credit reduced to 1 hour for students with credit in STAT 1772. Prerequisite(s): MATH 1421. (Same as STAT 3751) (Spring)
MATH 3752/5752. 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; junior standing. (Same as STAT 3752/5752) (Fall and Spring)
MATH 3780/5780. 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; junior standing. (Same as ACT SCI 3780/5780) (Spring)
MATH 4198. Independent Study.
(Variable)
MATH 4420/5420. Advanced Calculus 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; MATH 2500; MATH 2900 or consent of the instructor; junior standing. (Fall)
MATH 4421/5421. Advanced Calculus II — 3 hrs.
Riemann integration; sequences and series of functions; introduction to Lebesgue integration. Prerequisite(s): MATH 4420/5420; junior standing. (Spring)
MATH 4460/5460. Introduction to Complex Analysis — 3 hrs.
Algebraic and geometric structure of of complex number system; elementary functions and mappings; differentiation and integration of functions of a single complex variable; analytic and harmonic functions. Prerequisite(s): MATH 2422; junior standing. (Odd Falls)
MATH 4500/5500. Modern Algebra I — 3 hrs.
Basic properties of rings, integral domains, and fields. Polynomials over fields. Ideals and quotient rings. Introduction to groups. Prerequisite(s): MATH 2500; MATH 2900; junior standing. (Fall)
MATH 4501/5501. Modern Algebra II — 3 hrs.
Groups, homomorphisms, and quotient groups. Field extensions, straightedge and compass constructions. Additional topics from group theory and field theory. Prerequisite(s): MATH 4500/5500; junior standing. (Spring)
MATH 4510/5510. 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 2900; junior standing. (Spring and Even Falls)
MATH 4615/5615. 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; MATH 3610/5610 or MATH 3600/5600; junior standing. (Fall)
MATH 4641/5641. 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; MATH 2500; junior standing. (Even Springs)
MATH 4900. 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 and Spring)
MATH 4990. 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 and Spring)
MATH 6201. Foundations of Mathematics Education — 3 hrs.
Introduces current recommendations and policies regarding mathematics goals, content, frameworks, instructional strategies, and curricula. Investigates topics and documents with a focus on application and impact to classrooms. (Variable)
MATH 6205. 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 or consent of department. (Variable)
MATH 6209. Mathematics Curriculum and Assessment — 3 hrs.
In this course, students will explore various curricula and strategies and practices for assessing students' thinking and performance. Multiple curricula and forms of quality assessment will be considered, with an emphasis on formative assessment, aligning assessment to instruction, and interpreting evidence. (Even Falls)
MATH 6212. Foundations of Algebraic Reasoning — 3 hrs.
Examination of 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. (Summer)
MATH 6215. Foundations of Geometric Reasoning — 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. (Variable)
MATH 6216. Number and Operations — 3 hrs.
Examination of literature, problems, and issues related to the teaching of number and operations, with emphasis on whole numbers, decimals, and fractions. Reasoning about topics in the context and pedagogy of the K8 mathematics curriculum and exploration of innovative problem solving strategies. (Even Summers)
MATH 6225. Teaching and Learning Mathematics — 3 hrs.
Exploration of instructional strategies to support mathematical learning of K16 students with focus on your own practice. This includes establishing mathematical goals for learning, selecting appropriate tasks, facilitating classroom discourse, building conceptual understanding from procedural fluency, and using technology to enhance instruction. (Even Springs)
MATH 6227. Data Analysis, Probability, and Discrete Mathematical Reasoning — 3 hrs.
In this course, students will explore data collection, display, and interpretation methods including measures of central tendency; theoretical and empirical probability of single and multistage events; and apportionment, fair division, and counting. Concepts will be explored through and connected to best mathematical teaching practices. (Odd Falls)
MATH 6236. Equity and Mathematics Education — 3 hrs.
Examines theories of race, gender, social class, and sexuality and how these theories play out in K16 mathematics classrooms. Exploration of historical, political, and pedagogical issues within mathematics education. Includes history of treatment of minorities in mathematics education, teaching mathematics for social justice, culturally relevant mathematics pedagogy, and other pedagogies and theories related to teaching socioculturally diverse students. (Odd Springs)
MATH 6299. Research.
Prerequisite(s): consent of department. (Variable)
MATH 6370. Applied Linear Statistical Methods — 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, MATH 3751 or consent of instructor. (Fall and Spring)
MATH 6371. Probability and Statistical Inference — 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 or MATH 3751 or consent of instructor. (Variable)
MATH 6381. Current Research in Mathematics Education — 3 hrs.
Understand purposes and methods of research in mathematics education with a focus on action research. Review mathematics education research and its implications for instruction. Conduct a classroombased action research project. Prerequisite(s): MATH 6201 or consent of department. (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. Mathematical Analysis I — 3 hrs.
Set theory; the real number system; Lebesque measure; Lebesque integral. Prerequisite(s): MATH 4420/5420. Corequisite(s): MATH 4421/5421 or consent of instructor. (Odd Springs)
MATH 6421. Mathematical Analysis II — 3 hrs.
Differentiation and integration; classical Banach spaces; metric spaces; general measure and integration theory. Prerequisite(s): MATH 6420. (Spring)
MATH 6460. 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; MATH 4460/5460; or consent of instructor. (Spring)
MATH 6461. Complex Analysis II — 3 hrs.
Analytic continuation; harmonic functions; entire functions; conformal mapping; selected applications. Prerequisite(s): MATH 6460. (Variable)
MATH 6500. 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. Corequisite(s): MATH 4501/5501 or consent of instructor. (Fall)
MATH 6501. 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. (Spring)
MATH 6504. Advanced Linear Algebra — 3 hrs.
Vector spaces, linear transformations, matrices, eigenvalues and eigenvectors, canonical forms, bilinear and quadratic forms. Prerequisite(s): MATH 2500 or consent of instructor. (Odd Summers)
MATH 6510. Theory of Numbers — 3 hrs.
Mathematical study of integers: induction, divisibility, prime numbers, congruences, quadratic reciprocity, multiplicative functions. (Variable)
MATH 6530. 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 or MATH 4500/5500. (Variable)
MATH 6640. 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. (Variable)
MATH 6650. Topics in Mathematical Logic and Set Theory — 3 hrs.
Topics from the predicate calculus and firstorder mathematical theories; the Godel completeness and incompleteness theorems; algebraic and manyvalued 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. NonEuclidean Geometry — 3 hrs.
Historical development of geometry models that do not assume Euclid's fifth postulate. Emphasis on Poincare's disc and upper halfplane models, distance and area in the hyperbolic plane, and Mobius transformations. Prerequisite(s): MATH 2500; MATH 4500/5500; MATH 3610/5610 or MATH 3600/5600. (Variable)
MATH 6745. Deterministic Operations Research — 3 hrs.
Overview of optimization models, mathematical programming (linear, integer, goal), optimization software LINGO, transportation and assignment problems, network models (shortestpath, maximumflow), multiperiod planning problems. Prerequisite(s): MATH 2422; MATH 2500. (Fall and Spring)
MATH 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; MATH 2500, MATH 3752/5752. (Same as STAT 6746) (Fall and Spring)
MATH 6747. DiscreteEvent System Simulation — 3 hrs.
Discreteevent systems simulation theory including input analysis, output analysis; applications of simulation software ARENA to studying performances of systems such as bank services, call centers, materialhandling systems, and computer networks. Prerequisite(s): MATH 2422; STAT 1772. (Same as STAT 6747) (Fall and Spring)
MATH 6748. Modeling Industrial Systems Using Queueing Networks — 3 hrs.
Queueing networks, applications to modeling and evaluating industrial systems such as flexible manufacturing systems, pulltype production systems, polling systems in computer networks, handoff schemes in cellular mobile networks; computational package MATLAB. Prerequisite(s): MATH 2422; MATH 2500; MATH 3752/5752. (Same as STAT 6748) (Fall and Spring)
MATH 6779. Topics in Probability and Statistics — 3 hrs.
Topics from correlation and regression analysis, analysis of variance and covariance, nonparametric 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. 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)
MATH 6796. PSM Capstone Project — 3 hrs.
Mathematical/statistical modeling and analysis of a problem arising in industrial applications. Oral and written reports required on the project. Prerequisite(s): Approval of PSMIndustrial Mathematics coordinator and admittance to the PSM program in Industrial Mathematics. Completion of at least 9 hours in the PSMIndustrial Mathematics program. (Variable)
Statistics Courses
STAT 1772. 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. Students with credit in STAT 3770 should not enroll in STAT 1772. Prerequisite(s): Satisfactory score on ALEKS exam. (Fall, Spring, Summer)
STAT 1774. 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. Prerequisite(s): Satisfactory score on ALEKS exam. (Variable)
STAT 1780. Introduction to Data Science — 3 hrs.
Data acquisition, management, and visualization; selected methodologies of machine learning; applications and model evaluation; implementation in R; ethical issues in data science. Prerequisite(s): ALEKS Score of >50%. (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. No credit with credit in STAT 3770; credit reduced to 1 hour for students with credit in STAT 1772. Prerequisite(s): MATH 1421. (Same as MATH 3751) (Spring)
STAT 3752/5752. 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; junior standing. (Same as MATH 3752/5752) (Fall and Spring)
STAT 3771/5771. 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 or STAT 1772; junior standing. (Spring)
STAT 3775/5775. Introduction to Mathematical Statistics — 3 hrs.
Sampling distribution theory, point and interval estimation, Bayesian estimation, statistical hypotheses including likelihood ratio tests and chisquare tests, selected nonparametric methods. Prerequisite(s): MATH 3752/5752; junior standing. Prerequisite(s) or corequisite(s): MATH 2422. (Spring)
STAT 3776/5776. Regression Analysis — 3 hrs.
Regression analysis, analysis of variance, time series methods. Prerequisite(s): STAT 3775/5775; junior standing. (Fall)
STAT 3778/5778. 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 SPlus software. Prerequisite(s): STAT 1774 or STAT 1772 or SOC SCI 2020; junior standing. (Same as GEOG 3778/5778) (Odd Springs)
STAT 4772/5772. Statistical Computing I — 3 hrs.
Data management, graphical techniques and data analysis, computationallyintensive methods in statistics including Regression, Logistic Regression and Analysis of Variance. Emphasis on the use of statistical software such as SAS, SPSS, SPlus, and R. Prerequisite(s): STAT 1774 or STAT 1772; junior standing. (Fall)
STAT 4773/5773. Design and Analysis of Experiments — 3 hrs.
Planning and organizing experiments, onefactor experiments, randomized blocks, Latin squares and related designs, factorial designs and fractional factorial designs, response surface methodology, nested and splitplot designs. Prerequisite(s): STAT 3771/5771 or consent of instructor; junior standing. (Spring)
STAT 4777/5777. 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 or consent of instructor; junior standing. (Variable)
STAT 4779/5779. 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; STAT 3775/5775; junior standing. (Variable)
STAT 4782/5782. Statistical Computing II — 3 hrs.
Computationallyintensive methods in statistics including Multivariate and Categorical analyses. Emphasis on the use of statistical software such as SAS, SPSS, SPlus, and R. Prerequisite(s): STAT 4772/5772; Junior Standing. (Variable)
STAT 4784/5784. Introduction to Machine Learning — 3 hrs.
Models and Algorithms for Classification: kNN, Decision Trees, Neural Networks, Logistic Regression, Naive Bayes and Bayesian Networks, Support Vector Machines; Clustering: Hierarchical and kMeans, Kohonen Networks, Association Rules and Segmentation, Model Evaluation Techniques; Ensemble Methods: Bagging and Boosting. Prerequisite(s): CS 1510 or STAT 4772/5772; STAT 1772; junior standing; consent of instructor. (Fall)
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; MATH 2500; MATH 3752/5752. (Same as MATH 6746) (Fall and Spring)
STAT 6747. DiscreteEvent System Simulation — 3 hrs.
Discreteevent systems simulation theory including input analysis, output analysis; applications of simulation software ARENA to studying performances of systems such as bank services, call centers, materialhandling systems, and computer networks. Prerequisite(s): MATH 2422; STAT 1772. (Same as MATH 6747) (Fall and 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, pulltype production systems, polling systems in computer networks, handoff schemes in cellular mobile networks; computational package MATLAB. Prerequisite(s): MATH 2422; MATH 2500; MATH 3752/5752. (Same as MATH 6748) (Fall and Spring)
STAT 6772. 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. (Variable)
STAT 6779. Topics in Probability and Statistics — 3 hrs.
Topics from correlation and regression analysis, analysis of variance and covariance, nonparametric methods, order statistics. May be repeated on different topic with consent of instructor. Prerequisite(s): consent of instructor. (Same as MATH 6779) (Variable)