Departments & Centers
Department of Mathematical Sciences
Degree Requirements
Major Requirements
Pure Mathematics Option
With this option, students will be well prepared for graduate work in pure mathematics. However, students with undergraduate degrees in pure mathematics have also been successful with graduate studies in business administration, computer science, economics, educational research, engineering, law, medicine, operations research, physics, psychology, and statistics. Persons with advanced degrees in pure mathematics find careers primarily in college teaching, but careers in business, industry, or government service are also possible.
Courses taken to satisfy the Area IIIC requirements must include PHYS 15200 (or a more advanced physics course).
The Area IV major requirements are as follows:
- Core curriculum: MATH 16500, MATH 16600, MATH 17100, MATH 26100, MATH 26600, and MATH 35100 (or MATH 51100)
- MATH 45300 Beginning Abstract Algebra
- MATH 46200 Elementary Differential Geometry
- Two of the three: MATH 44400, MATH 42500, MATH 32101
- Twelve (12) additional credit hours selected from MATH 27600 and mathematics and statistics courses at the 300 level or above. Courses in computer science or courses in other departments of the School of Science that have appropriate mathematical content may be selected with the approval of the advisor. Normally, no more than 6 credit hours will be approved outside of mathematics and statistics.
- The 45 credit hours required above must include at least 6 credit hours by completing two of the course sequences listed below.
- Minimum two (2) credit hours of MATH 49200 Capstone Experience
Course Sequences
Two course sequences (each course 3 credit hours) are required. There must be at least one * sequence. No overlaps are allowed.
- *Foundations of Analysis: MATH 44400 and MATH 44500
- *Complex Analysis and Differential Equations: MATH 42500 and MATH 52000
- *Abstract Algebra: MATH 45300 and MATH 45400
- *Algebra and Number Theory: MATH 45600 and MATH 45300
- *Linear Algebra: MATH 35100 and MATH 35300
- *Differential Geometry: MATH 46200 and MATH 56200
- *Topology: MATH 32101 and MATH 57100
- Probability and Statistics: Two statistical-type courses at the STAT 35000 level or higher, with advisor's approval
- Modeling: MATH 41700 and MATH 42600
- Numerical Analysis: MATH 41400 and CSCI 51500
- Scientific computing: CSCI 47500 and 47600^{1}
- Theoretical computer science: CSCI 34000 and 47000^{1}
^{1} Students are generally allowed to select only one of these two course sequences.
Pure Mathematics Option Sample Program (124 credits required)
Freshman Year
First Semester | |
MATH 16500 Analytic Geometry and Calculus I | 4 |
MATH 17100 Multidimensional Mathematics | 3 |
SCI-I120 Windows on Science | 1 |
ENG-W131 Elementary Composition I | 3 |
Physical or biological science | 4 |
Total | 15 |
Second Semester | |
MATH 16600 Analytic Geometry and Calculus II | 4 |
CSCI 23000 Computing I | 4 |
COMM-R110 Fundamentals of Speech Communication | 3 |
Physical or biological science | 3 |
Free elective |
3 |
Total | 17 |
Sophomore Year
Third Semester | |
MATH 26100 Multivariate Calculus | 4 |
HIST-H114 History of Western Civilization II | 3 |
Second composition course | 3 |
PHYS 15200 Mechanics | 4 |
Free elective |
3 |
Total | 17 |
Fourth Semester | |
MATH 26600 Ordinary Differential Equations | 3 |
MATH 35100 Elementary Linear Algebra |
3 |
Physical or biological science | 3 |
Humanities-List H | 3 |
Free elective | 3 |
Total | 15 |
Junior Year
Fifth Semester | |
MATH 44400 Foundations of Analysis I |
3 |
MATH or STAT Elective | 3 |
Foreign language | 5 |
Social Sciences-List S | 3 |
Free elective | 3 |
Total | 17 |
Sixth Semester | |
MATH 44500 Foundations of Analysis II |
3 |
MATH 51000 Vector Calculus | 3 |
Comparative World Cultures-List C | 3 |
Free electives | 6 |
Total | 15 |
Senior Year
Seventh Semester | |
MATH 45300 Beginning Abstract Algebra | 3 |
MATH or STAT elective | 3 |
Free electives |
8 |
Total | 14 |
Eighth Semester | |
MATH or STAT electives | 6 |
MATH 49200 Capstone Experience | 2 |
Free electives | 6 |
CAND 99100 Candidate for Graduation | 0 |
Total | 14 |
Applied Mathematics Option
Graduates with training in applied mathematics are employed in business, industry, and government. They would probably work as part of a team and would often need to communicate mathematical ideas to persons trained in other subjects. In many instances, they would need to formulate problems for solution on a computer and interpret the answers. Thus, besides a fundamental knowledge of mathematics, a knowledge of what computers can do is essential. This option is also good preparation for graduate study in applied mathematics, computer science, statistics, and engineering.
Courses taken to satisfy the Area IIIC requirements must include PHYS 15200 and PHYS 25100 (or more advanced physics courses).
The Area IV major requirements are as follows:
- Core curriculum: MATH 16500, MATH 16600, MATH 17100, MATH 26100, MATH 26600, and MATH 35100 (or MATH 51100)
- MATH 41400 Numerical Methods or CSCI 47500 and CSCI 47600 Scientific Computing (6 cr.)
- MATH 51000 Vector Calculus or MATH 46200 Elementary Differential Geometry
- Mathematical modeling: MATH 42600 Introduction to Applied Mathematics or MATH 41700 Modeling and Game Theory
- MATH 44400 Foundations of Analysis I
- Twelve (12) additional credit hours selected from MATH 27600 and mathematics and statistics courses at the 300 level or above. Courses in computer science or courses in other departments of the School of Science that have appropriate mathematical content may be selected with the approval of the advisor. Normally, no more than 6 credit hours outside of mathematics and statistics will be approved.
- The 45 credit hours of courses required above must include at least 6 credit hours in each of two of the course sequences listed below. Students planning on attending graduate school in mathematics are advised to take MATH 44500.
- Minimum two (2) credit hours of MATH 49200 Capstone Experience
Course Sequences
Two course sequences (each course 3 credit hours) are required. No overlaps are allowed.
- Differential Equations: MATH 52000 and MATH 52200
- Foundations of Analysis: MATH 44400 and MATH 44500
- Complex Analysis and Differential Equations: MATH 42500 and MATH 52000
- Abstract Algebra: MATH 45300 and MATH 45400
- Algebra and Number Theory: MATH 45600 and MATH 45300
- Linear Algebra: MATH 35100 and MATH 35300
- Differential Geometry: MATH 46200 and MATH 56200
- Probability and Statistics: Two statistical-type courses at the STAT 35000 level or higher, with advisor's approval
- Modeling: MATH 41700 and MATH 42600
- Numerical Analysis: MATH 41400 and CSCI 51500
- Scientific computing: CSCI 47500 and 47600^{2}
- Theoretical computer science: CSCI 34000 and 47000^{2}
^{2}Students are generally allowed to select only one of these two course sequences.
Applied Mathematics Option Sample Program (124 credits required)
Freshman Year
First Semester | |
MATH 16500 Analytic Geometry and Calculus I |
4 |
MATH 17100 Multidimensional Mathematics |
3 |
SCI-I120 Windows on Science | 1 |
ENG-W131 Elementary Composition I | 3 |
Free elective | 3 |
Total | 14 |
Second Semester | |
MATH 16600 Analytic Geometry and Calculus II | 4 |
CSCI 23000 Computing I | 4 |
COMM-R110 Fundamentals of Speech Communication | 3 |
Second composition course |
3 |
HIST-H114 History of Western Civilization II |
3 |
Total | 17 |
Sophomore Year
Third Semester | |
MATH 26100 Multivariate Calculus | 4 |
PHYS 15200 Mechanics | 4 |
Humanities-List H | 3 |
Free electives | 6 |
Total |
17 |
Fourth Semester | |
MATH 26600 Ordinary Differential Equations | 3 |
MATH 35100 Elementary Linear Algebra | 3 |
PHYS 25100 Heat, Electricity, and Optics | 5 |
Free electives | 6 |
Total |
17 |
Junior Year
Fifth Semester | |
MATH 41400 Numerical Methods | 3 |
PHYS 31000 Intermediate Mechanics | 4 |
MATH or STAT Elective | 3 |
Social Sciences-List S | 3 |
Foreign language | 3 |
Total | 16 |
Sixth Semester | |
MATH 42600 Introduction to Applied Mathematics and Modeling or MATH 41700 Advanced Discrete Mathematics | 3 |
MATH 51000 Vector Calculus | 3 |
PHYS 34200 Modern Physics | 3 |
Comparative World Cultures-List C | 3 |
Foreign language | 3 |
Total | 15 |
Senior Year
Seventh Semester | |
MATH 44400 Foundations of Analysis I | 3 |
MATH or STAT Elective | 3 |
Free Electives | 8 |
Total | 14 |
Eighth Semester | |
MATH 49200 Capstone Experience | 2 |
MATH or STAT Electives | 6 |
Free electives | 6 |
CAND 99100 Candidate for Graduation | 0 |
Total | 14 |
Actuarial Science Option
The Actuarial Science Option for mathematics majors will provide students with the strong background in mathematics, statistics, and economics necessary to analyze financial risks. This concentration aims to prepare students for the first three actuarial examinations administered by the professional actuarial organizations. The secondary area of concentration for students in this option is fulfilled by required courses in business and economics.
Actuarial science deals with the analysis of financial consequences of risk. Actuaries are highly trained professionals, well versed in mathematical, statistical, and economic techniques that enable them to evaluate financial risk of uncertain future events, especially those pertaining to health care, insurance, and pension plans. Actuaries answer risk-related questions by developing, implementing, and interpreting sophisticated mathematical models.
The Area IV major requirements are as follows:
- Core Curriculum: MATH 16500, MATH 16600, MATH 17100, MATH 26100, MATH 26600, and MATH 35100 (or MATH 51100)
- ECON-S201, ECON-E202 or ECON-S202, ECON-E305, ECON-E321, ECON-E322
- BUS-A200, BUS-F300, BUS-F305
- MATH 37300 Mathematical Finance
- Mathematical Modeling: MATH 42600 Introduction to Applied Mathematics or MATH 41700 Modeling and Game Theory
- STAT 41600 Probability and STAT 41700 Statistical Theory
- Actuarial Models: STAT 47200 / STAT 47300
- Two (2)-credit hour or 3-credit hour STAT elective at the 300 level or above (not STAT 30100, 30200, or 31100) Suggested course: STAT 37100 (Prep for Actuarial Exam 1)
- Three (3) credit hour MATH or STAT course selected from MATH 27600 and mathematics and statistics courses at the 300 level or above (not STAT 30100, 30200, or 31100). Suggested course: STAT 35000 Introduction to Statistics
- Two (2) or three (3) credit hours of MATH 49200 Capstone Experience
Actuarial Science Option Sample Program (124 credits required)
Freshman Year
First Semester | |
MATH 16500 Analytic Geometry and Calculus I | 4 |
MATH 17100 Multidimensional Mathematics | 3 |
SCI-I120 Windows on Science | 1 |
ENG-W131 Elementary Composition I | 3 |
Physical or Biological Science Elective with Lab | 5 |
Total | 16 |
Second Semester | |
MATH 16600 Analytic Geometry and Calculus II | 4 |
CSCI 23000 Computing I | 4 |
COMM-R110 Fundamentals of Speech Communication |
3 |
Second composition course | 3 |
HIST-H114 History of Western Civilization II | 3 |
Total | 17 |
Sophomore Year
Third Semester | |
MATH 26100 Multivariate Calculus | 4 |
STAT 35000 Introduction to Statistics | 3 |
ECON-S201 Introduction to Microeconomics: Honors | 3 |
BUS-A200 Foundations of Accounting | 3 |
Physical or Biological Science Elective | 3 |
Total |
16 |
Fourth Semester | |
MATH 26600 Ordinary Differential Equations | 3 |
MATH 35100 Elementary Linear Algebra | 3 |
ECON-E202 or ECON-S202 Introduction to Macroeconomics | 3 |
Humanities-List H | 3 |
Free elective | 3 |
Total | 15 |
Junior Year
Fifth Semester | |
STAT 41600 Probability | 3 |
BUS-F300 Introduction to Financial Management | 3 |
ECON-E322 Intermediate Macroeconomic Theory | 3 |
Comparative World Cultures-List C | 3 |
Physical or biological science elective | 3 |
Total | 15 |
Sixth Semester | |
STAT 41700 Statistical Theory | 3 |
MATH 37300 Mathematical Finance | 3 |
STAT 37100 Prep for Actuarial Exam 1 | 2 |
BUS-F305 Intermediate Corporate Finance | 3 |
Foreign language | 5 |
Total | 16 |
Senior Year
Seventh Semester | |
STAT 47200 Actuarial Models I | 3 |
ECON-E305 Money and Banking | 3 |
Physical or biological science elective | 3 |
Free electives | 6 |
Total | 15 |
Eighth Semester | |
STAT 47300 Actuarial Models II |
3 |
MATH 42600 Introduction to Applied Mathematics and Modeling or MATH 41700 Modeling and Game Theory | 3 |
ECON-E321 Intermediate Microeconomic Theory | 3 |
MATH 49200 Capstone Experience | 2 |
Free elective | 3 |
CAND 99100 Candidate for Graduation | 0 |
Total | 14 |
Secondary School Teaching Option
Students who wish to teach in secondary schools must meet the requirements for teacher certification in the state in which they expect to teach. Interested persons can obtain these requirements by writing to the Department of Public Instruction, Certification Office, in the capital city of any state.
To satisfy Indiana law, a student should have 40 credit hours in generaleducation courses and a specified core of professional education courses as part of the requirement for a teaching license. Students should be sure to see an advisor to ensure that these hours are properly distributed and that the professional education requirements are met.
Courses taken to satisfy the Area IIIC requirements must include either PHYS 21800 or PHYS 15200 (or a more advanced physics course).
The Area IV major requirements are as follows:
- Core curriculum: MATH 16500, MATH 16600, MATH 17100, MATH 26100, MATH 26600, and MATH 35100 (or MATH 51100)
- MATH 27600 Discrete Math
- MATH 30000 Logic and the Foundations of Algebra
- MATH 45300 Abstract Algebra
- MATH 46300 Intermediate Euclidean Geometry for Secondary Teachers
- Probability and statistics: STAT 31100 or 35000 or 41600 or 51100
- MATH 58300 History of Elementary Mathematics
Secondary School Teaching Option Sample Program (124 credits required)
Freshman Year
First Semester | |
MATH 16500 Analytic Geometry and Calculus I | 4 |
MATH 17100 Multidimensional Mathematics | 3 |
SCI-I120 Windows on Science |
1 |
ENG-W131 Elementary Composition I | 3 |
PSY-B104 Psychology as a Social Science | 3 |
Total | 14 |
Second Semester | |
MATH 16600 Analytic Geometry and Calculus II | 4 |
MATH 27600 Discrete Mathematics | 3 |
COMM-R110 Fundamentals of Speech Communication | 3 |
Second composition course | 3 |
HIST-H114 History of Western Civilization II | 3 |
Total | 16 |
Sophomore Year
Third Semester | |
MATH 26100 Multivariate Calculus | 4 |
MATH 30000 Logic and the Foundations of Algebra | 3 |
EDUC-H341 American Culture and Education | 3 |
Foreign language | 5 |
Humanities-List H | 3 |
Total | 18 |
Fourth Semester | |
MATH 26600 Ordinary Differential Equations | 3 |
MATH 58300 History of Elementary Mathematics |
3 |
CSCI 23000 Computing I | 4 |
Comparative World Cultures-List C | 3 |
PHYS 21800 General Physics I | 4 |
Total | 17 |
Junior Year
Fifth Semester | |
MATH 35100 Elementary Linear Algebra | 3 |
EDUC-M322 Diversity/Learning: Reaching Every Adolescent | 6 |
+ Field Experience | 1 |
Physical or Biological Science with Lab | 4 |
Total | 14 |
Sixth Semester | |
MATH 46300 Intermediate Euclidean Geometry for Secondary Teachers | 3 |
Physical or biological science | 3 |
EDUC-M457 Methods of Teaching Senior High/Junior High/Middle School Mathematics | 4 |
EDUC-S420 Teaching/Learning in Middle School | 3 |
EDUC-M469 Content Area Literacy | 3 |
+ field experience | 1 |
Total | 17 |
Senior Year
Seventh Semester | |
MATH 45300 Abstract Algebra | 3 |
STAT 35000 Introduction to Statistics | 3 |
EDUC-S430 Teaching/Learning in the High School | 3 |
+ field experience |
1 |
Physical or biological science | 3 |
Total | 13 |
Eighth Semester | |
EDUC-M451 Student Teaching: Jr High/Middle School |
8 |
EDUC-M480 Student Teaching in the Secondary School | 8 |
CAND 99100 Candidate for Graduation | 0 |
Total | 16 |
Minor in the Mathematical Sciences
An undergraduate minor in mathematics is useful in many fields. A scientist or engineer may need knowledge of differential equations and linear algebra, while someone in business or a social science may need a background in probability or statistics.
Requirements
- The calculus sequence MATH 16500, MATH 16600, MATH 17100, and MATH 26100 (15 cr.)
- Two additional courses selected from mathematics courses numbered MATH 26600 or higher or from statistics courses numbered STAT 31100 or higher
- Nine (9) credit hours of the minor must be completed at IUPUI.
- The grade in each course submitted for the minor must be C (2.0) or higher.
Correspondence courses may not be used to fulfill requirements for the minor.