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Departments & Programs

Department of Mathematical Sciences
Degree Requirements

Major Requirements

IU Online Actuarial Science Option

With this option, students will study the key concepts of insurance, risk management, and interest theory. Solve conceptual and computational problems. Learn to price-risk to determine premiums, analyze data, determine suitable models and parameter values, and provide measures of confidence. Calculate present and accumulated values for various streams of cash flow.

Please contact the academic advisor for program-specific requirements.

IU Online Applied Statistics Option

With this option, students will study differentiation, integration, infinite series, properties of univariate and multivariate random variables, and discrete and continuous distributions. Students also study: 

  • Statistical methods and theory
  • Design of studies and exploratory data analysis
  • Statistical modeling and computation
  • Data analytics communication

Please contact the academic advisor for program-specific 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-I 152 (or a more advanced physics course).

The Area IV major requirements are as follows:

  1. Core curriculum: MATH-I 165, MATH-I 166, MATH-I 171, MATH-I 261, MATH-I 366, and MATH-I 351
  2. MATH-I 300 Logic & Foundations of Algebra
  3. MATH-I 321 Elementary Topology
  4. MATH-I 444 Foundations of Analysis I
  5. MATH-I 453 Beginning Abstract Algebra
  6. Nine (9) credit hours in the required advanced electives listed, and one additional advanced mathematics or statistics elective to be selected from 3-credit MATH courses numbered 300 and above or STAT courses numbered above 351 (STAT-I 416 is recommended). *500 level courses require departmental approval
  7. Minimum of two credit hours of MATH-I 492 Capstone Experience
  • MATH-I 425 Elements of Complex Analysis OR MATH-I 445 Foundations of Analysis II
  • MATH-I 454 Galois Theory OR MATH-I 456 Theory of Numbers
  • MATH-I 462 Elementary Differential Geometry OR MATH-I 571 Elementary Topology

 

Pure Mathematics Option Sample Program (120 credits required)

Freshman Year
First Semester
MATH-I 165 Analytic Geometry and Calculus I 4
MATH-I 171 Multidimensional Mathematics    3
SCI-I 120 Windows on Science 1
ENG-W 131 Reading, Writing and Inquiry 3
World Language 4
Total 15
Second Semester
MATH-I 166 Analytic Geometry and Calculus II 4
CSCI-C 200 Intro to Computers and Programming 4
COMM-R 110 Fundamentals of Speech Communication 3
Life and Physical Science (approved elective) 3
World Language 4
Total 18

Sophomore Year
Third Semester
MATH-I 261 Multivariate Calculus 4
PHYS-I 152 Mechanics 4
2nd Written Communication Course 3
MATH-I 300 Logic & Foundations of Algebra 3
Secondary Area elective 3
Total 17
Fourth Semester
MATH-I 366 Differential Equations 3
MATH-I 351 Elementary Linear Algebra 3
Life and Physical Science (approved elective) 3
Social Sciences (choose from list) 3
Secondary Area elective 3
Total 15

Junior Year
Fifth Semester
MATH-I 444 Foundations of Analysis I 3
Advanced MATH/STAT elective 3
Arts and Humanities elective(choose from list) 3
Secondary Area electives 6
Total 15
Sixth Semester
MATH-I 321 Elementary Topology 3
Advanced MATH/STAT elective 3
Life and Physical Sciences (approved elective) 3
Secondary Area electives 6
Total 15

Senior Year
Seventh Semester
MATH-I 453 Beginning Abstract Algebra 3
Arts & Humanities/Social Science (choose from list) 3
General electives 7
Total 13
Eighth Semester
Advanced MATH/STAT elective 3
Advanced MATH/STAT elective 3
General elective 3
MATH-I 492 Capstone Experience 3
Total 12

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-I 152 and PHYS-I 251 (or more advanced physics courses).

The Area IV major requirements are as follows:

  1. Core curriculum: MATH-I 165, MATH-I 166, MATH-I 171, MATH-I 261, MATH-I 366, MATH-I 300, and MATH-I 351
  2. MATH-I 414 Numerical Methods
  3. Mathematical modeling: MATH-I 426 Introduction to Applied Mathematics and either MATH-I 421 Linear Programming and Optimization Techniques or MATH-I 423 Discrete Modeling
  4. MATH-I 444 Foundations of Analysis I
  5. Nine (9) additional credit hours selected from MATH-I 276 and 3-credit mathematics courses at the 300 level or above and statistics courses numbered 350 or higher. 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.
  6. 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, economics, engineering, or physics are advised to take MATH-I 444 and MATH-I 445. Also, MATH-I 300 is a recommended advanced elective to be taken as a prerequisite for MATH-I 444.
  7. Minimum of two credit hours of MATH-I 492 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.

  • *Differential Equations: MATH-I 520 and MATH-I 522
  • *Biomathematics: Biomathematics course and STAT-I 350 or higher
  • Foundations of Analysis: MATH-I 444 and MATH-I 445
  • Complex Analysis and Differential Equations: MATH-I 425 and MATH-I 520
  • Abstract Algebra: MATH-I 453 and MATH-I 454
  • Algebra and Number Theory: MATH-I 456 and MATH-I 453
  • Linear Algebra: MATH-I 351 and MATH-I 353 or MATH-I 354
  • Differential Geometry: MATH-I 462 and MATH-I 562
  • *Probability and Statistics: Two statistical-type courses at the STAT-I 350 level or higher, with advisor's approval. STAT-I 416 and STAT-I 417, STAT-I 350 and STAT-I 414, or STAT-I 511 and STAT-I 512 recommended.
  • *Theoretical computer science: CSCI-C 241 and CSCI-B 401


Applied Mathematics Option Sample Program  (120 credits required)

Freshman Year
First Semester
MATH-I 165 Analytic Geometry and Calculus I 4
MATH-I 171 Multidimensional Mathematics 3
SCI-I 120 Windows on Science 1
ENG-W 131 Reading, Writing and Inquiry 3
World Language 4
Total 15
Second Semester
MATH-I 166 Analytic Geometry and Calculus II 4
CSCI-C 200 Intro to Computers and Programming 4
COMM-R 110 Fundamentals of Speech Communication 3
Life and Physical Science (approved elective) 3
World Language 4
Total 18

Sophomore Year
Third Semester
MATH-I 261 Multivariate Calculus 4
MATH-I 300 Logic & Foundations/Algebra 3
PHYS-I 152 Mechanics 4
2nd Written Communication Course 3
Secondary area elective 3
Total 17
Fourth Semester
MATH-I 366 Differential Equations (beginning Fall 2024) 3
MATH-I 351 Elementary Linear Algebra 3
PHYS-I 251 Heat, Electricity, and Optics 5
Secondary area elective 3
Total 14

Junior Year
Fifth Semester
MATH-I 444 Foundations of Analysis I 3
MATH/STAT sequence or elective 3
Arts and Humanities (choose from list) 3
Secondary area electives 6
Total 15
Sixth Semester
MATH-I 426 Introduction to Applied Mathematics and Modeling 3
MATH/STAT sequence or elective 3
Life and Physical Sciences (approved elective) 3
Secondary area electives 6

Total

15

Senior Year
Seventh Semester
MATH-I 414 Numerical Methods 3
MATH-I 421 Linear Programming and Opt. Tech. or MATH-I 423 Discrete Modeling 3
Social Sciences (choose from list) 3
General elective 3
Total 12
Eighth Semester
MATH-I 492 Capstone Experience 2
MATH/STAT sequence or electives 6
Arts and Humanities/Social Sciences (choose from list) 3
General elective 3
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.

Courses taken to satisfy Area IIIC requirements must include PHYS-I 152 (or a more advanced physics course).

The Area IV major requirements are as follows:

  1. Core Curriculum: MATH-I 165, MATH-I 166, MATH-I 171, MATH-I 261, MATH-I 266, and MATH-I 351
  2. ECON-E 201 or ECON-S 201, ECON-E 202 or ECON-S 202, ECON-E 305, ECON-E 321, ECON-E 322
  3. BUS-A 200, BUS-F 300, BUS-F 305
  4. MATH-I 373 Mathematical Finance
  5. Mathematical Modeling: MATH-I 426 Introduction to Applied Mathematics and Modeling or MATH-I 421 Linear Programming and Optimization Techniques or MATH-I 423 Discrete Modeling
  6. STAT-I 416 Probability and STAT-I 417 Statistical Theory
  7. Actuarial Models: STAT-I 472 and STAT-I 473
  8. Two credit hour or three credit hour STAT elective at the 300 level or above (not STAT-I 301, STAT-I 350, or STAT-S 351) Suggested course: STAT-I 512 or STAT-I 371 (Prep for Actuarial Exam 1)
  9. Three credit hour MATH or STAT course selected from STAT-I 421, STAT-I 433, STAT-I 512, or STAT-I 522.
  10. Two or three credit hours of MATH-I 492 Capstone Experience

Actuarial Science Option Sample Program (120 credits required)

Freshman Year
First Semester
MATH-I 165 Analytic Geometry and Calculus I 4
MATH-I 171 Multidimensional Mathematics 3
SCI-I 120 Windows on Science 1
ENG-W 131 Reading, Writing and Inquiry 3
World Language 4
Total 15
Second Semester
MATH-I 166 Analytic Geometry and Calculus II 4
Arts and Humanities (choose from list) 3
COMM-R 110 Fundamentals of Speech Communication 3
Life and Physical Science (approved elective) 3
World Language 4
Total 17
 Sophomore Year
Third Semester
MATH-I 261 Multivariate Calculus 4
Life and Physical Science (approved elective) 3
MATH-I 373 Financial Mathematics 3
ECON-S 201 Intro to Microeconomics: Honors 3
BUS-A 200 Foundations of Accounting 3
Total 16
Fourth Semester
MATH-I 351 Elementary Linear Algebra 3
MATH-I 266 Ordinary Differential Equations 3
PHYS-I 152 Mechanics 4
ECON-E 202 Intro to Macroeconomics 3
2nd Written Communication Course 3
Total 16
Junior Year
Fifth Semester
STAT-I 416 Probability 3
ECON-E 305 Money and Banking 3
BUS-F 300 Introduction to Finance 3
CSCI-C 200 Intro to Computers and Programming 4
Social Sciences (choose from list) 3
Total 16
Sixth Semester
STAT-I 371 Prep for Exam P/1 2
STAT-I 417 Statistical Theory 3
STAT-I 472 Actuarial Models 1 3
Arts and Humanities/Social Sciences (choose from list) 3
BUS-F 305 Intermediate Finance 3
Total 14
Senior Year
Seventh Semester
STAT-I 473 Actuarial Models II 3
ECON-E 321 Intermed. Microeconomic Theory 3
MATH-I 421 Linear Prog. and Optim. Tech. or  MATH-I 423 Discrete Modeling 3
STAT-I 512 Regression Analysis or STAT-I 421 Modern Statistical Methods 3
Elective or MATH-I 390 (Topics) 1
Total 13
Eighth Semester
MATH-I 492 Capstone Experience 3
ECON-E 322 Intermediate Macroeconomic Theory 3
Life and Physical Science (approved elective) 3
General elective 4
Total 13

Applied Statistics Option

The Applied Statistics Option for mathematics majors will provide students with the strong background in mathematics and statistics necessary to analyze risks.  The secondary area of concentration may be selected by the student or fulfilled by required courses in business and economics.

The Area IV major requirements are as follows:

  1. Core Curriculum: MATH-I 165, MATH-I 166, MATH-I 171, MATH-I 261, MATH-I 266, MATH-I 351.
  2. Math Major Concentration: STAT-I 416, STAT-I 417, STAT-I 421, STAT-I 512
  3. Twelve (12) additional credit hours of Advanced Electives, consisting of: MATH-I 414; one of MATH-I 421 or MATH-I 423 or MATH-I 426; one of STAT-I 414 or STAT-I 433 or STAT-I 522 or STAT-I 524; and one additional 3-credit advanced MATH or STAT course. Please contact the academic advisor for options.
  4. Secondary area of concentration selected by student.
  5. Two or three credit hours of MATH-I 492 Capstone Experience
Freshman Year
First Semester
MATH-I 165 Analytic Geometry and Calculus I 4
MATH-I 171 Multidimensional Mathematics 3
SCI-I 120 Windows on Science 1
ENG-W 131 Reading, Writing and Inquiry 3
World Language 4
Total 15
Second Semester
MATH-I 166 Analytic Geometry and Calculus II 4
CSCI-C 200 Intro to Computers and Programming 4
COMM-R 110 Fundamentals of Speech Communication 3
Life and Physical Science (approved elective) 3
World Language 4
Total 18
 Sophomore Year
Third Semester
MATH-I 261 Multivariate Calculus 4
Courses for concentration or minor 6
2nd Written Communication Course 3
General elective 3
Total 16
Fourth Semester
MATH-I 351 Elementary Linear Algebra 3
MATH-I 266 Ordinary Differential Equations 3
PHYS-I 152 Mechanics 4
Arts and Humanities (choose from list) 3
Course for concentration or minor 3
Total 16
Junior Year
Fifth Semester
STAT-I 416 Probability 3
MATH-I 414 Numerical Methods 3
Mathematics or Statistics elective 3
Courses for concentration or minor 3
Social Sciences (choose from list) 3
Total 15
Sixth Semester
STAT-I 417 Statistical Theory 3
STAT-I 421 Modern Statistical Modeling/R & SAS 3
Arts and Humanities/Social Sciences (choose from list) 3
Course for concentration or minor 2
Life and Physical Science (approved elective) 3
Total 14
Senior Year
Seventh Semester
STAT-I 512 Applied Regression Analysis 3
MATH-I 421 Linear Prog. & Opt. Techniques or MATH-I 423 Discrete Modeling 3
Course for concentration or minor 3
General electives 4
Total 13
Eighth Semester
MATH-I 492 Capstone Experience 3
STAT-I 414 Intro to Design of Experiments or STAT-I 433 Intro to Nonparametric Statistics 3
Course for concentration or minor 3
Life and Physical Science (approved elective) 3
General elective 1
Total 13

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 general education 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 PHYS-I 152 (or a more advanced physics course).

The Area IV major requirements are as follows:

  1. Core curriculum: MATH-I 165, MATH-I 166, MATH-I 171, MATH-I 261, MATH-I 266, and MATH-I 351
  2. MATH-I 276 Discrete Math
  3. MATH-I 300 Logic and the Foundations of Algebra
  4. MATH-I 453 Abstract Algebra
  5. MATH-I 463 Intermediate Euclidean Geometry for Secondary Teachers
  6. Probability and Statistics: STAT-I 350
  7. MATH-I 583 History of Elementary Mathematics
  8. EDUC-M 457 Methods of Teaching Senior High/Junior High/Middle School Mathematics

Secondary School Teaching Option Sample Program (124 credits required)
Freshman Year
First Semester
MATH-I 165 Analytic Geometry and Calculus I 4
MATH-I 171 Multidimensional Mathematics 3
SCI-I 120 Windows on Science 1
ENG-W 131 Reading, Writing and Inquiry 3
World Language 4
Total 15
Second Semester
MATH-I 166 Analytic Geometry and Calculus II 4
MATH-I 276 Discrete Mathematics 3
COMM-R 110 Fundamentals of Speech Communication 3
2nd Written Communication Course 3
World Language 4
Total 17
Sophomore Year
Third Semester
MATH-I 261 Multivariate Calculus 4
MATH-I 300 Logic and the Foundations of Algebra 3
EDUC-H 341 American Culture and Education 3
PSY-B 110 Introduction to Psychology 3
CSCI-C 200 Intro to Computers and Programming 4
Total 17
Fourth Semester
MATH-I 266 Ordinary Differential Equations 3
MATH-I 351 Elementary Linear Algebra 3
MATH-I 583 History of Mathematics 3
PHYS-I 152 Mechanics 4
Arts and Humanities (choose from list) 3
Total 16
Junior Year
Education Block IIA3
Fifth Semester
Block I-Diversity & Learning, Content Area Literacy, Field Exp. 10
Life and Physical Science (approved electives) 6
Total 16
Sixth Semester
MATH-I 463 Intermediate Euclidean Geometry for Secondary Teachers 3
Education Block IIA 7
Education Block IIB-EDUC-M 457 Methods of Teaching Senior High/Junior High/Middle School Mathematics 3
Arts and Humanities/Social Sciences (choose from list) 3
Total 16
Senior Year
Seventh Semester
MATH-I 453 Abstract Algebra 3
STAT-I 350 Introduction to Statistics 3
Block III-High School Methods, Field Exp. 4
Life and Physical Science (approved elective) 3
Total 13
Eighth Semester
Block IV-Student Teaching in Middle School/Junior High School  Student Teaching in High School 14
Total 14

 

Math-Physics Double Major

This option is for students intending to double major in mathematics and physics.
Courses taken to satisfy the Area IIIC requirements must include PHYS-I 152, PHYS-I 251, CHEM-C 105, and CHEM-C 106.
The Area IV major requirements are as follows:
  1. Core curriculum: MATH-I 165, MATH-I 166, MATH-I 171, MATH-I 261, MATH-I 266, and MATH-I 351
  2. MATH-I 300 Logic and the Foundations of Algebra
  3. MATH-I 414 Numerical Methods
  4. MATH-I 426 Introduction to Applied Mathematics
  5. MATH-I 444 Foundations of Analysis I
  6. Twelve (12) additional credit hours: three credit hours selected from MATH-I3 53/MATH-I 354/MATH-I 453; three credit hours selected from mathematics courses at the 300 level or above and statistics courses numbered 350 or higher; three additional credit hours from mathematics or statistics, or from physics courses numbered three hundred or above; and PHYS-I 442
  7. Students planning on attending graduate school in mathematics or physics are advised to take MATH-I 445 and MATH-I 453.
  8. The double major in mathematics and physics also requires the following additional courses in physics: PHYS-I 299, PHYS-I 310, PHYS-I 330, PHYS-I 342, PHYS-I 353, PHYS-I 400, PHYS-I 401, PHYS-I 418.
  9. Laboratory courses CHEM-C 125 and CHEM-C 126
  10. Minimum of two credit hours of PHYS-I 490 Capstone Experience
Math-Physics Double Major Option Sample Program (123 credits required)
Freshman Year
First Semester
MATH-I 165 Analytic Geometry and Calculus I 4
MATH-I 171 Multidimensional Mathematics 3
SCI-I 120 Windows on Science 1
ENG-W 131 Reading, Writing and Inquiry 3
CHEM-C 105/CHEM-C 125 Principles of Chemistry I Lecture/Lab 5
Total 16
Second Semester
MATH-I 166 Analytic Geometry and Calculus II 4
COMM-R 110 Fundamentals of Speech Communication 3
PHYS-I 152 Mechanics 4
CHEM-C 106/CHEM-C 126 Principles of Chemistry II Lecture/Lab 5
Total 16
Sophomore Year
Third Semester
MATH-I 261 Multivariate Calculus 4
MATH-I 300 Logic and the Foundations of Algebra 3
PHYS-I 251 Heat, Electricity & Optics 5
PHYS-I 299 Intro to Computational Physics 2
2nd Written Communication Course 3
Total 17
Fourth Semester
MATH-I 266 Ordinary Differential Equations 3
MATH-I 351/MATH-I 511 Elementary Linear Algebra 3
PHYS-I 342 Modern Physics 3
CSCI-C 200 Intro to Computers and Programming 4
Social Science (choose from list) 3
Total 16
Junior Year
Fifth Semester
MATH-I 444 Foundations of Analysis I 3
MATH-I 453 or MATH/STAT Elective 3
PHYS-I 310 Intermediate Mechanics 4
Arts and Humanities (Choose from List) 3
World Language 4
Total 17
Sixth Semester
MATH-I 353/MATH-I 354 or MATH/STAT Elective 3
MATH-I 426 Intro to Applied Math/Modeling 3
PHYS-I 330 Intermediate Electricity & Magnetism 3
PHYS-I 353 Electronics Laboratory 2
World Language 4
Total 15
Senior Year
Seventh Semester
MATH-I 414 Numerical Methods 3
PHYS-I 400 Physical Optics 3
PHYS-I 401 Physical Optics Laboratory 2
PHYS-I 442 Quantum Mechanics 3
Arts and Humanities or Social Science 3
Total 14
Eighth Semester
PHYS-I 490 (Capstone) 3
PHYS-I 418 Thermal and Statistical Physics 3
MATH/STAT/PHYS elective 3
General elective 3
Total 12