Bachelor of Science in Mathematics Program II (Bachelor of Science in Mathematics)

Students on Summer 2022, Fall 2022, or Spring 2023 requirements MATHBS2

View Degree MapA semester-by-semester path to completing degree and major requirements

Requirements

The major requires at least 33 credit hours, including the requirements listed below.

Linear Algebra. One (1) course:
- MATH-M 301 Linear Algebra and Applications
- MATH-M 303 Linear Algebra for Undergraduates
- MATH-S 303 Honors Course in Linear Algebra
MATH-M 301 Linear Algebra and Applications
Credits
3
Prerequisites
MATH-M 212, MATH-M 213, or MATH-S 212; or MATH-M 211 and CSCI-C 241; or MATH-S 211 and CSCI-C 241
Description
Solving systems of linear equations, matrix algebra, determinants, vector spaces, eigenvalues and eigenvectors. Selection of advanced topics. Applications throughout. Computer used for theory and applications.
Repeatability
Credit given for only one of MATH-M 301 or MATH-M 303.
- Summer 2025CASE NMcourse
  
  Spring 2025CASE NMcourse
  
  Fall 2024CASE NMcourse
MATH-M 303 Linear Algebra for Undergraduates
Credits
3
Prerequisites
MATH-M 212, MATH-M 213, or MATH-S 212; or MATH-M 211 and CSCI-C 241; or MATH-S 211 and CSCI-C 241
Description
Introduction to the theory of real vector spaces. Coordinate s, linear dependence, bases. Linear transformations and matrix calculus. Determinants and rank. Eigenvalues and eigenvectors.
Repeatability
Credit given for only one of MATH-M 301, MATH-M 303, or MATH-S 303.
- Summer 2025CASE NMcourse
  
  Spring 2025CASE NMcourse
  
  Fall 2024CASE NMcourse
MATH-S 303 Honors Course in Linear Algebra
Credits
3
Prerequisites
Consent of department
Description
Honors version of MATH-M 303. For students with unusual aptitude and motivation.
Repeatability
Not open to those who have had MATH-M 301 or MATH-M 303.
- Summer 2025CASE NMcourse
  
  Spring 2025CASE NMcourse
  
  Fall 2024CASE NMcourse
Calculus III. One (1) course:
- MATH-M 311 Calculus III
- MATH-S 311 Honors Course in Calculus III
MATH-M 311 Calculus III
Credits
4
Prerequisites
MATH-M 212, MATH-M 213, or MATH-S 212
Description
Elementary geometry of 2, 3, and n-space; functions of several variables; partial differentiation; minimum and maximum problems; multiple integration.
- Summer 2025CASE NMcourse
  
  Spring 2025CASE NMcourse
  
  Fall 2024CASE NMcourse
MATH-S 311 Honors Course in Calculus III
Credits
4
Prerequisites
MATH-S 212 or consent of instructor; and MATH M-301, MATH M-303, or MATH S-303
Description
Honors version of MATH-M 311, covering geometry of 2, 3, and n-space; functions of several variables; partial differentiation; minimum and maximum problems; and multiple integration. For students with unusual aptitude and motivation.
Repeatability
Credit given for only one of MATH-M 311 or MATH-S 311.
- Summer 2025CASE NMcourse
  
  Spring 2025CASE NMcourse
  
  Fall 2024CASE NMcourse
Calculus IV. One (1) course:
- MATH-M 312 Calculus IV
- MATH-S 312 Honors Course in Calculus IV
MATH-M 312 Calculus IV

Credits
3
Prerequisites
MATH-M 311 or MATH-S 311
Description
Differential calculus of vector-valued functions, transformation of coordinates, change of variables in multiple integrals. Vector integral calculus: line integrals, Green\'s theorem, surface integrals, Stokes\' theorem. Applications.
Repeatability
Credit given for only one of MATH-M 312 or MATH-S 312.

MATH-S 312 Honors Course in Calculus IV

Credits
3
Prerequisites
MATH-S 311 or consent of instructor
Description
For students with unusual aptitude and motivation.
Repeatability
Credit given for only one of MATH-M 312 or MATH-S 312.
Introduction to Differential Equations with Applications I. One (1) course:
- MATH-M 343
- MATH-S 343 Honors Course in Differential Equations
MATH-S 343 Honors Course in Differential Equations
Credits
3
Prerequisites
MATH-S 212 or consent of instructor
Description
Introduction, with historical examples, first order ordinary differential equations (ODEs) and applications, second order linear ODEs, linear ODEs of higher order, series solutions to linear ODEs, and numerical methods for ODEs. In addition, some theoretical aspects will be studied in detail such as the Picard existence/uniqueness theorem for initial-value problems, convergence of series solutions, and the matrix exponential exp(tA).
- Summer 2025CASE NMcourse
  
  Spring 2025CASE NMcourse
  
  Fall 2024CASE NMcourse
Introduction to Differential Equations with Applications II. One (1) course:
- MATH-M 344
- MATH-S 344 Honors Course in Differential Equations II
MATH-S 344 Honors Course in Differential Equations II
Credits
3
Prerequisites
MATH-M 212 or MATH-S 212; and MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-S 343
Description
Covers the topics of MATH-M 344, in addition to more theoretical material, which may include topics such as the uniqueness theorem for the inversion of the Laplace transform, introduction to the theory of distributions, derivation of the heat and wave equations, eigenvalues of Sturm-Liouville boundary problems, and oscillation theory applied to special functions. Meets with MATH-M 344, and the additional material will be incorporated in weekly homework sets. Exams will include some of this additional material.
Repeatability
Credit given for only one of MATH-M 344 or MATH-S 344.
- Summer 2025CASE NMcourse
  
  Spring 2025CASE NMcourse
  
  Fall 2024CASE NMcourse
Analysis I. One (1) course:
- MATH-M 413 Introduction to Analysis I
- MATH-S 413 Honors Course in Analysis I
MATH-M 413 Introduction to Analysis I

Credits
3
Prerequisites
MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311
Description
Modern theory of real number , limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics.

MATH-S 413 Honors Course in Analysis I

Credits
3
Prerequisites
MATH-S 312; or consent of instructor
Description
Differentiable transformations defined on Euclidean space, inverse and implicit function theorems. Lebesgue integration over Euclidean space and transformation of integrals. Exterior algebra, measure and integration on manifolds. Stokes\' theorem. Closed and exact forms.
Analysis II. One (1) course:
- MATH-M 414 Introduction to Analysis II
- MATH-M 415 Elementary Complex Variables with Applications
- MATH-S 414 Honors Course in Analysis II
- MATH-S 415 Honors Elementary Complex Variables
MATH-M 414 Introduction to Analysis II

Credits
3
Prerequisites
MATH-M 413 or MATH-S 413
Description
Continuation of MATH-M 413. Functions of several variables, Taylor series, extreme values. Manifolds in Euclidean space, Implicit Function Theorem, Inverse Function Theorem. Divergence Theorem and other classical theorems of vector calculus. Special topics.
Repeatability
Credit given for only one of MATH-M 414 or MATH-S 414.

MATH-M 415 Elementary Complex Variables with Applications

Credits
3
Prerequisites
MATH-M 311, MATH-S 311, or consent of instructor
Description
Algebra and geometry of complex numbers, elementary functions of a complex variable, power series, integrations, calculus of residues, conformal mapping. Application to physics.
Repeatability
Credit given for only one of MATH-M 415 or MATH-S 415.

MATH-S 414 Honors Course in Analysis II

Credits
3
Prerequisites
MATH-S 413; or consent of instructor
Description
Differentiable transformations defined on Euclidean space, inverse and implicit function theorems. Lebesgue integration over Euclidean space and transformation of integrals. Exterior algebra, measure and integration on manifolds. Stokes\' theorem. Closed and exact forms.
Repeatability
Credit given for only one of MATH-S 414 or MATH-M 414.

MATH-S 415 Honors Elementary Complex Variables

Credits
3
Prerequisites
MATH-S 311; or consent of instructor
Description
For students with unusual aptitude and motivation. Algebra and geometry of complex numbers, elementary functions of a complex variable, power series, contour integrals, calculus of residues, conformal mapping.
Repeatability
Credit given for only one of MATH-M 415 or MATH-S 415.
Applied Mathematics Courses. At least two (2) courses:
- MATH-M 441 Introduction to Partial Differential Equations with Applications I
- MATH-M 442 Introduction to Partial Differential Equations with Applications II
- MATH-M 451 The Mathematics of Finance
- MATH-M 463 Introduction to Probability Theory I
- MATH-M 464 Introduction to Probability Theory II
- MATH-M 471 Numerical Analysis I
- MATH-M 472 Numerical Analysis II
MATH-M 441 Introduction to Partial Differential Equations with Applications I

Credits
3
Prerequisites
MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311; and MATH-M 343 or MATH-S 343
Notes
R: MATH-M 312 or MATH-S 312
Description
Derivation and methods of solution of classical partial differential equations of mathematical physics: heat, wave, and Laplace equations. Separation of variables, Fourier series, Sturm-Liouville theory, special functions, Green\'s functions, Fourier transform, first order equations, characteristics and special topics.

MATH-M 442 Introduction to Partial Differential Equations with Applications II

Credits
3
Prerequisites
MATH-M 441
Description
Derivation and methods of solution of classical partial differential equations of mathematical physics: heat, wave, and Laplace equations. Separation of variables, Fourier series, Sturm-Liouville theory, special functions, Green\'s functions, Fourier transform, first order equations, characteristics and special topics.

MATH-M 451 The Mathematics of Finance

Credits
3
Prerequisites
MATH-M 311 or MATH-S 311; and MATH-M 365 or MATH-M 463 or MATH-S 463
Description
Course covers probability theory, Brownian motion, Ito\'s Lemma, stochastic differential equations, and dynamic hedging. These topics are applied to the Black-Scholes formula, the pricing of financial derivatives, and the term theory of interest rates.

MATH-M 463 Introduction to Probability Theory I

Credits
3
Prerequisites
MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311
Description
The meaning of probability. Random experiments, conditional probability, independence. Random variables, expected values and standard deviations, moment generating functions. Important discrete and continuous distributions. Poisson processes. Multivariate distributions, basic limit laws such as the central limit theorem.
Repeatability
Credit given for only one of MATH-M 463 or MATH-S 463.

MATH-M 464 Introduction to Probability Theory II

Credits
3
Prerequisites
MATH-M 463 or MATH-S 463
Description
Conditional distributions and expectation, linear and nonlinear regression; simple stochastic processes: Poisson process, process with independent increments, random walk, Markov chain with finite state space; information theory.

MATH-M 471 Numerical Analysis I

Credits
3
Prerequisites
MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311; and MATH-M 343 or MATH-S 343
Notes
Knowledge of a computer language such as FORTRAN, C, C++, etc., is essential for success in this course. Students with other programming backgrounds should consult the instructor
Description
Interpolation and approximation of functions, numerical integration and differentiation, solution of nonlinear equations, acceleration and extrapolation, solution of systems of linear equations, eigenvalue problems, initial and boundary value problems for ordinary differential equations, and computer programs applying these numerical methods.

MATH-M 472 Numerical Analysis II

Credits
3
Prerequisites
MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311; and MATH-M 343 or MATH-S 343
Notes
Knowledge of a computer language such as FORTRAN, C, C++, etc., is essential for success in this course. Students with other programming backgrounds should consult the instructor.
Description
Interpolation and approximation of functions, numerical integration and differentiation, solution of nonlinear equations, acceleration and extrapolation, solution of s of linear equations, eigenvalue problems, initial and boundary value problems for ordinary differential equations, and computer programs applying these numerical methods.
Addenda requirements*.
1. Computer Science**. One (1) course:
  - CSCI-A 201 Introduction to Programming I
  - CSCI-H 200 Introduction to Computers and Programming, Honors
  - CSCI-C 200 Introduction to Computers and Programming
  - CSCI-C 211 Introduction to Computer Science
  - CSCI-H 211 Introduction to Computer Science-Honors
  CSCI-A 201 Introduction to Programming I
  
  Description
  Fundamental programming constructs, including loops, arrays, classes and files. General problem-solving techniques. Emphasis on modular programming, user-interface design, and developing good programming style. Not intended for computer science majors.
  Additional information
  Credit hour, prerequisite, and other information cannot be displayed for this course. If this is a course outside of the College of Arts and Sciences, please see the appropriate school's bulletin for additional information.
  
  CSCI-H 200 Introduction to Computers and Programming, Honors
  
  Description
  Honors version of CSCI-C 200. This course is an introduction, broadly, to algorithmic thinking and, specifically, to programming. It teaches the basics of programming using real world applications in natural, physical and social sciences. Students will develop ability to program by identifying problems in real world and then creating a program that solves the problem.
  Additional information
  Credit hour, prerequisite, and other information cannot be displayed for this course. If this is a course outside of the College of Arts and Sciences, please see the appropriate school's bulletin for additional information.
  
  CSCI-C 200 Introduction to Computers and Programming
  
  Description
  This course is an introduction, broadly, to algorithmic thinking and, specifically, to programming. It teaches the basics of programming using real world applications in natural, physical and social sciences. Students will develop ability to program by identifying problems in real world and then creating a program that solves the problem.
  Additional information
  Credit hour, prerequisite, and other information cannot be displayed for this course. If this is a course outside of the College of Arts and Sciences, please see the appropriate school's bulletin for additional information.
  
  CSCI-C 211 Introduction to Computer Science
  
  Description
  A first course in computer science for those intending to take advanced computer science courses. Introduction to programming and to algorithm design and analysis. Using the Scheme programming language, the course covers several programming paradigms. Lecture and laboratory.
  Additional information
  Credit hour, prerequisite, and other information cannot be displayed for this course. If this is a course outside of the College of Arts and Sciences, please see the appropriate school's bulletin for additional information.
  
  CSCI-H 211 Introduction to Computer Science-Honors
  
  Description
  Honors version of CSCI-C 211.
  Additional information
  Credit hour, prerequisite, and other information cannot be displayed for this course. If this is a course outside of the College of Arts and Sciences, please see the appropriate school's bulletin for additional information.
2. Outside Focal Area. Nine (9) credit hours, approved by the Mathematics department, in one (1) of the following disciplines:
  - Astronomy
  - Biology
  - Chemistry
  - Cognitive Science
  - Computer Science
  - Economics
  - Geology
  - Physics
  - Statistics
  - Other departments with approval
Major GPA, Hours, and Minimum Grade Requirements.
1. Major GPA. A GPA of at least 2.000 for all courses taken in the major—including those where a grade lower than C- is earned—is required.
2. Major Minimum Grade. Except for the GPA requirement, a grade of C- or higher is required for a course to count toward a requirement in the major.
3. Major Upper Division Credit Hours. At least 18 credit hours in the major must be completed at the 300–499 level.
4. Major Residency. At least 18 credit hours in the major must be completed in courses taken through the Indiana University Bloomington campus or an IU-administered or IU co-sponsored Overseas Study program.

Notes

* Courses used to fulfill addenda requirements require a grade of C- or higher and do not count toward the Major GPA or Major Hours.
^** This requirement may be waived for students who can demonstrate proficiency in computer programming.

Major Area Courses

Unless otherwise noted below, the following courses are considered in the academic program and will count toward academic program requirements as appropriate:
- Any course at the 200–499 level with the MATH subject area prefix—as well as any other subject areas that are deemed functionally equivalent
- Any course contained on the course lists for the academic program requirements at the time the course is taken—as well as any other courses that are deemed functionally equivalent—except for those listed only under Addenda Requirements
- Any course directed to a non-Addenda requirement through an approved exception

Exclusions

The following courses cannot be applied toward major requirements:

Any MATH-E 100–499
Any MATH-K 100–499
MATH-M 330 Exploring Mathematical Ideas
MATH-M 333
MATH-M 347 Discrete Mathematics

Restrictions

The following restrictions apply to the minimum credit hours required in the major:

May be repeated for a maximum of 6 credit hours:
- MATH-X 170 Service Learning in Mathematics: Community Outreach
May be repeated once with approval of Department of Mathematics for a maximum of 6 credit hours:
- MATH-X 373 Internship in Professional Practice
May be repeated for a maximum of 12 credit hours:
- MATH-X 390 Readings and Research

This program of study cannot be combined with the following:

Bachelor of Arts in Economics and Mathematics (ECONMATHBA)
Bachelor of Arts in Mathematics (MATHBA)
Bachelor of Arts in Mathematics and Economics (MATHECONBA)
Bachelor of Science in Mathematics (MATHBS)
Bachelor of Science in Mathematics Program I (MATHBS1)
Minor in Mathematics (MATHMIN)

Exceptions to and substitutions for major requirements may be made with the approval of the unit's Director of Undergraduate Studies, subject to final approval by the College of Arts and Sciences.

The Bachelor of Science degree requires at least 120 credit hours, to include the following:

College of Arts and Sciences Credit Hours. At least 100 credit hours must come from College of Arts and Sciences disciplines.
Upper Division Courses. At least 36 credit hours (of the 120) must be at the 300–499 level.
College Residency. Following completion of the 60th credit hour toward degree, at least 36 credit hours of College of Arts and Sciences coursework must be completed through the Indiana University Bloomington campus or an IU-administered or IU co-sponsored Overseas Study program.
College GPA. A College grade point average (GPA) of at least 2.000 is required.
CASE Requirements. The following College of Arts and Sciences Education (CASE) requirements must be completed:
1. CASE Foundations
  1. English Composition: 1 course
  2. Mathematical Modeling: 1 course
2. CASE Breadth of Inquiry
  1. Arts and Humanities: 2 courses
  2. Natural and Mathematical Sciences: 4 courses
  3. Social and Historical Studies: 2 courses
3. CASE Culture Studies
  1. Diversity in the United States: 1 course
  2. Global Civilizations and Cultures: Not required
4. CASE Critical Approaches: 1 course
5. CASE Foreign Language: Proficiency in a single foreign language through the first semester of the second year of college-level coursework
6. CASE Intensive Writing: 1 course
7. CASE Public Oral Communication: 1 course
Major. Completion of the major as outlined in the Major Requirements section above.

Most students must also successfully complete the Indiana University Bloomington General Education program.

Bachelor of Science in Mathematics Program II (Bachelor of Science in Mathematics)

Requirements

Major hours and GPA

Major Area Courses

Exclusions

Restrictions

Restrictions on combining this major with other academic programs

Major requirement exceptions and substitutions