Department of Mathematics
Bachelor of Science in Mathematics Program II (Bachelor of Science in Mathematics)
Students on Summer 2018, Fall 2018, or Spring 2019 requirements MATHBS2
Bachelor of Science in Mathematics students study in depth the complex relationships between ideas in mathematics. This degree provides rigorous in-depth training in related areas such as astronomy, biology, chemistry, cognitive science, computer science, economics, finance, geology, or physics.
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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 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).
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 2024CASE NMcourse
- Introduction to Differential Equations with Applications II. One (1) course:
- MATH-M 344 Introduction to Differential Equations with Applications II
- MATH-S 344 Honors Course in Differential Equations II
MATH-M 344 Introduction to Differential Equations with Applications II
- Credits
- 3
- Prerequisites
- One of MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 343 or MATH-S 343
- Description
- Ordinary differential equations and methods for their solution, including series methods and the Laplace transform. Applications of differential equations. Systems, stability, and numerical methods. Partial differential equations of mathematical physics, Fourier series.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 2024CASE NMcourse
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.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourseSpring 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 Sequence. At least one of the following sequences:
- 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 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.
- Two (2) courses:
- MATH-M 463 Introduction to Probability Theory I
- MATH-M 464 Introduction to Probability Theory II
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.
- Two (2) courses:
- MATH-M 471 Numerical Analysis I
- MATH-M 472 Numerical Analysis II
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.
- Two (2) courses:
- Addenda requirements*.
- Computer Science. One (1) course:
- CSCI-A 201 INTRODUCTION TO PROGRAMMING I
- CSCI-C 200 Introduction to Computers and Programming
- CSCI-C 211 Introduction to Computer Science
- CSCI-H 200 INTRODUCTION TO COMPUTERS AND PROGRAMMING, HONORS
- CSCI-H 211 Introduction to Computer Science, Honors
CSCI-A 201 INTRODUCTION TO PROGRAMMING I
- Credits
- 3–4 credit hours
- Prerequisites
- None
- Description
- None
CSCI-C 200 Introduction to Computers and Programming
- Credits
- 4
- Prerequisites
- High school precalculus math
- 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.
- Repeatability
- Credit given for only one of CSCI-C 200, CSCI-C 211, CSCI-H 211, or CSCI-A 591.
CSCI-C 211 Introduction to Computer Science
- Credits
- 4
- Prerequisites
- High school precalculus math
- 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.
- Repeatability
- Credit given for only one of CSCI-C 200, CSCI-C 211, CSCI-H 211, or CSCI-A 591.
CSCI-H 200 INTRODUCTION TO COMPUTERS AND PROGRAMMING, HONORS
- Credits
- 4–4 credit hours
- Prerequisites
- None
- Description
- None
CSCI-H 211 Introduction to Computer Science, Honors
- Credits
- 4
- Prerequisites
- High school precalculus math
- Description
- Honors version of CSCI-C 211. 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.
- Repeatability
- Credit given for only one of CSCI-A 591, CSCI-C 200, CSCI-C 211, or CSCI-H 211.
- Outside focal area. A focal area approved by the department consisting of nine (9) credit hours in one of the following departments: Astronomy, Biology, Chemistry, Cognitive Science, Computer Science, Economics, Geology, Physics, Statistics, or other departments with approval of the mathematics department.
- Computer Science. One (1) course:
- Major GPA, Hours, and Minimum Grade Requirements.
- 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.
- At least 18 credit hours in the major must be completed at the 300–499 level.
- Except for the GPA requirement, a grade of C- or higher is required for a course to count toward a requirement in the major.
- 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.
- Exceptions to major requirements may be made with the approval of the department's Director of Undergraduate Studies, subject to final approval by the College of Arts and Sciences.
Notes
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 cumulative grade point average (GPA) of at least 2.000 is required for all courses taken at Indiana University.
- CASE Requirements. The following College of Arts and Sciences Education (CASE) requirements must be completed:
- CASE Foundations
- CASE Breadth of Inquiry
- CASE Culture Studies
- Diversity in the United States: Not required
- Global Civilizations and Cultures: Not required
- CASE Critical Approaches: 1 course
- CASE Foreign Language: Proficiency in a single foreign language through the first semester of the second year of college-level coursework
- CASE Intensive Writing: 1 course
- 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.