Department of Mathematics
Bachelor of Science in Mathematics Program I (Bachelor of Science in Mathematics)
Students on Summer 2019, Fall 2019, or Spring 2020 requirements MATHBS1
Bachelor of Science in Mathematics students study in depth the complex relationships between ideas in mathematics. This degree provides rigorous in-depth training suitable for graduate programs in mathematics.
Requirements
The major requires at least 39 credit hours, including the requirements listed below.
- Linear Algebra. One (1) course:
- MATH-M 303 Linear Algebra for Undergraduates
- MATH-S 303 Honors Course in Linear Algebra
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 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 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 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 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.
- Differential Equations or Probability and Statistics. One (1) course:
- MATH-M 343 Introduction to Differential Equations with Applications I
- MATH-M 365 Introduction to Probability and Statistics
- MATH-S 343 Honors Course in Differential Equations
MATH-M 343 Introduction to Differential Equations with Applications I
- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Notes
- R: MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Ordinary differential equations and methods for their solution, including series methods and the Laplace transform. Applications of differential equations. s, stability, and numerical methods. Partial differential equations of mathematical physics, Fourier series.
- Repeatability
- Credit given for only one of MATH-M 343 or MATH-S 343.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-M 365 Introduction to Probability and Statistics
- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Elementary concepts of probability and statistics. Combinatorics, conditional probability, independence, random variables, discrete and continuous distributions, moments. Statistical inference, point estimation, confidence intervals, test of hypotheses. Applications to social, behavioral, and natural sciences.
- Repeatability
- Credit given for only one of MATH-M 360 or MATH-M 365.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
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 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.
- Modern Algebra I. One (1) course:
- MATH-M 403 Introduction to Modern Algebra I
- MATH-S 403 Honors Course in Modern Algebra I
MATH-M 403 Introduction to Modern Algebra I
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Study of groups, rings, field extensions, with applications to linear transformations.
MATH-S 403 Honors Course in Modern Algebra I
- Credits
- 3
- Prerequisites
- MATH-S 303; or consent of instructor
- Notes
- For students of outstanding ability in mathematics
- Description
- Theory of groups, rings, integral domains, fields, and modules.
- Modern Algebra II. One (1) course:
- MATH-M 404 Introduction to Modern Algebra II
- MATH-M 405 Number Theory
- MATH-M 409 Linear Transformations
- MATH-M 453 Cryptography
- MATH-S 404 Honors Course in Modern Algebra II
MATH-M 404 Introduction to Modern Algebra II
- Credits
- 3
- Prerequisites
- None
- Notes
- Open only to graduate students
- Description
- Study of groups, rings, field extensions, with applications to linear transformations.
MATH-M 405 Number Theory
- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Numbers and their representation, divisibility and factorization, primes and their distribution, number theoretic functions, congruences, primitive roots, diophantine equations, quadratic residues, sums of squares.
MATH-M 409 Linear Transformations
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- The study of linear transformations on a finite dimensional vector space over the complex field. Canonical forms, similarity theory; inner products and diagonalization of normal transformations.
MATH-M 453 Cryptography
- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- The course covers encryption and decryption in secure codes. Topics include cryptos and their cryptanalysis, Data Encryption Standard, cryptanalysis, Euclidean algorithm, Chinese remainder theorem, RSA crypto, primality testing, factoring algorithms, EI Gamal crypto, discrete log problem, other public key cryptos, signature schemes, hash functions, key distribution and key agreement.
- Fall 2024CASE NMcourseSummer 2024CASE NMcourse
MATH-S 404 Honors Course in Modern Algebra II
- Credits
- 3
- Prerequisites
- MATH-S 403; or consent of instructor
- Description
- For students of outstanding ability in mathematics. Theory of groups, rings, integral domains, fields, and modules.
- Electives. Additional courses, including at least two (2) courses at the 400–599 level excluding MATH-M 491. MATH-M 490 may be used with the approval of the director of undergraduate studies.
- 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.
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.