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

Students on Summer 2020, Fall 2020, or Spring 2021 requirements MATHBS1

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

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.
- 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.
Differential Equations or Probability and Statistics. One (1) course:
- MATH-M 343
- MATH-M 365 Introduction to Probability and Statistics
- MATH-S 343 Honors Course in Differential Equations
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.
- Summer 2025CASE NMcourse
  
  Spring 2025CASE NMcourse
  
  Fall 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).
- 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.
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.
- Summer 2025CASE NMcourse
  
  Spring 2025CASE NMcourse
  
  Fall 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.
1. 400–599 Level Electives. At least two (2) additional courses:
  - Any MATH-M 400–499 except MATH-M 403; MATH-M 413; MATH-M 490
  - MATH-M 490 Problem Seminar (Departmental consent required)
  - Any MATH-S 400–499 except MATH-S 403; MATH-S 413; MATH-S 499
  - MATH-S 499 Reading for Honors Departmental consent required
  - MATH 500-599 (graduate level) course with approval from the Director of Undergraduate Studies
  MATH-M 490 Problem Seminar
  
  Credits
  3
  Prerequisites
  MATH-M 301, MATH-M 303 or MATH-S 303; and consent of instructor
  Notes
  R: MATH-M 343 or MATH-S 343, and MATH-M 441; and MATH-M 471
  Description
  Introduction to research techniques for advanced undergraduate and beginning graduate students, based on problems from parts of the regular curriculum, such as linear algebra, topology, probability, and analysis. Emphasis will be on problems of both current and historical interest but usually not in the standard literature.
  
  MATH-S 499 Reading for Honors
  
  Credits
  1–12 credit hours
  Prerequisites
  Approval of departmental honors committee
  Description
  None
  Repeatability
  May be repeated for a maximum of 12 credit hours.
2. 300–599 Level Electives. Additional courses, as needed, to complete remaining requirements:
  - Additional courses from the 400-599 Level Electives list
  - Any MATH-M 300–399 except MATH-M 303; MATH-M 311; MATH-M 312
  - Any MATH-S 300–399 except MATH-S 303; MATH-S 311; MATH-S 312
  - Any MATH-X 300–399
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.

Major Area Courses

MATH-M 119 Brief Survey of Calculus I
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 II (MATHBS2)
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 I (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