Department of Mathematics
Bachelor of Science in Mathematics Program I (Bachelor of Science in Mathematics)
Students on Summer 2024, Fall 2024, or Spring 2025 requirements MATHBS1
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 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 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 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 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.
- 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).
- 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.
- 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.
- 400–499 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.
- 400–499 Level Electives. At least two (2) additional courses:
- Major GPA, Hours, and Minimum Grade Requirements.
- 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.
- 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.
- Major Upper Division Credit Hours. At least 18 credit hours in the major must be completed at the 300–499 level.
- 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
- Any course at the 200–499 level with the
MATH-M 119 Brief Survey of Calculus I
- Credits
- 3
- Prerequisites
- None
- Notes
- R: To be successful, students will demonstrate mastery of two years of high school algebra, one year of high school geometry, and pre-calculus as indicated by an appropriate ALEKS score or completion of MATH-M 025 or MATH-M 027
- Description
- Introduction to calculus. Primarily for students from business and the social sciences.
- Repeatability
- Credit given for only one of MATH-J 113, MATH-M 119, MATH-V 119, MATH-M 211, or MATH-S 211.
- Fall 2024CASE MMcourse
- Fall 2024CASE NMcourse
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
MATH-M 330 Exploring Mathematical Ideas
- Credits
- 3
- Prerequisites
- MATH-M 211 or MATH-S 211
- Notes
- Does not count toward major requirements
- Description
- An experimental course to illustrate important ideas in major areas of mathematics, including number theory, group theory, topology, geometry, and probability. Additional topics may include newly emerging fields, such as chaos theory.
- Fall 2024CASE NMcourse
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
MATH-X 170 Service Learning in Mathematics: Community Outreach
- Credits
- 1
- Prerequisites
- MATH-M 211, MATH-S 211, or consent of instructor
- Corequisites
- Current enrollment in another mathematics course
- Description
- Students will work within the community to foster interest, knowledge, and appreciation in mathematics. Assignments will include assisting with activities designed for primary and secondary school levels, documenting those activities in a parental guide, and suggesting related activities for children to pursue at home.
- Repeatability
- May be repeated for a maximum of 6 credit hours in MATH-X 170 and MATH-Y 201
- Grading
- S/F graded.
MATH-X 373 Internship in Professional Practice
- Credits
- 1–3 credit hours
- Prerequisites
- Consent of department
- Description
- Professional work experience involving significant use of mathematics or statistics. Evaluation by employer and Department of Mathematics. Does not count toward major requirements.
- Repeatability
- May be repeated once with approval of Department of Mathematics for a maximum of 6 credit hours in MATH-X 373 and MATH-Y 398.
- Grading
- S/F grading
MATH-X 390 Readings and Research
- Credits
- 1–3 credit hours
- Prerequisites
- Consent of supervising member of Mathematics faculty
- Description
- Supervised problem solving.
- Repeatability
- May be repeated for a maximum of 12 credit hours in MATH-M 295 and MATH-X 390.
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:
- CASE Foundations
- CASE Breadth of Inquiry
- CASE Culture Studies
- Diversity in the United States: 1 course
- 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
- CASE Sustainability Literacy: 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.