Mathematics (Course 18)

Department of Mathematics

Bachelor of Science in Mathematics
(General Mathematics Option)

General Institute Requirements (GIRs)

The General Institute Requirements include a Communication Requirement that is integrated into both the HASS Requirement and the requirements of each major; see details below.

Summary of Subject Requirements Subjects
Science Requirement 6
Humanities, Arts, and Social Sciences (HASS) Requirement; at least two of these subjects must be designated as communication-intensive (CI-H) to fulfill the Communication Requirement. 8
Restricted Electives in Science and Technology (REST) Requirement [one subject can be satisfied by 18.03 in the Departmental Program] 2
Laboratory Requirement (12 units) 1
Total GIR Subjects Required for SB Degree 17
Physical Education Requirement
Swimming requirement, plus four physical education courses for eight points.

Departmental Program

Choose at least two subjects in the major that are designated as communication-intensive (CI-M) to fulfill the Communication Requirement.

Required SubjectsUnits
18.03Differential Equations12
Restricted Electives
Select eight 12-unit subjects of essentially different content, including at least six advanced subjects (first decimal digit one or higher). One of these eight subjects must be one of the following:96
Linear Algebra
Linear Algebra
Algebra I
Units in Major108
Unrestricted Electives84
Units in Major That Also Satisfy the GIRs(12)
Total Units Beyond the GIRs Required for SB Degree180

The units for any subject that counts as one of the 17 GIR subjects cannot also be counted as units required beyond the GIRs.

1

Students may substitute one of the more advanced subjects 18.152 Introduction to Partial Differential Equations or 18.303 Linear Partial Differential Equations: Analysis and Numerics for 18.03. 18.032 Differential Equations, which places more emphasis on theory, is also an acceptable option.

Communication-Intensive Subjects in the Major

To satisfy the requirement that students take two CI-M subjects, students must select one of the following options:
Option A
Select two of the following:
Seminar in Analysis
Undergraduate Seminar in Discrete Mathematics
Undergraduate Seminar in Physical Mathematics
Seminar in Information Theory
Seminar in Theoretical Computer Science
Seminar in Logic
Seminar in Algebra
Seminar in Number Theory
Project Laboratory in Mathematics
Seminar in Topology
Seminar in Geometry
Option B
Select one subject from Option A and one of the following:
Quantum Physics III
Research and Communication in Economics: Topics, Methods, and Implementation
Real Analysis
Real Analysis
Principles of Discrete Applied Mathematics
Topics in Mathematics with Applications in Finance

Bachelor of Science in Mathematics
(Applied Mathematics Option)

General Institute Requirements (GIRs)

The General Institute Requirements include a Communication Requirement that is integrated into both the HASS Requirement and the requirements of each major; see details below.

Summary of Subject Requirements Subjects
Science Requirement 6
Humanities, Arts, and Social Sciences (HASS) Requirement; at least two of these subjects must be designated as communication-intensive (CI-H) to fulfill the Communication Requirement. 8
Restricted Electives in Science and Technology (REST) Requirement [one subject can be satisfied by 18.03 in the Departmental Program] 2
Laboratory Requirement (12 units) 1
Total GIR Subjects Required for SB Degree 17
Physical Education Requirement
Swimming requirement, plus four physical education courses for eight points.

Departmental Program

Choose at least two subjects in the major that are designated as communication-intensive (CI-M) to fulfill the Communication Requirement.

Required SubjectsUnits
18.03Differential Equations 112
18.04Complex Variables with Applications12
or 18.112 Functions of a Complex Variable
18.06Linear Algebra 212
Select one of the following:12-15
Principles of Discrete Applied Mathematics (15 units, CI-M)
Principles of Discrete Applied Mathematics (12 units)
Principles of Continuum Applied Mathematics (12 units)
Restricted Electives
Select four additional 12-unit Course 18 subjects from the following two groups with at least one subject from each group: 348
Group I—Probability and statistics, combinatorics, computer science
Group II—Numerical analysis, physical mathematics, nonlinear dynamics
Units in Major96-99
Unrestricted Electives81-84
Units in Major That Also Satisfy the GIRs(12)
Total Units Beyond the GIRs Required for SB Degree168

The units for any subject that counts as one of the 17 GIR subjects cannot also be counted as units required beyond the GIRs.

1

Students may substitute one of the more advanced subjects 18.152 Introduction to Partial Differential Equations or 18.303 Linear Partial Differential Equations: Analysis and Numerics for 18.03. 18.032 Differential Equations, which places more emphasis on theory, is also an acceptable option.

2

Students may substitute 18.700 Linear Algebra, which places more emphasis on theory and proofs, or the more advanced subject, 18.701 Algebra I.

3

A list of acceptable subjects is available from Math Academic Services and on the department's website.

Communication-Intensive Subjects in the Major

To satisfy the requirement that students take two CI-M subjects, students must select one of the following options:
Option A
Select two of the following:
Seminar in Analysis
Undergraduate Seminar in Discrete Mathematics
Undergraduate Seminar in Physical Mathematics
Seminar in Information Theory
Seminar in Theoretical Computer Science
Seminar in Logic
Seminar in Algebra
Seminar in Number Theory
Project Laboratory in Mathematics
Seminar in Topology
Seminar in Geometry
Option B
Select one subject from Option A and one of the following:
Quantum Physics III
Research and Communication in Economics: Topics, Methods, and Implementation
Real Analysis
Real Analysis
Principles of Discrete Applied Mathematics
Topics in Mathematics with Applications in Finance

Bachelor of Science in Mathematics
(Pure Mathematics Option)

General Institute Requirements (GIRs)

The General Institute Requirements include a Communication Requirement that is integrated into both the HASS Requirement and the requirements of each major; see details below.

Summary of Subject Requirements Subjects
Science Requirement 6
Humanities, Arts, and Social Sciences (HASS) Requirement; at least two of these subjects must be designated as communication-intensive (CI-H) to fulfill the Communication Requirement. 8
Restricted Electives in Science and Technology (REST) Requirement [one subject can be satisfied by 18.03 in the Departmental Program] 2
Laboratory Requirement (12 units) 1
Total GIR Subjects Required for SB Degree 17
Physical Education Requirement
Swimming requirement, plus four physical education courses for eight points.

Departmental Program

Choose at least two subjects in the major that are designated as communication-intensive (CI-M) to fulfill the Communication Requirement.

Required SubjectsUnits
18.03Differential Equations 112
18.100BReal Analysis 212
18.701Algebra I12
18.702Algebra II12
18.901Introduction to Topology12
Restricted Electives
Select one of the following:12
Analysis and Manifolds
Introduction to Functional Analysis
Fourier Analysis: Theory and Applications
Select one undergraduate seminar from the following:12
Seminar in Analysis (CI-M)
Seminar in Logic (CI-M)
Seminar in Algebra (CI-M)
Seminar in Number Theory (CI-M)
Seminar in Topology (CI-M)
Seminar in Geometry (CI-M)
Select two additional 12-unit Course 18 subjects of essentially different content, with the first decimal digit one or higher24
Units in Major108
Unrestricted Electives84
Units in Major That Also Satisfy the GIRs(12)
Total Units Beyond the GIRs Required for SB Degree180

The units for any subject that counts as one of the 17 GIR subjects cannot also be counted as units required beyond the GIRs.

1

Students may substitute one of the more advanced subjects 18.152 Introduction to Partial Differential Equations or 18.303 Linear Partial Differential Equations: Analysis and Numerics for 18.03. 18.032 Differential Equations, which places more emphasis on theory, is also an acceptable option.

2

Alternate versions of this subject, 18.100A18.100P and 18.100Q, also satisfy this requirement.

Communication-Intensive Subjects in the Major

To satisfy the requirement that students take two CI-M subjects, students must select one of the following options:
Option A
Select two of the following:
Seminar in Analysis
Undergraduate Seminar in Discrete Mathematics
Undergraduate Seminar in Physical Mathematics
Seminar in Information Theory
Seminar in Theoretical Computer Science
Seminar in Logic
Seminar in Algebra
Seminar in Number Theory
Project Laboratory in Mathematics
Seminar in Topology
Seminar in Geometry
Option B
Select one subject from Option A and one of the following:
Quantum Physics III
Research and Communication in Economics: Topics, Methods, and Implementation
Real Analysis
Real Analysis
Principles of Discrete Applied Mathematics
Topics in Mathematics with Applications in Finance