## Mathematics (Major)

*Effective Winter 2021*

### Advising

Appointments are scheduled online at: lsa.umich.edu/math/undergraduates.. Students are strongly urged to consult with a department advisor each term before selecting courses for the following term.

### Grade Policies

All prerequisite courses must be satisfied with a grade of C– or above. Students with lower grades in prerequisite courses must receive special permission of the instructor to enroll in subsequent courses.

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

Most programs require completion of one of the sequences ending with MATH 215-217, 285-217, or 295-296. A working knowledge of a high-level computer language such as C++ or a computer algebra system (such as Maple or Mathematica), at a level equivalent to completion of a course of three or more credits, and eight credits of PHYSICS, preferably PHYSICS 140/141 and 240/241, are recommended for all programs and required for some. (A grade of C- or better is strongly suggested for MATH 217.)

### Requirements

A student considering a major in Mathematics should consult a mathematics department advisor in the Undergraduate Mathematics Office as early as possible and certainly by the first term of the sophomore year. The department offers many different submajors with varying requirements; failure to meet some of these at the intended time may delay completion of the program and graduation. A plan for the major must be designed with and approved by a department advisor.

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Pure Mathematics (Sub-Major)

*
Effective Winter 2022
*

### Advising

Appointments are scheduled online at: lsa.umich.edu/math/undergraduates. Students are strongly urged to consult with a department advisor each term before selecting courses for the following term.

### Grade Policies

All prerequisite courses must be satisfied with a grade of C– or above. Students with lower grades in prerequisite courses must receive special permission of the instructor to enroll in subsequent courses.

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

Completion of one of the sequences ending with MATH 215-217, 285-217, or 295-296. A working knowledge of a high-level computer language such as C++ or a computer algebra system (such as Maple or Mathematica), at a level equivalent to completion of a course of three or more credits, and eight credits of PHYSICS, preferably PHYSICS 140/141 and 240/241, are recommended for all programs and required for some. (A grade of C- or better is strongly suggested for MATH 217.)

**Additional prerequisites for the Pure Mathematics Submajor**

Completion of one of the sequences ending with MATH 215-217, 285-217, or 295-296. (A grade of C- or better is strongly suggested for MATH 217.)

All Pure Mathematics majors are also strongly encouraged to take PHYSICS 140-141 and 240-241 and to acquire a working knowledge of a high-level computer language (e.g., Fortran, C, or C++) at a level equivalent to the completion of EECS 183.

### Requirements

**Four basic courses**(one course from each of the following four groups), completed with a grade of at least C-:- Modern Algebra: MATH 312,412 or 493
- Differential Equations: MATH 286, or 316
- Analysis: MATH 351 or 451
- Geometry/Topology: MATH 431, 433, 490, or 590

**Four elective courses**(mathematics) chosen from a list of approved electives and approved by a department advisor.**One cognate course**outside the Mathematics Department, but with advanced mathematical content.

### Residency

Minimum number** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans)*:* Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.

### Mathematical Sciences (Sub-Major) (Winter 2021 - )

## Mathematics (Major)

*Effective Winter 2021*

### Advising

Appointments are scheduled online at: lsa.umich.edu/math/undergraduates.. Students are strongly urged to consult with a department advisor each term before selecting courses for the following term.

### Grade Policies

All prerequisite courses must be satisfied with a grade of C– or above. Students with lower grades in prerequisite courses must receive special permission of the instructor to enroll in subsequent courses.

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

Most programs require completion of one of the sequences ending with MATH 215-217, 285-217, or 295-296. A working knowledge of a high-level computer language such as C++ or a computer algebra system (such as Maple or Mathematica), at a level equivalent to completion of a course of three or more credits, and eight credits of PHYSICS, preferably PHYSICS 140/141 and 240/241, are recommended for all programs and required for some. (A grade of C- or better is strongly suggested for MATH 217.)

### Requirements

A student considering a major in Mathematics should consult a mathematics department advisor in the Undergraduate Mathematics Office as early as possible and certainly by the first term of the sophomore year. The department offers many different submajors with varying requirements; failure to meet some of these at the intended time may delay completion of the program and graduation. A plan for the major must be designed with and approved by a department advisor.

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Mathematical Sciences (Sub-Major)

*
Effective Winter 2021
*

### Advising

Appointments are scheduled online at: lsa.umich.edu/math/undergraduates. Students are strongly urged to consult with a department advisor each term before selecting courses for the following term.

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

Completion of one of the sequences ending with MATH 215-217, 285-217, or 295-296. A working knowledge of a high-level computer language such as C++ or a computer algebra system (such as Maple or Mathematica), at a level equivalent to completion of a course of three or more credits, and eight credits of PHYSICS, preferably PHYSICS 140/141 and 240/241, are recommended for all programs and required for some. (A grade of C- or better is strongly suggested for MATH 217.)

**Additional prerequisites for the Mathematical Sciences Submajor**

Completion of one of the sequences ending with MATH 215&217, 285&217, or 295&296. In addition, students must acquire a working knowledge of a high-level computer language (e.g., Fortran, C, or C++) at a level equivalent to the completion of EECS 183. Students pursuing the Mathematical Biology option are also required to take the Introductory Biology lectures (BIOLOGY 171 and either 172 or 174; or BIOLOGY 192; or BIOLOGY 195). For those not pursuing either a Physics major or minor, PHYSICS 140/141 and 240/241 are required for the Numerical and Mathematical Physics options and strongly recommended for the other options. Some of the options have additional requirements as noted below.

### Requirements

Each student must select one of the eight Program Options as a special area.

**Basic Courses**

The basic courses consist of one from each of the following four groups**completed with a grade of at least C-**:- Differential Equations: MATH 286, or 316
- Discrete Math/Modern Algebra: MATH 312, 412, 465, or 493
- Analysis: MATH 351, 354, 450, 451, or 454
- Probability: MATH 425 or 525

**Program Options**

At least three courses from ONE of the Program Options listed below (the list of possible electives for each option is given on the departmental website:- Discrete and Algorithmic Methods
- Numerical and Applied Analysis
- Operations Research and Modeling
- Probabilistic Methods
- Mathematical Economics
- Control Systems
- Mathematical Physics
- Mathematical Biology

**Advanced Courses**

Two additional advanced mathematics (or related) courses selected from either- courses taught outside the department which emphasize the application of significant mathematical tools (at least at the level of MATH 215) in another discipline at the 300 level or above, or
- mathematics courses numbered 400 or above

In all cases, approval of an advisor is required. This is a very flexible requirement to accommodate special interests and may be satisfied by a broad range of courses in other departments.

### Other Department Policies

- At least two of the courses used toward the Program Options and Advanced Courses must be MATH courses.
- At least one of the courses used toward the Program Options and Advanced Courses must be taken outside the department and be at the 300 level or above.

### Residency

** **Minimum number** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Mathematics (Major) (Winter 2021 - )

*
Effective Winter 2021
*

### Advising

Appointments are scheduled online at: lsa.umich.edu/math/undergraduates.. Students are strongly urged to consult with a department advisor each term before selecting courses for the following term.

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

Most programs require completion of one of the sequences ending with MATH 215-217, 285-217, or 295-296. A working knowledge of a high-level computer language such as C++ or a computer algebra system (such as Maple or Mathematica), at a level equivalent to completion of a course of three or more credits, and eight credits of PHYSICS, preferably PHYSICS 140/141 and 240/241, are recommended for all programs and required for some. (A grade of C- or better is strongly suggested for MATH 217.)

### Requirements

A student considering a major in Mathematics should consult a mathematics department advisor in the Undergraduate Mathematics Office as early as possible and certainly by the first term of the sophomore year. The department offers many different submajors with varying requirements; failure to meet some of these at the intended time may delay completion of the program and graduation. A plan for the major must be designed with and approved by a department advisor.

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.

### Pure Mathematics (Sub-Major) (Winter 2021 - Fall 2021)

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Pure Mathematics (Sub-Major)

*
Effective Winter 2021
*

### Advising

Appointments are scheduled online at: lsa.umich.edu/math/undergraduates. Students are strongly urged to consult with a department advisor each term before selecting courses for the following term.

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

Completion of one of the sequences ending with MATH 215-217, 285-217, or 295-296. A working knowledge of a high-level computer language such as C++ or a computer algebra system (such as Maple or Mathematica), at a level equivalent to completion of a course of three or more credits, and eight credits of PHYSICS, preferably PHYSICS 140/141 and 240/241, are recommended for all programs and required for some. (A grade of C- or better is strongly suggested for MATH 217.)

**Additional prerequisites for the Pure Mathematics Submajor**

Completion of one of the sequences ending with MATH 215-217, 285-217, or 295-296. (A grade of C- or better is strongly suggested for MATH 217.)

All Pure Mathematics majors are also strongly encouraged to take PHYSICS 140-141 and 240-241 and to acquire a working knowledge of a high-level computer language (e.g., Fortran, C, or C++) at a level equivalent to the completion of EECS 183.

### Requirements

**Four basic courses**(one course from each of the following four groups), completed with a grade of at least C-:- Modern Algebra: MATH 412 or 493
- Differential Equations: MATH 286, or 316
- Analysis: MATH 351 or 451
- Geometry/Topology: MATH 431, 433, 490, or 590

**Four elective courses**(mathematics) chosen from a list of approved electives and approved by a department advisor.**One cognate course**outside the Mathematics Department, but with advanced mathematical content.

### Residency

Minimum number** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans)*:* Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Mathematics of Finance and Risk Management (Sub-Major) (Winter 2021 - )

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Mathematics of Finance and Risk Management (Sub-Major)

*
Effective Winter 2021
*

### Advising

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- ECON 101, ECON 102, and EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

**Additional prerequisites for the Mathematics of Finance and Risk Management Submajor**

MATH 215&217, 285&217 or MATH 295&296. Each student must also complete: ECON 101 and 102 and EECS 183 all elected on a graded basis. The grade for ECON 101, ECON 102, and EECS 183 will be included in the major GPA.

### Requirements

A minimum of 10 courses, selected from the following:

**Four basic courses**(one from each of the following four groups), completed with a grade of at least C-:*Differential Equations:*MATH 286 or 316*Probability:*MATH 525*Statistics:*STATS 426*Analysis:*Math 351 or 451

**Four special courses for Financial Mathematics:**

MATH 423, MATH 474, MATH 472 (or 471), MATH 526.**Two additional courses**in areas relating to Financial Mathematics approved by an advisor.

### Residency

Minimum number** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Honors Mathematics (Sub-Major) (Winter 2021 - )

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Honors Mathematics (Sub-Major)

*
Effective Winter 2021
*

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

**Additional prerequisites for the Honors Mathematics Submajor**

Completion of one of the sequences ending with MATH 215-217, 285-217, 295-296, or 217-297. (A grade of C- or better is strongly suggested for MATH 217.)

Students intending an Honors major are strongly advised to take one of the Honors introductory sequences MATH 156-286, 175-286, 185-286, 295-396, or 217-297 or some combination of these five. The sequence MATH 295-396 is very theoretical. Eight credits of PHYSICS and familiarity with a high-level computer language are strongly recommended.

### Requirements

The Honors major program must include at least nine courses: (A) four basic courses, (B) four elective courses, and (C) one cognate course as described below.

- The basic courses consist of one from each of groups 1, 2, 3, and 4 or groups 1, 2, 5, 6 below, completed with a grade of at least C-:
- Linear Algebra: MATH 420, 494, or 571
- Analysis: MATH 451
- Modern Algebra: MATH 493
- Geometry/Topology: MATH 431, 433, 490, or 590
- Probability: MATH 525
- Differential Equations: MATH 404, 454, 556, 557, or 558

- Students who complete MATH 295&296 OR MATH 217&297, with a grade of at least a C- are exempt from MATH 451.

- Students who complete MATH 295&395 OR MATH 297&395, with a grade of at least a C- are exempt from MATH 420.

- B. The four elective courses must be chosen in consultation with an Honors advisor to provide a cohesive program which explores an area of mathematics in some depth. There is a good deal of freedom allowed here, but a random selection of courses will not satisfy this requirement. The courses should be chosen from the approved list or have a course number 600 or above. MATH 289 is a repeatable 1-credit course and can be used to satisfy the elective requirement only if taken for a total of 3 credits. A Mathematics Honors advisor may approve another mathematics course or a course from another department with advanced mathematical content as one of these elective courses. The Mathematics Honors advisor may ask that the student arrange supplemental work in a given class conform to expectations for an Honors elective. A student electing to satisfy requirement A by choosing courses from groups 1, 2, 5, and 6 must complete a course in Complex Analysis (MATH 555 or 596) as one of his/her electives.
- C. One cognate course from outside the Mathematics department, but containing significant mathematical content, chosen with the approval of the Honors advisor.

Students who, in the judgment of the Departmental Honors Committee, have completed an Honors major with distinction are granted a citation upon graduating. Interested students should discuss their program and the specific requirements for obtaining the citation with a Mathematics Honors advisor (appointments scheduled at: lsa.umich.edu/math/undergraduates) no later than the second term of their sophomore year.

### Residency

Minimum number** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Mathematics of Finance and Risk Management (Sub-Major) (Winter 2020 - Fall 2020)

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Mathematics of Finance and Risk Management (Sub-Major)

*
Effective Winter 2020
*

### Advising

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- ECON 101, ECON 102, and EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

Completion of one of the sequences ending with MATH 215-217, 256-217, 285-217, or 395-396. A working knowledge of a high-level computer language such as C++ or a computer algebra system (such as Maple or Mathematica), at a level equivalent to completion of a course of three or more credits, and eight credits of PHYSICS, preferably PHYSICS 140/141 and 240/241, are recommended for all programs and required for some. (A grade of C- or better is strongly suggested for MATH 217.)

**Additional prerequisites for the Mathematics of Finance and Risk Management Submajor**

MATH 215&217, 255&217, 285&217 or MATH 295&296. Each student must also complete: ECON 101 and 102 and EECS 183 all elected on a graded basis. The grade for ECON 101, ECON 102, and EECS 183 will be included in the major GPA.

### Requirements

A minimum of 10 courses, selected from the following:

**Four basic courses**(one from each of the following four groups), completed with a grade of at least C-:*Differential Equations:*MATH 286 or 316*Probability:*MATH 425*Statistics:*STATS 426*Analysis:*Math 351 or 451

**Four special courses for Financial Mathematics:**

MATH 423, MATH 472 (or 471), MATH 525, MATH 526.**Two additional courses**in areas relating to Financial Mathematics approved by an advisor.

### Residency

Minimum number** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Actuarial Mathematics (Sub-Major) (Winter 2020 - )

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Actuarial Mathematics (Sub-Major)

*
Effective Winter 2020
*

### Advising

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- ECON 101, ECON 102, and EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

Completion of one of the sequences ending with MATH 215-217, 256-217, 285-217, or 395-396. A working knowledge of a high-level computer language such as C++ or a computer algebra system (such as Maple or Mathematica), at a level equivalent to completion of a course of three or more credits, and eight credits of PHYSICS, preferably PHYSICS 140/141 and 240/241, are recommended for all programs and required for some. (A grade of C- or better is strongly suggested for MATH 217.)

**Additional prerequisites for the Actuarial Mathematics Submajor**

MATH 215&217, 255&217, 285&217 or MATH 295&296. Each student must also complete: ECON 101 and 102 and EECS 183 all elected on a graded basis. The grade for ECON 101, ECON 102, and EECS 183 will be included in the major GPA.

### Requirements

A minimum of 11 courses, selected from the following:

**Four basic courses**(one from each of the following four groups), completed with a grade of at least C-:*Differential Equations:*MATH 286 or 316*Probability:*MATH 425*Statistics:*STATS 426*Analysis:*MATH 351 or 451

**Five special courses for Actuarial Mathematics:**

MATH 423, MATH 424, MATH 520 MATH 523, and at least one of MATH 521 or MATH 524**Two additional courses**in areas relating to Actuarial Mathematics approved by an advisor.

### Residency

Minimum number** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include prerequisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Mathematics of Finance and Risk Management (Sub-Major) (Fall 2019)

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Mathematics of Finance and Risk Management (Sub-Major)

*
Effective Fall 2019
*

### Advising

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

Completion of one of the sequences ending with MATH 215-217, 256-217, 285-217, or 395-396. A working knowledge of a high-level computer language such as C++ or a computer algebra system (such as Maple or Mathematica), at a level equivalent to completion of a course of three or more credits, and eight credits of PHYSICS, preferably PHYSICS 140/141 and 240/241, are recommended for all programs and required for some. (A grade of C- or better is strongly suggested for MATH 217.)

**Additional prerequisites for the Mathematics of Finance and Risk Management Submajor**

MATH 215&217, 255&217, 285&217 or MATH 295&296. Each student must also complete: ECON 101 and 102 and EECS 183 all elected on a graded basis. The grade for ECON 101, ECON 102, and EECS 183 will be included in the major GPA.

### Requirements

**Four basic courses**(one from each of the following four groups), completed with a grade of at least C-:*Differential Equations:*MATH 286 or 316*Probability:*MATH 425*Statistics:*STATS 426*Finance:*MATH 423

**Four special courses for Financial Mathematics:**

MATH 351 (or 451), MATH 472 (or 471), MATH 525, MATH 526.- Two additional courses in areas relating to Financial Mathematics approved by an advisor.

### Residency

** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Honors Mathematics (Sub-Major) (Fall 2019 - Fall 2020)

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Honors Mathematics (Sub-Major)

*
Effective Fall 2019
*

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

**Additional prerequisites for the Honors Mathematics Submajor**

Completion of one of the sequences ending with MATH 215-217, 256-217, 285-217, or 395-396. (A grade of C- or better is strongly suggested for MATH 217.)

Students intending an Honors major are strongly advised to take one of the Honors introductory sequences MATH 156-256, 175-286, 185-286, or 295-396, or some combination of these four. The sequence MATH 295-396 is very theoretical. Eight credits of PHYSICS and familiarity with a high-level computer language are strongly recommended.

### Requirements

The Honors major program must include at least nine courses: (A) four basic courses, (B) four elective courses, and (C) one cognate course as described below.

- The basic courses consist of one from each of groups 1, 2, 3, and 4 or groups 1, 2, 5, 6 below, completed with a grade of at least C-:
- Linear Algebra: MATH 420 or 513
- Analysis: MATH 451
- Modern Algebra: MATH 493
- Geometry/Topology: MATH 433, 490, or 590
- Probability: MATH 525
- Differential Equations: MATH 404, 454, 556, 557, or 558

- Students who complete MATH 295&296 OR MATH 217&297, with a grade of at least a C- are exempt from MATH 451.

- Students who complete MATH 295&395 OR MATH 297&395, with a grade of at least a C- are exempt from MATH 420.

- The four elective courses must be chosen in consultation with an Honors advisor to provide a cohesive program which explores an area of mathematics in some depth. There is a good deal of freedom allowed here, but a random selection of courses will not satisfy this requirement. The courses should be chosen from the approved list or have a course number 600 or above. MATH 289 is a repeatable 1-credit course and can be used to satisfy the elective requirement only if taken for a total of 3 credits. A Mathematics Honors advisor may approve another mathematics course or a course from another department with advanced mathematical content as one of these elective courses. The Mathematics Honors advisor may ask that the student arrange supplemental work in a given class conform to expectations for an Honors elective. A student electing to satisfy requirement A by choosing courses from groups 1, 2, 5, and 6 must complete a course in Complex Analysis (MATH 555 or 596) as one of his/her electives.
- One cognate course from outside the Mathematics department, but containing significant mathematical content, chosen with the approval of the Honors advisor.

Students who, in the judgment of the Departmental Honors Committee, have completed an Honors major with distinction are granted a citation upon graduating. Interested students should discuss their program and the specific requirements for obtaining the citation with a Mathematics Honors advisor (appointments scheduled at: lsa.umich.edu/math/undergraduates) no later than the second term of their sophomore year.

### Residency

** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.

### Mathematical Sciences (Sub-Major) (Winter 2018 - Fall 2020)

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Mathematical Sciences (Sub-Major)

*
Effective Winter 2018
*

### Advising

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

**Additional prerequisites for the Mathematical Sciences Submajor**

Completion of one of the sequences ending with MATH 215&217, 256&217, 285&217, or 295&296. Students who have completed one of the sequences 255&256 or 285&286 may substitute MATH 513 for MATH 217. In addition, students must acquire a working knowledge of a high-level computer language (e.g., Fortran, C, or C++) at a level equivalent to the completion of EECS 183; and Introductory Biology sequence (BIOLOGY 171-172). For those not pursuing either a Physics major or minor, PHYSICS 140/141 and 240/241 are required for the Numerical and Mathematical Physics options and strongly recommended for the other options. Some of the options have additional requirements as noted below.

### Requirements

Each student must select one of the eight Program Options as a special area.

**Basic Courses**

The basic courses consist of one from each of the following four groups**completed with a grade of at least C-**:- Differential Equations: MATH 286, or 316
- Discrete Math/Modern Algebra: MATH 312, 412, 465, or 493
- Analysis: MATH 351, 354, 450, 451, or 454
- Probability: MATH 425 or 525

**Program Options**

At least three courses from ONE of the Program Options listed below (the list of possible electives for each option is given on the departmental website:- Discrete and Algorithmic Methods
- Numerical and Applied Analysis
- Operations Research and Modeling
- Probabilistic Methods
- Mathematical Economics
- Control Systems
- Mathematical Physics
- Mathematical Biology

**Advanced Courses**

Two additional advanced mathematics (or related) courses selected from either- courses taught outside the department which emphasize the application of significant mathematical tools (at least at the level of MATH 215) in another discipline at the 300 level or above, or
- mathematics courses numbered 400 or above

In all cases, approval of an advisor is required. This is a very flexible requirement to accommodate special interests and may be satisfied by a broad range of courses in other departments.

### Other Department Policies

- At least two of the courses used toward the Program Options and Advanced Courses must be MATH courses.
- At least one of the courses used toward the Program Options and Advanced Courses must be taken outside the department and be at the 300 level or above.

### Residency

** **Minimum number** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Actuarial Mathematics (Sub-Major) (Fall 2017 - Fall 2019)

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Actuarial Mathematics (Sub-Major)

*
Effective Fall 2017
*

### Advising

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

**Prerequisites for all Mathematics Majors**

**Additional prerequisites for the Actuarial Mathematics Submajor**

### Requirements

A minimum of 11 courses, selected from the following:

**Four basic courses**(one from each of the following four groups), completed with a grade of at least C-:*Differential Equations:*MATH 286 or 316*Probability:*MATH 425*Statistics:*STATS 426*Finance:*MATH 423

**Five special courses for Actuarial Mathematics:**

MATH 424, MATH 520 and 521 (or 522), and MATH 523 and 524.**Two additional courses**in areas relating to Actuarial approved by an advisor.

### Residency

Minimum number** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include prerequisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Mathematics of Finance and Risk Management (Sub-Major) (Fall 2017 - Summer 2019)

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Mathematics of Finance and Risk Management (Sub-Major)

*
Effective Fall 2017
*

### Advising

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

**Additional prerequisites for the Mathematics of Finance and Risk Management Submajor**

### Requirements

**Four basic courses**(one from each of the following four groups), completed with a grade of at least C-:*Differential Equations:*MATH 286 or 316*Probability:*MATH 425*Statistics:*STATS 426*Finance:*MATH 423

**Four special courses for Financial Mathematics:**

MATH 451, MATH 472 (or 471), MATH 525, MATH 526.- Two additional courses in areas relating to Financial Mathematics approved by an advisor.

### Residency

** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Secondary Mathematics Teaching Certificate (Sub-Major) (Fall 2016 - )

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Secondary Mathematics Teaching Certificate (Sub-Major)

*
Effective Fall 2016
*

### Advising

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

**Additional prerequisites for the Secondary Mathematics Teaching Certificate Submajor**

One of the pair of courses MATH 215&217, MATH 255&217, MATH 285&217, or MATH 295&296. Additionally, students must complete one term of computer programming, EECS 183 or equivalent.

### Requirements

Basic Courses = The basic courses for a candidate for a teaching certificate consist of one course from each of the following five groups (chosen with the approval of a teaching certificate advisor), completed with a grade of at least a C-:

- Modern Algebra/Number Theory: MATH 487 or 475
- Geometry: MATH 431 or 531
- Probability: MATH 425 or 525
- Analysis: MATH 351 or 451
- Secondary Mathematics: MATH 486

Specific Courses (or core/cognate courses) = The program requires 10 specific Education courses, listed below, totaling 30 credits. These are elected in the junior and senior years in a specified order. Consult with the School of Education Office of Student Services for the order and timing of these courses.

- Methods of Teaching Mathematics (or minor field): EDUC 413 (3 credits)
- Practicum in Teaching Methods: EDUC 307I and 307II (4 credits)
- Educational Psychology: EDUC 391 (3 credits)
- Reading and Writing: EDUC 402 (3 credits)
- Education in a Multi-cultural Society: EDUC 392 (3 credits)
- Directed Teaching: EDUC 302 (10 credits)
- Problems and Principles of Secondary Education: EDUC 304 (2 credits)
- Teaching with Digital Technologies 6-12: EDUC 446 (1 credit)
- Teaching Students with Exceptionalities in the General Education Middle and High School Classroom: EDUC 445 (1 credit)

The last four of these are to be elected concurrently. **Students must apply for admission to the certification program by January 15 of their sophomore year.** Application forms are available at the School of Education.

Additionally, every student must successfully complete:

- an introductory course in psychology (not PSYCH 112) that is to be taken before EDUC 391, and
- Michigan's licensure requirements (see www.soe.umich.edu/licensure_in_michigan/).

Every Teaching Certificate student must present a SOE major or SOE minor in another academic field. This normally requires 20-24 credits in a structured program in an area other than mathematics. Consult the *Bulletin* of the School of Education for acceptable programs.

### Residency

Minimum number** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) *Effective Fall 2015:* Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Actuarial Mathematics (Sub-Major) (Fall 2015 - Summer 2017)

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Actuarial Mathematics (Sub-Major)

*
Effective Fall 2015
*

### Advising

Appointments are scheduled online at: www.math.lsa.umich.edu/undergrad/. Students are strongly urged to consult with a department advisor each term before selecting courses for the following term.

### Prerequisites

### Requirements

A minimum of 11 courses, selected from the following:

**Four basic courses**(one from each of the following four groups), completed with a grade of at least C-:*Differential Equations:*MATH 216, 256, 286, or 316*Probability:*MATH 425*Statistics:*STATS 426*Finance:*MATH 423

**Five special courses for Actuarial Mathematics:**

MATH 424, MATH 520 and 521 (or 522), and MATH 523 and 524.- Two additional courses in areas relating to Actuarial approved by an advisor.

### Residency

** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Mathematical Sciences (Sub-Major) (Winter 2015 - Fall 2017)

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Mathematical Sciences (Sub-Major)

*
Effective Winter 2015
*

### Advising

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

**Additional prerequisites for the Mathematical Sciences Submajor**

Completion of one of the sequences ending with MATH 215&217, 256&217, 285&217, or 295&296. Students who have completed one of the sequences 255&256 or 285&286 may substitute MATH 513 for MATH 217. In addition, students must acquire a working knowledge of a high-level computer language (e.g., Fortran, C, or C++) at a level equivalent to the completion of EECS 183; and Introductory Biology sequence (BIOLOGY 171-172). For those not pursuing either a Physics major or minor, PHYSICS 140/141 and 240/241 are required for the Numerical and Mathematical Physics options and strongly recommended for the other options. Some of the options have additional requirements as noted below.

### Requirements

Each student must select one of the eight Program Options as a special area.

- Four basic courses (one course from each of the following four groups), completed with a grade of at least C-:
- Differential Equations: MATH 256, 286, or 316
- Discrete Math/Modern Algebra: MATH 312, 412, 465, or 493
- Analysis: MATH 351, 354, 450, 451, or 454
- Probability: MATH 425 or 525

- At least three courses from ONE of the Program Options listed below (the list of possible electives for each option is given on the departmental website: lsa.umich.edu/math/undergraduates):
- Discrete and Algorithmic Methods
- Numerical and Applied Analysis
- Operations Research and Modeling
- Probabilistic Methods
- Mathematical Economics
- Control Systems
- Mathematical Physics
- Mathematical Biology

- Two additional advanced mathematics (or related) courses, approved by a department advisor
- At least two of the courses in b and c must be MATH courses.

### Residency

** **Minimum number** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Mathematics (Major) (Winter 2014 - Fall 2020)

*
Effective Winter 2014
*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

Most programs require completion of one of the sequences ending with MATH 215-217, 256-217, 285-217, or 395-396. A working knowledge of a high-level computer language such as C++ or a computer algebra system (such as Maple or Mathematica), at a level equivalent to completion of a course of three or more credits, and eight credits of PHYSICS, preferably PHYSICS 140/141 and 240/241, are recommended for all programs and required for some. (A grade of C- or better is strongly suggested for MATH 217.)

### Requirements

- Pure Mathematics
- Mathematical Sciences
- Actuarial Mathematics
- Mathematics of Finance and Risk Management
- Honors Mathematics
- Secondary Mathematics Teaching Certificate

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Mathematics of Finance and Risk Management (Sub-Major) (Winter 2014 - Summer 2017)

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Mathematics of Finance and Risk Management (Sub-Major)

*
Effective Winter 2014
*

### Advising

Appointments are scheduled online at: www.math.lsa.umich.edu/undergrad/. Students are strongly urged to consult with a department advisor each term before selecting courses for the following term.

### Grade Policies

### Prerequisites

### Requirements

**Four basic courses**(one from each of the following four groups), completed with a grade of at least C-:*Differential Equations:*MATH 216, 256, 286, or 316*Probability:*MATH 425*Statistics:*STATS 426*Finance:*MATH 423

**Four special courses for Financial Mathematics:**

MATH 451, MATH 472 (or 471), MATH 525, MATH 526.- Two additional courses in areas relating to Financial Mathematics approved by an advisor.

### Residency

** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

No course used to fulfill a major requirement may be used toward the LSA Distribution Requirement. In addition, courses in the MATH subject area may not be used toward the Distribution Requirement.### Honors Mathematics (Sub-Major) (Fall 2012 - Summer 2019)

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Honors Mathematics (Sub-Major)

*
Effective Fall 2012
*

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

**Additional prerequisites for the Honors Mathematics Submajor**

Completion of one of the sequences ending with MATH 215-217, 256-217, 285-217, or 395-396. (A grade of C- or better is strongly suggested for MATH 217.)

Students intending an Honors major are strongly advised to take one of the Honors introductory sequences MATH 156-256, 175-286, 185-286, or 295-396, or some combination of these four. The sequence MATH 295-396 is very theoretical. Eight credits of PHYSICS and familiarity with a high-level computer language are strongly recommended.

### Requirements

The Honors major program must include at least nine courses: (A) four basic courses, (B) four elective courses, and (C) one cognate course as described below.

- The basic courses consist of one from each of groups 1, 2, 3, and 4 or groups 1, 2, 5, 6 below, completed with a grade of at least C-:
- Linear Algebra: MATH 420 or 513
- Analysis: MATH 451
- Modern Algebra: MATH 493
- Geometry/Topology: MATH 433, 490, or 590
- Probability: MATH 525
- Differential Equations: MATH 404, 454, 556, 557, or 558

- Students who complete MATH 295&296, with a grade of at least a C- are exempt from MATH 451. Students who complete MATH 295-395, with a grade of at least a C- are exempt from MATH 420.

- The four elective courses must be chosen in consultation with an Honors advisor to provide a cohesive program which explores an area of mathematics in some depth. There is a good deal of freedom allowed here, but a random selection of courses will not satisfy this requirement. The courses should be chosen from the approved list or have a course number 600 or above. MATH 289 is a repeatable 1-credit course and can be used to satisfy the elective requirement only if taken for a total of 3 credits. A Mathematics Honors advisor may approve another mathematics course or a course from another department with advanced mathematical content as one of these elective courses. The Mathematics Honors advisor may ask that the student arrange supplemental work in a given class conform to expectations for an Honors elective. A student electing to satisfy requirement A by choosing courses from groups 1, 2, 5, and 6 must complete a course in Complex Analysis (MATH 555 or 596) as one of his/her electives.
- One cognate course from outside the Mathematics department, but containing significant mathematical content, chosen with the approval of the Honors advisor.

Students who, in the judgment of the Departmental Honors Committee, have completed an Honors major with distinction are granted a citation upon graduating. Interested students should discuss their program and the specific requirements for obtaining the citation with a Mathematics Honors advisor (appointments scheduled at: lsa.umich.edu/math/undergraduates) no later than the second term of their sophomore year.

### Residency

** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans): Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

### Distribution Policy

### Pure Mathematics (Sub-Major) (Fall 2011 - Fall 2020)

## Mathematics (Major)

*Effective Winter 2021*

### Advising

### Grade Policies

**Major GPA Calculation**

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183
- ECON 101 and ECON 102 (actuarial mathematics submajor only).

### Prerequisites

### Requirements

### Residency

**Minimum number of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans) Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.

## Pure Mathematics (Sub-Major)

*
Effective Fall 2011
*

### Advising

### Grade Policies

For purposes of calculating grade point average, the term "field of the major" means the following:

- All MATH courses.
- All courses used to meet requirements for the major.
- All required cognate courses (if any).
- All mandatory prerequisites.
- EECS 183

### Prerequisites

**Prerequisites for all Mathematics Majors**

**Additional prerequisites for the Pure Mathematics Submajor**

Completion of one of the sequences ending with MATH 215-217, 256-217, 285-217, or 395-396. (A grade of C- or better is strongly suggested for MATH 217.)

All Pure Mathematics majors are also strongly encouraged to take PHYSICS 140-141 and 240-241 and to acquire a working knowledge of a high-level computer language (e.g., Fortran, C, or C++) at a level equivalent to the completion of EECS 183.

### Requirements

**Four basic courses**(one course from each of the following four groups), completed with a grade of at least C-:- Modern Algebra: MATH 412 or 493
- Differential Equations: MATH 256, 286, or 316
- Analysis: MATH 351 or 451
- Geometry/Topology: MATH 433, 490, or 590

**Four elective courses**(mathematics) chosen from a list of approved electives and approved by a department advisor.**One cognate course**outside the Mathematics Department, but with advanced mathematical content.

### Residency

Minimum number** of courses taken in residence for transfer students majoring in Mathematics** (applies to all sub-plans)*:* Students should take a minimum of 18 credits at the University of Michigan, Ann Arbor campus. Six of these credits must come from the basic courses and nine from the core courses and/or cognate courses. The 18 credits may include pre-requisites taken in Math.