## 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.

- 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.

## Honors Mathematics (Sub-Major)

*
Effective Winter 2021
*

### 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 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.

### Honors Mathematics (Sub-Major) (Fall 2019 - Fall 2020)

## 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.

- 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.

## 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**

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 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

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) (Fall 2012 - Summer 2019)

## 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

**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.

- 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.

## 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**

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 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

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 submajor (Fall 2011-Summer 2012)

**Effective Fall 2011-Summer 2012**

Outstanding students may elect an Honors major in Mathematics. The Honors Program is designed not only for students who expect to become mathematicians but also for students whose ultimate professional goal lies elsewhere (*e.g.,* in the humanities, law, ...).

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.

A. The basic courses consist of one from each of groups 1, 2, 3, and 4 or groups 1, 2, 5, and 6 below, completed with a grade of at least C-:

1. Linear Algebra: MATH 513

2. Analysis: MATH 451

3. Modern Algebra: MATH 512

4. Geometry/Topology: MATH 433, 490, or 590

5. Probability: MATH 525

6. 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 513.

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: www.math.lsa.umich.edu/undergrad/) no later than the second term of their sophomore year.