# Mathematics

## Overview

Mathematics, encompassing several of the original liberal arts, is valued for its exquisite intellectual beauty and its timeless exploration of all things spatial, quantitative and patterned through the lens of rigorous abstraction. As a vibrant modern science, it possesses an unparalleled analytical power for describing, detailing and deriving insight into numerous physical, biological, technological, economic and societal aspects of the world we all live in. The Mathematics department is committed to engaging a diverse range of students in the active study and creative application of the principles, ideas, and methods that characterize mathematics and the mathematical sciences, and offering preparation toward a wide variety of careers and educational pursuits.

Upon graduation, some mathematics majors go on to graduate or professional school while others begin careers in teaching, business, industry, or government. The major can be structured to provide a solid foundation in the mathematical sciences-pure and applied mathematics, statistics, and operations research-and fields close to mathematics like computer science, actuarial science, and engineering. A major or minor in mathematics can also provide an excellent technical and theoretical complement to a major or minor in other fields.

## Major Requirements

### COURSEWORK

The minimum requirements for the major outlined below allow a student great flexibility in designing a course of study to meet their own intellectual and career goals.

#### Fundamental courses

Calculus 1 | Scientific Modeling and Differential Calculus | 4 units |

Calculus 2 | Scientific Modeling and Integral Calculus | 4 units |

MATH 210 | Discrete Mathematics | 4 units |

MATH 212 | Multivariable Calculus | 4 units |

MATH 214 | Linear Algebra | 4 units |

Any student who places out of a Calculus 1 or Calculus 2 class satisfies the corresponding requirement for the Math Major.

Students must receive a grade of C or above in each of MATH 210, MATH 212, and MATH 214 in order to graduate with a Mathematics major. If a student does not receive a grade of C or higher, the department chair will support a Petition for Special Consideration requesting to repeat the course. Only the most recent grade will count towards satisfying the 200-level requirement.

At least two of the required 200-level Mathematics courses (MATH 210, MATH 212 and MATH 214) must be taken at Occidental College except by approval of the chair. Exceptions must be filed by submitting a Petition for Special Consideration.

#### Advanced Courses

Students must have 24 units of Mathematics courses numbered 310 or above (excluding MATH 400).

#### Colloquium Requirement

MATH 300 | Junior Colloquium | 2 units |

MATH 400 | Senior Colloquium | 2 units |

#### Breadth requirement

Students must take one course from the following approved list of courses (students can petition the department to have a course not on the list count for the breadth requirement):

CHEM 355 | Bioinformatics | 2 units |

COMP 131 | Fundamentals of Computer Science | 4 units |

COMP 229 | Data Structures | 4 units |

COMP 347 | Machine Learning | 4 units |

ECON 272 | Applied Econometrics | 4 units |

ECON 305 | Game Theory | 4 units |

ECON 306 | Advanced Econometrics | 4 units |

PHIL 350 | Metalogic | 4 units |

PHYS 110 | Introductory Mechanics | 4 units |

PHYS 115 | General Physics I | 4 units |

PHYS 117 | Waves and Thermal Physics | 4 units |

PHYS 230 | Introductory Electricity and Magnetism | 4 units |

PHYS 240 | Modern Physics | 4 units |

PHYS 261 | Simulations in Physics | 4 units |

PHYS 310 | Mathematical Methods in Physics | 4 units |

PHYS 320 | Analytical Dynamics | 4 units |

PHYS 350 | Statistical Physics | 4 units |

PHYS 361 | Computational Physics | 4 units |

PHYS 367 | Mathematical Methods in Physics II | 4 units |

The Mathematics department has prepared guidelines for majors considering future study or careers in pure and applied mathematics, education, actuarial science, and computer science. These guidelines are available in the Students section on our website.

## Second-Stage Writing Requirement

Students majoring in Mathematics should familiarize themselves with this requirement at the time of declaring the major. The Second-Stage Writing Requirement is addressed in MATH 300. Students not taking MATH 300 (e.g., study abroad students) may petition to satisfy the writing requirement at a different time.## Comprehensive Requirement

The comprehensive requirement has two parts. The first part measures competence in the five fundamental courses and is handled during MATH 300: Junior Colloquium. During Math 300 students take exams in each of the fundamental areas; a passing score on each exam is a 12 (or higher) out of 20. The second part is fulfilled by completing 4 units of MATH 400: Senior Colloquium. To pass the comprehensive requirements with distinction a student must pass all five exams on her/his first try, have at least an 80% overall average on the exams, and receive at least an A- in one section of MATH 400. Further information is available from the department.

## College Honors

Students who wish to be considered for honors in Mathematics should complete at least the five fundamental courses in their first two years with a grade point average greater than 3.0, and pass all five Comprehensive Exams on their first attempt. Honors students must also complete three approved upper-division courses beyond those required for the major by the end of their senior year. Honors students must obtain signed approval from a mentor by the end of the junior year, and should enroll in MATH 499 for the fall semester of senior year. For Honors students, MATH 499 is substituted for MATH 400 in satisfying the major requirements. To receive honors, a student must write a paper as well as give a talk to the department on the topic of the paper. The paper, which typically will be 20 pages long, is graded by the mentor along with a second reader; the entire department evaluates the talk, which is typically at least 30 minutes long. The paper and talk must both be completed **no later than April 1** of the Honors candidate's senior year. Consult the Mathematics Department and the Honors Program for additional details.

## Minor Requirements

The minor in Mathematics requires at least 20 units of Mathematics courses numbered 150 or above, taken at Occidental or through college transfer credit. Students must take at least one 4-unit course at the 300 level. Students are required to take at least 8 of the 20 units at Occidental College.

### COURSEWORK

#### Students must select at least three courses from the list below:

MATH 150 | Statistical Data Analysis | 4 units |

MATH 210 | Discrete Mathematics | 4 units |

MATH 212 | Multivariable Calculus | 4 units |

MATH 214 | Linear Algebra | 4 units |

## Calculus Placement

Placement in calculus courses (MATH 108, MATH 110, MATH 114, or MATH 128) is determined based on previous mathematical experience, advising, and the results of the Calculus Placement Exam. The Calculus Placement Exam is administered online prior to the beginning of Fall Semester.

Students with qualifying scores on the Advanced Placement or IB Examination in Calculus are most often placed in calculus courses as follows:

Calculus AP Exam Score | Which Math course to take |

BC 4 or 5 | MATH 150, MATH 210, MATH 212, or MATH 214. |

AB 4 or 5 |
MATH 120 or MATH 128 (after consultation with Math Dept) |

AB or BC 3 or less |
Take Calculus Placement Exam |

IB Exam Score |
Which Math course to take* |

IB HL 6 or 7 | MATH 150, MATH 210, MATH 212, or MATH 214 |

IB HL 5 | MATH 114 or MATH 120 or MATH 128 |

IB HL 4 | MATH 110 or MATH 114 |

IB HL 3 or less | Take Calculus Placement Exam |

IB SL (any score) |
Take Calculus Placement Exam |

In addition to the calculus courses, MATH 105, MATH 150, MATH 160, MATH 210, MATH 212, MATH 214, COMP 131, and COMP 146 may be taken by first-year students meeting the prerequisites.

Students with transfer credits should confer with the Department for advice on placement in an appropriate mathematics course.

**Students with IB Exam scores will be required to contact the instructor of the course for prerequisite override in order to register.*

### Mathematics Courses

Calculus is a prerequisite for all mathematics courses with the exceptions of MATH 105 and most Computer Science courses. All students planning to take Calculus must take the online Calculus Placement Exam prior to the beginning of the Fall Semester unless they are exempt due to having received an Advanced Placement exam score. (See Calculus Placement above or contact the Mathematics Department for further details.) Prerequisites for any course may be waived with permission of the instructor.

## Transfer Credit Policies

The Mathematics Department may accept online courses in transfer, both as general elective credit and as credit toward the major or minor.

Students who earned a score of 4 or 5 on the AP Calculus AB examination will earn four units of credit and will be considered to have completed the equivalent of MATH 110 (Calculus 1). Students who earned a score of 4 or 5 on the AP Calculus BC examination will earn four units of credit and will be considered to have completed the equivalent of MATH 120 (Calculus 2). Students who earned a score of 6 or 7 on the (higher level) IB examination or a grade of A or B on the A-level examination will earn four units of credit and will be considered to have completed the equivalent of both MATH 110 (Calculus 1) and MATH 120 (Calculus 2).

Students matriculating as frosh must take at least two of the required 200-level Mathematics courses (MATH 210, MATH 212 and MATH 214) at Occidental College except by approval of the chair.

Students transferring from another institution may transfer the 200-level Mathematics sequence (MATH 210, MATH 212, MATH 214) with approval from the department chair.

A student may apply no more than eight units of 300-level credit in transfer toward the major, except by permission of the chair.

Students should reference the Transfer Credit section for more details.

## Courses

## Faculty

### Regular Faculty

**Jim L. Brown**, chair

*Professor*

B.S., Michigan State University; Ph.D. University of Michigan

**Treena Basu**

*Associate Professor*

B.S. Jogamaya Devi College: University of Calcutta; M.S. University of Texas-Pan American; M.S. Bengal Engineering and Science University; Ph.D. University of South Carolina

**Ron Buckmire**

*Associate Dean for Curricular Affairs*

*Professor*

B.Sc., M.Sc., Ph.D., Rensselaer Polytechnic Institute

**Tamás Lengyel**

*Professor*

Diploma, Ph.D., Eotvos University, Budapest

**Ramin Naimi**

*Professor*

B.S., University of California, Los Angeles; Ph.D., California Institute of Technology

**Timothy Rainone**

*Assistant Professor, Mathematics*

B.S., M.S., McGill University; Ph.D., Texas A&M University

**Eric Sundberg**

*Associate Professor*

A.B., Occidental College; Ph.D., Rutgers University

**Nalsey Tinberg**

*Professor*

B.A., University of California, Los Angeles; M.S., Ph.D., University of Warwick

### On Special Appointment

**Nishu Lal**

* Non-Tenure Track Assistant Professor*

B.S., M.S., University of California, Irvine; Ph.D., University of California, Riverside

**Don Lawrence**

*Non-Tenure Track Professor*

B.A., Pomona College; M.A., Ph.D., University of California, Santa Barbara

**Jeffrey Miller**

*Non-Tenure Track Assistant Professor*

B.S., University of California, Davis; M.A., Ph.D., University of California, Santa Barbara

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