### Overview

To complete your MS in Mathematics degree, you have a choice of writing a master's degree thesis or passing two comprehensive exams. Most students choose the comprehensive exam option because

- The prerequisite is lower. To do a thesis, you need a GPA of 3.5 or better. To attempt the comprehensive exams, a GPA of 3.0 suffices.
- It's faster. Writing a thesis can take several terms. Comprehensive exams can be passed in one term.
- It's cheaper. If you don't pass the comprehensive exams on the first attempt, subsequent attempts cost $10 each - assuming that you are not taking any courses.

Even so, if you have ambitions to do a PhD, or are just enthusiastic about mathematical research, you should consider doing a thesis. When in doubt, seek advice from the graduate advisor.

### Comprehensive Exam Schedule

#### Fall 2020 Comprehensive Exam Committees and Schedule

The Fall 2020 Comprehensive Exam Schedule will be posted here in September.

Exams usually take place on Fridays, 9am-12pm in ST F213. (Unless the pandemic gets in the way...)

**Numerical Analysis****Topology****Algebra****Complex Analysis****Probability****Linear Analysis**

The star indicates the committee chair.

### Comprehensive Exam Policy

The following discussion elaborates the catalog description of the MS in Mathematics degree program and the university’s comprehensive exam policies.

**Semester/Quarter:** Except for students choosing to do a thesis, candidates for the MS degree in Mathematics must take comprehensive examinations. Students who joined the Math MS degree program before Fall 2016 may choose to follow the rules of the quarter system catalog or the semester system catalog. Students who joined the Math MS degree program in Fall 2016 or later must follow the rules of the semester system catalog.

**Semester catalog students:**

**Option 1 (General Math):** Students in Option 1 must pass two exams:

One of either Complex Analysis or Linear Analysis

One of either Abstract Algebra or Topology**Option 2 (Applied Mathematics): **Students in Option 2 must pass two exams:

One of either Complex Analysis or Linear Analysis

One of either Numerical Analysis or Probability

**Quarter catalog students: **

**Option 1 (General Math):** Students in Option 1 must pass two of the following three exams:

Topology, Abstract Algebra, Complex Analysis**Option 2 (Applied Math)**: Students in Option 2 must pass two of the following three exams:

Applied Linear Analysis, Complex Analysis, Numerical Analysis.

**Prerequisites:** Students taking comprehensive exams must be advanced to candidacy and have a current GPA of at least 3.0 on their program. A student taking comprehensive exams can have at most one course remaining on his/her degree program, not counting those being taken in the same semester as the comprehensive exam.

**Registration:** Students must register in Math 5960 in any semester they intend to take comprehensive examinations. This course is restricted and authorization must be obtained from the graduate advisor prior to registering. Registering in Math 5960 is otherwise subject to the same deadlines and rules as for other classes. Students may attempt one, two or more comprehensive exams in any semester.

**Re-examination:** A student, who started the Master’s program in Fall 2016 or after, may attempt any number of exams in each of, at most, 2 semesters. (In other words, a student may register for MATH 5960 a maximum of 2 times.) A student who started the Master’s program prior to Fall 2016 may attempt any number of exams in each of, at most, 3 semesters.

**No Shows:** Any semester in which a student registers in Math 5960 (and does not withdraw within the usual deadline or by the exam date) counts as an attempt at the comprehensive exams - even if the student does not show up for the exams.

**Special cases: **Matriculated students who are not otherwise taking classes must pay the Comprehensive Exam Fee (currently $10) at the cashier’s office before registering for Math 5960. These students do not need to pay any other fees since Math 5960 is a zero unit class.

Non-matriculated students (students who haven’t taken courses for a prolonged period and cannot enroll in courses) must apply for readmission to the university. This will require meeting the application deadline and paying the application fee. After being readmitted, such students are matriculated and register for Math 5960 as above.

**Frequency:** Comprehensive exams are given in all areas, assuming demand, each Fall and Spring semester. The exams are near the end of the semester. The exact time and date of each exam is set and posted by the graduate advisor.

**Exam Committees:** The exam committee for each exam is set and posted by the graduate advisor. Each exam committee has at least two, and normally three, members.

**Content:** The graduate advisor and Graduate Studies Committee maintain and review comprehensive exam syllabi. Each provides a list of topics for the given area and a list of reference texts. These syllabi, as well as copies of recent exams, are available on the department web site.

**Grading:** Each exam is graded A, B, C, D or F by the committee which prepared it. Student names do not appear on examination papers; code numbers are used instead. The committees report their grades by code number to the graduate advisor, who then advises the students of the results.

**Passing: **A student has passed the comprehensive exams if he/she achieves a B average in two exams (complying with the subject area restrictions for the option) with at least C in each. The semester(s), and the order, in which the exams are taken does not matter.

**Comprehensive Exams vs. Thesis:** Once a student has attempted a comprehensive exam, it is no longer possible to switch to the thesis option.

**Recommended Courses:** See below for courses that are recommended as preparation for each of the comprehensive exams. Exam syllabi can be found at the Math Department website.

- Probability: Math 4740 and Math 5740
- Applied Linear Analysis: Math 5021 and Math 5022
- Complex Analysis: Math 4680 and Math 5680
- Algebra: Math 5401 and Math 5402
- Numerical Analysis: Math 5700 and Math 5710
- Topology: Math 4690 and Math 5690

**Records:** The graduate advisor maintains copies of all comprehensive exams in accordance with the record retention policy of Cal State LA.

Revised: June 2018

### Comprehensive Exam Archive

**Comprehensive Exam Archive**

Most comprehensive exams since 2000 are available below. Some are missing because not all exams were offered in all terms.

**Algebra**

The Spring 2008 and later exams have solutions. The occasional references are to

- Fraleigh,
*A First Course in Abstract Algebra,*7th ed. - Dummit and Foote,
*Abstract Algebra,*3rd ed.

There is also a collection of miscellaneous solutions to older exam questions.

For some reason there was a Winter Quarter 2002 exam: Winter 02

**Topology**

Spring 00 | Fall 00 |

Spring 01 | Fall 01 |

Spring 02 | Fall 02 |

Spring 03 | Fall 03 |

Spring 04 | Fall 04 |

Spring 05 | Fall 05 |

Spring 06 | Fall 06 |

Spring 07 | Fall 07 |

Spring 08 | Fall 08 |

Spring 09 | Fall 09 |

Spring 10 | Fall 10 |

Spring 11 | Fall 11 |

Spring 12 | Fall 12 |

Spring 13 | Fall 13 |

Spring 14 | Fall 14 |

Spring 15 | Fall 15 |

Spring 16 | Fall 16 |

Spring 17 | Fall 17 |

Spring 18 | Fall 18 |

Spring 19 |

The exam offered in Fall 2006 is labeled as Spring 2006 because it was intended to be offered in Spring 2006.

The exam offered in Spring 2011 is labeled as Fall 2010 because it was intended to be offered in Fall 2010.

**Complex Analysis**

For some reason there was a Winter Quarter 2002 exam: Winter 02

**Linear Analysis**

Spring 00 | Fall 00 |

Spring 01 | Fall 01 |

Spring 02 | Fall 02 |

Spring 03 | Fall 03 |

Spring 04 | Fall 04 |

Spring 05 | Fall 05 |

Spring 06 | Fall 06 |

Spring 07 | Fall 07 |

Spring 08 | Fall 08 |

Spring 09 | Fall 09 |

Spring 10 | Fall 10 |

Spring 11 | Fall 11 |

Spring 12 | Fall 12 |

Spring 13 | Fall 13 |

Spring 14 | Fall 14 |

Spring 15 | Fall 15 |

Spring 16 | Fall 16 |

Spring 17 | Fall 17 |

Spring 18 | Fall 18 |

Spring 19 | Fall 19 |

Spring 20 |

For some reason there was a Winter Quarter 2002 exam: Winter 02

**Numerical Analysis**

Spring 10 | Fall 10 |

Spring 11 | Fall 11 |

Spring 12 | Fall 12 |

Spring 13 | Fall 13 |

Spring 14 | Fall 14 |

Spring 15 | Fall 15 |

Spring 16 | Fall 16 |

Spring 17 | Fall 17 |

Spring 18 | Fall 18 |

Spring 19 | |

Spring 20 |

**Probability**

Spring 17 | Fall 17 |

Spring 18 | Fall 18 |

Comprehensive exams in probablility were not offered until Spring 2017.