**Math Graduate Advisor:** Dr. Michael Krebs**Office:** Simpson Tower 317**Email:** [email protected]

Our current catalog (we made major program changes that went into effect in Fall 2020):

2021-2022 Catalog description of the Math MS degree

2021-2022 Catalog descriptions of all MATH courses

Roadmap for catalog

For students who are on previous catalogs:

2020-2021 Catalog description

2019-2020 Catalog description

2018-2019 Catalog description

Graduate Resource Center - Resources from the Graduate Studies Department

Graduate Student Handbook (2018-2019)

NSS College Graduate Programs Website** **- Resources from the Graduate Studies Department (including lots of forms)

Click on the links on the left for information on the comprehensive exams and thesis options for completing your MS degree.

Thinking about getting a PhD in Math? Check out these links:

General information about admission to graduate studies at Cal State LA can be found at the Office of Graduate Studies. The following provides specific information about admission into the MS in Mathematics degree program. For any remaining questions, feel free to contact the Graduate Advisor, or the Mathematics Department at (323) 343-2150.

**Application Deadlines:**

__Please see this website for admissions deadlines.__

You are encouraged to apply earlier because the department will start to make an admission decision as soon as your application is complete.

**How to apply:**

- You can apply for fall or spring semester admission.
- To apply, go to Cal State LA graduate admissions, which will link you to the application process through Cal State Apply. (See the important note below before you apply.)
__Important:__When you apply to the school through Cal State Apply, they will want certain information from you including that you send official transcripts to the admissions office. In addition to this, the Math Department requires you to upload unofficial (or official) transcripts at the time of application in Cal State Apply. These go directly to the Math Department. Please make sure to do this step on Cal State Apply so that we can process your application.

**Admission process**

The minimum GPA requirement for admission to the MS in Mathematics degree program is 2.75 in upper division courses in the applicant's major. The admissions committee especially looks at all the applicant's grades in mathematics courses. Students with a mathematics degree who have a GPA of between 2.5 and 2.74 might be admitted but, if admitted, may be required to take preparatory upper-division mathematics courses (to be specified by the graduate advisor) to strengthen their preparation. The GPA earned in these courses must be 3.0 or higher.

We require at the minimum that you have completed at least the following courses to apply for admission into the program:

- MATH 2110 (Calculus I)
- MATH 2120 (Calculus II)
- MATH 2130 (Calculus III)
- MATH 2150 (Differential Equations)
- MATH 2550 (Introduction to Linear Algebra)
- MATH 2450 (Foundations of Mathematics I: Discrete Mathematics)
- MATH 3450 (Foundations of Mathematics II: Mathematical Reasoning) -- or a similar introduction to proofs course or proof based upper-division mathematics course.

Most of the above courses are offered at community colleges in the Los Angeles area. For example, MATH 2450 above is comparable to MATH 10 (Discrete Structures) at Santa Monica College or MATH 272 (Methods of Discrete Mathematics) at ELAC. Some schools have Math 2450 and Math 3450 bundled as one course.

In addition to the above, to be admitted non-conditionally into the program we require the following three courses with a B or better grade in each:

- Math 4650 (Analysis I)
- Math 4550 (Modern Algebra I)
- Math 4570 (Advanced Linear Algebra)

You may still apply to the program if you have not completed Math 4650, 4550, 4570 with a B or better. However, if you are admitted then you will be admitted conditionally. You will then have to take the missing courses while you are a student here. These three courses do not count towards the masters degree units. Usually you are given two semesters to complete these prerequisite classes. Depending on your case you may be able to take other courses at the same time that do count towards the masters degree. This will be determined by the graduate advisor upon admission. Once you have completed these prerequisite courses you will no longer be conditional and you will become what is called classified (ie non-conditional).

**Transfer credit**

Post-undergraduate courses taken elsewhere can count toward your MS degree. Such courses count as transfer credit and are limited to a total of 9 semester units, and no more than 6 graduate level units. You can consult with the graduate advisor to see if courses you have taken, or plan to take, can be transferred to your MS degree.

If, for example, you want to get started on your degree before you are admitted to the university, you can take courses through Open University. Courses taken through Open University can be transferred to your MS degree but are considered transfer credit and are subject to the above limits.

**Financial aid**

All university financial aid programs are administered by the Center for Student Financial Aid & Scholarships. The Mathematics Department is not involved.

**Teaching associates**

Many of our graduate students work as Teaching Associates in the department. For detailed information, scroll below to TA RESOURCES.

Graduating students will:

- Demonstrate understanding and devise proofs of mathematical theorems. This includes the roles of definitions, axioms, logic, and particular proof techniques such as proof by induction, proof by contradiction, etc.
- Demonstrate advanced understanding of linear analysis, group theory and complex analysis together with two other fields chosen from topology, numerical linear algebra, probability and real analysis.
- Demonstrate a broad understanding of mathematics through electives chosen from a range of topics including abstract algebra, real analysis, complex analysis, logic, geometry, differential equations, probability, number theory, topology, graph theory, numerical analysis, and applied mathematics.

## Comprehensive Exams

#### Fall 2024 Comprehensive Exam Schedule

- Saturday, Nov. 16, 10am - 1pm

Algebra

- Saturday, Nov. 23, 10am - 1pm

Analysis

Complex Analysis

An archive of old comprehensive exams for students who started their MS before Fall 2020: Old Comprehensive Exams

#### Algebra Comprehensive Exam

Here is the** syllabus.**

Here is a** sample test**

__Here are all the previous exams:__

Spring 2021 | |

Fall 2021 | Spring 2022 |

Fall 2022 test and solutions |
Spring 2023 Test and solutions |

Fall 2023 Test and solutions |
Spring 2024 Test and solutions |

**Here is some extra Math 4570 practice material:**

**Here is some extra Math 5401 practice material:**

You can also look at the older Algebra comps from the pre-Fall 2020 period and do problems in the group theory section of those comps.

#### Analysis Comprehensive Exam

Here is the** syllabus.**

Here is a** sample test. **

Here are the previous exams:

Spring 2021 | |

Fall 2021 | Spring 2022 |

Fall 2022 test and solutions |
Spring 2023 test and solutions |

Fall 2023 test and solutions |
Spring 2024 test and solutions |

**Here is some extra Math 4650 practice material:**

- Shaheen website (lecture notes, homework and solutions)
- Krebs 4650 quizes and tests
- Akis 4650 final
- Mijares quizes and midterms

**Here is some extra Math 5021 practice material:**

You can also look at the older Linear Analysis comps from the pre-Fall 2020 period and do problems that correspond to the Math 5021 class.

The following discussion elaborates the catalog description of the MS in Mathematics degree program and the university’s comprehensive exam policies. Except for students choosing to do a thesis, candidates for the MS degree in Mathematics must pass two comprehensive exams:

- Algebra (Group Theory and Linear Algebra, i.e. the equivalent of Math 4570 and Math 5401)
- Analysis (Linear Analysis and Analysis, i.e. the equivalent of Math 4650 and Math 5021)

**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 courses 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 or both comprehensive exams in any semester.

**Re-examination:** A student may attempt any number of exams in each of, at most, 3 semesters. (In other words, a student may register for MATH 5960 a maximum of 3 times and take any number of exams each time they register.)

**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 both 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 both exams 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.

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

Last edited 3/4/22

## Master's Thesis

Students completing a master’s thesis will produce a written work (thesis) and give an oral presentation (defense) on a topic chosen with consultation of a thesis supervisor.

**Time:** A thesis typically takes at least two or three semesters of solid work.

**Length:** A thesis is typically 50 to 100 pages.

**Requirements:** A student is required to have a GPA of 3.5 or better on the MS degree program, EXCLUDING DIRECTED STUDY COURSES, and have completed at least 3 5000-level courses from his/her MS degree program when a faculty member agrees to be the thesis supervisor. The GPA must also be 3.5 or more when submitting the GS-10 and registering in Math 5990 (Thesis).

**Content and Presentation:** The thesis should contain an original research result or consist of an expository discussion of a topic, organized in an original way. If the thesis contains an original research result, it should also discuss the broad context in which the result occurs (e.g., other related results or conjectures in the field, historical development, etc.). The thesis must contain some content of theoretical significance, e.g., some theorems and their proofs. The writing should be grammatically correct and structurally sound, i.e., the presentation of the results and their context should follow a logical order. The introduction to the thesis should be readable by a person who has some mathematical knowledge, but is not necessarily an expert in the subject.

**Research:** The thesis must draw from multiple sources in the mathematical literature.

**Oral Defense:** The oral defense of a thesis is a public event. An announcement of an upcoming thesis defense should be posted in the Math Department at least a week in advance. A student’s defense presentation will typically last one hour, followed by questions from the thesis committee and other members of the audience.

**Prospectus and Committee:** At least one to two semesters before the planned thesis defense, the student, in consultation with the proposed thesis supervisor, will write a 1-2 page thesis prospectus, including a tentative title and a research plan. The prospectus will then be used to recruit a thesis committee, normally consisting of the thesis supervisor and two other math department faculty members able to evaluate the thesis and oral defense. Faculty members from other departments can serve on a thesis committee that is interdisciplinary in nature. At least two of the thesis committee members must be from the math department (typically the advisor and one other faculty member).

Revised: April 2021

**Thesis Template**

Below are the Math Department LaTex thesis template links. Insert your own title, abstract, chapters, graphics, committee member names, etc. The template takes care of the margins, pagination, formating, references, appedices, etc. To compile/typeset the thesis template you will also need the cycloid graphic pdf file below. This graphic is there to illustrate how to use graphics in your own file. You should put the pdf file in the same folder that the tex file is in so the latex program can find it. Try downloading the files and compiling them as is. The resulting pdf will teach you many of the things you will need to know so you can write your thesis.

▪ Thesis template in LaTeX form

▪ Thesis template in .pdf form

▪ Cycloid graphic in .pdf form

Here are some latex programs and websites that you can use:

- MikTeX works on PC, Mac, and Linux.
- MacTeX is for Macs.
- The LaTeX Project is a general LaTeX information website.

**Submission**

Details on the submission process, deadlines, and general information about writing a thesis is at the Office of Graduate Studies website.

## TA Resources

Teaching Associates are graduate students who teach mathematics courses. In the first semester of teaching, TAs usually get only one class. TAs typically teach GE math courses (Math 1000, 1090) or the associated workshops. With more experience, some teach precalculus and other courses.

TAs are currently paid just over $1100 per unit of teaching. The Math Department Chair and Associate Chair are responsible for hiring and scheduling TAs.

Even graduate students who don't need the money should consider that teaching experience obtained as a TA is important for their futures. This is obvious for students who want to teach in community colleges after graduating, but is also true for students who want to go into a PhD program.

**When to apply:** The earlier the better. Teaching assignments are made on a continuing basis starting six months before the start of the semester.

**What to submit:** For initial employment as a TA you need to provide the following to the Math Department.

- Cal State LA Employment Application
- Three letters of recommendation. Should be on official letterhead. Original signature needed. Not more than two years old.
- Official transcript from your highest degree (if not obtained from Cal State LA).
- Your curriculum vitae (CV) (or resume). Use Google to find examples and suggestions.

For continuing employment, it suffices to email your availability and course preferences as below.

**Teaching preferences/availability: **Email the days and times you are available to teach, and course preferences to the Associate Chair, Gary Brookfield.

- New TAs usually teach GE courses and/or workshops for, at most, four units.
- Experienced TAs are generally limited to 7.5 units of teaching.
- Wider availability increases the probability of getting an assignment and/or getting more units.
- You should update this information each semester.

**Appointments**Appointments are made based on evidence of, or potential for, academic achievement and success as a Teaching Associate.**Number of units:**Any TA will have a maximum of 7.5 units of teaching in any semester. TAs will receive very limited teaching assignments the first time they teach here, so that we can first evaluate teaching performance before assigning additional classes.**Office hours:**TAs who teach six units or fewer will schedule a minimum of one office hour per week. TAs who teach more than six units will schedule a minimum of two office hours per week.**Class visits:**Faculty will visit each TA’s classes to evaluate the performance and provide feedback. Such visits occur in each of the first two semesters of teaching; in subsequent terms, if the teaching performance was low; and otherwise, once per academic year**NSS/Cal State LA/CSU rules:**All college, university, and CSU rules also apply.

April 2023