# Master's Degree in Mathematics

### University Catalog Information

### Advisement

**Math Graduate Advisor:** Tony Shaheen**Office:** ST F317**Phone:** (323) 343-2159**Email:** [email protected] (over the summer, email both Shaheen and the department chair ([email protected]) with your questions)

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:

### Admission

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, Tony Shaheen, or the Mathematics Department at (323) 343-2150.

**Application Deadlines:**

- Spring 2023 application deadline is November 1, 2022; but you are encouraged to apply earlier because the department will make an admission decision as soon as your application is complete.

- Fall 2023 application deadline is April 15, 2023.

**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 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.

### Program Learning Outcomes

Graduating students will:

- Have a broad exposure to advanced mathematics through electives chosen from a wide range of topics including abstract algebra, advanced calculus, geometry, differential equations, linear algebra, probability, number theory, and topology.
- Understand and devise proofs of mathematical theorems. This includes understanding the role of definitions, axioms, logic, and particular proof techniques such as proof by induction, proof by contradiction, etc.
- Be able to write a coherent, clear article on a mathematical theme, and to present this orally.
- Be able to search the mathematical literature to research a topic of interest.
- Understand and be able to apply basic results of complex analysis including: the relationship between complex analytic functions and harmonic functions, conformal mapping, and applications to Dirichlet problems; Cauchy’s integral formulas and their consequences including the fundamental theorem of algebra; series expansions, classification of singularities, and the application of residue calculus to definite integrals and sums.

## Comprehensive Exams

### Exam Schedule

#### Spring 2022 Comprehensive Exam Schedule

- Saturday April 30th, 10am - 1pm.... Complex analysis, Analysis (new)
- Saturday May 7, 10am - 1pm.... Algebra (old), Algebra (new)
- Friday May 13, 3pm - 6pm....Numerical Analysis

### Syllabi and Sample Exams

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

#### Algebra Comprehensive Exam

Spring 2021 | |

Fall 2021 | Spring 2022 |

**Math 4570 practice material:**

**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

**Math 4650 practice material:**

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

**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.

### Comprehensive Exam Policy

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

### Thesis Policy

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

### LaTeX Thesis Template

You can download the Math Department LaTeX thesis template, edit as needed, then typeset and print out your completed thesis. The template takes care of the margins, pagination, the formats of the title page, copyright page, references, appendices, etc. Comments in the LaTeX files provide information on how to use the templates. Portable Document File (.pdf) versions of these files are also provided in case they are useful.

If you don't have LaTeX or don't know how to use LaTeX you might start at the Consolidated TeX Archive Network or at The LaTeX Project.

**Abstract**

You can use the following templates to make an prospectus/abstract for your thesis to distribute to your committee.

▪ Abstract template in LaTeX form

▪ Abstract template in .pdf form

**Thesis Template**

In theory, you can take this LaTeX thesis template, insert your own title, abstract, chapters, graphics, committee member names, etc. and then not have to worry about the margins, pagination, the formats of the title page, copyright page, references, appendices, etc.

To typeset the template, you will need the cycloid graphic. This graphic serves only to demonstrate how such graphics can be included in a LaTeX document. If you don't care about that, you don't need the graphics file, and the first change you might make to the thesis template is to remove all the \includegraphics commands. This graphics file needs to be put somewhere your LaTeX application can find it - for example, it could be placed in the same folder as the thesis template itself.

▪ Thesis template in LaTeX form

▪ Thesis template in .pdf form

▪ Cycloid graphic in .pdf form

**Submission**

Details on the submission process, and submission deadlines are found in the University Thesis Guidelines. You upload your completed thesis in .pdf format (without signatures) to ProQuest. You must also obtain the signatures of all committee members and the department chair on the GS-13 Form. Submit the signed GS-13 Form with original ink signatures to your Thesis/Dissertation Reviewer. The department graduate advisor would also like a signed copy of this form.

## TA Resources

### Overview

Teaching Associates are graduate students who teach mathematics courses. Before taking on this responsibility, TAs are expected to pass Math 4950 (College Instruction I). 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 $1000 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.

### How to apply

**Are you ready to be a Teaching Associate?:** Before applying, make sure you qualify, or will qualify, to be a TA. Click on TA Policies below.

**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, Borislava Gutarts.

- 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.

### TA Policies

**TAs should be making satisfactory progress towards the MS degree.**

- TAs must be classified math graduate students: MATH MS G2 on GET. In other words, conditionally admitted students may not be TAs.

- TAs must maintain a 3.0 GPA on their MS degree programs.

- No TA may teach more than a total of 30 units while in the MS degree program.

- TAs must be registered in some Cal State LA class in any semester they teach.

- Students who do not get B or better on at least one comprehensive exam on the first attempt, and students who have made a second attempt at the comprehensive exams, will not be TAs in subsequent terms. After completing the course work of the degree, TAs should attempt the comprehensive exams in any semester they are offered.

**Teaching Record:**Continued TA appointments are contingent on a satisfactory teaching record**(**as evidenced by visitation reports, student evaluations and other feedback).

**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.

**MATH 4950 for prospective TAs:**Students are required to pass MATH 4950 (2 units) before becoming a TA. The Chair or Associate Chair may allow an exception to this rule for students who already have experience as a lead classroom teacher (not just a tutor or lab instructor). MATH 4950 can be taken as an undergraduate. It does not count towards the MS (or any other) degree. The Chair or Associate Chair may allow an exception to this rule for TAs if registration in MATH 4950 would result in additional tuition fees. TAs who do not register in MATH 4950 because of such an exception are still expected to participate in and successfully complete all requirements of MATH 4950. We currently plan to offer MATH 4950 every Fall.

**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.

**Exceptions**: The Chair or Associate Chair may waive any of the above rules (except 1a and 1d) in special circumstances.

**NSS/Cal State LA/CSU rules:**All college, university, and CSU rules also apply.

August 2018