### Resources

**Math Graduate Advisor:** Vladimir Akis**Office:** E&T A311 and ST F311**Phone:**(323) 343-6694 and (323) 343-5255**Email:** vakis@calstatela.edu

**Office Hours: **Dr. Akis is off duty for the summer. Questions can be directed to the department chair.

**Catalog description of the Math MS degree**

**NSS College Graduate Programs Website **- with NSS Graduate Studies Handbook and lots of forms

### Admission

We hope that this will answer some of your immediate questions about admission into the MS Program in Mathematics at Cal State LA. For any remaining questions, feel free to contact the Mathematics Department by calling (323) 343-2150.

**How to apply**

Step 1: Start at Cal State LA graduate admissions for information on the deadlines and application process. Your actual application is made through Cal State Apply. This CSU website that has information about degree programs at all CSU campuses. As part of this Cal State LA application process you will have to send official transcripts from your school(s) (other than Cal State LA) to the Admissions Department.

Step 2: In addition to the Cal State Apply application and materials, the Mathematics Department requires that you submit a department application form and unofficial transcripts (other than from Cal State LA) directly to the Mathematics Department: __DOC__ or __PDF__.

**Admission process**

The minimum GPA requirement for admission to the Department 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.

For students without an undergraduate degree in Mathematics, we require at the minimum that you have taken at least the following courses, or their equivalents, to be admitted 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) -- or a similar introduction to proofs course or proof based upper-division mathematics course.

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.

See the course catalog for more information on these courses.

In order to attain classified graduate status, students with a Mathematics degree or an equivalent degree must have a minimum B or better grade in each of MATH 4650 – Analysis I and MATH 4550 – Modern Algebra I (or equivalent courses at other institutions) for Option 1 (General Mathematics); or a minimum B or better grade in each of MATH 4650 – Analysis I and MATH 4570 – Advanced Linear Algebra (or equivalent courses at other institutions) for Option 2 (Applied Mathematics).

If you have an undergraduate degree in mathematics and you meet the grade requirements given in the paragraphs above, then the graduate advisor will map out a course program with you and classify you. If you have an undergraduate degree in mathematics and do not meet the requirements given in the above paragraphs, then the graduate advisor will map out with you how to satisfy these requirements so that you can become classified. In this second case, you may have to take some preparatory classes before becoming classified.

If your background is not “substantially equivalent” to a BA/BS in mathematics, you will be required to take prerequisite undergraduate mathematics courses before becoming classified. The number of prerequisite courses will depend on your undergraduate degree. The prerequisite courses will include, if not already completed, MATH 4650 (Analysis I) and MATH 4550 (Modern Algebra I) for Option 1, or MATH 4650 (Analysis I) and MATH 4570 (Advanced Linear Algebra) for Option 2, with grade requirements as described above. The prerequisite courses may take up to a year to complete depending on how many upper-division mathematics courses you took during your undergraduate education. Note that the prerequisite courses will not count towards your master’s degree; they will be required prerequisite courses to prepare you for the program. The graduate advisor will determine these prerequisite courses in an initial meeting with the student.

**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. 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 9 semester unit limit.

**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 on being a TA, go to the TA Resources page

### Comprehensive Exams

### Thesis Policies

If you are interested in writing a thesis (or in the process of writing a thesis), you should be aware of the Math Department's policies and guidelines below, as well as those of the college and university:

#### Math Department 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-12 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.

**Abstract:** One semester before the defense, the student, in consultation with the thesis supervisor, should choose a title for the thesis and write an abstract. The abstract and a GS-12 form are submitted to the College Associate Dean for approval.

Revised 2016

### 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**

The GS-12 form and a thesis abstract need to be sent to the Associate Dean of the college at least one semester before the thesis defense. The abstract accompanying the GS-12 does not actually need to be in the same, precisely specified, form as the abstract in the thesis, but why not make it the same.

▪ 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**

Review details on the submission process, and submission deadlines. 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.

Revised: June 2018

### Learning Outcomes

In the Mathematics MS program students choose one of two options: Option 1 (General Mathematics) and Option 2 (Applied Mathematics). The learning outcomes are somewhat different for each as seen below.

#### Graduating students in both options 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.

#### Graduating students in Option 1 (General Math) will:

- Have a broad understanding at the graduate level of the content of the required courses of the option. This includes the theory of groups, rings and fields, topology, complex analysis, and real or functional analysis.
- Understand the basic theories of groups, rings and fields, including the structure of finite groups, polynomial rings and Galois theory.
- Understand how the main topological concepts (connectedness, compactness, products and separation properties) are introduced and used in abstract spaces where the topological structure is not derived from an underlying metric.
- Understand basic set theory including axiom of choice, basic topological properties of the real line; properties of real functions, sequences of real functions and various notions of convergence such as pointwise and uniform convergence.
- Understand the notions of outer-measure, measurability of sets, non-measurable sets, Riemann and Lebesgue integrability, convergence in measure, differentiation of functions, functions of bounded variation, absolutely continuous functions, basic properties of L^p spaces.
- Have an understanding of metric spaces, sequences, completeness; normed linear spaces, Banach spaces, classical sequence spaces, linear functionals and linear operators and their representations; the Hahn-Banach, Banach-Steinhaus and Open Mapping theorems; innerproduct and Hilbert spaces, orthonormal sets and sequences, representation of linear functionals on Hilbert spaces, Fourier series.

#### Graduating students in Option 2 (Applied Math) will:

- Have a broad understanding at the graduate level of the content of the required courses of the option. This includes numerical analysis, linear analysis, mathematical modeling and complex analysis.
- Be able to use a variety of mathematical tools (differential equations, linear algebra, etc) to formulate a mathematical model of real world problems. Understand the balance between the complexity of a model and its mathematical tractability. Understand the iterative process of modeling and the necessity to test a model against data.
- Be able to apply numerical methods to solve problems, such as large systems of linear equations, eigenvalue/eigenvector problems, and understand the theoretical underpinnings of these methods.
- Be able to solve partial differential equations numerically and be able to analyze the stability and convergence of these approximate solutions. This includes the understanding of the fundamental differences among parabolic, elliptic and hyperbolic partial differential equations, the Max/Min principle for certain elliptic partial differential equations and the method of characters for and second order hyperbolic partial differential equations.
- Understand metrics, norms, and inner products on important spaces of functions, including Banach spaces and Hilbert spaces and be able to use important applications including Fourier series and solutions of integral equations by contraction. They will be familiar with basic properties of linear operators, especially on Hilbert spaces, invertiblity and spectrum, and be able to apply these to solution of integral equations and differential equations.