Comprehensive Exams

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.   This is 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

Info for catalogs before 2020-2021

This tab is for students who are on a program from a year before the 2020-2021 school year.   You will know if you are on one of these catalogs if you started in our program before Fall 2020 and you have an option such as General Mathematics or Applied Mathematics.

Comprehensive Exam Policies:

    For students whose catalog is before 2020-2021 see here for the department comprehensive exam policies:

    In addition to the above policies, the department will allow the following two substitutions for students on the older catalogs before Fall 2020.   (1) You may substitute the newer Algebra comp exam for the older Algebra comp exam, and/or (2) you may substitute the newer Analysis comp exam for the older Linear Analysis comp exam.   To do either of these substitutions, you must tell the graduate advisor when you sign up for Math 5960 to take the exams.

    Syllabi and past exams:

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

      Algebra

      Syllabus

      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

      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 Fall 20
      Spring 21 Fall 21

       

      Topology

      Syllabus

      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  
      Spring 21 Fall 21

      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

      Syllabus

      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
      Fall 20

      Note: #6 should have been z^4+4z-1
      Spring 21 Fall 21

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

      Linear Analysis

      Syllabus

      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  
      Spring 21  

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

      Numerical Analysis

      Syllabus

      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 Fall 20
      Spring 21  

       

      Probability

       

      Syllabus

      Spring 17 Fall 17
      Spring 18 Fall 18
        Fall 20
      Spring 21  

      Comprehensive exams in probablility were not offered until Spring 2017.

      Info for catalogs after 2020-2021

      This tab is for students who are on the 2020-2021 catalog year or after.    You will know if you are on this catalog if you started the graduate program in Fall 2020 or afterwards.




      THIS IS AN OLD WEBPAGE.   GO HERE FOR THE NEW WEBPAGE:

      https://www.calstatela.edu/nss/math/masters-degree-mathematics
       



      Comprehensive Exam Policies:

        For students whose catalog is 2020-2021 and after see here for the department comprehensive exam policies:

        Syllabi and sample exams:

        Algebra

        Syllabus

        Sample test

         Spring 21   Fall 21

        4570 practice material:

        • Shaheen website (lecture notes, homework and solutions)
        • Liu final

        5401 more practice:

        • 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

        Syllabus 

        Sample test 

         Spring 21     Fall 21

        4650 practice material:

        5021 more 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 5021 class.