Pure Mathematics (M.S.)

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Curriculum for Pure Mathematics (M.S.)

 The masters programs in mathematical sciences are flexible enough to accommodate students with diversified background training. In consultation with the Graduate Committee, each student develops a course of study in mathematics areas most relevant to his or her professional and career objectives. Each student must take 15 credit hours of required courses, and complete an additional 18 hours either in the Thesis Option or the Non-Thesis Option.
 
Required Courses
All of these five courses:
 

 

Course No.
Course Name
Credits
25-500
Foundations of Mathematics
3 Hours
25-511
Introduction to Abstract Algebra
3 Hours
25-561
Real Analysis I
3 Hours
25-562
Real Analysis II
3 Hours
25-571
Complex Analysis
3 Hours

 

 
Select one of the following two courses:
           

 

Course No.
Course Name
Credits
25-541
Advanced Probability Theory
3 Hours
25-521
General Topology
3 Hours

 

Total:           18 Hours
 
 
THESIS OPTION: Pure Mathematics
 
  1.      Electives of 6 credit hours from the Pure Mathematics Courses:
           
Course No.
Course Name
Credits
25-525
 Logic
3 Hours
25-531
Number Theory
3 Hours
25-621
Introduction to Functional Analysis
3 Hours
25-504
Modern Geometry
3 Hours
25-611
Topics in Pure Mathematics
3 Hours

  2.      25-699        Thesis                                                                       6 Hours

  3.      Electives from Pure Mathematics and/or applied Mathematics and/or Other Graduate level courses with the approval of the student’s advisor.         3 Hours

 Total:          15 Hours

 
The students who select thesis option must defend their thesis before the Department Graduate Committee. A student must complete a six-hour research thesis.
 
 
NON-THESIS OPTION
 
The student who selects either one of the following non-thesis options must pass a written examination within two attempts.
 
This written examination is administered in February. A student must pass the written exam by the beginning of his/her 6th semester of study. A second and final attempt is permitted in the following August. In this examination a student must choose 2 topics from Algebra, Analysis, and Applied Mathematics. The exam is based on both 25-561 for Analysis, 25-511 for Algebra, and (or) 25-651 and 25-643 for Applied Mathematics. Another topic, such as Ordinary Differential Equations, Partial Differential Equations, or Statistics, may be substituted for one of the above by petition to the graduate committee based on two graduate level courses and supported by a faculty member.
 
Pure Mathematics
1.         Electives from the Pure Mathematics Courses                               9 Hours
 
2.         Electives from Pure Mathematics and/or Applied Mathematics and/or Graduate level courses with the approval of the student’s advisor.             6 Hours
                                                                                               
 Total:        15 Hours