Ph.D. degree in Mathematical Sciences: Core Group A (Mathematics)
Pure Mathematics or Applied Mathematics Focus
This fouryear program assumes a strong entering background in mathematics, including a oneyear sequence in probability and statistics. If your entering background is average, add one or two years at the outset for MATH 520, 521, 530, 531, 534, 542 and 550, and STAT 570 and 572 as necessary.
You should register for two hours of MATH 792 each fall and spring semester before the working phase of your Applications Involvement Component (AIC).
Semester 
Courses 
First semester, year one 
 Math 620 Algebraic Structures I
 Math 630 Real Analysis I
 Math 636 Ordinary Differential Equations I*

Second semester, year one 
 Math 621 Algebraic Structures II
 Math 632 Complex Analysis
 Math 650 Topology*

Summer, year one 
 Foreign language course, research tool, other elective or written Ph.D. qualifying examination

First semester, year two 
 Math 631 Real Analysis II (Functional analysis)*
Math 640 Applied Mathematics (or other elective) Math 662 Numerical Analysis

Second semester, year two 
 Math 642 Partial Differential Equations I*
 600level elective
 700level seminar

Year two 
 Written Ph.D. qualifying examination

First semester, year three 
 600level elective
 700level seminar or reading course
 700level seminar or reading course

Second semester, year three 
 Applications Involvement Component (internship)
 700level seminar or reading course

Year three 
 Oral Ph.D. candidacy examination

First semester, year four 
 700level seminar or reading course
 Math 799 Doctoral Research and Dissertation

Second semester, year four 
 Math 799 Doctoral Research and Dissertation

Summer, year four 
 Math 799 Doctoral Research and Dissertation
 Complete dissertation and graduate

*This program requires 4 of these 5 courses.
Ph.D. degree in Mathematical Sciences: Core Group D (Mathematics)
Computational Mathematics Focus
This fouryear program assumes a strong entering background in mathematics, including a oneyear sequence in probability and statistics. If your entering background is average, add one or two years at the outset for MATH 520, 521, 530, 531, 534, 542 and 550, and STAT 570 and 572 as necessary.
You should register for two hours of MATH 792 each fall and spring semester before the working phase of your AIC.
Semester 
Courses 
First semester, year one 
 Math 620 Algebraic Structures I
 Math 630 Real Analysis I
 Math 662 Numerical Analysis

Second semester, year one 
 Math 621 Algebraic Structures II*
Math 632 Complex Analysis Math 664 Numerical Linear Algebra

Summer, year one 
 Foreign language course, research tool, other elective or written Ph.D. qualifying examination

First semester, year two 
 Math 631 Real Analysis II (Functional analysis)*
 Math 636 Ordinary Differential Equations*
 Math 668 Nonlinear Programming

Second semester, year two 
 Math 666 Numerical Differential Equations
 Math 642 Partial Differential Equations I*
 Math 650 Topology*

Summer, year two 
 Written Ph.D. qualifying examination

First semester, year three 
 Math 640 Applied Mathematics (or other elective)
 700level seminar or reading course
 700level seminar or reading course

Second semester, year three 
 Applications Involvement Component (internship)
 700level seminar or reading course

Summer, year three 
 Oral Ph.D. candidacy examination
 Math 799 Doctoral Research and Dissertation

First semester, year four 
 700level seminar or reading course
 Math 799 Doctoral Research and Dissertation

Second semester, year four 
 Math 799 Doctoral Research and Dissertation

Summer, year four 
 Math 799 Doctoral Research and Dissertation
 Complete dissertation and graduate

*This program requires 4 of these 5 courses.
Ph.D. degree in Mathematical Sciences: Core Group B (Mathematics Education)
A typical 4year schedule for this degree is given below. Special schedules may be designed to fit the needs of parttime or other students. You should register for two hours of MATH 792 each fall and spring semester before the working phase of your AIC.
Semester 
Courses 
First semester, year one 
 Math 610 Theoretical Foundations of Mathematics Education
 Math 520 Algebra I**
 Math 530 Advanced Calculus I**

Second semester, year one 
 Math 614 The Teaching of Geometry
 Math 521 Algebra II
 Math 531 Advanced Calculus II

Summer, year one 
 Math 612 The Teaching of Mathematics, Grades 69
 Foreign language, research tool or elective course

First semester, year two 
 Math 613 The Teaching of Algebra
 Math 620 Algebraic Structures I
 Math 630 Real Analysis I or Math 562 Numerical Analysis

Second semester, year two 
 Math 611 Introduction to Mathematics Education Research
 Math 615 Using Microcomputers in Teaching Mathematics
 Math 632 Complex Analysis

Summer, year two 
 Written Ph.D. qualifying examination

First semester, year three 
 Initiate AIC
 Math 662 Numerical Analysis or Math 630 Real Analysis I
 Elective topics course or seminar outside mathematics education

Second semester, year three 
 Math 710A or B Topics in Mathematics Education
 Elective topics course or seminar outside mathematics education
 Oral Ph.D. candidacy examination

Summer, year three 
 Math 799 Doctoral Research and Dissertation
 AIC completed

First semester, year four 
 700level elective topics course or seminar
 Math 710A or B Topics in Mathematics Education
 Math 799 Doctoral Research and Dissertation

Second semester, year four 
 Math 710A or B Topics in Mathematics Education
 Math 799 Doctoral Research and Dissertation

Summer, year four 
 Math 799 Doctoral Research and Dissertation
 Complete dissertation and graduate

**Math 520 and Math 530 both carry graduate credit, but only one of these two courses may be counted toward a mathematical sciences graduate degree.