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Sample PhD Study Plans

This appendix contains sample PhD study plans for students wanting to focus in one of the following areas:

Students who pass one or both of the preliminary exams before the start of their first fall semester can skip the corresponding Master’s core courses, and follow the plans for Year 2 and on. Please keep in mind that these are just sample plans. Each student need to work with their advisor to design a plan that best suits them.

Sample Study Plan for Algebra

First Year

Fall

  • Math 586 – Introduction to Real Analysis I
  • Math 572 – Linear Algebra
  • Elective

Spring

  • Math 587 –  Introduction to Real Analysis II
  • Math 570 – Prin. Modern Algebra I
  • Elective
  • GTA Training

Second Year

Fall

  • MATH 571 – Modern Algebra II
  • MATH 565 – Intro General Topology
  • MATH 580 – Real Analysis I

Spring

  • MATH 573 – Abstract Algebra I
  • MATH 566 – Intro Algebraic Topology
  • MATH 681 – Real Analysis II

Third Year

Fall

  • MATH 583 – Complex Analysis I
  • MATH 674 – Abstract Algebra II
  • Elective

Spring

  • MATH 677 – Topics in Algebra
  • MATH 560 – Introduction to Differential Geometry
  • Math 598 – Non-Thesis Research or Math 698 – Non-Dissertation Research

Fourth/Fifth/Sixth Years

Electives and MATH 699 – Dissertation Research.

Preferred electives: MATH 684 Complex Analysis II; MATH 686 Functional Analysis. MATH 677 Topics in Algebra may be taken more than once. There is an applied math requirement which can be satisfied by taking MATH 510 Numerical Linear Algebra; MATH 554 Mathematical Statistics I or other applied PhD courses.

Sample Study Plan for Analysis

First Year

Fall

  • Math 586 – Introduction to Real Analysis I
  • Math 572 – Linear Algebra
  • Elective

Spring

  • Math 587 –  Introduction to Real Analysis II
  • Math 570 – Prin. Modern Algebra I
  • Elective
  • GTA Training

Second Year

Fall

  • MATH 565 – Intro General Topology
  • MATH 541 – Boundary Value Problems
  • MATH 580 – Real Analysis I

Spring

  • MATH 566 – Intro Algebraic Topology or MATH 560 Intro Diff. Geom.
  • MATH 642 – Partial Differential Equations
  • MATH 681 – Real Analysis II

Third Year

Fall

  • MATH 583 – Complex Analysis I
  • MATH 686 – Functional Analysis I
  • MATH 571 – Prin Modern Algebra II

Spring

  • MATH 566 – Intro Algebraic Topology
  • MATH 573 – Abstract Algebra I
  • MATH 598 – Non-Thesis Research or MATH 698 Non-Dissertation Research

Fourth/Fifth/Sixth Years

Electives and MATH 699 – Dissertation Research

Preferred electives: MATH 510 Numerical Linear Algebra; MATH 511 Numerical Analysis; MATH 688 Topics in Analysis; MATH 554 Mathematical Statistics I; MATH 557 Stochastic Processes I; MATH 588 Theory of Differential Equations.

Sample Study Plan for Scientific Computing

First Year

Fall

  • MATH 586 – Introduction to Real Analysis I
  • MATH 572 – Linear Algebra
  • MATH 537 – Applied Math Topics

Spring

  • Math 587 –  Introduction to Real Analysis II
  • Math 510 – Numerical Linear Algebra
  • Elective
  • GTA Training

Second Year

Fall

  • MATH 511 – Numerical Analysis I
  • MATH 541 – Boundary Value Problems
  • MATH 520 – Optimization I

Spring

  • MATH 512 – Numerical Analysis II
  • MATH 642 – Partial Differential Equations
  • MATH 521  Nonlinear Optimization Theory

Third Year

Fall

  • MATH 610 – Iterative Methods
  • MATH 554 – Mathematical Statistics I
  • Electives

Spring

  • MATH 611 – Numerical Methods for PDEs
  • MATH 555 – Mathematical Statistics II
  • MATH 598 – Non-Thesis Research or MATH 698 Non-Dissertation Research

Fourth/Fifth/Sixth Years

Electives and MATH 699 – Dissertation Research

Preferred electives: MATH 554 Mathematical Statistics I; MATH 555 Mathematical Statistics II; MATH 588 Theory of Differential Equations I; MATH 580 Real Analysis I; MATH 681 Real Analysis II; MATH 686 Functional Analysis I.

Sample Study Plan for Partial Differential Equations

First Year

Fall

  • MATH 586 – Introduction to Real Analysis I
  • MATH 572 – Linear Algebra
  • Elective

Spring

  • MATH 587 –  Introduction to Real Analysis II
  • MATH 510 – Numerical Linear Algebra or MATH 570 – Prin Modern Algebra I
  • Elective
  • GTA Training

Second Year

Fall

  • MATH 511 – Numerical Analysis I
  • MATH 541 – Boundary Value Problems
  • MATH 580 – Real Analysis I

Spring

  • MATH 512 – Numerical Analysis II
  • MATH 642 – Partial Differential Equations
  • MATH 681 – Real Analysis II

Third Year

Fall

  • MATH 586 Intro General Topology
  • MATH 686 Functional Analysis
  • Elective

Spring

  • MATH 688 – Topics in Analysis
  • Elective
  • MATH 598 – Non-Thesis Research or MATH 698 Non-Dissertation Research

Fourth/Fifth/Sixth Years

Electives and MATH 699 – Dissertation Research

Preferred electives: MATH 520 Linear Optimization Theory; MATH 521 Nonlinear Optimization The- ory; MATH 588 Theory of Differential Equations I; MATH 557 Stochastic Processes I; MATH 554 MATH Statistics I; MATH 555 Math Statistics II; MATH 611 Numerical Methods for PDEs.

Sample Study Plan for Topology

First Year

Fall

  • MATH 586 – Introduction to Real Analysis I
  • MATH 572 – Linear Algebra
  • Elective

Spring

  • MATH 587 –  Introduction to Real Analysis II
  • MATH 570 – Prin Modern Algebra I
  • Elective
  • GTA Training

Second Year

Fall

  • MATH 565 – Intro General Topology
  • MATH 571 – Modern Algebra II
  • MATH 580 – Real Analysis I

Spring

  • MATH 566 – Intro Algebraic Topology
  • MATH 573 – Abstract Algebra I
  • MATH 681 – Real Analysis II

Third Year

Fall

  • MATH 583 – Complex Analysis I
  • MATH 661 – Algebraic Topology
  • Elective

Spring

  • MATH 560 – Intro Differential Geometry
  • Elective
  • MATH 598 – Non-Thesis Research or MATH 698 Non-Dissertation Research

Fourth/Fifth/Sixth Years

Electives and MATH 699 – Dissertation Research

Preferred electives: MATH 510 Numerical Linear Algebra; MATH 541 Boundary Value Problems; MATH 642 Partial Differential Equations; MATH 688 Topics in Analysis; MATH 684 Complex Analysis II.

Sample Study Plan for Mathematics Education

This program is designed so that students have a strong background in all major areas of mathematics in order to be prepared to teach any undergraduate mathematics course or research the teaching and learning of undergraduate mathematics. Note that some students may need to take prerequisite coursework for the first year of study.

First Year

Fall

  • MATH 586 – Introduction to Real Analysis I
  • MATH 572 – Linear Algebra
  • Elective

Spring

  • MATH 587 –  Introduction to Real Analysis II
  • MATH 570 – Prin Modern Algebra I
  • Elective
  • GTA Training

Second Year

Fall

  • MATH 571 – Modern Algebra II
  • MATH 580 – Real Analysis
  • MATH 565 – Intro General Topology

Spring

  • MATH 573 – Abstract Algebra I
  • MATH 566 – Intro Algebraic Topology or MATH 681 Real Analysis II
  • MATH 591 or 593

Third Year

Fall

  • MATH 554 – Mathematical Statistics I
  • BER 600 or BER 631
  • Elective

Spring

  • MATH 555 – Mathematical Statistics II
  • BER 600 or BER 631
  • Elective

Fourth Year

Fall

  • Mathematics Elective
  • Educational Elective
  • MATH 699 Dissertation Research

Spring

  • Educational Elective
  • MATH 699 Dissertation Research

Fifth/Sixth Years

During this period, students take MATH 699, complete and defend the dissertation.

Courses in Educational Research and Mathematics Education will be selected from courses offered by the College of Education to reflect a balance between research methods and educational theory. Choices will be made to reflect student interest and advisor recommendation in preparation for research in mathematics education.

Preferred Math electives: MATH 510 Numerical Linear Algebra; MATHH 511 Numerical Analysis I; MATH 512 Numerical Analysis II; MAATH 557 Stochastic Processes ; MATH 585 Introduction to Complex Variables.

Sample Study Plan for Optimization

First Year

Fall

  • MATH 586 – Introduction to Real Analysis I
  • MATH 572 – Linear Algebra
  • MATH 537 – Applied Math Topics

Spring

  • Math 587 –  Introduction to Real Analysis II
  • Math 510 – Numerical Linear Algebra
  • Elective
  • GTA Training

Second Year

Fall

  • MATH 520 – Linear Optimization
  • MATH 511 – Numerical Analysis
  • MATH 580 – Real Analysis I

Spring

  • MATH 521 – Optimization Theory II
  • MATH 512 – Numerical Analysis
  • MATH 681 – Real Analysis II

Third Year

Fall

  • MATH 554 – Mathematical Statistics I
  • MATH 541 – Boundary Value Problems
  • MATH 557 – Stochastic Processes I

Spring

  • MATH 555 – Mathematical Statistics II
  • Elective
  • MATH 598 Non-Thesis Research or MATH 698 Non-Dissertation Research

Fourth/Fifth/Sixth Years

Electives and MATH 699 – Dissertation Research

Preferred electives: MATH 583 Complex Analysis I; MATH 588 Theory of Differential Equations I; MATH 610 Iterative Methods for Linear Systems; MATH 642 Partial Differential Equations; MATH 686 Functional Analysis I. General electives can be any 500 or 600 courses from another department (if the student is interested in a particular area of application).

Sample Study Plan for Statistics

First Year

Fall

  • MATH 586 – Introduction to Real Analysis I
  • MATH 572 – Linear Algebra
  • Elective

Spring

  • Math 587 –  Introduction to Real Analysis II
  • Math 510 – Numerical Linear Algebra
  • Elective
  • GTA Training

Second Year

Fall

  • MATH 554 – Mathematical Statistics I
  • MATH 511 – Numerical Analysis I
  • MATH 580 – Real Analysis I

Spring

  • MATH 555 – Mathematical Statistics II
  • MATH 512 – Numerical Analysis II
  • MATH 681 – Real Analysis II

Third Year

Fall

  • MATH 520 Linear Optimization Theory
  • MATH 557 – Stochastic Processes I
  • Elective

Spring

  • MATH 521 – Nonlinear Optimization Theory
  • Elective
  • MATH 598 Non-Thesis Research or MATH 698 Non-Dissertation Research

Fourth/Fifth/Sixth Years

Electives and MATH 699 – Dissertation Research

Preferred electives: MATH 541 Boundary Value Problems; MATH 583 Complex Analysis I; MATH 588 Theory of Differential Equations I; MATH 559 Stochastic Processes II; MATH 610 Iterative Methods for Linear Systems; MATH 642 Partial Differential Equations; MATH 686 Functional Analysis I. Non-math electives can be any three of the following courses: Applied Multivariate Analysis (ST 553), Applied Design Experiments (ST 561), Statistical Quality Control (ST 575), Nonparametric Statistics (ST 635), Advanced Data Mining II (ST 532).