MATHPHD - Mathematics

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Students must take 18 units from the following courses and receive a grade of "B" or better in both semesters, or earn a high pass on the corresponding written qualifying exam.

Math 511A: Algebra (3 units)

Math 511B: Algebra (3 units)

Math 523A: Real Analysis (3 units)

Math 523B: Real Analysis (3 units)

Math 534A: Topology-Geometry (3 units)

Math 534B: Topology-Geometry (3 units)

Core coursework: See website - http://math.arizona.edu/academics/grads/requirements/phd
Language requirements: See website - http://math.arizona.edu/academics/grads/requirements/phd
Other requirements:

Students may choose a minimum of 37 units from the following list or from other courses with the approval of the DGS.

Math 500A: Research on the Learning of Mathematics for Teachers (3 units)

Math 501A: Symbolic Logic (3 units)

Math 501B: Symbolic Logic (3 units)

Math 504: History of Mathematics (3 units)

Math 505C: Algebra for Elementary & Middle School Teachers (3-4 units)

Math 505D: Data Analysis and Probability for K-8 Teachers (3-4 units)

Math 505E: Number and Operations for K-8 Teachers (3-4 units)

Math 505F: Geometry and Measurement for K-8 Teachers (3-4 units)

Math 506A: Research on the Learning of Mathematics (3 units)

Math 506B: Research Methods in Math Education (3 units)

Math 506C: Research on the Teaching of Mathematics (3 units)

Math 507C: Problem Solving for Secondary Mathematics Teachers (3 units)

Math 507D: Modern Algebra for Secondary Mathematics Teachers (3 units)

Math 507E: Principles of Calculus for Secondary School Teachers (3 units)

Math 507F: Probability and Statistics for Secondary Math Teachers (3 units)

Math 509C: Statistics for Research (3 units)

Math 513: Linear Algebra (3 units)

Math 514A: Algebraic Number Theory (3 units)

Math 514B: Algebraic Number Theory (3 units)

Math 516: Commutative Algebra (3 units)

Math 517A: Group Theory (3 units)

Math 517B: Group Theory (3 units)

Math 518: Topics in Algebra (3 units), may be repeated)

Math 519: Topics in Number Theory and Combinatorics (3 units), may be repeated)

Math 520A: Complex Analysis (3 units)

Math 520B: Complex Analysis (3 units)

Math 527A: Principles of Analysis (3 units)

Math 527B: Principles of Analysis (3 units)

Math 528A: Banach and Hilbert Spaces (3 units)

Math 528B: Banach and Hilbert Spaces (3 units)

Math 529: Topics in Modern Analysis (3 units), may be repeated)

Math 532: Topological Spaces (3 units)

Math 536A: Algebraic Geometry (3 units)

Math 536B: Algebraic Geometry (3 units)

Math 537A: Global Differential Geometry (3 units)

Math 537B: Global Differential Geometry (3 units)

Math 538: Topics in Geometry and Topology (3 units, may be repeated)

Math 539: Algebraic Coding Theory (3 units)

Math 541: Introduction to Mathematical Physics (3 units)

Math 553A: Partial Differential Equations (3 units)

Math 553B: Partial Differential Equations (3 units)

Math 554: Ordinary Differential Equations (3 units)

Math 556: Applied Partial Differential Equations (3 units)

Math 557A: Dynamical Systems and Chaos (3 units)

Math 557B: Dynamical Systems and Chaos (3 units)

Math 559A: Lie Groups and Lie Algebras (3 units)

Math 559B: Lie Groups and Lie Algebras (3 units)

Math 563: Probability Math (3 units)

Math 564: Theory of Probability (3 units)

Math 565A: Stochastic Processes (3 units)

Math 565B: Stochastic Processes (3 units)

Math 565C: Stochastic Differential Equations (3 units)

Math 566: Theory of Statistics (3 units)

Math 567A: Theoretical Statistics I (3 units)

Math 567B: Theoretical Statistics II (3 units)

Math 568: Applied Stochastic Processes (3 units)

Math 571A: Advanced Statistical Regression Analysis (3 units)

Math 571B: Design of Experiments (3 units)

Math 573: Theory of Computation (3 units)

Math 574E: Environmental Statistics (3 units)

Math 574G: Introduction to Geostatistics (3 units)

Math 574M: Statistical Machine Learning (3 units)

Math 574T: Time Series Analysis (3 units)

Math 575A: Numerical Analysis (3 units)

Math 575B: Numerical Analysis (3 units)

Math 576A: Numerical Analysis PDE (3 units)

Math 576B: Numerical Analysis PDE (3 units)

Math 577: Topics in Applied Mathematics (3 units, may be repeated)

Math 580: Mathematical Models in Biology (3 units)

Math 582: Applied Complex Analysis (3 units)

Math 583A: Principles and Methods of Applied Mathematics (3 units)

Math 583B: Principles and Methods of Applied Mathematics (3 units)

Math 585: Mathematical Modeling (3 units)

Math 586: Case Studies in Applied Mathematics (3 units)

Math 587: Perturbation Methods in Applied Mathematics (3 units)

Math 588: Topics in Mathematical Physics (3 units, may be repeated)

Math 593: Internship 1-6 units

Math 595A: Math Instruction (3 units)

Math 595C: Research in Applied Mathematics (3 units)

Math 595D: Research in Mathematics Education (3 units)

Math 596A: Topics in Mathematics (3 units)

Math 596B: Mathematics Mentoring Methods (3 units)

Math 596C: Mathematics Instruction for English Language Learners (3 units)

Math 596F: Topics in Math for Elementary and Middle School Teachers (3 units)

Math 599: Independent Study (1-6 units, may be repeated)

Math 636: Information Theory (3 units)

Math 697B: Applied Mathematics Laboratory (3 units)

Math 699: Independent Study (3 units)

Math 900: Research (2-6 units, may be repeated)

Students must take the following 5 units:

Math 596G: Research Tutorial Group (1 unit in the spring of the first year, 3 units in the fall of the second year)

Math 597T: Professional Development Workshop in Teaching Mathematics (1 unit)

Additional requirements for the PhD include:

Qualifying examinations

Two year-long Mathematics course sequences that are not co-convened and are not part of the required core of algebra, real analysis, and geometry-topology. These two sequences must be in two of the three general areas: algebra and number theory, analysis and geometry, mathematical physics and applied mathematics. 

Comprehensive examination

Prospectus

PhD students must complete a series of professional development requirements consiting of:

• Professional Development

• Community Development

• Broader Impact

• Equity

All students in the Mathematics Ph.D. program are required to have a Graduate Faculty Advisor (also called Major Professor)

The University requires that PhD students declare a minor. PhD students in mathematics may declare their minor in mathematics or in a supporting discipline. Requirements for the minor are determined by the minor department. Up to 12 units of course work may be in the minor. Students contemplating a minor should consult with the Associate Head for the Graduate Program and their dissertation advisor regarding the suitability of their plans.

Please refer to the Graduate Student Handbook for students who are pursuing this program of study.