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Sample Programs of Study

These are just examples. Students are free to pursue  other fields and courses of study. Each student's program will be worked out in consultation with his or her advisor and the Graduate Group Chair.

MATHEMATICAL BIOLOGY  (There are 2 options here)


Professor Joshua Plotkin

Genomics and bioinformatics

Year 1:  

Required courses plus an elective such as:


BIOL 410 Evolution of Populations
BIOL 535. Mathematical Ecology.


Year 2:

STAT 540. Statistical Methods and Computation. 
BIOL 536. Computational Biology 
BSTA 630. Statistical Methods for Data Analysis I. 
BIOL 537. Advanced Computational Biology. 
BSTA 631. Statistical Methods and Data Analysis II. 
GCB 531. Introduction to Genome Science. 
BSTA 651. Introduction to Linear Models and Generalized Linear Models. 
MATH 640. Ordinary Differential Equations. 
PHYS 580. (BCHE580) Biological Physics. 
STAT 512. (BSTA621, STAT432) Mathematical Statistics. 
CIS 520. Artificial Intelligence and Machine Learning. 

Year 3:

MATH 547. (STAT531) Stochastic Processes. 
CIS 535.  Introduction to Bioinformatics. 
MEAM 613. (CBE 617, CIS 613, ESE 617) Nonlinear Control Theory. 
BMB 604. (BE  619) Statistical Mechanics. 
MATH 590. Advanced Applied Mathematics. 
STAT 901. (OPIM931) Stochastic Processes II. 
BIOL 540. (CAMB541, MOLB541) Genetic Analysis. 
BMB 619. Protein Folding. 
CAMB752 Genomics. 
BE 539. (ESE 539) Neural Networks, Chaos, and Dynamics: Theory and Application. 
STAT 927. Bayesian Statistical Theory and Methods. 
STAT 910. Forecasting and Time Series Analysis. 
BSTA 771 Applied Bayesian Analysis



Professor Phil Nelson

Year 1:
Students must take the first year courses in Applied Analysis, Algebra and Probability and a fourth elective.
Student should pick a course at a level, and in a field, that picks up from their prior background:
BMB 604. (BE619) Statistical Physics
PHYS 581 Thermodynamics and the Introduction to Statistical Mechanics and Kinetic Theory. (A)
PHYS 611. Statistical Mechanics. (A)
CHEM 521. Statistical Mechanics I. (A)
CHEM 522. Statistical Mechanics II. (B)
MEAM 670. Statistical Mechanics of Solids. (A)

Year 2:

Require: PHYS580. (BCHE580) Biological Physics. (C)
PHYS529 Modern Optics. (J)
BIO 536.(BIOL536, CIS 536) Computational Biology. (M) 
BE 505. Quantitative Human Physiology. (B) 
BE517. (ESE 517) Optical Imaging. (C) 
CHEM 559. BIOMOLEC IMAGING. (B) Dmochowski. 
CIS 535. (BIOL535, GCB 535) Introduction to Bioinformatics. (A) 

Year 3:

Any 500+ level course in BMB (offerings change every year). 
Any 500+ level course in BE, e.g. 
BE 519. Cellular-Level Neural Simulation and Modeling. (M) Finkel. 
BE 520. (INSC594) Computational Neuroscience and Neuroengineering. (B) Finkel. 
BE 539. (ESE 539) Neural Networks, Chaos, and Dynamics: Theory and Application. (B) 
BE 546. (BMB 546) Quantitative Image Analysis. (H)


Imaging Science 

Prof James Gee.

Year 1: 

601-602. Algebraic Techniques for Applied Mathematics and Computational Science. 
605-606. Probability, Stochastic Processes and Statistics for Applied  Mathematics and Computational Science 
608-609. Analytic techniques for Applied Mathematics and Computational Science 
1st year electives: 
CIS 520 - Artificial Intelligence and Machine Learning. 
CIS 580 - Machine Perception. 
ESE 531 - Digital Signal Processing. 
Math 500/501 - Geometry-Topology, Differential Geometry. 
Math 546 ( Stat 530 ) - Probability. 
Math 547 (Stat 531) - Stochastic Processes. 
Math 584/585. (BE  584/585) - The Mathematics of Medical Imaging and  Measurement. 
517. (ESE 517) Optical Imaging. 
584. (MATH584) Mathematics of Medical Imaging and Measurements. 
Year 2: 

500. Geometry-Topology, Differential Geometry I. 
501. Geometry-Topology, Differential Geometry II. 
511. Foundations of Engineering Mathematics 
520. Artificial Intelligence and Machine Learning. 
--> CIS 580 Machine Perception (missing) 
510. (CSE 410) Curves and Surfaces: Theory and Applications. 
502. (ENM 402) Numerical Methods and Modeling. 
504. (OPIM910) Introduction to Optimization Theory 
More advanced courses 
CIS 620 - Advanced Topics in Artificial Intelligence. 
CIS 680 - Advanced Topics in Machine Perception. 
ESE 605 - Modern Convex Optimization. 
Math 600 - Topology and Geometric Analysis. 
Math 608/609 - Real Analysis, Complex Analysis. 
Math 640/641 - Ordinary Differential Equations. 
Year 3: 

600-601. Topology and Geometric Analysis. 
654. Lie Groups. 
674. Information Theory 
618-619. Algebraic Topology, Part I 
Math 644/645 - Partial Differential Equations. 
Math 676 (CIS 610) - Advanced Geometric Methods in Computer Science. 
Math 650-657 - Functional Analysis Electives (Lie Algebras, Operator 
Theory, Lie Groups, Representation of Continuous Groups) .
Math 680/681 - Applied Linear Analysis.

Materials Science


Professor Pedro Ponte-Castaneda

Year  1:
1 year course in Analysis 
1 year course in Algebra 
1 year course in Probability and Statistics 
MEAM 530 OR 630. Continuum Mechanics 
MSE 520 Structure of Materials OR PHYS 518 Intro to Condensed Matter 
Year 2:

2 courses from list A 
2 courses from list B 
2 courses from lists C, or D

Year 3:
2 courses from lists A or B 
2 courses from lists C, or D 


List A. Math Courses 
MATH 542. Variational Calculus 
MATH 594. Advanced Applied Math  OR  ENM 510-511 Engineering Math 
MATH 640-641. ODEs 
MATH 644-645. PDEs 
MATH 660-661. Differential Geometry 
ENM 601. Special Topics in Engineering Math 

List B. Computational Math Courses 
ENM 520. PDE/ODE Constrained Optimization 
ENM 540. Numerical Methods 
AMCS 601-602. Algebraic Techniques for AMCS 
AMCS 605-606. Probability, Stochastic Processes and Statistics for AMCS 
AMCS 608-609. Analytic Techniques for AMCS 
MATH 693-694. Numerical Analysis 
List C. Engineering Courses 
MSE 570-571. Physics of Materials 
MSE 580-581. Polymer Physics 
MSE 660. Atomistic Modeling in Materials Science 
MEAM 631. Advanced Elasticity 
MEAM 632. Plasticity 
MEAM 633. Fracture Mechanics 
MEAM 634. Rods and Shells (Structural Mechanics) 
MEAM 635. Composite Materials 
MEAM 646. Computational Mechanics 
List D. Chemistry and Physics Courses 
CHEM 521-522. Statistical Mechanics  OR  PHYS 611. Statistical Mechanics. 
PHYS 531-532. Quantum Mechanics 
PHYS 581. Thermodynamics 
PHYS 601. Introduction to Field Theory