AMCS MODEL
CURRICULA for SEVERAL POSSIBLE AREAS of CONCENTRATION
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.
Alternatives/Additions:
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.
Alternative/Additions:
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
Biophysics
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.
Inverse Problems
Professor John Schotland
Year 1:
Required courses plus an elective such as
PHYS 516 Electromagnetic Theory
ESE 510 Electromagnetic and Optical Theory
PHYS 514 Classical Mechanics
MATH 584 Mathematics of Medical Imaging
Year 2:
Electives:
BE 517 (ESE 517) Optical Imaging
ESE 504 Introduction to Optimization Theory
ENM 520 Theory and Computation for ODE/PDE Constrained Optimization
MATH 692 Numerical Analysis
MATH 644 Partial Differential Equations
MATH 645 Partial Differential Equations
PHYS 531 Quantum Mechanics I
PHYS 532 Quantum Mechanics II
Year 3:
Electives:
BE 619 Statistical Physics
ESE 605 Modern Convex Optimization
PHYS 611 Statistical Mechanic
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
Electives
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