Ph.D. Sample Program - Biomedical Engineering
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Year 1
1st year Medical School basic sciences curriculum. (Molecules and Cells, Immunology, Neuroscience, and Physiology). This program fulfills the biology curriculum, although students will usually want to take additional advanced seminars in neuroscience. These courses usually fill a student’s time during the first year and are supplemented with rotations.
Year 2 or Years 1 & 2 Electives in the Engineering and Physical Sciences
The following curriculum is to be completed in Year 2 if taking the SOM basic life sciences track or in Years 1-2 if taking the alternative track. Students are required to take at least 2 courses per semester in Year 2, with at least one of these being at the 600/700 level. Curricula are to be designed with the guidance of the student’s mentor. Suggested electives are given below for each track (choose 4 of 6 each semester). Qualifiers are taken either at the end of the second year or in the middle of the third year.
| Medical Imaging Systems |
Computational Vision and Image Understanding |
Geometry, Shape and Computational Anatomy |
| Fall |
| 110.405 |
Analysis I |
| 520.414 |
Image Processing and Analysis I |
| 520.651 |
Random Signals |
| 550.420 |
Introduction to Probability |
| 550.437 |
Information, Statistics and Perception |
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TBN (Radiology) |
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| Spring |
| 110.406 |
Analysis II |
| 520.415 |
Image Processing and Analysis II |
| 550.426 |
Stochastic Processes |
| 580.472 |
Medical Imaging Systems |
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TBN (Radiology) |
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TBN (Radiology) |
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| Fall |
| 110.405 |
Analysis I |
| 520.414 |
Image Processing and Analysis I |
| 520.651 |
Random Signals |
| 550.420 |
Introduction to Probability |
| 550.437 |
Information, Statistics and Perception |
| 600.357 |
Computer Graphics |
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| Spring |
| 110.406 |
Analysis II |
| 520.415 |
Image Processing and Analysis II |
| 520.630 |
Introduction to the Calculus of Variations and Optimal Control |
| 520.652 |
Filtering & Smoothing |
| 550.426 |
Stochastic Processes |
| 550.730 |
Topics in Statistics: Statistical Pattern Recognition |
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| Fall |
| 110.405 |
Analysis I |
| 110.439 |
Introduction to Differential Geometry |
| 520.414 |
Image Processing and Analysis I |
| 520.651 |
Random Signals |
| 530.648 |
Group Theory in Engineering Design |
| 550.420 |
Introduction to Probability |
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| Spring |
| 110.406 |
Analysis II |
| 110.417 |
Partial Differential Equations for Applications |
| 520.415 |
Image Processing and Analysis II |
| 520.630 |
Introduction to the Calculus of Variations and Optimal Control |
| 520.652 |
Filtering & Smoothing |
| 550.426 |
Stochastic Processes |
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Year 3 (Choose 4 of following) and Year 4 (Choose 2 of following)
| Applied Mathematics and Statistics |
| 550.361 |
Linear Optimization |
| 550.420 |
Introduction to Probability |
| 550.426 |
Introduction to Stochastic Processes |
| 550.430 |
Introduction to Statistics |
| 550.434 |
Nonparametric and Robust Methods |
| 550.437 |
Statistics, Information and Perception |
| 550.620 |
Probability Theory I |
| 550.621 |
Probability Theory II |
| 550.626 |
Stochastic Processes II |
| 550.630 |
Statistical Theory |
| 550.631 |
Statistical Inference |
| 550.632 |
Multivariate Statistical Theory |
| 550.633 |
Time Series Analysis |
| 550.634 |
Nonparametric and Robust Inference |
| 550.661 |
Foundations of Optimization |
| 550.662 |
Optimization Algorithms |
| 550.672 |
Graph Theory |
| 550.681 |
Numerical Analysis |
| 550.692 |
Matrix Analysis and Linear Algebra |
| 550.723 |
Markov Chains |
| 550.730 |
Topics in Statistics: Statistical Pattern Recognition |
| 550.764 |
Optimization of Functionals |
| 550.790 |
Topics in Applied Mathematics: Deformation Analysis for Images and Shapes |
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| Mechanical Engineering |
| 530.601 |
Continuum Mechanics |
| 530.648 |
Group Theory in Engineering Design |
| 530.669 |
Computational Methods of Engineering |
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| Biomedical Engineering |
| 580.473 |
Magnetic Resonance in Medicine |
| 580.472 |
Medical Imaging Systems |
| 580.744 |
Pattern Theory: From representation to Inference |
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| Electrical and Computer Engineering |
| 520.414 |
Image Processing and Analysis I |
| 520.415 |
Image Processing and Analysis II |
| 520.432 |
Medical Imaging Systems |
| 520.435 |
Digital Signal Processing |
| 520.447 |
Introduction to Information Theory and Coding |
| 520.497 |
Information Theory |
| 520.608 |
Image Reconstruction and Restoration |
| 520.614 |
Linear Systems Theory |
| 520.630 |
Introduction to the Calculus of Variations and Optimal Control |
| 520.643 |
Digital Multimedia Coding and Processing |
| 520.644 |
Pattern Theory: From representation to Inference |
| 520.645 |
Adaptive Filtering |
| 520.646 |
Wavelets and Filter Banks |
| 520.651 |
Random Signal Analysis |
| 520.652 |
Filtering and Smoothing |
| 520.674 |
Information Theoretic Methods in Statistics |
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| Bioethics Elective |
| 306.655 |
Ethical Issues in Public Health |
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| Computer Science |
| 600.303 |
High Performance Computing |
| 600.357 |
Computer Graphics |
| 600.441 |
Vision-Based Interaction for Man and Machine |
| 600.445 |
Computer-Integrated Surgery I |
| 600.446 |
Computer-Integrated Surgery II |
| 600.461 |
Computer Vision |
| 600.462 |
Applications of Computer Vision |
| 600.630 |
Advanced Topics in Physics-Based Computer Vision |
| 600.646 |
Advanced Computer-Integrated Surgery |
| 600.652 |
Advanced Computer-Integrated Surgery Seminar |
| 600.746 |
Medical Image Analysis Seminar |
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| Mathematics |
| 110.405 |
Analysis I |
| 110.406 |
Analysis II |
| 110.413 |
Introduction to Topology |
| 110.417 |
Partial Differential Equations for Applications |
| 110.423 |
Lie Groups |
| 110.427 |
Introduction to Calculus of Variation |
| 110.439 |
Introduction to Differential Geometry |
| 110.605 |
Real Variables |
| 110.619/110.620 |
Lie Groups and Lie Algebras |
| 110.631/110.632 |
Partial Differential Equations |
| 110.645/110.646 |
Riemannian Geometry |
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