BME MS pre-2021 Program Requirements

The principal objective for the program is to provide an educational environment and experience for students to acquire the analytical skills required to perform academic or industrial activities that result in technological innovations. The two specific programmatic goals include:

• Providing each student with an individualized, advanced course of study that delivers the analytical tools to perform fundamental and applied research in each track’s focus area.
• Obtaining the requisite technical knowledge that can be applied to management, marketing, sales, entrepreneurial, and other activities related to biomedical engineering.

The program’s three MS degree tracks include specific course sequences that ensure that a student is prepared to pursue a career in their field of interest. Further, within each track, students can elect to pursue research in laboratories at NYU Tandon School of Engineering, NYU School of Medicine, and other NYU-affiliated schools and hospitals.

The BME MS program will consider applications for admission from students with a BS/BA or a more advanced degree in biomedical, chemical, mechanical, or electrical engineering; computer engineering or science; physics; mathematics, chemistry; or biological sciences. We also consider applications from students with medical, dental, nursing and legal degrees.

The program requires that all applicants must have taken two semesters of college-level calculus and two semesters of calculus-based physics. It further highly recommends that each student’s undergraduate preparation include the following sequence of math and science courses:

•     1 semester of linear algebra
•     1 semester of ordinary differential equations
•     1 semester of multivariable calculus
•     2 semesters of biology with labs
•     2 semesters of general chemistry with labs

For those focusing on the Biomaterials track, additional background in organic chemistry and biochemistry is desirable. For those choosing the Medical Imaging or Bioinstrumentation tracks, additional advanced mathematics courses, e.g. complex variables, partial differential equations are recommended. Though not required, exposure to CAD/FEA, Matlab, C++ /Python computer programming experience is highly desirable.

For International Students:

Applications can only be considered from international students who have completed all of the undergraduate math and science courses listed above.

For Domestic Students:

Applicants pursuing a career change and lacking some of the undergraduate courses listed above may be admitted conditionally if they present a strong record of achievement in their undergraduate field of study and agree to enroll in the missing undergraduate courses to raise their level of knowledge so that they are better prepared for the analytically rigorous coursework that is part of the BME MS program. Such undergraduate courses do not count toward the MS degree’s credit requirements.

Find out more about Admission Requirements.

The Biomedical Engineering MS program offers 3 tracks:

•     Biomaterials Track
•     Medical Imaging Track
•     Bioinstrumentation Track

Each track includes 2 options. The first specifies course requirements that include research with submission of a master's thesis. The second option specifies course requirements plus research performed as guided studies. If you choose to perform a thesis research-based degree, you must register for at least 6 credits of BE-GY 997X and then write and defend a master’s thesis according to School guidelines. You will also be required to take training in laboratory safety.

To meet graduation requirements in your chosen track, you must achieve an overall B average in all courses (including MS thesis or guided studies) and must not have more than two grades of C in required (core) subjects.

Required Courses

3 Credits Anatomy, Physiology, & Biophysics I BE-GY 6103

Anatomy and Physiology are the sciences that identify body structures and how they function and interact, respectively. Therefore, academic training for biomedical engineering must include a sound, comprehensive knowledge of human anatomy and physiology. While the course emphasizes normal functions, it also considers the consequences of disease and injury and deals with the body's potential for recovery and compensation. The Biophysics' component examines the underlying physical principles of organ function. Part I of this two-part sequence focuses on Cell Physiology and Homeostasis, Cardiac, Nervous, and Respiratory systems. The course will be taught using a "systems engineering" approach and introduce the design considerations for artificial organs. The material includes hands-on demonstration of technology to measure EEGs, EKG and respiratory function.

3 Credits Anatomy, Physiology, & Biophysics II BE-GY 6113

Part II of this sequence focuses on the muscular, skeletal, renal and endocrine systems and includes discussions on skin and basic oncology. This part is taught using a ?systems? approach and link concepts from BE-GY 6013. The material includes hands-on demonstration of technology to measure EMG.
Prerequisites: BE-GY 6013.

3 Credits Statistics for Biomedical Engineers BE-GY 6463

This course reviews various methods of analysis for biomedical data. Contents: population and sample, confidence interval, hypothesis test, Bayesian logic, correlation, regression, design of studies, t test, chi-square test, analysis of variance, multiple regression, survival curves. Multivariable Calculus knowledge required; Probability Theory knowledge is preferred.

3 Credits Orthopedic Biomechanics and Biomaterials BE-GY 6753

The course provides fundamental knowledge of the relevant background science, theory, practice and materials required to provide modern orthopedic and trauma care. Students learn about biomaterials used in orthopedics and how materials engineering has made them increasingly sophisticated. The course covers important clinical applications as well as fundamental concepts in biomechanics of bone and other tissues; materials used; wear and corrosion during use; dental implants; joint-replacement devices; stress-strain analysis, beam theory; introduction to finite element analysis design for prosthesis; and more.
Prerequisite: Calculus with ordinary diff. eq.; BE-GY 6703 Materials in Medicine.

3 Credits Biomaterials: Engineering Principles and Design Consideration BE-GY 6803

This course will provide the student with an overview of the techniques used to evaluate and design with materials used in biomedicine in the context of reconstructing, repairing, replacing or augmenting diseased or injured tissue or organs in the human body.
Prerequisites: Calculus I, Calculus II and Ordinary Differential Equations.

Course objective:
1. Introduce the concepts of CAD/FEA used with the design of non-orthopedic devices that interface to the neurologic and cardiovascular systems.
2. To present the various classes of biomaterials such as metals, ceramics, man-made polymers and those derived from nature.
3. To simulate and identify the pertinent interactions between materials and composites with living tissue and their durability.
4. To give specific examples for the design of an artificial organ, i.e. artificial heart.

3 Credits Tissue Engineering BE-GY 9443

This courses teaches basic biological processes that occur during blood contact with artificial surfaces; how to critically read and review literature on tissue engineering; how to anticipate biocompatibility issues with a variety of implant devices students may later encounter; current approaches directed toward the engineering of cell-based replacements for various tissue types.
Prerequisite: Adviser's approval.

3 Credits Immunology: Concepts, Mechanisms and Applications in Biotechnology BT-GY 6063

The purpose of this course is to develop a general understanding of the established biochemical, molecular, cellular, and organ-level principles that govern the workings of the mammalian immune system, and to prepare the student for immunological research in the academic, government, or industrial laboratory. Topics covered include cells of the immune system and their development, pattern recognition receptors and innate immunity, molecular mechanisms of antigen processing and presentation, long distance communication and immune cells? migration, homing, and trafficking. Applications in Biotechnology and autoimmune diseases and the use of immunotherapy in industry will also be discussed.
Advisor/Instructor Permission Required

3 Credits Protein Engineering CM-GY 9433

This course introduces modern protein engineering techniques available to researchers to understand protein structure and function and to create entirely new proteins for a variety of purposes. This is a new field that lies on the interface of chemistry, biology and engineering. The first part of the course discusses protein composition and structure and various genetic, biochemical and chemical techniques required to engineer proteins?all followed by specific topics. Topics include designing proteins that are highly structured and active at high temperatures and in non-aqueous solvents; that selectively interact with other proteins, small molecules and nucleic acids for therapeutic purposes; and that catalyze new reactions.
Prerequisite: CM-GY 9413 or adviser's approval.

Taken once per year: 

Colloquium in Biomedical Engineering BE-GY 9730

Engineers and scientists from industry and academia present recent developments in biomedical engineering. Students will be required to attend the department colloquium series each semester.

Seminar in Biomedical Engineering BE-GY 9740

Students present research findings if engaged in MS or PhD thesis research, or make presentations from their critical analysis of recent biomedical-engineering publications. The seminar gives students the opportunity to prepare a scientific presentation on a biomedical-engineering topic of interest and to speak before their peers, who will question them. Two and four semesters are required for master's and PhD students, respectively.

Electives or Research

You may choose up to 6 credits from the list of electives below.  With permission from a graduate adviser, you may substitute a course not listed. You may also elect to do research as Guided Studies in Biomedical Engineering  (BE-GY 873x, 3 to 6 credits) without writing a thesis, or MS Thesis in Biomedical Engineering (BE-GY 997x, 6 credits).

Required Courses

3 Credits Anatomy, Physiology, & Biophysics I BE-GY 6103

Anatomy and Physiology are the sciences that identify body structures and how they function and interact, respectively. Therefore, academic training for biomedical engineering must include a sound, comprehensive knowledge of human anatomy and physiology. While the course emphasizes normal functions, it also considers the consequences of disease and injury and deals with the body's potential for recovery and compensation. The Biophysics' component examines the underlying physical principles of organ function. Part I of this two-part sequence focuses on Cell Physiology and Homeostasis, Cardiac, Nervous, and Respiratory systems. The course will be taught using a "systems engineering" approach and introduce the design considerations for artificial organs. The material includes hands-on demonstration of technology to measure EEGs, EKG and respiratory function.

3 Credits Anatomy, Physiology, & Biophysics II BE-GY 6113

Part II of this sequence focuses on the muscular, skeletal, renal and endocrine systems and includes discussions on skin and basic oncology. This part is taught using a ?systems? approach and link concepts from BE-GY 6013. The material includes hands-on demonstration of technology to measure EMG.
Prerequisites: BE-GY 6013.

3 Credits Digital Signal Processing I BE-GY 6403

Discrete and continuous-time linear systems. Z-transform. Fourier transforms. Sampling. Discrete Fourier transform (DFT). Fast Fourier transform (FFT). Digital filtering. Design of FIR and IIR filters. Windowing. Least squares in signal processing. Minimum-phase and all-pass systems. Digital filter realizations. Matlab programming exercises.

or

3 Credits Digital Signal Processing I ECE-GY 6113

Discrete and continuous-time linear systems. Z-transform. Fourier transforms. Sampling. Discrete Fourier transform (DFT). Fast Fourier transform (FFT). Digital filtering. Design of FIR and IIR filters. Windowing. Least squares in signal processing. Minimum-phase and all-pass systems. Digital filter realizations. Matlab programming exercises. Co-listed as BE-GY 6403
Prerequisites: Graduate status. *Online version available.

3 Credits Biomedical Imaging I BE-GY 6203

This course introduces the physics, instrumentation and signal-processing methods used in X-ray imaging (projection radiography), X-ray computed tomography, nuclear medicine (SPECT/PET), ultrasound imaging and magnetic resonance imaging. Also listed under: EL-GY 6813

Prerequisites: Undergraduate level courses in multivariable calculus (MA-UY 2112 & MA-UY 2122 or MA-UY 2114), physics (PH-UY 2033), probability (MA-UY 3012), signals and systems (EE-UY 3054). Students who do not have prior courses in signals ans systems must take EL-GY 6113 / BE-GY 6403 - Digital Signal Processing I as a prerequisite or must obtain instructor's approval; EL-GY 6123 - Image and Video Processing is also recommended but not required.

or

3 Credits Medical Imaging I ECE-GY 6813

This course introduces the physics, instrumentation and signal processing methods used in X-ray imaging (projection radiography), X-ray computed tomography, nuclear medicine (SPECT/PET), ultrasound imaging, magnetic resonance imaging and optical imaging. Co-listed with BE-GY 6203

Prerequisites: Undergraduate level courses in multivariable calculus (MA-UY 2112 & MA-UY 2122 or MA-UY 2114), physics (PH-UY 2033), probability (MA-UY 3012), signals and systems (EE-UY 3054). Students who do not have prior courses in signals ans systems must take EL-GY 6113 / BE-GY 6403 - Digital Signal Processing I as a prerequisite or must obtain instructor's approval; EL-GY 6123 - Image and Video Processing is also recommended but not required.

3 Credits Probability and Stochastic Processes BE-GY 6453

Continuous and discrete random variables and their joint probability distribution and density functions; Functions of one random variable and their distributions; Independent random variables and conditional distributions; One function of one and two random variables; Two functions of two random variables and their joint density functions; Jointly distributed discrete random variables and their functions; Characteristic functions and higher order moments; Covariance, correlation, orthogonality; Jointly Gaussian random variables; Linear functions of Gaussian random variables and their joint density functions. Stochastic processes and the concept of Stationarity; Strict sense stationary (SSS) and wide sense stationary (WSS) processes; Auto correlation function and its properties; Poisson processes and Wiener processes; Stochastic inputs to linear time-invariant (LTI) systems and their input-output autocorrelations; Input-output power spectrum for linear systems with stochastic inputs; Minimum mean square error estimation (MMSE) and orthogonality principle; Auto regressive moving average (ARMA) processes and their power spectra. Co-listed as EL-GY 6303.
Prerequisites: Graduate status

or

3 Credits Probability and Stochastic Processes ECE-GY 6303

Continuous and discrete random variables and their joint probability distribution and density functions; Functions of one random variable and their distributions; Independent random variables and conditional distributions; One function of one and two random variables; Two functions of two random variables and their joint density functions; Jointly distributed discrete random variables and their functions; Characteristic functions and higher order moments; Covariance, correlation, orthogonality; Jointly Gaussian random variables; Linear functions of Gaussian random variables and their joint density functions. Stochastic processes and the concept of Stationarity; Strict sense stationary (SSS) and wide sense stationary (WSS) processes; Auto correlation function and its properties; Poisson processes and Wiener processes; Stochastic inputs to linear time-invariant (LTI) systems and their input-output autocorrelations; Input-output power spectrum for linear systems with stochastic inputs; Minimum mean square error estimation (MMSE) and orthogonality principle; Auto regressive moving average (ARMA) processes and their power spectra. Co-listed as BE-GY 6453.
Prerequisite: Graduate status. *Online version available.

3 Credits Image and Video Processing ECE-GY 6123

This course introduces fundamentals of image and video processing, including color image capture and representation; color coordinate conversion; contrast enhancement; spatial domain filtering (linear convolution, median and morphological filtering); two-dimensional (2D) Fourier transform and frequency domain interpretation of linear convolution; 2D Discrete Fourier Transform (DFT) and DFT domain filtering; image sampling and resizing; geometric transformation and image registration; video motion characterization and estimation; video stabilization and panoramic view generation; basic compression techniques (entropy coding, vector quantization, predictive coding, transform coding); JPEG image compression standard; wavelet transform and JPEG2000 standard; video compression using adaptive spatial and temporal prediction; video coding standards (MPEGx/H26x); Stereo and multi-view image and video processing (depth from disparity, disparity estimation, video synthesis, compression). Students will learn to implement selected algorithms in MATLAB or C-language.
Prerequisites: Graduate Standing or Undergraduate Standing having completed EE-UY 3054 and EE-UY 2233. Suggested Corequisites: EL-GY 6113 and EL-GY 6303 (not required)

3 Credits Applied Mathematics in Engineering CBE-GY 6153

This course covers mathematical formulation of chemical engineering problems in terms of ordinary, partial differential and differential equations. Topics include solutions of boundary and initial value problems using Green's functions and other techniques; characterization of second-order partial differential equations and properties of their solutions; asymptotic methods and numerical techniques.
Prerequisite: MA-UY 2122 and MA-UY 2132 or adviser's approval.

Taken once per year:

Colloquium in Biomedical Engineering BE-GY 9730

Engineers and scientists from industry and academia present recent developments in biomedical engineering. Students will be required to attend the department colloquium series each semester.

Seminar in Biomedical Engineering BE-GY 9740

Students present research findings if engaged in MS or PhD thesis research, or make presentations from their critical analysis of recent biomedical-engineering publications. The seminar gives students the opportunity to prepare a scientific presentation on a biomedical-engineering topic of interest and to speak before their peers, who will question them. Two and four semesters are required for master's and PhD students, respectively.

Electives or Research

You may choose up to 9 credits from the list of electives below. With permission from a graduate adviser, you may substitute a course not listed. You may also elect to do research as Guided Studies in Biomedical Engineering  (BE-GY 873x, 3 to 6 credits) without writing a thesis, or MS Thesis in Biomedical Engineering (BE-GY 997x, 6 to 9 credits).

Required Courses

3 Credits Anatomy, Physiology, & Biophysics I BE-GY 6103

Anatomy and Physiology are the sciences that identify body structures and how they function and interact, respectively. Therefore, academic training for biomedical engineering must include a sound, comprehensive knowledge of human anatomy and physiology. While the course emphasizes normal functions, it also considers the consequences of disease and injury and deals with the body's potential for recovery and compensation. The Biophysics' component examines the underlying physical principles of organ function. Part I of this two-part sequence focuses on Cell Physiology and Homeostasis, Cardiac, Nervous, and Respiratory systems. The course will be taught using a "systems engineering" approach and introduce the design considerations for artificial organs. The material includes hands-on demonstration of technology to measure EEGs, EKG and respiratory function.

3 Credits Anatomy, Physiology, & Biophysics II BE-GY 6113

Part II of this sequence focuses on the muscular, skeletal, renal and endocrine systems and includes discussions on skin and basic oncology. This part is taught using a ?systems? approach and link concepts from BE-GY 6013. The material includes hands-on demonstration of technology to measure EMG.
Prerequisites: BE-GY 6013.

3 Credits Biomedical Instrumentation BE-GY 6503

This course gives an overview on the theory, design and application of biomedical instrumentation used for dagnosis, monitoring, treatment and scientific study of physiological systems. The objective of this course is to enable students to design, build and test useful circuits, and to interface them with a computer using a data acquisition system for further signal analysis and processing. Cross-listed with BE-GY 6503.
Prerequisite: EE-UY 2024 or equivalent course in circuits, programming experience.

3 Credits Bio-optics BE-GY 6303

Recent growth in using optics technology for biomedical research and health care has been explosive. New applications are made possible by emerging technologies in lasers, optoelectronic devices, fiber optics, physical and chemical sensors and imaging?all of which are now applied to medical research, diagnostics and therapy. This sequence course on optics for biomedical students combines fundamental knowledge of the generation and interaction of electromagnetic waves with applications to the biomedical field. The goal is for this approach is to provide tools for researchers in bio-physics and to familiarize researchers, technologists and premed students with cutting-edge approaches.
Prerequisite(s): An undergraduate course in physics that includes electricity, magnetism and waves such as PH-UY 2023, an undergraduate course in physics that includes electricity, magnetism and waves such as PH-UY 2023 and multivariable calculus such as MA-UY 2122 and MA-UY 2122.

3 Credits Digital Signal Processing I BE-GY 6403

Discrete and continuous-time linear systems. Z-transform. Fourier transforms. Sampling. Discrete Fourier transform (DFT). Fast Fourier transform (FFT). Digital filtering. Design of FIR and IIR filters. Windowing. Least squares in signal processing. Minimum-phase and all-pass systems. Digital filter realizations. Matlab programming exercises.

or

3 Credits Digital Signal Processing I ECE-GY 6113

Discrete and continuous-time linear systems. Z-transform. Fourier transforms. Sampling. Discrete Fourier transform (DFT). Fast Fourier transform (FFT). Digital filtering. Design of FIR and IIR filters. Windowing. Least squares in signal processing. Minimum-phase and all-pass systems. Digital filter realizations. Matlab programming exercises. Co-listed as BE-GY 6403
Prerequisites: Graduate status. *Online version available.

3 Credits Probability and Stochastic Processes BE-GY 6453

Continuous and discrete random variables and their joint probability distribution and density functions; Functions of one random variable and their distributions; Independent random variables and conditional distributions; One function of one and two random variables; Two functions of two random variables and their joint density functions; Jointly distributed discrete random variables and their functions; Characteristic functions and higher order moments; Covariance, correlation, orthogonality; Jointly Gaussian random variables; Linear functions of Gaussian random variables and their joint density functions. Stochastic processes and the concept of Stationarity; Strict sense stationary (SSS) and wide sense stationary (WSS) processes; Auto correlation function and its properties; Poisson processes and Wiener processes; Stochastic inputs to linear time-invariant (LTI) systems and their input-output autocorrelations; Input-output power spectrum for linear systems with stochastic inputs; Minimum mean square error estimation (MMSE) and orthogonality principle; Auto regressive moving average (ARMA) processes and their power spectra. Co-listed as EL-GY 6303.
Prerequisites: Graduate status

or

3 Credits Probability and Stochastic Processes ECE-GY 6303

Continuous and discrete random variables and their joint probability distribution and density functions; Functions of one random variable and their distributions; Independent random variables and conditional distributions; One function of one and two random variables; Two functions of two random variables and their joint density functions; Jointly distributed discrete random variables and their functions; Characteristic functions and higher order moments; Covariance, correlation, orthogonality; Jointly Gaussian random variables; Linear functions of Gaussian random variables and their joint density functions. Stochastic processes and the concept of Stationarity; Strict sense stationary (SSS) and wide sense stationary (WSS) processes; Auto correlation function and its properties; Poisson processes and Wiener processes; Stochastic inputs to linear time-invariant (LTI) systems and their input-output autocorrelations; Input-output power spectrum for linear systems with stochastic inputs; Minimum mean square error estimation (MMSE) and orthogonality principle; Auto regressive moving average (ARMA) processes and their power spectra. Co-listed as BE-GY 6453.
Prerequisite: Graduate status. *Online version available.

3 Credits Applied Mathematics in Engineering CBE-GY 6153

This course covers mathematical formulation of chemical engineering problems in terms of ordinary, partial differential and differential equations. Topics include solutions of boundary and initial value problems using Green's functions and other techniques; characterization of second-order partial differential equations and properties of their solutions; asymptotic methods and numerical techniques.
Prerequisite: MA-UY 2122 and MA-UY 2132 or adviser's approval.

Taken once per year:

Colloquium in Biomedical Engineering BE-GY 9730

Engineers and scientists from industry and academia present recent developments in biomedical engineering. Students will be required to attend the department colloquium series each semester.

Seminar in Biomedical Engineering BE-GY 9740

Students present research findings if engaged in MS or PhD thesis research, or make presentations from their critical analysis of recent biomedical-engineering publications. The seminar gives students the opportunity to prepare a scientific presentation on a biomedical-engineering topic of interest and to speak before their peers, who will question them. Two and four semesters are required for master's and PhD students, respectively.

Electives or Research

You may choose up to 9 credits from the list of electives below. With permission from a graduate adviser, you may substitute a course not listed. You may also elect to do research as Guided Studies in Biomedical Engineering  (BE-GY 873x, 3 to 6 credits) without writing a thesis, or MS Thesis in Biomedical Engineering (BE-GY 997x, 6 to 9 credits).

Courses available to students pursuing an MS degree in either the Biomaterials, Medical Imaging or Bioinstrumentation tracks.

3 Credits Biomedical Imaging I BE-GY 6203

This course introduces the physics, instrumentation and signal-processing methods used in X-ray imaging (projection radiography), X-ray computed tomography, nuclear medicine (SPECT/PET), ultrasound imaging and magnetic resonance imaging. Also listed under: EL-GY 6813

Prerequisites: Undergraduate level courses in multivariable calculus (MA-UY 2112 & MA-UY 2122 or MA-UY 2114), physics (PH-UY 2033), probability (MA-UY 3012), signals and systems (EE-UY 3054). Students who do not have prior courses in signals ans systems must take EL-GY 6113 / BE-GY 6403 - Digital Signal Processing I as a prerequisite or must obtain instructor's approval; EL-GY 6123 - Image and Video Processing is also recommended but not required.

3 Credits Medical Imaging I ECE-GY 6813

This course introduces the physics, instrumentation and signal processing methods used in X-ray imaging (projection radiography), X-ray computed tomography, nuclear medicine (SPECT/PET), ultrasound imaging, magnetic resonance imaging and optical imaging. Co-listed with BE-GY 6203

Prerequisites: Undergraduate level courses in multivariable calculus (MA-UY 2112 & MA-UY 2122 or MA-UY 2114), physics (PH-UY 2033), probability (MA-UY 3012), signals and systems (EE-UY 3054). Students who do not have prior courses in signals ans systems must take EL-GY 6113 / BE-GY 6403 - Digital Signal Processing I as a prerequisite or must obtain instructor's approval; EL-GY 6123 - Image and Video Processing is also recommended but not required.

3 Credits Bio-optics BE-GY 6303

Recent growth in using optics technology for biomedical research and health care has been explosive. New applications are made possible by emerging technologies in lasers, optoelectronic devices, fiber optics, physical and chemical sensors and imaging?all of which are now applied to medical research, diagnostics and therapy. This sequence course on optics for biomedical students combines fundamental knowledge of the generation and interaction of electromagnetic waves with applications to the biomedical field. The goal is for this approach is to provide tools for researchers in bio-physics and to familiarize researchers, technologists and premed students with cutting-edge approaches.
Prerequisite(s): An undergraduate course in physics that includes electricity, magnetism and waves such as PH-UY 2023, an undergraduate course in physics that includes electricity, magnetism and waves such as PH-UY 2023 and multivariable calculus such as MA-UY 2122 and MA-UY 2122.

3 Credits Special Topics in Biomedical Engineering BE-GY 6353

Topics of special interest in Biomedical Engineering are announced before the semester in which they are offered.
Prerequisite: adviser's approval.

3 Credits Digital Signal Processing I BE-GY 6403

Discrete and continuous-time linear systems. Z-transform. Fourier transforms. Sampling. Discrete Fourier transform (DFT). Fast Fourier transform (FFT). Digital filtering. Design of FIR and IIR filters. Windowing. Least squares in signal processing. Minimum-phase and all-pass systems. Digital filter realizations. Matlab programming exercises.

3 Credits Digital Signal Processing I ECE-GY 6113

Discrete and continuous-time linear systems. Z-transform. Fourier transforms. Sampling. Discrete Fourier transform (DFT). Fast Fourier transform (FFT). Digital filtering. Design of FIR and IIR filters. Windowing. Least squares in signal processing. Minimum-phase and all-pass systems. Digital filter realizations. Matlab programming exercises. Co-listed as BE-GY 6403
Prerequisites: Graduate status. *Online version available.

3 Credits Probability and Stochastic Processes BE-GY 6453

Continuous and discrete random variables and their joint probability distribution and density functions; Functions of one random variable and their distributions; Independent random variables and conditional distributions; One function of one and two random variables; Two functions of two random variables and their joint density functions; Jointly distributed discrete random variables and their functions; Characteristic functions and higher order moments; Covariance, correlation, orthogonality; Jointly Gaussian random variables; Linear functions of Gaussian random variables and their joint density functions. Stochastic processes and the concept of Stationarity; Strict sense stationary (SSS) and wide sense stationary (WSS) processes; Auto correlation function and its properties; Poisson processes and Wiener processes; Stochastic inputs to linear time-invariant (LTI) systems and their input-output autocorrelations; Input-output power spectrum for linear systems with stochastic inputs; Minimum mean square error estimation (MMSE) and orthogonality principle; Auto regressive moving average (ARMA) processes and their power spectra. Co-listed as EL-GY 6303.
Prerequisites: Graduate status

3 Credits Probability and Stochastic Processes ECE-GY 6303

Continuous and discrete random variables and their joint probability distribution and density functions; Functions of one random variable and their distributions; Independent random variables and conditional distributions; One function of one and two random variables; Two functions of two random variables and their joint density functions; Jointly distributed discrete random variables and their functions; Characteristic functions and higher order moments; Covariance, correlation, orthogonality; Jointly Gaussian random variables; Linear functions of Gaussian random variables and their joint density functions. Stochastic processes and the concept of Stationarity; Strict sense stationary (SSS) and wide sense stationary (WSS) processes; Auto correlation function and its properties; Poisson processes and Wiener processes; Stochastic inputs to linear time-invariant (LTI) systems and their input-output autocorrelations; Input-output power spectrum for linear systems with stochastic inputs; Minimum mean square error estimation (MMSE) and orthogonality principle; Auto regressive moving average (ARMA) processes and their power spectra. Co-listed as BE-GY 6453.
Prerequisite: Graduate status. *Online version available.

3 Credits Statistics for Biomedical Engineers BE-GY 6463

This course reviews various methods of analysis for biomedical data. Contents: population and sample, confidence interval, hypothesis test, Bayesian logic, correlation, regression, design of studies, t test, chi-square test, analysis of variance, multiple regression, survival curves. Multivariable Calculus knowledge required; Probability Theory knowledge is preferred.

3 Credits Biomedical Instrumentation BE-GY 6503

This course gives an overview on the theory, design and application of biomedical instrumentation used for dagnosis, monitoring, treatment and scientific study of physiological systems. The objective of this course is to enable students to design, build and test useful circuits, and to interface them with a computer using a data acquisition system for further signal analysis and processing. Cross-listed with BE-GY 6503.
Prerequisite: EE-UY 2024 or equivalent course in circuits, programming experience.

3 Credits Drug Delivery BE-GY 6603

The course provides an integrated approach to the basic and clinical science of drug delivery. Topics: the history drug delivery; kinds of drugs to be delivered, including genes and proteins; various targeting mechanisms; transport phenomena and thermodynamic concepts; pharmacokinetics and pharmacodynamics of drug delivery, polymeric drug-delivery systems; various devices developed for controlled delivery.
Prerequisite: calculus with ordinary diff. eq.; undergraduate courses in biology, chemistry and physiology (minimum grade B).

3 Credits Orthopedic Biomechanics and Biomaterials BE-GY 6753

The course provides fundamental knowledge of the relevant background science, theory, practice and materials required to provide modern orthopedic and trauma care. Students learn about biomaterials used in orthopedics and how materials engineering has made them increasingly sophisticated. The course covers important clinical applications as well as fundamental concepts in biomechanics of bone and other tissues; materials used; wear and corrosion during use; dental implants; joint-replacement devices; stress-strain analysis, beam theory; introduction to finite element analysis design for prosthesis; and more.
Prerequisite: Calculus with ordinary diff. eq.; BE-GY 6703 Materials in Medicine.

3 Credits Biomaterials: Engineering Principles and Design Consideration BE-GY 6803

This course will provide the student with an overview of the techniques used to evaluate and design with materials used in biomedicine in the context of reconstructing, repairing, replacing or augmenting diseased or injured tissue or organs in the human body.
Prerequisites: Calculus I, Calculus II and Ordinary Differential Equations.

Course objective:
1. Introduce the concepts of CAD/FEA used with the design of non-orthopedic devices that interface to the neurologic and cardiovascular systems.
2. To present the various classes of biomaterials such as metals, ceramics, man-made polymers and those derived from nature.
3. To simulate and identify the pertinent interactions between materials and composites with living tissue and their durability.
4. To give specific examples for the design of an artificial organ, i.e. artificial heart.

3 Credits Tissue Engineering BE-GY 9443

This courses teaches basic biological processes that occur during blood contact with artificial surfaces; how to critically read and review literature on tissue engineering; how to anticipate biocompatibility issues with a variety of implant devices students may later encounter; current approaches directed toward the engineering of cell-based replacements for various tissue types.
Prerequisite: Adviser's approval.

3 Credits Bioethics Seminar BE-GY 9753

This graduate-level seminar course discusses the ethical issues relevant to today's bioengineers and molecular and cell biologists. Topics include: Darwin's theory of evolution; science and religion in twentieth-century America; Intelligent Design Theory; social Darwinism and the concomitant rise of eugenics in Europe and the U.S., the ways in which molecular genetics has challenged historical categories of race; the ethical, social, and legal implications of the Human Genome Project (specifically genetic privacy and testing, human genes and intellectual property); argo-biotechnology and the science, ethics, and politics of genetically modified organisms (GMOs); and the science, politics, and ethics of human-embryonic-stem-cell research. The student is encouraged to think about the way in which debates concerning ?nature versus nurture? have been framed historically, in order to understand current controversies over that distinction.

3 Credits Immunology: Concepts, Mechanisms and Applications in Biotechnology BT-GY 6063

The purpose of this course is to develop a general understanding of the established biochemical, molecular, cellular, and organ-level principles that govern the workings of the mammalian immune system, and to prepare the student for immunological research in the academic, government, or industrial laboratory. Topics covered include cells of the immune system and their development, pattern recognition receptors and innate immunity, molecular mechanisms of antigen processing and presentation, long distance communication and immune cells? migration, homing, and trafficking. Applications in Biotechnology and autoimmune diseases and the use of immunotherapy in industry will also be discussed.
Advisor/Instructor Permission Required

3 Credits Applied Mathematics in Engineering CBE-GY 6153

This course covers mathematical formulation of chemical engineering problems in terms of ordinary, partial differential and differential equations. Topics include solutions of boundary and initial value problems using Green's functions and other techniques; characterization of second-order partial differential equations and properties of their solutions; asymptotic methods and numerical techniques.
Prerequisite: MA-UY 2122 and MA-UY 2132 or adviser's approval.

3 Credits Protein Engineering CM-GY 9433

This course introduces modern protein engineering techniques available to researchers to understand protein structure and function and to create entirely new proteins for a variety of purposes. This is a new field that lies on the interface of chemistry, biology and engineering. The first part of the course discusses protein composition and structure and various genetic, biochemical and chemical techniques required to engineer proteins?all followed by specific topics. Topics include designing proteins that are highly structured and active at high temperatures and in non-aqueous solvents; that selectively interact with other proteins, small molecules and nucleic acids for therapeutic purposes; and that catalyze new reactions.
Prerequisite: CM-GY 9413 or adviser's approval.

3 Credits Computer Vision CS-GY 6643

An important goal of artificial intelligence (AI) is to equip computers with the capability of interpreting visual inputs. Computer vision is an area in AI that deals with the construction of explicit, meaningful descriptions of physical objects from images. It includes as parts many techniques from image processing, pattern recognition, geometric modeling, and cognitive processing. This course introduces students to the fundamental concepts and techniques in computer vision.
Knowledge of Data Structures and Algorithms, proficiency in programming, and familiarity with matrix arithmetic. Prerequisites: Graduate standing.

3 Credits Image and Video Processing ECE-GY 6123

This course introduces fundamentals of image and video processing, including color image capture and representation; color coordinate conversion; contrast enhancement; spatial domain filtering (linear convolution, median and morphological filtering); two-dimensional (2D) Fourier transform and frequency domain interpretation of linear convolution; 2D Discrete Fourier Transform (DFT) and DFT domain filtering; image sampling and resizing; geometric transformation and image registration; video motion characterization and estimation; video stabilization and panoramic view generation; basic compression techniques (entropy coding, vector quantization, predictive coding, transform coding); JPEG image compression standard; wavelet transform and JPEG2000 standard; video compression using adaptive spatial and temporal prediction; video coding standards (MPEGx/H26x); Stereo and multi-view image and video processing (depth from disparity, disparity estimation, video synthesis, compression). Students will learn to implement selected algorithms in MATLAB or C-language.
Prerequisites: Graduate Standing or Undergraduate Standing having completed EE-UY 3054 and EE-UY 2233. Suggested Corequisites: EL-GY 6113 and EL-GY 6303 (not required)

3 Credits Digital Signal Processing Laboratory ECE-GY 6183

Real-time implementation of algorithms for digital signal processing (DSP) with an emphasis on audio processing. Audio input-output and buffering. Filtering (recursive and non-recursive filters, structures). Fast Fourier transform and windowed spectral analysis. Digital audio effects (delay line, amplitude modulation, reverberation, distortion, phase vocoder). Time-varying and adaptive filters. Students with learn to implement these algorithms for real-time audio processing in software (e.g., Matlab and Python).
Prerequisites: EE-UY 3054 or equivalent (for undergraduate students) or Graduate Standing.

3 Credits Machine Learning ECE-GY 6143

This course is an introduction to the field of machine learning, covering fundamental techniques for classification, regression, dimensionality reduction, clustering, and model selection. A broad range of algorithms will be covered, such as linear and logistic regression, neural networks, deep learning, support vector machines, tree-based methods, expectation maximization, and principal components analysis. The course will include hands-on exercises with real data from different application areas (e.g. text, audio, images). Students will learn to train and validate machine learning models and analyze their performance. May not take if student has already completed ECE-UY 4563.
Prerequisite: Graduate status with undergraduate level probability theory

3 Credits Real Time Embedded Systems ECE-GY 6483

This course provides an overview of the unique concepts and techniques needed to design and implement computer systems having real-time response requirements in an embedded environment. It contrasts the concepts and techniques of real time and embedded systems with those of more traditional computer systems. Topics include: Basic concepts of real time and embedded systems, hardware features, programming languages, real time operating systems, synchronization techniques, performance optimization and current trends in real time and embedded systems such as incorporating internet connectivity.
Prerequisite: Knowledge of C, Pascal or other programming language and a basic understanding of computer architecture.

MA-GA 2852 Please refer to the bulletin for more information

3 Credits Special Topics ME-GY 7863

These course numbers are reserved for special topics offered periodically by the Mechanical Engineering Program and are open to first-year graduate students. When offered, the subject matter is indicated as part of the title after the words ?Special Topics,? and the complete title appears on the student's transcript.
Prerequisite: tailored to the offering.
Prerequisite: Graduate standing or advisor approval

3 Credits Physical Concepts of Polymer Nanocomposites PH-GY 6403

This course presents fundamental aspects of polymer nanocomposites and updates on recent advancements and modern applications. Topics include nanostructured materials; assembly at interfaces; interactions on surfaces; properties of polymer nanocomposites; reliability; nanodevices.

BMSC-GA 4404 Please refer to the bulletin for more information

BMSC-GA 4409 Please refer to the bulletin for more information

BMSC-GA 4427 Please refer to the bulletin for more information

BMSC-GA 4428 Please refer to the bulletin for more information

BMSC-GA 4469 Please refer to the bulletin for more information