The core of this program is 29 credits of required math courses and 30 credits of required physics courses. In addition, you must take 9 credits of math electives and 12 credits of physics electives. 16 credits are reserved for free electives and independent study courses, of which 6 to 8 credits are recommended for a project. The remaining credits are used to satisfy other Institute and state requirements.

- 4.00 Credits Calculus I MA-UY 1024
- This course covers library of Functions: functions of one variable. Limits, derivatives of functions defined by graphs, tables and formulas, differentiation rules for power, polynomial, exponential and logarithmic functions, derivatives of trigonometric functions, the product and quotient rule, the chain rule, applications of the chain rule, maxima and minima, optimization. MA 1324 is for students who wish to take MA 1024 but need more review of precalculus. MA1324 covers the same material as MA1024 but with more contact hours a week, incorporating a full discussion of the required precalculus topics.

Prerequisite: Placement Exam or MA-UY 912 or MA-UY 914. Corequisite: EX-UY 1 - 4.00 Credits Calculus II MA-UY 1124
- This course covers definite integrals, theorems about integrals, anti-derivatives, second fundamental theorem of calculus, techniques of integration, introduction to ordinary differential equations, improper integrals, numerical methods of integration, applications of integration, sequences, series, power series, approximations of functions via Taylor polynomials, Taylor series.

Corequisite: EX-UY 1. - 2.00 Credits Multivariable Calculus A MA-UY 2112
- This course introduces Multivariable Calculus. Analysis of functions of several variables, vector valued functions, partial derivatives and multiple integrals.

Prerequisite: MA-UY 2012. - 2.00 Credits Multivariable Calculus B MA-UY 2122
- This course continues Multivariable Calculus. Optimization techniques, parametric equations, line integrals, surface integrals and major theorems concerning their applications.

Prerequisite: MA-UY 2112. - 2.00 Credits Elements of Linear Algebra I MA-UY 2012
- This course introduces vector concepts. Linear transformations.Matrices and Determinants. Characteristic roots and eigenfunctions.

Prerequisite: MA-UY 1124 or equivalent. - 2.00 Credits Ordinary Differential Equations MA-UY 2132
- This course covers first order differential equations: modeling and solving. Stability of autonomous equations. Higher order linear ordinary differential equations: Solution bases, Wronskian and initial value problems. Linear system of first-order differential equations with constant coefficients: Elimination and eigenvalue method of solution. Elementary concepts of numerical analysis. Numerical solution of initial value problems for ordinary differential equations.

Prerequisite or Corequisite: MA-UY 2012. - 2.00 Credits Introduction to Probability I MA-UY 3012
- This course covers probability of events. Random variables. Discrete and continuous distributions. Joint distributions. Expectation. Functions of a random variable. Central limit theorem.

Prerequisite: MA-UY 2112 or MA-UY 2114. - 2.00 Credits Complex Variables I MA-UY 3112
- This course covers functions of a complex variable. Derivatives and Cauchy-Riemann equations. Integrals and Cauchy integral theorem. Power and Laurent Series. Residue theory.

Prerequisite: MA-UY 2122 or equivalent. - 3.00 Credits Introduction to Mathematical Statistics MA-UY 4113
- This is a standard first course in mathematical statistics, recommended for those who will take advanced courses in statistics. Topics covered: Sampling distributions, tests of hypotheses, significance tests, point and interval estimation, regression and analysis of variance.

Prerequisite: MA-UY 3012. - 3.00 Credits Applied Partial Differential Equations MA-UY 4413
- This course looks at the heat equation, homogeneous and non-homogeneous boundary conditions, Green’s function, separation of variables, Fourier series and Fourier transform, Maximum principle, existence and uniqueness, Poisson integral formula, the wave equation. Shock waves, conservation laws.

Prerequisite: MA-UY 2132 and MA-UY 3112. - 3.00 Credits Introductory Numerical Analysis MA-UY 4423
- This course covers: Polynomial interpolation and approximation of functions. Divided differences. Least-squares data fitting, orthogonal polynomials. Numerical differentiation and integration. Solution of nonlinear equations. Gaussian elimination, pivoting, iterative refinement, conditioning of matrices. Numerical solution of ordinary differential equations.

Prerequisites: MA-UY 2132 and some experience in computer programming.

- 4.00 Credits Introductory Physics I PH-UY 1004
- This course is the first of a two-semester integrated lecture and laboratory sequence in general physics for science and engineering students. One-dimensional motions. Vectors and two-dimensional motions. Newton’s laws of motion. Conservation of energy and momentum. Rotational motions. Gravity. Statics and elasticity. Fluids. Oscillations. Heat and the laws of thermodynamics.

Prerequisite: MA-UY 1024 or an approved equivalent. Co-requisite: MA-UY 1124 or an approved equivalent, and EX-UY 1 - 4.00 Credits Introductory Physics II PH-UY 2004
- This is the second course of a two-semester, integrated lecture and laboratory sequence in general physics for science and engineering students. Electric forces and fields. Electric potential and capacitance. Electric current. Magnetic forces and fields. Faradays law and inductance. Maxwell’s equations. Mechanical and electromagnetic waves. Geometrical optics. Interference and diffraction.

Prerequisites: PH-UY 1004, MA-UY 1124 or an approved equivalent. Corequisite: EX-UY 1 - 4.00 Credits Introduction to Modern and Solid State Physics PH-UY 2344
- Special theory of relativity, Michelson Morley experiment. Planck’s quantum hypothesis, photoelectric effect, Compton effect, Rutherford scattering, Bohr’s atom, DeBroglie wavelength, electron diffraction, wave function, uncertainty principle, Schrodinger equation. Application to: square well potential, one electron atom. Atomic nucleus, fission and fusion. Energy bands in a periodic lattice, Kronig Penney model, valence, conduction bands, impurity states, electron mobility. Semiconductor properties. Introduction to superconductivity; electron pairs, energy gap, Josephson effect.

Prerequisite: PH-UY 2004 or PH-UY 2023; Co-requisites: PH-UY 2033. - 4.00 Credits Analytical Mechanics PH-UY 2104
- The course covers statics by virtual work and potential energy methods. Stability of equilibrium. Particle dynamics, harmonic oscillator and planetary motion. Rigid body dynamics in two and three dimensions. Lagrangian mechanics. Dynamics of oscillating systems.

Prerequisites: MA-UY 2122, and PH-UY 2004 or PH-UY 2023. - 4.00 Credits Electricity and Magnetism PH-UY 3234
- The course covers properties of the electrostatic, magnetostatic and electromagnetic field in vacuum and in material media. Maxwell’s equations with applications to elementary problems.

Prerequisites: MA-UY 2122, and PH-UY 2004 or PH-UY 2033. - 4.00 Credits Thermodynamics and Statistical Physics PH-UY 4124
- The course covers fundamental laws of macroscopic thermodynamics, heat, internal energy and entropy. Topics include an introduction to statistical physics, and applications of Maxwell, Fermi-Dirac and Bose-Einstein distributions.

Prerequisites: MA-UY 2122 and PH-UY 2344. - 4.00 Credits Introduction to the Quantum Theory PH-UY 4364
- The course introduces quantitative introduction to the quantum theory, which describes understanding light, electrons, atoms, nuclei and solid matter. Superposition principle, expectation values, momentum operator and wave function, duality, current vector, Hermitian operators, angular momentum, solution of the radial equation, electron in a magnetic field, perturbation theory, WKB approximation, identical particles. Applications include alpha decay, electrons in a periodic lattice, hydrogen spectrum, helium atom, neutron-proton scattering, and quark model of baryons.

Prerequisites: MA-UY 2122 and PH-UY 2344. - 2.00 Credits Senior Seminar in Physics PH-UY 4912
- Senior physics students, in consultation with the instructor, study and prepare presentations on several current research topics in the general area of interdisciplinary physics. Students’ performance is based on the mastery of the material chosen and also on the quality of the presentation made to the instructor and the seminar members.

- 4.00 Credits General Chemistry for Engineers CM-UY 1004
- This is a one-semester introductory course in general chemistry. It covers chemical equations, stoichiometry, thermodynamics, gases, atomic and molecular structure, periodic table, chemical bonding, states of matter, chemical equilibrium, organic, inorganic and polymeric materials and electrochemistry.

Corequisite: EX-UY 1 - 4.00 Credits Introduction to Programming & Problem Solving CS-UY 1114
- This course introduces problem solving and computer programming and is for undergraduate Computer Science and Computer Engineering majors who have limited prior experience in programming in any language. The course covers fundamentals of computer programming and its underlying principles using the Python programming language. Concepts and methods introduced in the
course are illustrated by examples from various disciplines. ABET competencies: a,b,c, e, f, g, k

Corequisite: EX-UY 1 - 4.00 Credits Writing & Humanities 1 EN-UY 1014
- 4.00 Credits Writing & Humanities 2 EN-UY 1204
- 4.00 Credits Modern World History HI-UY 2104

You should select 9 credits from the following list of math elective courses.

- 3.00 Credits Problem Solving and Proofs MA-UY 3103
- This course covers mathematical problem-solving, proofs and innovative reasoning. Discussion of independent challenging problems from Analysis, Complex Analysis, Probability, Combinatorics, Linear Algebra, Number Theory and Graph Theory.

Prerequisites: MA-UY 2312, MA-UY 2012. - 3.00 Credits Differential Geometry MA-UY 3303
- This course covers curves and Surfaces. Curvature. First and second fundamental form. Gaussian curvature. Geodesics, Minimal Surfaces. Gauss-Bonnet Theorem.

Prerequisite: MA-UY 2122. - 3.00 Credits Analysis I MA-UY 4613
- This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, uniform convergence, continuity, partial differentiation, extreme value problems with constraints, Riemann integrals, line integrals, improper integrals, integrals with parameters, transformations, Riemann-Stieltjes integral, uniform and absolute convergence of integrals. Beta and Gamma functions.

Prerequisites: MA-UY 2122 and MA-UY 2132. - 3.00 Credits Analysis II MA-UY 4623
- This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, uniform convergence, continuity, partial differentiation, extreme value problems with constraints, Riemann integrals, line integrals, improper integrals, integrals with parameters, transformations, Riemann-Stieltjes integral, uniform and absolute convergence of integrals. Beta and Gamma functions.

Prerequisites: MA-UY 4613 - 3.00 Credits Linear Optimization MA-UY 3203
- This course examines linear optimization problems with constraints; optimality conditions and duality theory, the simplex method, complexity of the simplex method, interior point methods, selected applications, network flow problems and the network simplex method.

Prerequisites: MA-UY 2312, MA-UY 2112. - 3.00 Credits Introduction to Number Theory MA-UY 4013
- This course covers properties of integers and prime numbers. Congruences. Theorems of Fermat, Euler and Wilson. Quadratic residues. Diophantine equations.

Prerequisite: MA-UY 1124 or equivalent. - 3.00 Credits Elements of Abstract Algebra MA-UY 4023
- This course covers basic properties of groups, rings, fields, Euclidean rings and modules. Field extensions and Galois theory. Finite fields.

Prerequisite: MA-UY 2012.

You should select 12 credits from the following list of physics elective courses.

- 3.00 Credits Astronomy and Astrophysics PH-UY 2813
- This course covers historical development of observational astronomy. Traditional and modern observational techniques. Theories of formation and evolution of stars, planets and galaxies. Current developments in astronomy, cosmology and astrophysics.

Prerequisite: PH-UY 2031 and PH-UY 2033 - 4.00 Credits Introduction to Polymer Physics PH-UY 3054
- This course introduces polymer physics and its applications in engineering. The course includes polymer assemblies, morphology and motion, mechanical and dielectric response, transitions and relaxations, time-temperature equivalence, yield and fracture, conducting polymers, optics of polymers, oriented structures, nanofibers, composites.

Prerequisite: CM-UY 1004 or C-UY 1014; Co-requisites: PH-UY 2004 or PH-UY 2023. - 4.00 Credits Concepts of Nanotechnology PH-UY 3244
- This course is the first of an interdisciplinary, two-semester sequence on concepts, techniques and applications of nanotechnology. Introduction to nanotechnology, examples of nanoscale systems. Systematics in miniaturization from the mm to the nm scale. Limits to miniaturization. Quantum concepts and elementary Schrodinger theory. Quantum effects in the behavior of chemical matter. Examples of self-assembled nanosystems from nature and from contemporary industrial products.

Prerequisite: PH-UY 2004 or PH-UY 2033. - 4.00 Credits Light and Lighting PH-UY 3424
- The course explores physical concepts in conversion of electric energy into visible light. Nature of light. Visualization of light. Principles of operation and characteristics of modern light sources. Incandescent and tungsten halogen lamps. Fluorescent mercury lamps. Low-pressure sodium lamps. High intensity discharge (HID) lamps. Solid-state light sources. Latest trends in lighting technology. (Crosslisted as EE-UY 3424.)

Prerequisites: CM-UY 1004, and PH-UY 2033 or PH-UY 2004. - 4.00 Credits Introduction to Modern Optics PH-UY 3474
- This course covers the physics of optics using both classical and semi-classical descriptions. The classical and quantum interactions of light with matter. Diffraction of waves and wave packets by obstacles. Fourier transform optics, holography, Fourier transform spectroscopy. Coherence and quantum aspects of light. Geometrical optics. Matrix optics. Crystal optics. Introduction to electro-optics and nonlinear optics.

Prerequisite: PH-UY 2004 or PH-UY 2033. - 4.00 Credits Techniques and Applications of Nanotechnology PH-UY 4244
- This is the second of a two-course sequence on concepts and techniques of nanotechnology. Novel function and performance can occur with materials or devices of size scales of one to 100 nanometers, a range extending from molecular scale to that of typical linewidths in contemporary microelectronics. Nanosystems may provide entirely new functions, by virtue of access enabled by the small size. Photo and x-ray lithographic patterning. Scanning probe microscopes for observation and for fabrication. Molecular machines as envisioned by Drexler. The role of Van der Waals force. Questions of machine manufacturability on the nm scale. The IBM GMR hard-drive read head. Micro- and nano-electromechanical devices and systems. Single-electron electronics. Molecular electronics.

Prerequisite: PH-UY 3244. - 4.00 Credits Quantum Optics PH-UY 4444
- Beginning with a review of classical optics and quantum mechanics, this course covers foundations of spectroscopy, including atomic transition rates, selection rules and spectral line shapes. The course explores the quantum nature of light. Topics include photon statistics, coherent states, squeezed light, resonant light-atom interactions, atoms in cavities and laser cooling.

Prerequisite: PH-UY 3474. - 4.00 Credits Solid State Physics PH-UY 4554
- The course covers basic concepts in condensed matter physics and preparation for the advanced quantum theory of solid state.

Prerequisite: PH-UY 2344.

*Graduate courses may be substituted with adviser's approval for the following physics elective courses:*

- 3.00 Credits Physical Basis of Nanotechnology PH-GY 5343
- This course focuses on the underlying physical basis of nanotechnology. Introduction to nanotechnology, examples of nanoscale systems. Systematics in miniaturization from the mm to the nm scale. Limits to miniaturization. Quantum concepts and elementary Schrodinger theory. Quantum effects in the behavior of chemical matter. Examples of self-assembled nanosystems from nature and from contemporary industrial products.

Prerequisite: PH-UY 2004 or PH-UY 2033 - 3.00 Credits Physical Techniques and Application of Nanotechnology PH-GY 5443
- This course focuses on physical techniques and applications of nanotechnology. Scanning probe microscopes for observation and fabrication. Photolithographic methods of patterning, deposition techniques. Dense memory based on arrays of cantilevers. Magnetic Tunnel Junctions as elements of magnetic disc memory read heads and in Magnetic Random Access Memory. Nanoscale high-electric-field devices. Nanoscale confinement techniques and devices. Applications of carbon nanotubes and semiconductor nanowires. Assembly methods for nanoscale objects.

Prerequisite: PH-UY 2004 or PH-UY 2033 - 3.00 Credits Modern Optics PH-GY 5473
- The course covers the physics of optics, using both classical and semi-classical descriptions. Topics include the classical and quantum interactions of light with matter. Diffraction of waves and wave packets by obstacles. Fourier transform optics, holography, Fourier transform spectroscopy. Coherence and quantum aspects of light. Geometrical optics. Matrix optics. Crystal optics. Introduction to electro-optics and nonlinear optics.

Prerequisites: MA-UY 2122 and PH-UY 3234 equivalents. - 3.00 Credits Physics of Nanoelectronics PH-GY 5493
- This course covers limits to the ongoing miniaturization (Moore’s Law) of the successful silicon-device technology imposed by physical limitations of energy dissipation, quantum tunneling and discrete quantum electron states. Quantum physical concepts and elementary Schrodinger theory. Conductance quantum and magnetic flux quantum. Alternative physical concepts appropriate for devices of size scales of 1 to 10 nanometers, emphasizing role of power dissipation. Tunnel diode, resonant tunnel diode, electron wave transistor; spin valve, tunnel valve, magnetic disk and random access memory; single electron transistor, molecular crossbar latch, quantum cellular automata including molecular and magnetic realizations. Josephson junction and “rapid single flux quantum” computation. Photo- and x-ray lithographic patterning, electron beam patterning, scanning probe microscopes for observation and for fabrication; cantilever array as dense memory, use of carbon nanotubes and of DNA and related biological elements as building blocks and in self-assembly strategies.

Prerequisites: PH-UY 2004 or PH-UY 2033. - 3.00 Credits Physics of Quantum Computing PH-GY 5553
- This course explores limits to the performance of binary computers, traveling salesman and factorization problems, security of encryption. The concept of the quantum computer based on linear superposition of basis states. The information content of the qubit. Algorithmic improvements enabled in the hypothetical quantum computer. Isolated two-level quantum systems, the principle of linear superposition as well established. Coherence as a limit on quantum computer realization. Introduction of concepts underlying the present approaches to realizing qubits (singly and in interaction) based on physical systems. The systems in present consideration are based on light photons in fiber optic systems; electron charges in double well potentials, analogous to the hydrogen molecular ion; nuclear spins manipulated via the electron-nuclear spin interaction, and systems of ions such as Be and Cd which are trapped in linear arrays using methods of ultra-high vacuum, radiofrequency trapping and laser-based cooling and manipulation of atomic states. Summary and comparison of the several approaches.

Prerequisites: PH-UY 2004 or PH-UY 2033 - 3.00 Credits Physics of Alternative Energy PH-GY 5663
- The course examines non-petroleum sources of energy including photovoltaic cells, photocatalytic generators of hydrogen from water, and nuclear fusion reactors. The advanced physics of these emerging technical areas are introduced in this course. Semiconductor junctions, optical absorption in semiconductors, photovoltaic effect. Energy conversion efficiency of the silicon solar cell. Single crystal, polycrystal, and thin film types of solar cells. Excitons in bulk and in confined geometries. Excitons in energy transport within an absorbing structure. Methods of making photocatalytic surfaces and structures for water splitting. Conditions for nuclear fusion. Plasmas and plasma compression. The toroidal chamber with magnetic coils as it appears in recent designs. Nuclear fusion by laser compression (inertial fusion). Small scale exploratory approaches to fusion based on liquid compression and electric field ionization of deuterium gas.

Prerequisites: PH-UY 2004 or PH-UY 2033

You are required to take 12 credits in the humanities and social sciences, with EN 1204 and HI 2104 as prerequisites. To gain depth of knowledge, it is recommended that one or more of these electives be taken at advanced level.

Sixteen credits are reserved for free electives and independent study courses, of which 6 to 8 credits are recommended for use on a project or thesis topic.

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