You must complete 128 credits, as defined below, to graduate from the School of Engineering with a Bachelor of Science in Physics and Mathematics. Please note that the curriculum that follows applies to students who began classes in the fall of 2014 or later. If you entered the School of Engineering prior to that date, please review the curriculum and typical course schedule for students entering prior to fall 2014.

- 3 Credits Mechanics PH-UY 1013
- This course is the first of a three-semester lecture sequence in general physics for science and engineering students. Motion of particles and systems of particles. One-dimensional motion. Vectors and two-dimensional motions. Forces and acceleration. Conservation of energy and momentum. Rotations. The free and driven harmonic oscillator. Gravitation. (This class meets four hours per week for lectures and recitation.)

Prerequisites: MA-UY 1024 or an approved equivalent. Corequisites: MA-UY 1124 or approved equivalent, and EX-UY 1 - 3 Credits Electricity, Magnetism, & Fluids PH-UY 2023
- This is the second course of a three-semester lecture sequence in general physics for science and engineering students. Fluids at rest and in motion. An introduction to electric and magnetic forces and fields. Electric charge density. Electric fields from simple charge distributions. Electric potential. Capacitance.
Magnetic forces. Magnetic field from a current loop. Inductance. Magnetism
in matter. Current and resistance. (This class meets four hours per week for lectures and recitation.)

Prerequisites: PH-UY 1013 and MA-UY 1124 or an approved equivalent. Co-requisite: PH-UY 2121 General Physics Laboratory I, and EX-UY 1 - 3 Credits Waves, Optics, & Thermodynamics PH-UY 2033
- This is the third course of a three-semester lecture sequence in general physics for science and engineering students. Water, sound and electromagnetic waves. Reflection, scattering and absorption. Standing waves and spectra. Superposition, diffraction and beats. Geometrical optics. Introduction to thermodynamics; temperature, heat, and entropy. (This class meets four hours per week for lectures and recitation.)

Prerequisites: PH-UY 2121 and PH-UY 2023. Co-requisites: PH-UY 2131, and EX-UY 1. - 4 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.

Prerequisite: PH-UY 2023; Co-requisite: MA-UY 2034 - 1 Credits General Physics Laboratory I PH-UY 2121
- PH-UY 2121 General Physics Laboratory I (0.5:1:0:1). An introductory level experimental course. Fundamental laboratory experiments in classical mechanics and electrostatics. Stresses basic experimental techniques, error analysis, and written presentation of experiment results. Experiments require progressively more detailed and sophisticated analysis. This laboratory class meets for three hours on alternate weeks.

Prerequisites: PH-UY 1013 and MA-UY 1124 or equivalent. Co-requisite: PH-UY 2023. - 1 Credits General Physics Laboratory II PH-UY 2131
- PH 2131 General Physics Laboratory II (0.5:1:0:1). The second part of the introductory physics laboratory program. Fundamental laboratory experiments in E&M, waves, optics, and thermodynamics. Stresses experimental models and design, error and data analysis. This laboratory class meets for three hours on alternate weeks.

Prerequisites: PH-UY 2121 and PH-UY 2023. Corequisite: PH-UY 2033 - 4 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.

Prerequisites: PH-UY 2023 and MA-UY 2034; Co-requisite: PH-UY 2033. - 2 Credits Junior Physics Laboratory PH-UY 3002
- An intermediate level laboratory course providing in depth exposure to a selection of classic physics experiments. Students' experimental skill set is expanded and data analysis and communication skills developed.

Prerequisites: PH-UY 2131 and PH-UY 2033; Co-requisites: PH-UY 2344 and MA-UY 2224. - 4 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: PH-UY 2033 and MA-UY 2114. - 4 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: PH-UY 2344, MA-UY 2114, and MA-UY 2224. - 4 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: PH-UY 2344, MA-UY 2114, and MA-UY 2224.

- 4 Credits Calculus I for Engineers 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 Credits Calculus II for Engineers 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. - 4 Credits Linear Algebra and Differential Equations MA-UY 2034
- MA-UY 2034 is an introduction to ordinary differential equations and linear algebra. The course develops the techniques for the analytic and numeric solutions of ordinary differential equations (and systems) that are widely used in modern engineering and science. Linear algebra is used as a tool for solving systems of linear equations as well as for understanding the structure of solutions to linear (systems) of differential equations. Topics covered include the fundamental concepts of linear algebra such as Gaussian elimination, matrix theory, linear transformations, vector spaces, subspaces, basis, eigenvectors, eigenvalues and the diagonalization of matrices, as well as the techniques for the analytic and numeric solutions of ordinary differential equations (and systems) that commonly appear in modern engineering and science.

Prerequisite: MA-UY 1124, MA-UY 1424 or MA-UY 1132. - 4 Credits Calculus III: Multi-Dimensional Calculus MA-UY 2114
- Functions of several variables. Vectors in the plane and space. Partial derivatives with applications, especially Lagrange multipliers. Double and triple integrals. Spherical and cylindrical coordinates. Surface and line integrals. Divergence, gradient, and curl. Theorems of Gauss and Stokes.

Prerequisite: MA-UY 1124, MA-UY 1424, or MA-UY 1132. - 4 Credits Data Analysis MA-UY 2224
- An introductory course to probability and statistics. It affords the student some acquaintance with both probability and statistics in a single term. Topics in Probability include mathematical treatment of chance; combinatorics; binomial, Poisson, and Gaussian distributions; the Central Limit Theorem and the normal approximation. Topics in Statistics include sampling distribution of sample mean and sample variance; normal, t-, and Chi-square distributions; confidence intervals; testing of hypotheses; least square regression model. Applications to scientific, industrial, and financial data are integrated into the course. NOTE: Cannot be taken if student is also taking or has already taken MA-UY 3012 or MA-UY 3022.

Prerequisite: MA-UY 1124, MA-UY1424, or MA-UY 1132 - 3 Credits Advanced Linear Algebra and Complex Variables MA-UY 3113
- This course provides a deeper understanding of topics introduced in MA 2012 and MA 2034 and continues the development of those topics,while also covering functions of a Complex Variable. Topics covered include: The Gram-Schmidt Process,inner product spaces and applications , Singular value decomposition,LU decomposition. Derivatives and Cauchy-Riemann equations, Integrals and Cauchy integral theorem. Power and Laurent Series, Residue theory.

Prerequisites: MA-UY 2122 or MA-UY 2114 AND MA-UY 2012 or MA-UY 2034. Note: Course not open to students who have taken MA-UY 3112. - 3 Credits Applied Partial Differential Equations MA-UY 4413
- Modeling of physical processes. Classification of equations. Formulation and treatment of boundary- and initial-value problems. Greens functions. Maximum principle. Separation of variables. Fourier series and integrals. Quasilinear first-order equations and characteristics. DAlembert solution of wave equation. Conservation laws and shock waves.

Prerequisites: MA-UY 108 or Departmental adviser’s approval. - 3 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, MA-UY 2034 or MA-UY 108.

Select 7 credits from the list of undergraduate applied physics elective courses. Graduate courses may be substituted with advisor’s approval.

Select 10 credits from the list of undergraduate math elective courses. Graduate courses may be substituted with advisor’s approval.

14 credits are reserved for free electives and independent study courses, of which 8 credits are reserved for a 6 credit applied physics project plus a 2 credit senior physics seminar or a 4 credit math project/thesis and an extra 4 credit math elective.

You are required to take 16 credits in the humanities and social sciences requiring EXPOS-UA1 and EXPOS-UA2 as prerequisites. To gain some breadth and depth of knowledge, it is required that you take courses in at least two disciplines and at least one course at an advanced level.

- 1 Credits Engineering and Technology Forum EG-UY 1001
- In this course the notion of invention, innovation and entrepreneurship (i2e) is introduced to the students’ educational experience. Students will be exposed to elements of a research-intensive institution and diverse research performed by leading engineers, scientists, inventors and entrepreneurs.
- 4 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 Credits Writing the Essay: EXPOS-UA 1
- This foundational writing course is required for CAS, Stern, Nursing, Social Work, Steinhardt and Tandon incoming undergraduates. Writing The Essay provides instruction and practice in critical reading, creative and logical thinking, and clear, persuasive writing. Students learn to analyze and interpret written texts, to use texts as evidence, to develop ideas, and to write exploratory and argumentative essays. Exploration, inquiry, reflection, analysis, revision, and collaborative learning are emphasized. In Fall, sections 16-125 are available to incoming undergraduates on the WSQ campus and sections 126-167 are available to incoming undergraduates on the BROOKLYN campus. Students are NOT permitted to add or switch sections after the first week of classes without first obtaining EWP permission. Contact: dm1@nyu.edu Two special versions requiring department consent are available to qualifying undergraduates. Writing the Essay, Science (sections 1-7 offered both Fall and Spring) is tailored for UA students with a STRONG interested in science, medicine or psychology. Students must contact an advisor to discuss this option and obtain access. Writing The Essay, Goddard (sections 8-13, offered in Fall only) is offered ONLY for students who live in the Goddard Residential College. Writing the Essay, Rubin (sections 14-15, offered in Fall only) is offered ONLY for students who have been selected for the Rubin Themed Writing the Essay Community. Students placed in these sections will receive instructions for enrollment.
- 4 Credits The Advanced College Essay EXPOS-UA 2
- The course follows Writing the Essay (EW 1013) and provides advanced instruction in analyzing and interpreting written texts from a variety of academic disciplines, using written texts as evidence, developing ideas, and writing argumentative essays. It stresses analysis, argument, reflection, revision, and collaborative learning.

Prerequisite(s): EW 1013 - 4 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

And either of these courses can be taken:

- 2 Credits Physics: the Genesis of Technology PH-UY 1002
- This course introduces contemporary topics in physics, along with readings and discussions of topics with technological implications.

Prerequisite: Only first-year students are permitted to enroll in this introductory level course. - 2 Credits The Art of Mathematics MA-UY 1002
- This is an introductory course about Mathematics. Areas of Mathematics. History of Mathematics. Mathematical Methods. Great Mathematicians. Famous open and solved mathematical problems. The study of Mathematics. Mathematical Software.

Prerequisite: Only first-year students are permitted to enroll in this introductory level course.

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