
Academics
Physics and Mathematics, B.S.
Mathematics deals with abstraction, logic, and quantitative reasoning. Because it has applications to nearly every branch of science and engineering, it’s essential for mathematicians to think about how their work infiltrates other branches of learning. Advances in physics — for example, those in electromagnetism and thermodynamics — often resonate deeply with mathematics.
At the School of Engineering, the BS in Applied Physics and Mathematics program serves as a means to bridge these 2 disciplines. The dual major allows you to gain a foothold in separate but substantial fields. In addition to learning the fundamentals of physics and math, our students pursue a specialized course of study that a minor in either field just can’t match.
But we also want to make sure your skills transfer over to the real world. That’s why we provide internship opportunities at major financial, insurance, and technology firms in the New York area.
Students with experience in both mathematics and physics enjoy diverse and interesting careers. Our graduates have the freedom to explore such stimulating fields as chemistry, biology, medicine, and engineering. They’re also qualified for positions in software design, economics, aerospace engineering, law, and business.
Curriculum
OverviewYou 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.
Physics Requirements (33 credits)
 3 Credits Mechanics PHUY1013
 This course is the first of a threesemester lecture sequence in general physics for science and engineering students. Motion of particles and systems of particles. Onedimensional motion. Vectors and twodimensional 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: MAUY 1024 or an approved equivalent. Corequisites: MAUY 1124 or approved equivalent, and EXUY 1  3 Credits Electricity, Magnetism, & Fluids PHUY2023
 This is the second course of a threesemester 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: PHUY 1013 and MAUY 1124 or an approved equivalent. Corequisite: PHUY 2121 General Physics Laboratory I, and EXUY 1  3 Credits Waves, Optics, & Thermodynamics PHUY2033
 This is the third course of a threesemester 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: PHUY 2121 and PHUY 2023. Corequisites: PHUY 2131, and EXUY 1.  4 Credits Analytical Mechanics PHUY2104
 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: PHUY 2023; Corequisite: MAUY 2034  1 Credits General Physics Laboratory I PHUY2121
 PHUY 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: PHUY 1013 and MAUY 1124 or equivalent. Corequisite: PHUY 2023.  1 Credits General Physics Laboratory II PHUY2131
 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: PHUY 2121 and PHUY 2023. Corequisite: PHUY 2033  4 Credits Introduction to Modern and Solid State Physics PHUY2344
 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: PHUY 2023 and MAUY 2034; Corequisite: PHUY 2033.  2 Credits Junior Physics Laboratory PHUY3002
 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: PHUY 2131 and PHUY 2033; Corequisites: PHUY 2344 and MAUY 2224.  4 Credits Electricity and Magnetism PHUY3234
 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: PHUY 2033 and MAUY 2114.  4 Credits Thermodynamics and Statistical Physics PHUY4124
 The course covers fundamental laws of macroscopic thermodynamics, heat, internal energy and entropy. Topics include an introduction to statistical physics, and applications of Maxwell, FermiDirac and BoseEinstein distributions.
Prerequisites: PHUY 2344, MAUY 2114, and MAUY 2224.  4 Credits Introduction to the Quantum Theory PHUY4364
 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, neutronproton scattering, and quark model of baryons.
Prerequisites: PHUY 2344, MAUY 2114, and MAUY 2224.
Math Requirements (29 credits)
 4 Credits Calculus I for Engineers MAUY1024
 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 rules, the chain rule, applications of the chain rule, maxima and minima, optimization. The definite integral, the Fundamental Theorem of Calculus and interpretations, theorems about definite integrals, antiderivatives. MAUY 1324 is for students who wish to take MAUY 1024 but need more review of precalculus. MAUY 1324 covers the same material as MAUY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.
Prerequisite: Placement Exam or MAUY 912 or MAUY 914 (with a grade of B or better). Corequisite: EXUY 1  4 Credits Calculus II for Engineers MAUY1124
 This course covers 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, functions of two variables, graphs of functions of two variables, contour diagrams, linear functions, functions of three variables. MAUY 1424 is for students who wish to take MAUY 1124 but need more review of precalculus. MAUY 1424 covers the same material as MAUY 1124 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.
Prerequisites: MAUY 1022 (with a grade of B or better) or MAUY 1024 or MAUY 1324 (with a grade of B or better).
Corequisite: EXUY 1.  4 Credits Linear Algebra and Differential Equations MAUY2034
 MAUY 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: MAUY 1124, MAUY 1424 or MAUY 1132. Note: Not open to students who have taken MAUY 3044 or MAUY 3054 or MAUY 3083 or MAUY 4204.  4 Credits Calculus Iii: Multidimensional Calculus MAUY2114
 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: MAUY 1124 or MAUY 1424 or MAUY 1132.  4 Credits Data Analysis MAUY2224
 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 distributions of sample mean and sample variance; normal, t, and Chisquare distributions; confidence intervals; testing of hypotheses; least squares regression model. Applications to scientific, industrial, and financial data are integrated into the course.NOTE: Not open to students who have taken MAUY 2233 or MAUY 3012 or MAUY 3022.
Prerequisite: MAUY 1124, MAUY1424, or MAUY 1132  3 Credits Advanced Linear Algebra and Complex Variables MAUY3113
 This course provides a deeper understanding of topics introduced in MAUY 2012 and MAUY 2034 and continues the development of those topics, while also covering functions of a Complex Variable. Topics covered include: The GramSchmidt process, inner product spaces and applications, singular value decomposition, LU decomposition. Derivatives and CauchyRiemann equations, integrals and Cauchy integral theorem. Power and Laurent Series, residue theory.
Prerequisites: (MAUY 2122 or MAUY 2114) AND (MAUY 2012 or MAUY 2034). Note: Not open to students who have taken MAUY 1533, MAUY 3112 or MAUY 4433.  MAUY4413 Please refer to the bulletin for more information
 MAUY4423 Please refer to the bulletin for more information
Physics Electives (7 Credits)
Select 7 credits from the list of undergraduate applied physics elective courses. Graduate courses may be substituted with advisor’s approval.
Math Electives (10 Credits)
Select 10 credits from the list of undergraduate math elective courses. Graduate courses may be substituted with advisor’s approval.
Free Electives, Independent Study and Projects (14 Credits)
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.
Electives in the Humanities and Social Sciences (16 Credits)
You are required to take 16 credits in the humanities and social sciences requiring EXPOSUA1 and EXPOSUA2 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.
Other Required Courses (19 Credits)
 1 Credits Engineering and Technology Forum EGUY1001
 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 researchintensive institution and diverse research performed by leading engineers, scientists, inventors and entrepreneurs.
 4 Credits General Chemistry for Engineers CMUY1004
 This is a onesemester 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: EXUY 1  4 Credits Writing the Essay: EXPOSUA1
 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 2019, sections 001, 002, 004, 005, 006, and 007 are reserved for CAS firstyear students with a strong interest in science and/or prehealth who were placed in these sections as part of the virtual advising process (in spring, sections 1,2,4, 6). They are not open to other students and there are no exceptions. In Fall, sections 16125 are available to incoming undergraduates on the WSQ campus and sections 126167 are available to incoming undergraduates at Tandon on the BROOKLYN campus. Writing The Essay, ResidentLife (sections 815, offered in Fall only) is reserved ONLY for students who have been selected for the Goddard or Rubin "Themed Writing the Essay Community." No exceptions. Students are enrolled by a ResidentLife administrator. Students are advised NOT to add or switch sections after the first week of classes without first obtaining EWP permission. English Language Learners uncertain about placement into “Writing the Essay” might qualify for the “International Writing Workshop” sequence, an alternative to the core requirement. For more information contact ewpwritingsurvey@nyu.edu.
 4 Credits The Advanced College Essay EXPOSUA2
 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 CSUY1114
 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: EXUY 1
And either of these courses can be taken:
 2 Credits Physics: the Genesis of Technology PHUY1002
 This course introduces contemporary topics in physics, along with readings and discussions of topics with technological implications.
Prerequisite: Only firstyear students are permitted to enroll in this introductory level course.  2 Credits The Art of Mathematics MAUY1002
 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 firstyear students are permitted to enroll in this introductory level course.
Sample Course Schedule
OverviewThis schedule lists specific courses you might take during your 4 years at the School of Engineering; it does not indicate required courses. It applies to students who begin classes in the fall of 2009 and onwards. 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 2009.
First Year
Fall Semester
Choose one:
 2 Credits Physics: the Genesis of Technology PHUY1002
 This course introduces contemporary topics in physics, along with readings and discussions of topics with technological implications.
Prerequisite: Only firstyear students are permitted to enroll in this introductory level course.  2 Credits The Art of Mathematics MAUY1002
 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 firstyear students are permitted to enroll in this introductory level course.
Take all:
 4 Credits Calculus I for Engineers MAUY1024
 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 rules, the chain rule, applications of the chain rule, maxima and minima, optimization. The definite integral, the Fundamental Theorem of Calculus and interpretations, theorems about definite integrals, antiderivatives. MAUY 1324 is for students who wish to take MAUY 1024 but need more review of precalculus. MAUY 1324 covers the same material as MAUY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.
Prerequisite: Placement Exam or MAUY 912 or MAUY 914 (with a grade of B or better). Corequisite: EXUY 1  4 Credits General Chemistry for Engineers CMUY1004
 This is a onesemester 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: EXUY 1  4 Credits Writing the Essay: EXPOSUA1
 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 2019, sections 001, 002, 004, 005, 006, and 007 are reserved for CAS firstyear students with a strong interest in science and/or prehealth who were placed in these sections as part of the virtual advising process (in spring, sections 1,2,4, 6). They are not open to other students and there are no exceptions. In Fall, sections 16125 are available to incoming undergraduates on the WSQ campus and sections 126167 are available to incoming undergraduates at Tandon on the BROOKLYN campus. Writing The Essay, ResidentLife (sections 815, offered in Fall only) is reserved ONLY for students who have been selected for the Goddard or Rubin "Themed Writing the Essay Community." No exceptions. Students are enrolled by a ResidentLife administrator. Students are advised NOT to add or switch sections after the first week of classes without first obtaining EWP permission. English Language Learners uncertain about placement into “Writing the Essay” might qualify for the “International Writing Workshop” sequence, an alternative to the core requirement. For more information contact ewpwritingsurvey@nyu.edu.
 1 Credits Engineering and Technology Forum EGUY1001
 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 researchintensive institution and diverse research performed by leading engineers, scientists, inventors and entrepreneurs.
Spring Semester
 3 Credits Mechanics PHUY1013
 This course is the first of a threesemester lecture sequence in general physics for science and engineering students. Motion of particles and systems of particles. Onedimensional motion. Vectors and twodimensional 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: MAUY 1024 or an approved equivalent. Corequisites: MAUY 1124 or approved equivalent, and EXUY 1  4 Credits Calculus II for Engineers MAUY1124
 This course covers 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, functions of two variables, graphs of functions of two variables, contour diagrams, linear functions, functions of three variables. MAUY 1424 is for students who wish to take MAUY 1124 but need more review of precalculus. MAUY 1424 covers the same material as MAUY 1124 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.
Prerequisites: MAUY 1022 (with a grade of B or better) or MAUY 1024 or MAUY 1324 (with a grade of B or better).
Corequisite: EXUY 1.  4 Credits Introduction to Programming & Problem Solving CSUY1114
 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: EXUY 1  4 Credits The Advanced College Essay EXPOSUA2
 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
Second Year
Fall Semester
 3 Credits Electricity, Magnetism, & Fluids PHUY2023
 This is the second course of a threesemester 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: PHUY 1013 and MAUY 1124 or an approved equivalent. Corequisite: PHUY 2121 General Physics Laboratory I, and EXUY 1  1 Credits General Physics Laboratory I PHUY2121
 PHUY 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: PHUY 1013 and MAUY 1124 or equivalent. Corequisite: PHUY 2023.  4 Credits Analytical Mechanics PHUY2104
 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: PHUY 2023; Corequisite: MAUY 2034  4 Credits Linear Algebra and Differential Equations MAUY2034
 MAUY 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: MAUY 1124, MAUY 1424 or MAUY 1132. Note: Not open to students who have taken MAUY 3044 or MAUY 3054 or MAUY 3083 or MAUY 4204.
HuSS Elective 1, Credits: 4.00*
Spring Semester
 3 Credits Waves, Optics, & Thermodynamics PHUY2033
 This is the third course of a threesemester 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: PHUY 2121 and PHUY 2023. Corequisites: PHUY 2131, and EXUY 1.  1 Credits General Physics Laboratory II PHUY2131
 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: PHUY 2121 and PHUY 2023. Corequisite: PHUY 2033  4 Credits Calculus Iii: Multidimensional Calculus MAUY2114
 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: MAUY 1124 or MAUY 1424 or MAUY 1132.
MA ***3 Math Elective, Credits: 3.00
HuSS Elective 2, Credits: 4.00*
*To gain some breadth and depth of knowledge, take courses in at least two disciplines and at least one course at an advanced level.
Third Year
Fall Semester
 4 Credits Introduction to Modern and Solid State Physics PHUY2344
 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: PHUY 2023 and MAUY 2034; Corequisite: PHUY 2033.  4 Credits Data Analysis MAUY2224
 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 distributions of sample mean and sample variance; normal, t, and Chisquare distributions; confidence intervals; testing of hypotheses; least squares regression model. Applications to scientific, industrial, and financial data are integrated into the course.NOTE: Not open to students who have taken MAUY 2233 or MAUY 3012 or MAUY 3022.
Prerequisite: MAUY 1124, MAUY1424, or MAUY 1132  Chemical Laboratory Safety CMGY5040
 This course discusses problems of health and safety in chemical laboratories, including how to work safely with dangerous chemicals. This course must be completed by graduate and undergraduate chemistry students before they begin laboratory research.
PH ***4 Physics Elective, Credits: 4.00
HuSS Elective 3, Credits: 4.00*
Spring Semester
 2 Credits Junior Physics Laboratory PHUY3002
 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: PHUY 2131 and PHUY 2033; Corequisites: PHUY 2344 and MAUY 2224.  4 Credits Electricity and Magnetism PHUY3234
 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: PHUY 2033 and MAUY 2114.  3 Credits Advanced Linear Algebra and Complex Variables MAUY3113
 This course provides a deeper understanding of topics introduced in MAUY 2012 and MAUY 2034 and continues the development of those topics, while also covering functions of a Complex Variable. Topics covered include: The GramSchmidt process, inner product spaces and applications, singular value decomposition, LU decomposition. Derivatives and CauchyRiemann equations, integrals and Cauchy integral theorem. Power and Laurent Series, residue theory.
Prerequisites: (MAUY 2122 or MAUY 2114) AND (MAUY 2012 or MAUY 2034). Note: Not open to students who have taken MAUY 1533, MAUY 3112 or MAUY 4433.
MA ***3 Math Elective, Credits: 4.00
HuSS Elective 4, Credits: 4.00*
*To gain some breadth and depth of knowledge, take courses in at least two disciplines and at least one course at an advanced level.
Fourth Year
Fall Semester
Take all:
 4 Credits Introduction to the Quantum Theory PHUY4364
 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, neutronproton scattering, and quark model of baryons.
Prerequisites: PHUY 2344, MAUY 2114, and MAUY 2224.  MAUY4413 Please refer to the bulletin for more information
PH ***3 Physics Elective, Credits: 3.00
XYZ ***3 Free Elective, Credits: 3.00
and either take both:
 2 Credits Introduction to Senior Project in Physics PHUY4902
 A qualified senior physics student or group of students work with a faculty member (and possibly graduate students) on an advanced problem in physics. In this introductory phase the student(s) and adviser select a suitable theoretical or experimental problem in the subject area and use various resources to solve it.
 2 Credits Senior Seminar in Physics PHUY4912
 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.
or take:
MA ***4 Math Elective, Credits: 4.00
Spring Semester
Take all:
 4 Credits Thermodynamics and Statistical Physics PHUY4124
 The course covers fundamental laws of macroscopic thermodynamics, heat, internal energy and entropy. Topics include an introduction to statistical physics, and applications of Maxwell, FermiDirac and BoseEinstein distributions.
Prerequisites: PHUY 2344, MAUY 2114, and MAUY 2224.  MAUY4423 Please refer to the bulletin for more information
MA ***3 Math Elective, Credits: 3.00
XYZ ***3 Free Elective, Credits: 3.00
Choose one:
 4 Credits Senior Project in Physics PHUY4904
 In the project’s concluding phase, senior physics students or group of students work with a faculty member (and possibly graduate students) to solve an advanced problem in interdisciplinary physics. The conclusion of the project is a written report and an oral presentation made to the supervising faculty.
 4 Credits Project in Mathematics I MAUY3914
 In this course, students read, study, and investigate selected topics in mathematics. Problems are discussed and presented by participating students.
Prerequisite: approval of departmental adviser. Note: This course is repeatable for credit, but does not allow multiple enrollment in the same term.