# Mathematics, BS

### Mathematics forms the backbone of many scientific fields. It provides the theory and methods essential to understanding the fundamentals of such areas as physics, engineering, and computer science. With a firm grasp of mathematics, you’ll have the widest possible base from which to launch explorations of related disciplines.

The School of Engineering's BS in Mathematics program prepares you for success. Our students benefit not only from a full spectrum of math courses but from hands-on experience in the real world. We provide this through unique internship opportunities at organizations such as MIT Lincoln Laboratories, Verizon, Credit Suisse First Boston, New York Hall of Science, and the CIA.

Our students have the freedom to pursue varied and exciting careers, math majors can become software designers, biostatisticians, industrial engineers, imaging scientists, aerospace mathematicians, and economists. Today, mathematicians find rewarding work in a wide range of companies, including investment banks and government organizations like the National Security Agency.

## Curriculum

Goals and Objective- Command of core areas in both pure and applied mathematics, including but not limited to real and complex analysis, linear algebra, ordinary and partial differential equations.
- Mastery of a particular applied or engineering field and how mathematics is used in that field.
- Readiness for a variety of career options following graduation, including, but not limited to graduate study in applied mathematics, engineering, medicine, as well as professional careers in consulting, business & finance, and technology.

Rationale

The Tandon B.S. in Mathematics program is designed to provide a student with the knowledge and skills needed to both start a career in a mathematically-oriented field and adapt easily to changes in both the field and one’s career directions. The program has the following components:

- A core set of required fundamental mathematics courses
- Mathematics electives
- A cohesive set of courses that focus on a particular field of engineering or applied science. The student works together with their advisor to choose these courses appropriately.

Students must complete 121 credits, as defined below, to graduate from the NYU Tandon School of Engineering with a Bachelor of Science in Mathematics. **Please note that the curriculum that follows applies to students who begin classes in the Fall of 2017 or later. ** For students who enter the NYU Tandon School of Engineering prior to that date, please refer to the bulletin website: curriculum and typical course schedule for students entering prior to Fall 2017.

The NYU Tandon School of Engineering also offers a Physics and Mathematics, B.S. which is a dual major in both subjects.

Courses

### Required Courses

Core Mathematics Requirements (41 Credits)

- 2 Credits The Art of Mathematics MA-UY1002
- 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.

- 4 Credits Calculus I for Engineers MA-UY1024
- 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, anti-derivatives. MA-UY 1324 is for students who wish to take MA-UY 1024 but need more review of precalculus. MA-UY 1324 covers the same material as MA-UY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

Prerequisite: Placement Exam or MA-UY 912 or MA-UY 914 (with a grade of B or better). Corequisite: EX-UY 1

Or

- 4 Credits Integrated Calculus I for Engineers MA-UY1324
- 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, anti-derivatives. MA-UY 1324 is for students who wish to take MA-UY 1024 but need more review of precalculus. MA-UY 1324 covers the same material as MA-UY 1024 but with more contact hours per 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-UY1124
- 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. MA-UY 1424 is for students who wish to take MA-UY 1124 but need more review of precalculus. MA-UY 1424 covers the same material as MA-UY 1124 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

Prerequisites: MA-UY 1022 (with a grade of B or better) or MA-UY 1024 or MA-UY 1324 (with a grade of B or better).

Corequisite: EX-UY 1.

Or

- 4 Credits Integrated Calculus II for Engineers MA-UY1424
- This course MA-UY 1424 is for students who wish to take MA-UY 1124 but need more review of precalculus. MA-UY 1424 covers the same material as MA-UY 1124 but with more contact hours a week, incorporating a full discussion of the required precalculus topics.

Prerequisites: MA-UY 1022 or MA-UY 1024 or MA-UY 1324. Note: credit for this course may be used to satisfy the minimum credit requirement for graduation. Corequisite: EX-UY 1

- MA-UY153 Please refer to the bulletin for more information
- 4 Credits Calculus Iii: Multi-dimensional Calculus MA-UY2114
- 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 or MA-UY 1424 or MA-UY 1132. - 3 Credits Analysis I MA-UY4613
- This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, continuity, partial differentiation, extreme value problems with constraints.

Prerequisites: (MA-UY 2122 or MA-UY 2114) and (MA-UY 2132 or MA-UY 2034) - 3 Credits Diff Equat & Num Methods MA-UY108
- 3 Credits Introduction to Probability MA-UY2233
- Standard first course in probability, recommended for those planning further work in probability or statistics. Probability of events, random variables and expectations, discrete and continuous distributions, joint and conditional distributions, moment generating functions, the central limit theorem.

Prerequisites: MA-UY 109, MA-UY 2112, OR MA-UY 2114. Note: Not open to students who have taken MA-UY 2224 or MA-UY 3012 or MA-UY 3022. - 3 Credits Applied Partial Differential Equations MA-UY4413
- Modeling of physical processes. Classification of equations. Formulation and treatment of boundary- and initial-value problems. Green’s functions. Maximum principle. Separation of variables. Fourier series and integrals. Quasilinear first-order equations and characteristics. D’Alembert solution of wave equation. Conservation laws and shock waves.

Prerequisite: MA-UY 2114 and (MA-UY 3083 or MA-UY 4204) - 3 Credits Complex Variables MA-UY4433
- This course covers: Functions of a complex variable. Derivatives and Cauchy-Riemann equations. Integrals and Cauchy integral theory. Power and Laurent series. Residue theory. Conformal mappings. Schwarz-Christoffel transformations.

Prerequisites: MA-UY 2132 and MA-UY 3112. Note: Not open to students who have taken MA-UY 3113. - 3 Credits Introduction to Mathematical Statistics MA-UY4113
- 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.

Prerequisites: MA-UY 2233. - MA-UY4423 Please refer to the bulletin for more information
- MA-UY239 Please refer to the bulletin for more information

Other Required Courses (28 Credits)

- 1 Credits Engineering and Technology Forum EG-UY1001
- 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 Introduction to Programming & Problem Solving CS-UY1114
- 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 Credits General Chemistry for Engineers CM-UY1004
- 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 - 3 Credits Mechanics PH-UY1013
- 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-UY2023
- 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-UY2033
- 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. - 1 Credits General Physics Laboratory I PH-UY2121
- 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-UY2131
- 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 - EXPOS-UA1 Please refer to the bulletin for more information
- EXPOS-UA2 Please refer to the bulletin for more information

**Electives**

#### Math Electives (9 Credits)

Students should select three math elective courses totaling at least 9 credits.

#### Other Electives (28 Credits)

- Students are required to take 16 credits in the humanities and social sciences.
**Note:**EXPOS-UA 1 and EXPOS-UA 2**do not**count toward the Humanities and Social Sciences Elective requirement of 16 credits. - 12 credits are reserved for free electives, with advisor’s approval.

### Engineering Component (15 Credits)

Students should select five engineering courses totaling at least 15 credits in Engineering Components. The Engineering Component of the B.S. in Mathematics Program must be in at least one of the following disciplines:

- Chemical and Biomolecular Engineering
- Civil Engineering
- Computer Engineering
- Computer Science
- Electrical Engineering
- Mechanical Engineering

Interdisciplinary components involving two or more of the fields above will be considered. The courses comprising a math major’s engineering component must be approved in advance by an official Mathematics Department advisor.

Sample engineering courses in Engineering Components are listed under the Sample Course Schedule section.

**Total: 121 Credits**

Minor and Double Major

### Minor in Mathematics

A student not majoring in math or math/physics can obtain a minor in mathematics by fulfilling the following requirements:

- 16 credits of math courses
- At least 8 credits of math courses must be in addition to the major's math requirements
- At least 8 of the 16 credits must be taken while enrolled at Tandon
- Minimum 2.0 minor GPA

All courses used for the Minor in Mathematics must be pre-approved by the Math Department Advisor. Courses with similar content cannot be used towards the minor.

### Dual Major in Mathematics and Physics

You may also pursue a dual major in mathematics and physics. Advisers from both the mathematics and physics programs must approve specific course requirements for the 128-credit degree.

## Sample Course Schedule

B.S. in MathematicsHere's a look at what your schedule might look like as you pursue a Bachelor of Science in Mathematics at the School of Engineering.

### First Year

#### Fall Semester

- 4 Credits Calculus I for Engineers MA-UY1024
- 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, anti-derivatives. MA-UY 1324 is for students who wish to take MA-UY 1024 but need more review of precalculus. MA-UY 1324 covers the same material as MA-UY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

Prerequisite: Placement Exam or MA-UY 912 or MA-UY 914 (with a grade of B or better). Corequisite: EX-UY 1

or

- 4 Credits Integrated Calculus I for Engineers MA-UY1324
- 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, anti-derivatives. MA-UY 1324 is for students who wish to take MA-UY 1024 but need more review of precalculus. MA-UY 1324 covers the same material as MA-UY 1024 but with more contact hours per 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.

- 2 Credits The Art of Mathematics MA-UY1002
- 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. - 4 Credits General Chemistry for Engineers CM-UY1004
- 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 - EXPOS-UA1 Please refer to the bulletin for more information
- 1 Credits Engineering and Technology Forum EG-UY1001
- 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.

#### Spring Semester

- 4 Credits Calculus II for Engineers MA-UY1124
- 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. MA-UY 1424 is for students who wish to take MA-UY 1124 but need more review of precalculus. MA-UY 1424 covers the same material as MA-UY 1124 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.

Prerequisites: MA-UY 1022 (with a grade of B or better) or MA-UY 1024 or MA-UY 1324 (with a grade of B or better).

Corequisite: EX-UY 1.

or

- 4 Credits Integrated Calculus II for Engineers MA-UY1424
- This course MA-UY 1424 is for students who wish to take MA-UY 1124 but need more review of precalculus. MA-UY 1424 covers the same material as MA-UY 1124 but with more contact hours a week, incorporating a full discussion of the required precalculus topics.

Prerequisites: MA-UY 1022 or MA-UY 1024 or MA-UY 1324. Note: credit for this course may be used to satisfy the minimum credit requirement for graduation. Corequisite: EX-UY 1

- 3 Credits Mechanics PH-UY1013
- 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 - EXPOS-UA2 Please refer to the bulletin for more information
- 4 Credits Introduction to Programming & Problem Solving CS-UY1114
- 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

### Second Year

#### Fall Semester

- MA-UY153 Please refer to the bulletin for more information
- 3 Credits Electricity, Magnetism, & Fluids PH-UY2023
- 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 - 1 Credits General Physics Laboratory I PH-UY2121
- 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.

Engineering Course #1, Credits: 3.00

#### Spring Semester

- 4 Credits Calculus Iii: Multi-dimensional Calculus MA-UY2114
- 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 or MA-UY 1424 or MA-UY 1132. - 3 Credits Waves, Optics, & Thermodynamics PH-UY2033
- 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. - 1 Credits General Physics Laboratory II PH-UY2131
- 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

Engineering Course #2, Credits: 3.00

### Third Year

#### Fall Semester

- 3 Credits Analysis I MA-UY4613
- This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, continuity, partial differentiation, extreme value problems with constraints.

Prerequisites: (MA-UY 2122 or MA-UY 2114) and (MA-UY 2132 or MA-UY 2034) - 3 Credits Diff Equat & Num Methods MA-UY108

Engineering Course #3, Credits: 3.00

Free Elective #1, Credits: 3.00

#### Spring Semester

- 3 Credits Introduction to Probability MA-UY2233
- Standard first course in probability, recommended for those planning further work in probability or statistics. Probability of events, random variables and expectations, discrete and continuous distributions, joint and conditional distributions, moment generating functions, the central limit theorem.

Prerequisites: MA-UY 109, MA-UY 2112, OR MA-UY 2114. Note: Not open to students who have taken MA-UY 2224 or MA-UY 3012 or MA-UY 3022. - 3 Credits Applied Partial Differential Equations MA-UY4413
- Modeling of physical processes. Classification of equations. Formulation and treatment of boundary- and initial-value problems. Green’s functions. Maximum principle. Separation of variables. Fourier series and integrals. Quasilinear first-order equations and characteristics. D’Alembert solution of wave equation. Conservation laws and shock waves.

Prerequisite: MA-UY 2114 and (MA-UY 3083 or MA-UY 4204) - 3 Credits Complex Variables MA-UY4433
- This course covers: Functions of a complex variable. Derivatives and Cauchy-Riemann equations. Integrals and Cauchy integral theory. Power and Laurent series. Residue theory. Conformal mappings. Schwarz-Christoffel transformations.

Prerequisites: MA-UY 2132 and MA-UY 3112. Note: Not open to students who have taken MA-UY 3113.

Engineering Course #4, Credits: 3.00

### Fourth Year

#### Fall Semester

- 3 Credits Introduction to Mathematical Statistics MA-UY4113
- 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.

Prerequisites: MA-UY 2233. - MA-UY4423 Please refer to the bulletin for more information

Free Elective #2, Credits: 3.00

Engineering Course #5, Credits: 3.00

#### Spring Semester

Math Elective #2, Credits: 3.00Math Elective #3, Credits: 3.00

Free Elective #3, Credits: 3.00

Free Elective #4, Credits: 3.00

Sample Engineering Components

#### Chemical & Biomolecular Engineering

- 2 Credits Introduction to Chemical & Biomolecular Engineering CBE-UY1002
- This course introduces the chemical and biomolecular engineering profession, its history and its career potential. The course containsselected topics on basic chemical and biomolecular engineering, plant visits, and seminars covering the full range of chemical and biomolecular engineering profession from

emerging areas to those found in more traditional positions.

Prerequisites: CM-UY 1004, EG-UY 1003 and First-year standing - 4 Credits Analysis of Chemical and Biomolecular Processes CBE-UY2124
- This course prepares students to formulate and solve material and energy balances on chemical and biomolecular process systems and lays the foundation for subsequent courses in thermodynamics, unit operations, kinetics and process dynamics, and control. The course introduces the fundamental engineering approach to problem solving: breaking down a process into its components, establishing the relations between known and unknown process variables, assembling the information needed to solve for the unknowns and, finally, obtaining the solution using relevant computational methods.

Prerequisites: CM-UY 1004 and MA-UY 1024 (B- or better). - 3 Credits Chemical and Biomolecular Engineering Thermodynamics CBE-UY3153
- The course covers thermodynamics of flow systems. Topics include properties of fluids with advanced equations of state; properties of non-ideal mixtures; activity-coefficient models for non-electrolyte and electrolyte solutions; phase-equilibrium calculations at low and elevated pressures by computer procedures; and chemical reaction equilibria.

Prerequisites: CBE-UY 2124 and CM-UY 2614. - 3 Credits Transport I CBE-UY3313
- The course establishes fundamental concepts in momentum and mass transfer and their applications in chemical and biomolecular systems. Topics in Momentum Transfer include macroscopic (integral) balances on finite control volumes of fluids (determination of inflow, outflow quantities), and microscopic (differential) balances on infinitesimal volumes of fluids (determination of fluid-velocity profiles and pressure profiles). Topics in Mass Transfer include diffusion and convection with applications in separation processes and biomolecular systems.

Prerequisites: MA-UY 2132 or MA-UY 2034 and CBE-UY 2124. - 3 Credits Transport II CBE-UY3323
- The course expands understanding in mass transfer, establishes fundamental concepts in heat transfer, and introduces engineering aspects of transport. Topics in Mass Transfer include diffusion-limited reactions with applications in biomolecular systems, transport in porous media, and mass transfer across membranes with applications in chemical and biomolecular systems. Topics in Heat Transfer include the basic mechanisms of conduction and convection. Topics in engineering aspects of transport include flow in closed conduits, heat-transfer equipment, and examples of simultaneous Heat and Mass Transfer.

Prerequisite: CBE-UY 3313.

#### Civil Engineering

- 3 Credits Statics CE-UY2113
- The course covers: Vector treatment of static and dynamic equilibrium of particles and rigid bodies; equivalent forces and couple systems; distributed forces; static analysis of determinate trusses, frames and machines; friction; centroid and center of gravity, and moment of inertia.

Prerequisite: PH-UY 1013 and MA-UY 1024 or MA-UY 1324 or equivalent (C or better). - 3 Credits Mechanics of Materials CE-UY2123
- This course introduces basic principles of stress and strain in axial loading, shear, torsion and bending, along with principles of transformation of stress for design. Laboratory experiments provide hands-on experience.

Prerequisite: PH-UY 1013 and CE-UY 2113 (C or better) or equivalents. - 3 Credits Fluid Mechanics and Hydraulics CE-UY2213
- The course examines the basic principles of fluid mechanics with beginning applications to hydraulic design. Topics include fluid properties, fluid statics, elementary fluid dynamics and Bernoulli equation, continuity, energy and momentum equations, and fluid kinematics. Additional topics are laminar

and turbulent flow, boundary layer characteristics, drag and lift concepts (flow over immersed bodies), dimensional analysis, and fluid measurements.

Prerequisite: CE-UY 2113 or equivalent. - 2 Credits Structural Dynamics CE-UY3122
- The course covers: Three-dimensional treatment of the kinetics of particles and rigid bodies using various coordinate systems; Newton’s law, work, energy, impulse and momentum; and an introduction to dynamics of one, two and multi-degree of freedom systems, with and without damping.

Prerequisites: MA-UY 2034 (or MA-UY 2012) and CE-UY 2113 or equivalents: Co-requisite: CE-UY 3133 or equivalent. - 3 Credits Structural Analysis CE-UY3133
- This course offers in-depth coverage of structural analysis techniques. Topics: analysis of statically determinate structures; deflection calculations using energy methods; analysis of statically indeterminate structures using superposition; influence lines; and slope deflection, moment distribution and matrix analysis of structures. Computer applications are included.

Prerequisites for Brooklyn Engineering Students: MA-UY 2034; and CE-UY 2123 or CE-UY 2113 with a grade of B+ or better.

Prerequisites for Abu Dhabi Students: MATH-AD 116 and MATH-AD 121; and ENGR-AD 237 or ENGR-AD 111. - 3 Credits Transportation Engineering CE-UY2343
- This course provides an introduction to transportation engineering. The course will cover travel demand forecasting, road user and vehicle characteristics, traffic engineering studies, engineering economic analysis, and highway design. The highway design element will focus on the basic design concepts of horizontal and vertical alignment, superelevation, and cross-section design. The course will also cover flexible pavement design, design of parking facilities, as well as bikeway and walkway design.

Prerequisites: CE-UY 1002 or CE-UY 1502 or permission of Civil Engineering Program Advisor

#### Computer Engineering

- 4 Credits Introduction to Programming & Problem Solving CS-UY1114
- 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 - EE-UY1012 Please refer to the bulletin for more information
- EE-UY2013 Please refer to the bulletin for more information
- EE-UY2024 Please refer to the bulletin for more information
- 4 Credits Digital Logic and State Machine Design CS-UY2204
- This course covers combinational and sequential digital circuits. Topics: Introduction to digital systems. Number systems and binary arithmetic. Switching algebra and logic design. Error detection and correction. Combinational integrated circuits, including adders. Timing hazards. Sequential circuits, flipflops, state diagrams and synchronous machine synthesis. Programmable Logic Devices, PLA, PAL and FPGA. Finite-state machine design. Memory elements. A grade of C or better is required of undergraduate computer-engineering majors.

Prerequisite: CS-UY 1114 (C- or better) or CS-UY 1133 (C- or better). ABET competencies: a, c, e, k.

#### Computer Science

- 4 Credits Introduction to Programming & Problem Solving CS-UY1114
- 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 Credits Discrete Mathematics MA-UY2314
- Logic, proofs, set theory, functions, relations, asymptotic notation, recurrences, modeling computation, graph theory.

Prerequisite: Math Diagnostic Exam or MA-UY 912 or MA-UY 914 (minimum calculus level required)

Prerequisite for Shanghai students: MATH-SHU 110. Note: This course and CS-GY 6003 cannot both be taken for credit. - 4 Credits Object Oriented Programming CS-UY2124
- This intermediate-level programming course teaches object-oriented programming in C++. Topics: Pointers, dynamic memory allocation and recursion. Classes and objects including constructors, destructors, methods (member functions) and data members. Access and the interface to relationships of classes including composition, association and inheritance. Polymorphism through function overloading operators. Inheritance and templates. Use of the standard template library containers and algorithms.

Prerequisite: CS-UY 1134 (C- or better); Corequisite: EX-UY 1 - 4 Credits Data Structures and Algorithms CS-UY1134
- This course covers abstract data types and the implementation and use of standard data structures along with fundamental algorithms and the basics of algorithm analysis. Not open to students who have taken CS-UY 2134.

Prerequisite: CS-UY 1114 (C- or better); Corequisite: EX-UY 1 - 3 Credits Design & Analysis of Algorithms CS-UY2413
- This course covers fundamental principles of the design and analysis of algorithms. Topics include asymptotic notation, recurrences, randomized algorithms, sorting and selection, balanced binary search trees, augmented data structures, advanced data structures, algorithms on strings, graph algorithms, geometric algorithms, greedy algorithms, dynamic programming and NP completeness.

Prerequisites for Brooklyn Engineering Students: (CS-UY 2134 or CS-UY 1134) and (CS-UY 2124 or CS-UY 1124) (C- or better) and MA-UY 2314

Prerequisites for Abu Dhabi Students: (CS-UY 2134 or CS-UY 1134) and (CS-UY 2124 or CS-UY 1124) (C- or better) and MATH-AD 131

Prerequisites for Shanghai Students: CSCI-SHU 210 (C- or better) and CSCI-SHU 2314 or MATH-SHU 120.

#### Electrical Engineering

- EE-UY2013 Please refer to the bulletin for more information
- EE-UY2024 Please refer to the bulletin for more information
- EE-UY3054 Please refer to the bulletin for more information
- EE-UY3114 Please refer to the bulletin for more information
- EE-UY3124 Please refer to the bulletin for more information

#### Mechanical Engineering

- 3 Credits Introduction to Materials Science ME-UY2813
- Students in this course become familiar with atomic structure and bonding, atomic arrangement in crystals, crystal imperfections, mechanical behavior and failure of materials and binary phase diagrams.

Prerequisites: PH-UY 1013 and CM-UY 1004 (or CM-UY 1014 and CM-UY 1024). Co-requisite: ME-UY 2811. - 1 Credits Materials Science Laboratory ME-UY2811
- Students learn to characterize the microstructure and crystal structure of a material by optical and scanning electron microscopy and X-ray diffraction. The mechanical characterization is accomplished by hardness, tensile and yield strength, impact and fatigue testing.

Prerequisites: PH-UY 1013, CM-UY 1004 (or CM-UY 1014 and CM-UY 1024). Co-requisite: ME-UY 2813. - 3 Credits Statics ME-UY2213
- The course covers three-dimensional vector treatment of the static equilibrium of particles and rigid bodies. Topics: Equivalent force and couple systems. Distributed force systems. Static analysis of trusses, frames and machines. Friction, impending motion. Methods of virtual work.

Prerequisite: PH-UY 1013 and MA-UY 1024. Co-requisite: ME-UY 2211. - 1 Credits Statics Laboratory ME-UY2211
- The course deals with measurement and calculations of bending stress, bending moment, shear forces and deflections in beams, buckling of struts and equilibrium analysis of structures.

Co-requisite: ME-UY 2213. - 3 Credits Thermodynamics ME-UY3333
- The course centers on properties of pure substances; concepts of work and heat; closed and open systems. Topics: Fundamental laws of thermodynamics. Carnot and Clasius statements of the 2nd law; entropy and entropy production; heat engines, refrigerators, heat pumps; efficiencies, coefficients of performance.

Prerequisite: PH-UY 2033, MA-UY 1124 and MA-UY 2132 or MA-UY 2034. - 3 Credits Mechanics of Materials ME-UY3213
- The course examines the Concept of Stresses and Strains in two and three dimensions, Stress-strain relationships, Stress transformation, Strain transformation, Axial members, Torsion of shafts, Bending of beams.

Prerequisites: ME-UY 2213, MT-UY 2813 and MA-UY 2132 or MA-UY 2034. Co-requisite: ME-UY 3211. - 3 Credits Fluid Mechanics ME-UY3313
- This course introduces fluid kinematics, hydrostatics and thermodynamics. Topics: Basic conservation laws in integral form for a control volume. Conservation of mass, momentum, angular momentum and energy for flow. Inviscid flow: Bernoulli’s and Euler’s equations. Viscous flow: flows in pipes and ducts, head loss and friction factor.

Prerequisites: ME-UY 3333, MA-UY 2132 or MA-UY 2034 and MA-UY 2122 or MA-UY 2114. Co-requisite: ME-UY 3311.