You need 128 credits to graduate from the Bachelor of Science in Mathematics program, as outlined below.

Advanced placement (AP) courses may be awarded toward the first year of calculus. Students who receive a grade of 4 or 5 in Calculus BC on AP examinations in calculus given the College Entrance Examination Board may be granted a maximum of 8 credits to be applied toward the 128-credit requirement for this degree.

### Required Courses

#### Mathematics (42 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. - 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 - Integrated Calculus I for Engineers MA-UY 1324
- 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 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. - 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. - Integrated Calculus II for Engineers MA-UY 1424
- 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: For MA-UY 1124: MA-UY 1024 or MA-UY 1324; for MA-UY 1424: MA-UY 1324 or MA-UY 1024. Note: credit for this course may be used to satisfy the minimum credit requirement for graduation. Corequisite: EX-UY 1 - 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. - 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. - 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. - 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. - Data Analysis I MA-UY 2212
- This course covers basic theory of probability. Random variables. Distributions. Expectation. Functions of a random variable. Descriptive statistics. Data description. Sampling distributions. Use of statistical software is integrated with previous topics.

Prerequisite: MA-UY 1124 or equivalent. - Data Analysis II MA-UY 2222
- This course covers point and interval estimation. Hypothesis testing. Linear regression. One-way analysis of variance. Use of statistical software is integrated with the previous topics.

Prerequisite: MA-UY 2212. - Probability II MA-UY 3022
- This course covers multivariate random variables, moment generating functions, properties of expectation, limit theorems and gives an introduction to random processes and their applications.

Prerequisites: MA-UY 2224, MA-UY 2233 or MA-UY 3012 - 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. - 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. - 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 or MA-UY 2114 and MA-UY 2132 or MA-UY 2034. - 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

May be substituted by another course with adviser's approval:

- Discrete Math 1 MA-UY 2312
- This course covers logic and induction. Sets and functions. Recursive definitions. Counting techniques. Inclusion-exclusion principle.

Prerequisite: MA-UY 1124 or equivalent. - Discrete Math 2 MA-UY 2322
- This course covers recurrence relations and generating functions. Equivalence relations and partial orderings. Graphs and connectivity of graphs. Trees and sorting. Boolean algebra, languages and finite state machines.

Prerequisite: MA-UY 2312. - 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.

#### Computer Science (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

#### Physics (10 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 - 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 - 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. - PH-UY 2021 (Please refer to the bulletin)
- PH-UY 2031 (Please refer to the bulletin)

#### English/Writing (8 Credits)

- Writing the Essay: EXPOS-UA 1
- This foundational writing course is required for CAS, Engineering, Stern, Nursing, Social Work, and Steinhardt 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 126-160 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 or UN 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 8-15, offered in Fall only) is offered ONLY for students who live in the Goddard Residence. Each stream focuses on some aspect of New York City and the Arts: All The World's a Stage, Global New York, Writing New York, and Poverty and Affluence. For access contact Ethan Youngerman: ewy200@nyu.edu
Please note: EXPOS-UA 4 International Writing Workshop 1 is equivalent to and will substitute for EXPOS-UA 1 Writing The Essay for incoming freshmen or transfers for whom English is a second language. Only International students in UA, UE, UB, US, UN and UY may qualify to take this course instead of Writing The Essay. For information on eligibility or to learn about the course contact your advisor, visit our website, or contact Denice Martone at dm1@nyu.edu.
- 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

#### Chemistry (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

#### Humanities/Social Science Electives (16 Credits)

#### Free Electives with Adviser's Approval (26 Credits)

These can be courses offered by any department, provided they do not duplicate material studied in other courses and that you meet the prerequisites for the courses.

#### Concentration Specialties (18 Credits)

These consist of at least 9 credits in a single area of study other than mathematics and beyond the required courses found below. The sequence must be well integrated and consistent to insure you gain knowledge in an area other than mathematics. When selecting electives, you should consult with the adviser of the department that interests you. This work is in addition to the courses you take under other categories of the programs. For instance, required courses in physics do not count toward a minor in physics.

The following are possible minor concentrations:

- Chemical Engineering
- Chemistry
- Computer Engineering
- Computer Science
- Electrical Engineering
- Management
- Mechanical Engineering
- Physics
- Transportation

### Minor in Mathematics

You may obtain a minor in mathematics by taking 15 credits of mathematics courses, 8 credits of which are in addition to the major department’s requirement in mathematics and must include 2 courses in Real Analysis. You must take at least 6 of those 8 credits while enrolled at the School of Engineering.

### 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 this 128-credit degree.

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