You need 127 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 127-credit requirement for this degree.

- 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.

- 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

Or

- 4 Credits 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.

- 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.

Or

- 4 Credits 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

- 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 - 2 Credits 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 or MA-UY 3012 (Note: Not open to students who have taken MA-UY 2233) - 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 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. - 3 Credits Analysis I MA-UY 4613
- This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, uniform convergence, continuity, partial differentiation, extreme value problems with constraints, Riemann integrals, line integrals, improper integrals, integrals with parameters, transformations, Riemann-Stieltjes integral, uniform and absolute convergence of integrals. Beta and Gamma functions.

Prerequisites: MA-UY 2122 or MA-UY 2114 and MA-UY 2132 or MA-UY 2034. - 3 Credits Analysis II MA-UY 4623
- This course covers the study of basic topics in analysis with emphasis on methods. Sequences, series, functions, uniform convergence, continuity, partial differentiation, extreme value problems with constraints, Riemann integrals, line integrals, improper integrals, integrals with parameters, transformations, Riemann-Stieltjes integral, uniform and absolute convergence of integrals. Beta and Gamma functions.

Prerequisites: MA-UY 4613

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

- 4 Credits Discrete Mathematics MA-UY 2314
- 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 Project in Mathematics I MA-UY 3914
- In this course, students reading, study and investigation of selected topics in mathematics. Problems are discussed and presented by participating students.

Prerequisite: approval of departmental adviser. - 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.

- 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

- 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. - 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 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.
- 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 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

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.

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

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.

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.

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