Mathematics Placement

 

During the summer prior to your first semester at NYU Shanghai, you will be initially placed into a Mathematics course based on high school Mathematics performance. Students who wish to be initially placed in MATH-SHU 131 (Calculus) and/or MATH-SHU 140 (Linear Algebra) must meet one of the following prerequisites:

 

 

Students who did not meet any of the criteria above will be placed in MATH-SHU 009 (Precalculus). Students who are placed into Precalculus and do not wish to continue to enroll in Calculus also have the option to take MATH-SHU 10 (Quantitative Reasoning: Great Ideas in Math). Students should work with their advisor on this course selection.

 

Students who wish to be initially placed into MATH-SHU 201 (Honors Calculus) and/or MATH-SHU 141 (Honors Linear Algebra I) must meet one of the following prerequisites:

 

Students who wish to enroll in MATH-SHU 151 (Multivariable Calculus) must meet one of the following prerequisites:

 

 

Students who are placed into Precalculus and do not wish to continue to enroll in Calculus also have the option to take MATH-SHU 10 (Quantitative Reasoning: Great Ideas in Math) in Spring 2020. This course cannot serve as a prerequisite for Calculus and would be suitable if you are quite sure you do not wish to pursue a major that requires Calculus. Majors that require Calculus include Science majors, Business, Computer Science, Data Science, Economics, Mathematics, and Engineering. This course will not be offered in Fall 2019. If you are certain that you want to take this course, you can take it in Spring 2020, and in Fall 2019 you will enroll in 2 elective courses.

 

Taking a Mathematics placement examination is optional at NYU Shanghai. NYU Shanghai offers three Mathematics placement examinations:
 
Exam I: Placement into Calculus and Linear Algebra
Exam II: Placement out of Calculus
Exam III: Place into Honors Calculus and Honors Linear Algebra

 

Please note that NYU Shanghai abides by the following policies for Mathematics placement.

 

1.    No student may move to a higher level of Mathematics except by placement examination.
2.    A student may attempt the same placement exam only twice, with at least three months between each attempt.
3.    Within the NYU Shanghai add/drop period, a student is allowed to move to a lower level of Mathematics at his/her own discretion (provided that student has not already taken the lower-level course at NYU Shanghai). The student must inform his/her advisor of this change. Instructor approval is not required for such a change. No such movement may occur after the add/drop period has ended.

 

 

Sample Placement Exam I: Placement into Calculus and Linear Algebra  Examination | Solutions
Sample Placement Exam II: Placement out of Calculus Examination | Solutions

Sample Placement Exam III: Placement into Honors Calculus and Honors Linear Algebra I Examination

 

 

Please note that the course syllabi are example ones for your reference only. You will receive the most updated syllabi in class.

 

MATH-SHU 9 Precalculus
This course is designed as a preparation for calculus, including study of basic properties of polynomials, rational functions, exponential and logarithmic functions, and trigonometric functions. Systems of linear equations are also covered. Prerequisite: None.Click here to view course syllabus.

 

This one-semester course serves as an introduction to great ideas in mathematics. During the course we will examine a variety of topics chosen from the following broad categories.

1) A survey of pure mathematics: What do mathematicians do and what questions inspire them? 2) Great works: What are some of the historically big ideas in the field? Who were the mathematicians that came up with them? 3) Mathematics as a reflection of the world we live in: How does our understanding of the natural world affect mathematics (and vice versa)? 4) Computations, proofs, and mathematical reasoning: Quantitative skills are crucial for dealing with the sheer amount of information available in modern society. 5) Mathematics as a liberal art: Historically, some of the greatest mathematicians have also been poets, artists, and philosophers. How is mathematics a natural result of humanity's interest in the nature of truth, beauty, and understanding? Why is math a liberal art? Prerequisite: None.

 

This course presents the foundations of calculus for functions of a single variable. Topics addressed include limits, continuity, rules of differentiation, approximation, antiderivatives, indefinite and definite integrals, the fundamental theorem of calculus, integration techniques, and improper integrals. Prerequisite: Sufficient high school grades, or NYU SH “Calculus and Linear Algebra” placement exam, or a grade of C or better in MATH-SHU 9 (Precalculus).

Click here to view course syllabus.

 

This is a rigorous course in single-variable calculus, providing preparation for advanced, courses in analysis. It emphasizes proofs and therefore also provides a strong formation to logical thinking and argumentation, which are valuable in other disciplines. Topics covered include basic logic and set theory, functions, sequences, series, limits of functions, continuity, derivatives, and Taylor expansions. Prerequisite: Faculty review of high school grades, or NYU SH “Honors Calculus and Honors Linear Algebra” placement exam, or authorization of the instructor. This course can replace MATH-SHU 131 (Calculus) as a prerequisite. Not of ered to students who took MATH-SHU 143 (Foundations of Mathematical Methods).

Click here to view course syllabus.

 

This is the first semester of a 2-semester sequence in linear algebra for advanced mathematics majors. This course starts with introducing the basic practical knowledge of linear algebra, that is operations on matrices and techniques in order to solve a system of linear equations. These notions are covered on both practical and theoretical levels. After this, the focus is on operators and an introduction to spectral theory. The following topics are studied: vector spaces, linear independence, bases, dimension, determinants, characteristic polynomials, Cayley-Hamilton theorem, as well as eigenvalues and eigenvectors. The goal of this course is, on one hand, to provide the practical tools for application in various disciplines and courses such as Differential Equations, Analysis, or Probability and, on the other hand, to acquire the theoretical knowledge necessary to properly write mathematical proofs. Prerequisite: Faculty review of high school grades, or NYU SH “Honors Calculus and Honors Linear Algebra” placement exam, or authorization of the instructor. This course can
replace MATH-SHU 140 (Linear algebra) as a prerequisite.

Usually taken concurrently with MATH-SHU 201 Honors Calculus. Click here to view course syllabus.

 

This course is a continuation of calculus, focusing on sequences, series, and the calculus of functions of several variables. The first part is focused on real sequences and series, power series, Taylor expansions and Landau’s notation. The second part concerns functions of several variables, including continuity, differentiation, gradient, extrema, Lagrange multipliers, multiple integrals, and an introduction to vector calculus. Prerequisite: Grade of C or better in MATH-SHU 131 (Calculus).

Click here to view course syllabus.