Courant Institute New York University FAS CAS GSAS

V63.009: Algebra and Calculus


Author: Selin Kalaycioglu and the CIMS/NYU Calculus III Faculty <>
Date: January 24,2011


Welcome to Precalculus!  In this course we will prepare you for the rigors of the CIMS Calculus sequence.  Specifically, you will work with a standard library of single variable functions in order to understand their algebraic and geometric properties.  These functions will form the foundations of a mathematical toolbox on which you will rely throughout any future mathematics course.


We will begin by understanding what a function is and how it can be represented geometrically as a graph.  We will then learn some standard function manipulations (algebraic combinations, composition, inverses, etc.) focusing on how such manipulations affect the shape of the graph.  Then we will go through a list of classic functions (polynomial, rational, trigonometric, exponential, logarithmic, etc.) learning their algebraic and geometric properties, emphasizing the relationship between them.

Course Details

Class Meetings

The lectures for this course meet MW from 9:30-10:45, along with a 75 minute recitation session. You must register for lecture and recitation separately.

Textbook and Materials

You need a textbook and you need WebAssign access.

PreCalculus by Faires and DeFranza is the official textbook for the course. NYU offers this text bundled with access to Enhanced WebAssign.  However, you need not purchase the bundled option if you can find a cheaper option for the text, since you can purchase access to webassign directly through Blackboard.

The calculator question

A graphing calculator is encouraged for class discussion and on homework, but not allowed for exams. No specific calculator is endorsed, so do not buy a new one. If you have one already, continue to use that one; if you do not, try free alternatives such as Wolfram Alpha.


There are two media for homework in Precalculus.

There will be weekly online assignments administered through WebAssign (This is why a WebAssign software license is one of the required course materials), WebAssign problems are computational in nature and assess the techniques introduced in class. Many of these problems will resemble examples in the textbook or from class. You will get immediate feedback on your progress and will get several chances to ensure it.  WebAssign is available directly through the course's Blackboard website available at your account.

There will also be problems to write up on paper each week and turn in. These problems will require more than just procedure, might connect two more more things together, and will more closely resemble the harder exam problems.  Homework assignments and webassign due dates will be available under the Assignments tab in your lecture's Blackboard site.

One of the major goals of college-level mathematics education is to move students from computational processes to conceptual thinking and communication. That is the biggest difference between this course and a high school course, even an Advanced Placement course. Mathematics is more than a bag of tricks and there are not a limited number of "types" of problems that can be asked. The goal in class is to prepare you to do the homework and not necessarily to show you how to do your homework. The learning occurs when you can move yourself into the unknown territory.

Graders will grade the written homework promptly, and solutions will be made available on the course website. Graders will be expecting you to express your ideas clearly, legibly, and completely, often requiring complete English sentences rather than merely just a long string of equations or unconnected mathematical expressions. This means you could lose points for unexplained answers. See the homework page for a more detailed rubric.

In fairness to fellow students and to graders, late homework will generally not be accepted. Because sometimes things more important than math homework come up, you have some free passes: Your two lowest written assignment score and your three lowest WebAssign scores (one week's worth in both cases) will be dropped in the final grade calculation.

By all means you may work in groups on the homework assignments. Collaboration is a big part of learning and of scholarship in general. However, each student must turn in his or her own write-up of the solutions, with an acknowledgment of collaborators.

There is free math tutoring sponsored by the math department, meeting in room 524 of Warren Weaver Hall. Check the signs posted throughout WWH and the tutoring web page.


There will be two midterm exams held in class.  Please see the class calender.

The final exam for all sections will be  Thursday May 12 from 2:00–3:50pm. Please make a note of it and plan your travel schedule accordingly.

Exams will contain a mixture of computational and conceptual problems. Some of them will resemble homework problems, while some will be brand new to you.

In-Class Work

There will also be in class assignments given during recitation. These may be any type of worksheets, quizzes, exercises, presentations, etc.  The schedule will be determined by your teaching team and published in advance (i.e., no pop quizzes). Quizzes are intended to provide practice for the exams and to give students feedback on how well they know the most important core topics of this course. If a student has a weakness in a particular area, it is better to find out on a quiz rather than on an exam. Quizzes will be timed at fifteen minutes and will be given at the beginning of each recitation session. Each quiz will be based on the sections covered by the preceeding HW problems and examples covered in class. Classwork scores will be averaged together, again dropping the two lowest.

Policy on missed in-class assignments

We are only able to accommodate a limited number of out-of-sequence exams due to limited availability of rooms and proctors. For this reason, we may approve out-of-sequence exams in the following cases:

  1. A documented medical excuse.
  2. A University sponsored event such as an athletic tournament, a play, or a musical performance. Athletic practices and rehearsals do not fall into this category. Please have your coach, conductor, or other faculty advisor contact your instructor.
  3. A religious holiday.
  4. Extreme hardship such as a family emergency.

We will not be able to accommodate out-of-sequence exams, quizzes, and finals for purposes of more convenient travel, including already purchased tickets.

If you require additional accommodations as determined by the Center for Student Disabilities, please let your instructor know as soon as possible.


Your course score will be determined as the following weighted average:

Item Weight
Midterm 1
Midterm 2
WebAssign 10%
Written Homework 10%
In-Class work
Final 30%
Total 100%

We will convert this score to a letter grade beginning with these values as cutoffs:

Cutoff Letter Grade
93 A
90 A-
87 B+
83 B
80 B-
75 C+
65 C
50 D

These cutoffs might be adjusted, but only in the downward direction (to make letter grades higher).


A tentative day-by-day schedule is also available.

CAS Policy on Academic Integrity

The College is a “community of the mind.” Its students, faculty, and staff all share the goal of pursuing truth through free and open inquiry, and we support one another’s endeavors in this regard. As in any community, membership comes with certain rights and responsibilities. Foremost among these is academic integrity. Cheating on an exam, falsifying data, or having someone else write a paper undermines others who are “doing it on their own”; it makes it difficult or impossible to assess fairly a student’s interest, aptitude, and achievement; and it diminishes the cheater, depriving him or her of an education. Most important, academic dishonesty is a violation of the very principles upon which the academy is founded. Thus, when students enter the College, one of the first things that they are asked to do is to sign a community compact, recognizing these principles of academic integrity. For this reason also, violations of these principles are treated with the utmost seriousness.


We look forward to seeing you in Precalculus!