Courant Institute New York University FAS CAS GSAS

V63.0009: Algebra and calculus

Coordinator:
Selin Kalaycioglu
Term: Spring 2011
Recitations:
Students must enroll in a corresponding recitation
Office: 725 WWH
Office hours: TBD and by appointment
Phone: 212-998-3375
Email: kalaycioglu@cims.nyu.edu
Website:
cims.nyu.edu/~kalaycioglu

Prerequisites

Students who wish to enroll in Algebra and Calculus must meet the following prerequisites:

  • Prerequisite:  High school math or permission of the department.

Goals

  • In this course you will be prepared 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.

Topics

  • 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

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 and a cheaper
option for the text, since you can purchase access to webassign directly through Blackboard.

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.

Class Meetings

The lectures for this course are on Monday and Wednesdays from 9:30-10:45 am, along with a 75 minute recitation session. You must register for lecture and recitation separately.

Homework

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 home.nyu.edu 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.

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 2
1lowest written assignment score and your three lowest WebAssign scores 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.


In-Class Work

In-Class Work There will also be in class assignments given during recitation. These may be any type
of worksheets, exercises, presentations, quizzes etc. 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 and 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
sessions. The quiz questions will consist of exercises that are similar to HW problems and examples
covered in class. Each quiz will be based on the sections covered by the preceding HW assignment.
Before computing the overall semester quiz score, the lowest two scores will be dropped. In general,
missed quizzes may NOT be made up.

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. An extreme hardship such as a family emergency

We will not be able to accommodate out-of-sequence exams, quizzes, and finals for pur-
poses 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.

Exams

There will be two midterm exams held in class. The tentative midterm schedule is as follows:

Midterm 1: Wednesday, March 9th
Midterm 2: Wednesday, April 13th

The final exam will be Thursday, May 12 from 2:00-3:50pm. Please make a note of it and plan your
summer 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.

Grading policy

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

Midterm 1 20%
Midterm 2 20%
WebAssign 10%
Written Homework 10%
In-Class work 10%
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

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 anothers 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 students 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.

Tentative Calendar

Week Topic
1 1.2, 1.3 The real line, the coordinate plane
1.3 Equations and Graphs
2 1.6 Functions
1.7 Linear Functions
3 1.8 Quadratic functions
2.2 Other common functions
4 2.3 Arithmetic combinations of functions
2.4 Combinations of functions
5 2.5 Inverse Functions
6 3.2 Polynomial Functions
3.3 Finding factors and zeros of polynomials
7 Review MIDTERM 1
8 Spring Break-No Classes
9 3.4 Rational functions
3.5 Other algebraic functions
10 4.2 Measuring angles
4.3 The sine and cosine functions
11 4.4 Graphs of sine and cosine functions
4.5 Other trigonometric functions
12 Review Midterm II
13 4.6, 4.7 Trigonometric identities, Right-triangle trigonometry
4.8 Inverse trigonometric functions
14
4.9 Applications of trigonometric functions
5.2 The natural exponential function
15
5.3 Logarithm functions
5.4 Exponential growth and decay
16
Review for final exam