David Darmon
MA 115, Pre-Calculus Modeling for the Biological Sciences, Section 01
Fall 2020
Wednesday, 10:05 AM – 11:25 AM, Bey Hall Auditorium
Friday, 10:05 AM – 11:25 AM, Remote via Zoom
This course covers the prerequisites necessary to develop and use mathematical models as they appear in the biological sciences. It is centered around the concept of a function: a way to map from one set of things to another. We will develop the language of functions, which requires knowledge of its vocabulary and grammar. We begin with a refresher on algebra, including variables, arithmetic with variables, expressions, equations and inequalities, and functions and their graphs. We then cover the elementary functions: polynomial, exponential, logarithmic, and trigonometric. We will consider these functions in context, both historical and scientific, emphasizing why they were invented in the first place and where you are likely to find them in biological models. We finish the class with a taste of more advanced topics, including systems of linear equations and sequences and summations.
Prerequisites
MA 101 passed with a grade of C- or higher or Math Placement Level 3 or 4.
Professor
| Dr. David Darmon | | ddarmon [at] monmouth.edu |
| | Howard Hall 241 |
Topics, Notes, Readings
This is currently a tentative listing of topics, in order.
- Review of algebra: Integer exponents as shorthand for repeated multiplication or division. Radicals. Rational exponents as another notation for radicals. What does it mean for two expressions to be equal? Inequalities. The coordinate plane. Plotting graphs of equations in the coordinate plane.
- Polynomial functions: Three viewpoints of a function: tables, graphs, equations. Linear polynomials. Quadratic polynomials. General polynomials.
- Exponential and logarithmic functions: Exponentiation as repeated multiplication. The exponential function. Contrasting the exponential function with a monomial function. The natural exponent. The logarithm as the inverse of the exponential function. Rules for manipulating expressions involving logarithms.
- Trigonometric functions: The unit circle. Sine, cosine, and tangent. Harmonic motion. Periodic behavior.
- Systems of linear equations: Moving from equality in a single equation to equality in a group (system) of equations. Systems of two linear equations. Types of solutions for systems of two linear equations. Solving systems of linear equations by substituting, eliminating, or graphing. Systems of more than two linear equations.
- Sequences and summation: Sequences as functions of counting numbers. Recursive sequences. Difference equations. "Sigma" notation as shorthand for summing a sequence. Arithmetic sequences. Geometric sequences.
See the end for the current lecture schedule, subject to revision. Lecture notes will be linked there, as available.
Course Mechanics
Office Hours
I will have office hours at the following four times each week:
| Tuesday, 01:30–02:30 PM | Howard Hall 241 |
| Thursday, 10:00–11:00 AM | Howard Hall 241 |
| Thursday, 01:30–02:30 PM | Howard Hall 241 |
| Friday, 09:00–10:00 AM | Howard Hall 241 |
I will be available for office hours both in-person and on Zoom. For in-person office hours, please email me to make an appointment during one of the times above.
If you are struggling with the homework, having difficulty with the quizzes, or just want to chat, please visit me during my office hours. I am here to help.
Grading Policy
Your final grade will be determined by:
- 50% for 4 in-class exams (12.5% each)
- 15% for a cumulative final exam
- 15% for in-class quizzes
- 15% for homework problem sets
- 5% for class participation
I will use the standard 10-point breakdown to assign letter grades to numerical grades:
- \([90, 100] \to \text{A}\)
- \([80, 90) \,\,\, \to \text{B}\)
- \([70, 80) \,\,\, \to \text{C}\)
- \([60, 70) \,\,\, \to \text{D}\)
- \([0, 60) \,\,\,\,\,\, \to \text{F}\)
with pluses and minuses assigned by dividing the intervals into thirds.
Quizzes
Quizzes will be given during the first 10 minutes of some class sessions. Quizzes may not be every week: I will announce quizzes at least one class session before they will occur. If you miss a quiz your grade will be zero for that quiz. Your lowest two quiz grades of the semester will be dropped.
Homework
Homework will be assigned at the end of every class meeting, and listed on WebAssign. Homework assignments are due at the beginning of the next class meeting.
See this Quick Start Guide provided by WebAssign for details on setting up your account. The class key for this course is below.
Class Key: MONMOUTH 1536 7156
Attendance
Required. If you expect to miss 2-3 sessions of the course, you should take the course during another semester.
Class Participation
You are expected to actively participate during each lecture. This includes responding to questions I pose to the class, as well as raising additional questions you may have as I present the material. I will regularly call on both volunteers and non-volunteers and you are expected to either attempt to answer the question or explain your current confusion.
Zoom
We will use Zoom for our remote meetings. During a remote meeting, try to make your surroundings conducive to learning: find a quiet place, close applications and windows on your computer unrelated to class, and clear your work area of other possible distractions. While you are not required to have your video on during the lecture, having it on is highly encouraged. You are expected to have the ability to talk during lecture. Under extenuating circumstances where you are unable to talk, you may interact with the class via the Chat feature in Zoom.
In the event that a quiz or test must be taken remotely, I will provide guidelines for how we will hold the quiz or test over Zoom. For these sessions, you will be expected to have your video on.
Examination Absences
If you miss an examination your grade will be zero for that exam. If you know you will be absent for an exam you must let me know at least one week in advance to schedule a make-up exam.
Textbook
The required textbook is:
- James Stewart, Lothar Redlin, and Saleem Watson, Precalculus: Mathematics for Calculus, 7th edition (Cengage Learning, 2015, ISBN: 9781305701618). Link to University Store
Collaboration, Cheating, and Plagiarism
All submitted work should be your own. You are welcome and encouraged to consult with others while working on an assignment, including other students in the class and tutors in the Mathematics Learning Center. However, whenever you have had assistance with a problem, you must state so at the beginning of the problem solution. Unless this mechanism is abused, there will be no reduction in credit for using and reporting such assistance. This policy applies to both individual and group work. In group work, you only need to acknowledge help from outside the group. This policy does not apply to examinations.
Statement on Special Accommodations
Students with disabilities who need special accommodations for this class are encouraged to meet with me or the appropriate disability service provider on campus as soon as possible. In order to receive accommodations, students must be registered with the appropriate disability service provider on campus as set forth in the student handbook and must follow the University procedure for self-disclosure, which is stated in the University Guide to Services and Accommodations for Students with Disabilities. Students will not be afforded any special accommodations for academic work completed prior to the disclosure of the disability, nor will they be afforded any special accommodations prior to the completion of the documentation process with the appropriate disability office.
School of Science Commitment to Equity and Inclusion
The School of Science does not discriminate based on race, gender, ethnicity, sexual orientation, or religion. We strive to create a learning environment that allows everyone to succeed and grow. Towards that end, we are here to assist you in any way we can. Should you experience any difficulties or challenges due to discriminatory or harassing behaviors of any sort in your classes, please know that many people are available to help. You can contact your professor, your academic advisor, the department chair, or any of the Deans (Dean Bachrach, Associate Dean Duckett and Assistant Dean Tiedemann) by email or phone or to meet in person by appointment. There are also resources available in the larger University community including the Office of Equity and Diversity and the Intercultural Center.
COVID-19 and In-person Meetings
During the COVID-19 pandemic, it is critically important that we care for ourselves and each other by taking strict measures to avoid spreading SARS-CoV-2. It is therefore a requirement that face masks are worn properly and appropriate physical distancing is maintained at all times during all classes.
When entering a room, please pick up disinfectant wipes and move as far into the classroom as possible in order to help maintain physical distances. Similarly, leave the room in an orderly fashion and dispose of the wipes on the way out.
Students should wipe down their desktops upon arrival.
Students are expected to wipe down keyboards and monitors with disinfectant wipes (provided) both before and after use.
For further information about COVID-19-related policies, please refer to the Student Handbook.
FERPA Video Prohibition
Under the Family Educational Rights and Privacy Act (FERPA), your education records as a student are confidential and protected. Under most circumstances your records will not be released without your written and signed consent. Part of a student's protected and confidential education records include video and / or audio recordings of students within the classroom. As such, students are strictly prohibited from video or audio recording distance learning lectures off of any platform utilized by professors (Zoom, Webex, etc.). A prohibited recording includes, but is not limited to recordings using the platform, a cell phone, tablet, video camera, audio capture device, etc. Students may be subject to disciplinary action under the Student Code of Conduct if found to have made any video and/or audio recording distance learning lectures without proper consent.
Schedule
Subject to revision. Assignments and solutions
will all be linked here, as they are available. All readings are from
the textbook by Stewart et al., unless otherwise noted.
- September 9, Lecture 1:
- Topics: Exponents and Radicals. Algebraic Expressions.
- Sections: 1.2, 1.3
- Learning Objectives
- Reich Lab COVID-19 Forecast Hub
- Nowcasting COVID-19 Cases in Monmouth County, NJ
- September 11, Lecture 2:
- Topics: Rational Expressions. Equations.
- Sections: 1.4, 1.5
- Learning Objectives
- September 16, Lecture 3:
- Topics: Inequalities. The Coordinate Plane; Graphs of Equations; Circles.
- Sections: 1.8, 1.9
- Learning Objectives
- September 18, Lecture 4:
- Topics: Lab.
- Sections: Lab
- Lab 1 Handout
- Lab 1 Excel File
- September 23, Lecture 5:
- Topics: Functions. Average Rate of Change of a Function. Linear Functions and Models.
- Sections: 2.1, 2.4, 2.5
- Learning Objectives
- Desmos Demo for Average Rate of Change of a Function
- Desmos Demos for Linear Functions: Standard Form, Point-Slope Form, Two-Point Form
- September 25, Lecture 6:
- Topics: Review.
- Sections: Review
- September 30, Lecture 7:
- Topics: Exam.
- Sections: Chapter 1
- Exam 1 Study Guide
- October 2, Lecture 8:
- Topics: Quadratic Functions and Models.
- Sections: 3.1
- Learning Objectives
- Desmos Demos for Quadratic Functions: Non-Standard Form, Standard Form
- October 7, Lecture 9:
- Topics: Polynomial Functions and Their Graphs.
- Sections: 3.2
- Learning Objectives
- October 9, Lecture 10:
- Topics: Review.
- Sections: Review
- October 14, Lecture 11:
- Topics: Exam.
- Sections: Exam
- Exam 2 Study Guide
- October 16, Lecture 12:
- Topics: Exponential Functions. The Natural Exponential Function.
- Sections: 4.1, 4.2
- Learning Objectives
- Excel Demo of Approximating Irrational Exponents with Rational Exponents
- Desmos Demo of Approximating Irrational Exponents with Rational Exponents
- Desmos Demo of Graphs of Exponential Functions (Basic)
- Desmos Demo of Graphs of Exponential Functions (Transformations)
- October 21, Lecture 13:
- Topics: Logarithmic Functions. Laws of Logarithms.
- Sections: 4.3, 4.4
- Learning Objectives
- Desmos Demo of the Relationship Between Exponential and Logarithmic Functions
- October 23, Lecture 14:
- Topics: Modeling with Exponential Functions.
- Sections: 4.6
- Learning Objectives
- October 28, Lecture 15:
- Topics: The Unit Circle.
- Sections: 5.1
- Learning Objectives
- Unit Circle Demo
- October 30, Lecture 16:
- Topics: Review.
- Sections: Review
- Exam 3 Study Guide
- Link to Lab 2
- November 4, Lecture 17:
- Topics: Exam.
- Sections: Exam
- November 6, Lecture 18:
- Topics: Trigonometric Functions of Real Numbers.
- Sections: 5.2
- Learning Objectives
- November 11, Lecture 19:
- Topics: Trigonometric Graphs. More Trigonometric Graphs.
- Sections: 5.3, 5.4
- Learning Objectives
- Sine, Cosine, and the Unit Circle Demo
- Transformations of Sine and Cosine Demo
- Tangent and Cotangent Demo
- Cosecant and Secant Demo
- November 13, Lecture 20:
- Topics: Modeling Harmonic Motion.
- Sections: 5.6
- Learning Objectives
- Spring-Mass Demo
- Sound Wave Demo
- Tone Generator
- November 18, Lecture 21:
- Topics: Review.
- Sections: Review
- Exam 4 Study Guide
- November 20, Lecture 22:
- Topics: Exam.
- Sections: Exam
- December 2, Lecture 23:
- Topics: Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables.
- Sections: 10.1, 10.2
- Learning Objectives
- December 4, Lecture 24:
- Topics: Sequences and Summation Notation.
- Sections: 12.1
- Learning Objectives
- Graphing Sequences Demo
- December 9, Lecture 25:
- Topics: Arithmetic Sequences. Geometric Sequences.
- Sections: 12.2, 12.3
- Learning Objectives
- December 11, Lecture 26:
- Topics: Review for Final.
- Sections: Review for Final
- Final Exam Study Guide
- December 16, Final Exam:
- Time: 8:30 AM - 11:20 AM
- Location: Via Zoom