Math 120: Calculus I Fall 2021 Syllabus

Prof. Andrew Ross, Eastern Michigan University

Eastern Michigan University Creed

We believe the INTEGRITY of our work and the RESPECT we show for our fellow students, faculty, alumni and staff are an integral part of our ongoing EDUCATION.

We believe that the RELATIONSHIPS we have and those we continue to develop will support us as we learn and grow together as a community.

INTEGRITY adds value to our educational experience.

RESPECT promotes unity and understanding through individual differences within our community.

EDUCATION allows us to develop socially, intellectually, and emotionally.

RELATIONSHIPS are the foundation of our growth.

Something You Would Hope Wouldn’t Need To Be Said, But It Does

I stand against white supremacy and racism in all forms in my career, as part of my profession, and in my everyday life.

I can supply you a lot of reading about white supremacy and racism in math--please ask! In the meantime, here are a few links or thoughts:

(not that I am perfect at it. Please tell me ways that I can improve, if you have time and energy)

A Sense of Belonging

I hope that everyone knows that they belong in this class, and that our class atmosphere contributes to that sense of belonging. You belong in this class even if nobody else (or only a few people) look like you--that’s the fault of racist/sexist/ableist systems, not your fault. You belong in this class even if you feel like your precalculus skills aren’t where you want them to be--we’ll work together on that.

Basic Information

Note: this syllabus is temporary, and may change up to the first day of class.

This version posted on: 2020-08-29

Official Course Catalog Entry

Calculus of functions of a single variable; differential calculus, including limits, derivatives, techniques of differentiation, the mean value theorem and applications of differentiation to graphing, optimization and rates. Integral calculus, including indefinite integrals, the definite integral, the fundamental theorem of integral calculus, and applications of integration to area and volume.

General Education rationale

MATH 120 is an introductory four credit course in calculus. Students in this course will develop the mathematical skills associated with the core topics of limits, derivatives and integration, and learn the wider context for these skills within the mathematical sciences. In a unified fashion, the course makes the case for using functions to model physical phenomena and simultaneously teaches methods to analyze these functions in a meaningful way. Applications of calculus abound in the physical and life sciences and, increasingly, in social sciences like economics as well. It is the theoretical engine that is used in these client disciplines when it comes time to reason in a quantitative way. For these reasons, MATH 120 will count for the Quantitative Reasoning requirement in the General Education program Education for Participation in the Global Community.

Very important notice

This course does not automatically count as a QR course for every student who takes it. If you plan to count this course for your QR requirement, it is essential that you check with an advisor to see if it will count for you before taking the course. It is your responsibility to check and follow the rules. No exceptions can be made. For more information go to www.emich.edu/gened

Prerequisites

Placement or (at least a C in any of the following group of courses: (MATH 105 and MATH 107) or in (MATH 112) or in (MATH 210 and MATH 107))

Related Courses

For math majors and statistics majors (but not math-education majors), I recommend that you take COSC 146 Applied Programming as soon as you can, even this semester if possible. For those who are going farther in the calculus sequence, I STRONGLY recommend that you sign up for Math 121 (Calculus II) as soon as possible after Calc I, and then Calc III the semester after that. Calculus is sort of like a language, and if you skip it for a semester, your skills will decay. Also, take Math 122 (Linear Algebra) as soon as you can, since it is a prerequisite (or co-requisite) for Calc III. You could even take it simultaneously with Calc I.

Class Meetings

Online section

Section 12, asynchronous+Supplemental Instruction, CRN 10351

The course is "asynchronous"--students are not required to all meet online at the same time. I will hold some optional (but highly encouraged!) synchronous sessions several times a week.

For each new topic (section of the textbook), I will post a few short videos for you to watch, on this playlist, then try some straightforward practice problems (some that are on the homework, some that are not). Then as you try the more challenging problems on the homework, you can email me for help, or drop by the synchronous video session, or email me for an appointment for a video chat if the scheduled synchronous session doesn't work for you. The synchronous sessions will include some groupwork on the harder problems.

If we take the point of view of an in-person class: To succeed in Math 120 it usually takes 12 hours per week outside of class during a regular (Fall or Winter) semester, or twice that (24 hours/week) during a double-pace Summer semester. The federal standard for what a credit-hour means is a _minimum_ of 2-hours-outside-class for every credit hour, and our class is 4 credit hours, so that's at least 8 hours/week outside class.

For an asynchronous online class, add 4 hours/week for a regular semester (total of 20 hours/week) or 8 hours/week for a fast summer semester (total of 32 hours/week) for most people to succeed.

In-Person class

Section 10, Mon/Tue/Wed/Thu 11:00-11:50am (Ross) and 11:50-12:15 (supplemental instruction), CRN 10349

Regular attendance is strongly recommended. There will be material discussed in class that is not in the textbook, yet will be very useful. Similarly, there are things in the textbook that might not be covered in class, but are still very useful. If you must miss a class, arrange to get a copy of the notes from someone, and arrange for someone to ask your questions for you.

My discussions mostly use the document camera, along with demonstrations in Desmos and Excel and other mathematical software. I do not usually have PowerPoint-like presentations, and thus cannot hand out copies of slides.

To succeed in Math 120 it usually takes 12 hours per week outside of class during a regular (Fall or Winter) semester, or twice that (24 hours/week) during a double-pace Summer semester. The federal standard for what a credit-hour means is a _minimum_ of 2-hours-outside-class for every credit hour, and our class is 4 credit hours, so that's at least 8 hours/week outside class.

Instructor information

Professor Andrew Ross

Office: Pray-Harrold 515m

andrew.ross@emich.edu

http://people.emich.edu/aross15/

(734) 487-1658, but I strongly prefer e-mail instead of phone contact.

Math department main office: Pray-Harrold 515, (734) 487-1444

You can make an appointment with me using my Google Calendar Appointment Page

Office Hours and other help

In-Person: This is in flux, because faculty have been told to not do office hours in-person in their actual office, and to use Zoom instead, but it’s hard to see how to do that based on my schedule. For now, let’s say: if there’s no Supplemental Instruction session, I’ll hold office hours in the same room as the classroom for 15 minutes after class, and I’ll publish some times for online office hours too.

Online class: Again, things are in flux. I’ll publish a schedule for online office hours as soon as I can.

I am also happy to make appointments if you cannot come to the general office hours. Please send me e-mail to arrange an appointment, or use my Google Calendar Appointment Page.

The Mathematics Student Services Center (or "Math Lab") is also here to help you, in Pray-Harrold 411. Their hours are posted here. Please give them a call at 734-487-0983 or just drop by.

During an in-person semester: A good place to study, if the Math Lab doesn't suit you, is the Math Den, Pray-Harrold room 501.

Another resource on campus is the Holman Success Center, formerly the Holman Learning Center.

Teaching philosophy, interests

I am a very applied mathematician. Applied, applied, applied. Not pure. Impure. I try to focus on real-world problems, or at least formulas that are related to real-world problems, rather than artificial drill problems (though I do recognize the need for some drill). My classes spend much more time on formulating problems (going from the real world to math notation and back) than on proving theorems. If you want the theoretical basis for anything we are discussing, please ask!

My general math interests are in Industrial Engineering and Operations Research (IEOR). In particular, I do research in applied probability and queueing theory, the mathematics of predicting how long it takes to wait in line for service. You can learn more about this in Math 319 and 419 when I teach them. I also enjoy teaching about cost-minimizing/profit-maximizing methods called Non-Linear Programming (NLP) in Math 319 and Math 560.

I was a licensed amateur radio operator, and enjoy bringing aspects of electronics and the physics of sound/music into the classroom. You will see lots of sines and cosines in my classes, and exponentials/logarithms, but not much in the way of tangent, secant, etc.

Required materials and Technology Requirements

Online class, and in-person if you want to do an interview online: A webcam or cell phone video camera capability is required for identity verification and the video structured interviews. Similarly, some way to take photos of your by-hand work so you can upload it is required.

We will use Excel and/or Google Sheets fairly often. This is often difficult to do on a tablet without a keyboard, and very difficult on a phone, so try to have a laptop/desktop handy. Similarly, we’ll be using Desmos.com (a free graphing calculator website), and that is better on a laptop/desktop than on a phone.

Our required text is APEX Calculus Version 4.0, Volume 1 (chapters 1-6), which is freely available online at APEX Calculus. I recommend that you have a hard copy, whether you print it from a PDF or buy the cheap (about $20 total) printed copy online.

Reading a math textbook takes certain skills! Here are some guides:

A TI-83/84 is allowed, but is not ideal, since there are many problems in the world that can't be solved by a graphing calculator. I would advise you to learn more professional technology tools than just a TI. A TI-89 or TI-Nspire is not required, but is allowed just as much as a TI-84 sort of calculator.

Course Web Page

I will post data files, homework assignment files, etc. in Canvas, and possibly also at my home page and my youtube channel. A record of all homework assignments is at this Google Doc (or, this link in case the bitly link fails)

We will use the Canvas system to record scores. You are expected to keep an eye on your scores using the system, and get extra help if your scores indicate the need.

Supplementary Materials

Course Content

QR outcomes

The Quantitative Reasoning (QR) outcomes defined by the General Education program are:

(short form): Students will learn to solve real-life problems using a mathematical modeling process. They will learn to:

  1. Build an appropriate model.
  2. Use the model to solve the problem.
  3. Communicate the results of their analysis.
  4. Evaluate the model.

(full version): Students will learn to solve real-life problems using a mathematical modeling process. They will learn to:

  1. Build an appropriate model.
  1. Estimate an answer to the problem.
  2. Identify important components of the model.
  3. Collect or generate appropriate data.
  4. Analyze the situation using arithmetic, geometric, algebraic, and/or probabilistic or statistical methods.
  1. Use the model to solve the problem.
  1. Propose a solution.
  2. Evaluate the reasonableness of the solution.
  1. Communicate the results of their analysis.
  1. Share the findings in oral or written reports using appropriate mathematical language.
  2. Write summaries to explain how they reached their conclusions.
  3. Communicate quantitative relationships using symbols, equations, graphs, and tables.
  1. Evaluate the model.
  1. Draw other inferences from the model.
  2. Identify the assumptions of the model.
  3. Discuss the limitations of the model.

Math 120 Student Learning outcomes

Upon successful completion of MATH 120 - Calculus I, a student will be able to:

  1. Master the functions from precalculus, using numerical, graphical, algebraic representations, while recognizing and explaining functions in context
  2. Use the derivative of a function to determine the properties of the graph of the function and use the graph of a function to estimate its derivative
  3. Solve problems in a range of mathematical applications using the derivative or the integral, including optimization, related rates, in-depth graphing problems, linearizations as approximations, and simple differential equations
  4. Explain and apply the Mean Value Theorem and the Fundamental Theorem of Calculus
  5. Determine the continuity and differentiability of a function at a point and on a set
  6. Use appropriate modern technology to explore calculus concepts
  7. (From precalculus): construct, interpret, and critique mathematical models of data obtained from applied scenarios
  8. Compute limits and derivatives of algebraic, trigonometric, transcendental, implicit, and piecewise defined functions, both algebraically and graphically
  9. Compute definite and indefinite integrals of algebraic and trigonometric functions using formulas and substitution

I will add: I want my students to learn reproducible/debug-able/transmit-able work skills! This means doing things in a way that can be emailed to a co-worker or supervisor so that they can re-run your calculations automatically if needed. Common tools for this include spreadsheets, computer code like Python or R, and to a lesser extent Desmos and WolframAlpha. Definitely not on the list are calculators.

Course Topic Outline

The topics we will cover are:

Differential Equations in Spreadsheets

Modeling: building, using, communicating, evaluating.

An introduction to Limits

Finding Limits Analytically

One-Sided Limits

Continuity

Limits Involving Infinity

Computer methods; forward, backward, and central difference quotient

Modeling with Graphs and Functions

Instantaneous Rates of Change: The Derivative

Interpretations of the Derivative

Basic Differentiation Rules

The Product and Quotient Rules

The Chain Rule

Implicit Differentiation

Extreme Values

The Mean Value Theorem

Increasing and Decreasing Functions

Concavity and the Second Derivative

Curve Sketching

Related Rates

Optimization

Differentials (and linear approx)

Antiderivatives and Indefinite Integration

The Definite Integral

Riemann Sums

The Fundamental Theorem of Calculus

Numerical Integration

u-Substitution for integrals

Fourier Methods (bonus)

preview of Taylor series (bonus)

but I might be mixing the order up a bit. See the homework file for the schedule: this Google Doc (or, this link in case the bitly link fails)

Grading Policies

Attendance

In the asynchronous online class, there is no real concept of "attendance". There are some things that are like attendance: any online discussions within Canvas, and the optional synchronous sessions.

In the in-person class, regular attendance is strongly recommended. There will be material discussed in class that is not in the textbook, yet will be very useful. Similarly, there are things in the textbook that might not be covered in class, but are still very useful. If you must miss a class, it’s great to email me and let me know what is going on--not because I require attendance, but because I care about my students.

My classes mostly use the document camera, along with demonstrations in Desmos and Excel and other mathematical software. I do not usually have PowerPoint-like presentations, and thus cannot hand out copies of slides.

Homework

Homework will be assigned just about every day, often 2 new homeworks a day in a fast summer semester.

In general, you should write out your homework by hand, take pictures of it (and hopefully turn them into a PDF using something like GeniusScan), and upload it to Canvas. Another (fancier and more time consuming) option is to type it out, in Excel or in a Python notebook or Rmarkdown document, or using Word/Google Docs and equation editor.

I encourage you to work together in study groups, but the learning doesn’t tend to sink in unless each person works out and writes out their own homework--so, no copying from each other. As in any academic work, you should "cite your sources": write down who you received help from (including tutors, but not including me) on any particular problem, or at the top of the homework paper if it's more efficient.

Overall Grades

No scores will be dropped by default, unless a valid excuse (possibly with evidence) is given. In the unfortunate event of a need, the appropriate grade or grades might be dropped entirely (at the professor's discretion), rather than giving a make-up. You are highly encouraged to still complete the relevant assignments and consult with me during office hours to ensure you know the material.

Your overall score will be computed as follows:

Why is the homework worth so much? There are very important problems that are too long to do on an exam, but work well as homework, and I want to make sure you get a chance to work on them and contemplate them. Each of the 2 standard projects (where everyone does the same projects) are worth 4 homeworks.

Interviews/Quizzes

Online class: "Small structured technical interviews" will consist of me asking you a question or two via video chat, and you answering. Plan on about 5-10 minutes each, usually on a Thursday or Friday. Note that these kind of skills-based interview questions are quite common in some fields when interviewing for a job, like software engineering. I will set up some sort of appointment system for them. The default conditions for our interviews will be: camera on, closed-book, closed-notes. You should do the work by hand initially, but then you can/should check on Desmos or a spreadsheet or with a graphing calculator (but not those that can do symbolic derivatives/integrals, and not Wolfram Alpha or similar tools that can do symbolic math).

In-person Class: we will take about 10 minutes at the end of some class sessions to do a quiz that is equivalent to the online class’s interview.

Both in-person and online:

Final Project

The final project that you do is on a topic that you choose (with my help), and then you present to me in person or via video and I ask you questions. It will involve:

In the project proposal, describe 3 things: what problem do you want to solve (and any details about it that I should know), where will you get data if a dataset is important, and what basic methods are you thinking of using?

The project report could be written in a forward-thinking format, such as a Python notebook, R markdown file, or spreadsheet with paragraphs interleaved with computation, if a Word file is not appropriate. The project report should include a section where traditional skills (derivative and integral) related to the project topic are used, even if they are not the main focus of the project. For example, if the project uses differential equations that result in a curve that does not have a nice precise formula, you should still give an approximate formula for the result, and take its integral and derivative, and discuss. I will help you figure out what direction to go with that, as needed.

If the interview reveals that you do not understand the project, it will put in jeopardy any points on the project report as well. I plan to record all interviews so I can go back to them if I need to check something in them. If the structured-interview process is just not working, we will convert to a more traditional assessment method--perhaps Zoom-proctored exams, with a few different times offered.

Grading Scale

Because grading students "on a curve" sets them against each other rather than encouraging cooperation, I use a grading system where everyone works together to achieve great learning. The following scale will be used:

From:        To:        Grade:

-infinity 56 F

56        59.33333333        D-

59.33333333        62.66666667        D

62.66666667        66        D+

66        69.33333333        C-

69.33333333        72.66666667        C

72.66666667        76        C+

76        79.33333333        B-

79.33333333        82.66666667        B

82.66666667        86        B+

86        89.33333333        A-

89.33333333        infinity        A

This scale is based on student performance from a previous semester. If absolutely necessary, the cutoffs might be adjusted.

Notice that there are about 40 homeworks (not including the projects), so each is worth about 1 percentage point on your grade. This means that missing one homework can easily move you from an A to an A-, or a B to a B-, etc, and missing two will almost DEFINITELY knock you down!

General Caveat

The instructor reserves the right to make changes to this syllabus throughout the semester. Notifications will happen via email and/or Canvas.

Advice from Other Calculus Students

In the last few years, I've asked my calculus students to give advice to you, future calculus students, based on their experiences in my course. Here are some of the highlights:

Advice from Research on How Students Learn

From the book "Learning and Motivation in the Postsecondary Classroom" by Marilla D. Svinicki: "researchers have demonstrated that students who are initially allowed to generate their own ideas about a problem before they receive a lecture on it better understand the concepts behind the problem than students who are simply told what those concepts are." What does this mean for you in this class? Most of the time, after the first class meeting about a new section of the book, it's best to do the homework that night and ask questions during the next class meeting, then turn it in that day to get the most rapid feedback from me. There is a temptation to not try it the first night, and just sit and try to absorb information about the problems from the discussion the next day. The research cited above says this is not good for your learning.

Also, "students who learn to monitor their own understanding and take steps to modify their thinking in light of that monitoring become much better problem solvers in the long run." I almost always want you to check your work by comparing to sensible upper and lower bounds, guesses, etc., or by taking a derivative to check an integral formula you just found. This way, you are monitoring how well you can do the problems in real-time, without having to wait for feedback from me grading your paper. The research I just mentioned shows that this makes you a better problem solver. AND, you get more credit because you can fix the problems you find you got wrong, even before turning it in!

Growth Mindset Statements

from @sylviaduckworth (but modified a bit) What can I say to myself?

Instead of I'm not good at this,

try: what am I missing?

Instead of I'm awesome at this,

try: I'm on the right track.

Instead of I give up,

try: I'll use some of the strategies we've learned (or email the professor!)

Instead of This is too hard,

try: This may take more time and effort

Instead of I can't make this any better,

try: I can always improve so I'll keep trying.

Instead of I just can't do calc,

try: I'm going to train my brain in calculus

Instead of I made a mistake,

try: Mistakes (and spotting them) help me to learn better

Instead of She's so smart. I will never be that smart,

try: I'm going to figure out how she does it.

Instead of It's good enough,

try: Is it really my best work (in the time available)?

Instead of Plan "A" didn't work,

try: Good thing the alphabet has 25 more letters!

Standard University Policies and Resources

Resources

https://www.emich.edu/studenthandbook/campus-resources/index.php In particular, I encourage you to use Swoop's Food Pantry if you need it, or donate/volunteer if you are able to.

EMU COVID Policies, etc.

www.emich.edu/emusafe

Academic Honesty

Academic dishonesty, including all forms of cheating, falsification, and/or plagiarism, will not be tolerated in this course. Penalties for an act of academic dishonesty may range from receiving a failing grade for a particular assignment to receiving a failing grade for the entire course. In addition, you might be referred to the Office of Student Conduct and Community Standards for discipline that can result in either a suspension or permanent dismissal. The Student Conduct Code contains detailed definitions of what constitutes academic dishonesty but if you are not sure about whether something you are doing would be considered academic dishonesty, consult with the course instructor. You may access the Code online at: www.emich.edu/responsibility/

Some schools have an Honor Code. EMU doesn't yet but together we can all work toward it!

Classroom Behavior

For in-person classes: Those who use laptops during class other than when everyone is using them should sit in the back row or sides if possible, to avoid distracting others with what is on their screens.

For online classes: To avoid distracting others with random noises from your environment and/or echoes, please keep yourself muted when possible. In many video chat apps, you can hold down the space bar to temporarily unmute, and then when you let up on the space bar, you're muted again, so you don't have to remember to re-mute. For the most part, please keep your video on if you can, to promote personal relations. Students who deliberately disrupt group video chats will lose the privilege of doing group video chats. Please be considerate about what appears behind you in video chats, mainly about things that would likely offend or unfairly distract other people.

Land Acknowledgement

The campus of Eastern Michigan University is located on the traditional territory (ceded in the 1807 Treaty of Detroit) of the Anishinaabeg, which refers collectively to the Ojibwe, Odawa, and Potawatomi (also known as the People of the Three Fires), and was also home to the Wendat/Wyandot people. This acknowledgement is included here to honor the elders and stewards of these heritages.

Standard University Policies

In addition to the articulated course specific policies and expectation, students are responsible for understanding all applicable university guidelines, policies, and procedures. The EMU Student Handbook is the primary resource provided to students to ensure that they have access to all university policies, support resources, and student's rights and responsibilities. Changes may be made to the EMU Student Handbook whenever necessary, and shall be effective immediately, and/or as of the date on which a policy is formally adopted, and/or the date specified in the amendment. Electing not to access the link provided below does not absolve a student of responsibility. For questions about any university policy, procedure, practice, or resources, please contact the Office of the Ombuds: 248 Student Center, 734.487.0074, emu_ombuds@emich.edu, or visit the website at www.emich.edu/ombuds.

CLICK HERE to access the University Course Policies

Refusals to comply with COVID mitigation requirements are a disruption of the classroom learning environment.  This includes examples such as refusing to wear a face mask, maintain appropriate distancing, or otherwise comply with the University’ COVID-19 policies. Steps that instructors may take in the event of a classroom disruption include:

  1. Make reasonable efforts to resolve the classroom disruption within the classroom.  This includes reminding the student that they must wear a face mask, class will not begin and instructors are not permitted to conduct a class session until they do so.  Failure to comply with University policy will subject the student to disciplinary action.
  2. If the behavior persists and the student does not comply with the policy, the instructor has the right to (and with masking violations SHOULD) discontinue the class session and immediately report the behavior to their department head/school director who will contact the Office of Wellness and Community Responsibility.
  3. If the situation escalates and an instructor feels an immediate threat to themselves or others, they may contact DPS (911 or 734-487-1222) for support.

University Writing Center

The University Writing Center Virtual (UWCV) offers writing support to all undergraduate and graduate students. In doing so, we value the diversity of our campus and honor all students and the languages they bring with them to the University.

 

Holman Success Center

Provides Academic Support through a variety of virtual and in-person services

 

Disabilities Resource Center

The DRC works collaboratively with students, faculty and staff to create an accessible, sustainable, and inclusive educational environment.

 

University Library

Research support is available to all students, 24/7. This includes getting started with research, identifying sources to search, developing search strategies, evaluating resources, and more. See https://www.emich.edu/library/help/ask.php for all of the ways in which you can get help with research. Some University Library services have changed, and may continue to change, in response to the pandemic. Please check for current information at https://www.emich.edu/library/news/covid.php

 

Title IX regarding discrimination on the basis of sex

Title IX of the Education Amendments of 1972 prohibits discrimination on the basis of sex under any education program or activity receiving federal financial aid. Sexual assault and sexual harassment is a form of sex discrimination prohibited by Title IX. What you need to know about Title IX

 

Student and Exchange Visitor Statement (SEVIS):

The Student Exchange Visitor Information System (SEVIS) requires F and J students to report numerous items to the Office of International Students & Scholars (OISS)

Food Pantry

Swoop's Pantry (104 Pierce Hall, https://www.emich.edu/swoopspantry/   , 734 487 4173) offers food assistance to all EMU students who could benefit. Students are able to visit twice per month to receive perishable and non-perishable food items, personal hygiene items, baby items, and more. Students can visit our website for hours of operation and more information. If you are in a position to donate to Swoop's, I encourage you to do so!