Math 120: Calculus 1 Winter 2022 Syllabus
Prof. Andrew Ross, Eastern Michigan University
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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)
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.
Parenting is hard work, and doubly so when combined with being a student. I recognize that there may occasionally be times when the way to make it possible is to have your child accompany you to class (or be on a video call), whether that is because it's how your new baby gets fed, or because your older child's school doesn't meet that day. Know that they are welcome! I trust your judgment on what your child can be present for, and that you will provide supervision/quiet activities for them during class. I honor the hard work that you are doing. I also appreciate the issues involved in taking care of other friends and relatives (such as elders).
Note: this syllabus is temporary, and may change up to the first day of class.
This version posted on: 2022-01-08
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.
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.
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
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))
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.
Section 12, asynchronous, CRN 20676
The course is "asynchronous"--students are not required to all meet online at the same time.
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 make an appointment for a video chat.
If we take the point of view of an in-person class: Research has shown that to succeed in Math 120 it usually takes 12 hours per week outside of class during a regular (Fall or Winter) semester. For an asynchronous online class, add 4 hours/week for a regular semester (total of 16 hours/week) for most people to succeed.
Just to highlight that again:
As one person put it, it's well more than twice what it takes for Math 107 Trigonometry (which is a 2-credit course, while Math 120 is a 4-credit course that is known to be harder than trig).
FYI, 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 extremely well-prepared students.
If it’s a twice-as-fast Summer semester (7 weeks instead of 14), then plan on double the hours/week, of course: 32 hours/week.
Professor Andrew Ross
Office: Pray-Harrold 515m
andrew.ross@emich.edu
http://emunix.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
For online classes, please make appointments with me using my Google Calendar Appointment Page. You can reserve as many 10-minute appointments in a row as you need. If you can’t find an appointment time that works for you, please email me with your availability for the next few days and we will find a time that works.
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.
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.
Online class: 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. I strongly prefer that people use a camera/scanner phone app like GeniusScan or CamScanner.
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.
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. It is a good idea to keep an eye on your scores using the system, and get extra help if your scores indicate the need.
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:
(full version): Students will learn to solve real-life problems using a mathematical modeling process. They will learn to:
Though it’s not explicitly part of the official EMU math modeling process, I think it’s also important to:
For more on these ideas, see the book “Becoming a Teacher of Mathematical Modeling, Grades 6-12”, page 67.
Upon successful completion of MATH 120 - Calculus I, a student will be able to:
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.
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: Google Doc (or, this link in case the bitly link fails)
In the asynchronous online class, there is no real concept of "attendance".
My classes and videos 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 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 or CamScanner), 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.
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.
My students often say that there is more homework than expected in my classes. This is very likely true. On the other hand, you will probably spend less time “studying for exams”, since the Interviews aren’t as big, stressful, or make-or-break as ordinary exams are.
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. Note that this kind of skills-based interview questions are quite common in some fields when interviewing for a job, like software engineering. 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).
Interviews/Quizzes are on a Mastery-Based Grading system, which means that if you haven’t achieved mastery of a topic yet, you should plan on doing a retake after getting help with it (from me, the math lab, or anyone else), and plan on retaking until you have mastered the topic. I hope this lowers anxiety about them, since retakes are possible (and encouraged/expected!)
While the target time is about 5-10 minutes, there is no actual time limit. I do not mean this to be a speed test. For online courses, you might need to stay in the Zoom waiting room until the person ahead of you finishes.
The final project that you do is on a topic that you (and perhaps a partner) 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.
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 affect your grade downward.
The instructor reserves the right to make changes to this syllabus throughout the semester. Notifications will happen via email and/or Canvas.
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:
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!
I’m not going to pretend that a growth mindset solves everything, but not having a growth mindset can definitely get in the way!
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!
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.
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!
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.
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, and to prompt more conversation about returning land to its rightful owners.
Let’s consider this:
https://theconversation.com/land-acknowledgments-meant-to-honor-indigenous-people-too-often-do-the-opposite-erasing-american-indians-and-sanitizing-history-instead-163787 which concludes with
“Land acknowledgments are not harmful, we believe, if they are done in a way that is respectful of the Indigenous nations who claim the land, accurately tell the story of how the land passed from Indigenous to non-Indigenous control, and chart a path forward for redressing the harm inflicted through the process of land dispossession.
What many Indigenous persons want from a land acknowledgment is, first, a clear statement that the land needs to be restored to the Indigenous nation or nations that previously had sovereignty over the land.
This is not unrealistic: There are many creative ways to take restorative measures and even to give land back, such as by returning U.S. national parks to the appropriate tribes. Following from this, land acknowledgments must reveal a sincere commitment to respecting and enhancing Indigenous sovereignty.
If an acknowledgment is discomforting and triggers uncomfortable conversations versus self-congratulation, it is likely on the right track.”
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.
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Student expectations from instructors
Students may expect impartial and respectful treatment from instructors, including:
1. Reasonable opportunities to ask questions and express ideas;
2. Respect for his or her right to privacy (FERPA) for certain educational, personal, and health related information;
3. Knowledge of the grading system early in the semester and the absence of unfair, capricious or discriminatory grading categories. This should include explicit and early description of the instructor's policy for penalties regarding failure to attend and/or participate in class;
4. Prompt return of examinations and other assignments with verbal and/or written explanations of deficiencies;
5. Posted office hours, scheduled at times most beneficial to students and advance knowledge, when possible, of cancellation of class or office hours;
6. Reasonable accommodations upon the provision of documentation provided by the Disability Resource Center.
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!