---
tags: mth225, course-documentation
---
# Specifications for Satisfactory Work in MTH 225
## Overview
As the syllabus details, your work in MTH 225 is graded on a two-level scale: Either 1 or **Satisfactory** if the work meets our class' standards for quality, or 0 or **Unsatisfactory** if it does not meet those standards. **This document gives the details of those standards for every piece of work in the course.** Next to the syllabus and the calendar, this is therefore the most important document for the course. You need to make sure you read it carefully and refer back to it regularly as you work. **Use this document as a "pre-flight" checklist** to self-evaluate your work before you hand it in; this will improve your work dramatically and save you lots of time having to revise Unsatisfactory work.
## Standards for Daily Prep assignments
Daily Prep assignments have two parts: a **pre-class** exercise set based on videos and reading, and an **in-class** group quiz over the same material.
| Part | Earn **1** if: |
|:---: | :-----------: |
| Pre-class | The work is **submitted before the deadline** and <br> **every non-optional item has a response representing a good-faith effort to be right**. |
| In-class | At least 2/3 or 3/4 of the items have a correct answer. |
:::warning
Please note that on the pre-class portion, a **0** is given if *any* of the following occur:
- The work is submitted after the deadline; or
- A required item has been left blank, even if accidentally; or
- A required item has been given a response that indicates low effort in attempting to be right, such as an obvious guess, a frivolous answer, or an "I don't know".
:::
## Standards for Weekly Challenges
Weekly Challenges typically consist of three kinds of work: practice exercises on basic computations, application or extension problems, and writing prompts. **Practice Exercises** are optional and are not graded. However, answers (or a tool for checking your answers) will be provided, and any work submitted for a practice exercise (even if it's partial or just a question) will receive feedback you can use to help you learn. These are for your own growth. **Application/Extension Problems** are graded on the basis of the correctness of the result and, especially and primarily, on the correctness and clarity of the explanation. **Writing Prompt** responses are evaluated based on whether you gave given a good-faith effort to provide an honest and substantive response.
:::warning
When grading a Weekly Challenge, the entire body of work you submit is considered and given a mark of either **Satisfactory** or **Unsatisfactory**. A Weekly Challenge is considered **Satisfactory** if all of these standards are met:
- Every Application/Extension Problem has a solution that **demonstrates strong understanding of the concepts involved**, is **complete and well-communicated**, and contains **at most only a few minor errors**, none of which demonstrate gaps in understanding or communication.
- Every writing prompt has a response that represents a **good-faith effort at honest communication** regarding the subject and is **well-communicated**.
:::
Some items may contain additional expectations or requirements (for example, if a problem involves computer code), and **Satisfactory** will require meeting those expectations as well as the two baseline expectations above.
**Incomplete (IC) work on Weekly Challenges:** A special designation of **Incomplete** (abbreviated **IC** in the Blackboard gradebook) may be given to Weekly Challenge submissions. A Weekly Challenge is graded **IC** if:
- All or part of a required item is blank, only partially complete, or has a response that is not a good-faith effort at a complete response. For example, completing part of a problem and then explaining that you didn't know how to complete the other parts will result in an **IC**. Or,
- There are significant and numerous major errors or misconceptions on mathematics or logic that occur throughout the work. Or,
- The submission is disorganized, illegible, messy, or unprofessionally written up. Written responses for Weekly Challenges are acceptable, but all writeups *must* show good-faith effort to present the work in an orderly, professional-looking manner.
Weekly Challenges that are marked **IC** will receive feedback only on why it was so marked; little to no feedback will be given on the content of the submission. You may revise and resubmit an **IC** Weekly Challenge, but ~~**you must spend a token** to do so, and~~ you will be doing it without the benefit of feedback on the math content of your work. *(Update: We removed the token requirement in the October update.)*
## Standards for Learning Target work
Becoming "fluent" on a Learning Target, in the language of the syllabus, requires **two successful demonstrations of skill** on that target that can be done in various ways, all detailed in the syllabus. A "demonstration of skill" typically means working out a problem or small group of problems that have something to do with the skills in the learning target. Those problems will vary throughout the semester but will always focus on the same set of skills. For example, no matter how you choose to demonstrate skill on Learning Target L.3, you will always be asked to do work involving determining whether a predicate is true, determining whether a quantified predicate is true, and stating the negation of a quantified predicate --- because that's what the Learning Target says (*"I can identify the truth value of a predicate, determine whether a quantified predicate is true or false,and state the negation of a quantified statement."*)
:::warning
**Regardless of the precise work you do, a demonstration of skill is considered "successful" if**:
- All parts of the work you are asked to do have an attempted response. That is, you may not skip or decline to respond to a part of a problem.
- The response contains **no more than two simple errors** (see below for a definition) and **no non-simple errors**. That is, the work can contain no significant errors that cast doubt on your skill.
- The response cannot *just* consist of a correct answer, unless it specifically says so --- you must also clearly communicate the thought processes that led to the answer, through clearly-written mathematical work, verbal explanations, or both.
:::
For MTH 225, a "simple" error is defined to be **an error in logic, computation, or communication that does not pertain to the learning target and does not oversimplify the problem**.
**Example:** In a hypothetical Algebra II class using our grading system, students are demonstrating their skill at solving quadratic equations ($ax^2 + bx + c = 0$) using the quadratic formula ($x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$). On a quiz, the class is asked to do this by finding the solutions to $3x^2 + 4x + 1 = 0$. (The correct answers are $x = -1$ and $x=-1/3$.) Here are some errors that students might commit, and whether they are considered "simple" or "non-simple".
| Error | Simple? | Why |
| :---: | :--------: | :---: |
| Alice copies the problem down incorrectly as $3x^2 - 4x + 1 = 0$ (changing $+4x$ to $-4x$), then *correctly* solves this incorrect problem to get $x=1$ and $x=1/3$. | SIMPLE | The copy error doesn't pertain to the learning target (being able to show skill with the quadratic formula) and doesn't make the problem any harder or easier. |
| Bob copies the problem down incorrectly as $3x + 4x + 1 = 0$ (dropping the square on $3x^2$), simplifies this to $7x + 1 = 0$, then solves without the quadratic formula to get $x=-1/7$. | NOT SIMPLE | The copy error oversimplifies the problem, and it no longer demonstrates skill on the learning target. |
| Chuck copies the problem down correctly but mistakenly uses $b^2 + 4ac$ in the quadratic formula instead of $b^2-4ac$. | NOT SIMPLE | That's a fundamental error directly related to the learning target. |
| Diane copies the problem down correctly and starts the solution correctly, but at one point she mistakenly switches a plus/minus sign, which leads to an incorrect answer. | SIMPLE | A basic sign error made in the process of a correctly-set up solution does not pertain to this learning target and does not make the problem trivially easy. |
Note that **an error that is considered "simple" in one situation may be "non-simple" in another**. For example, Learning Targets SF.5 and C.2 both involve the factorial function. Making an error in computing this function, for example computing $10! = 1000$, would be *non-simple* for SF.5 since the entire target is about computing these functions correctly; but might be simple in C.2 since the emphasis there is in using the factorial as part of a larger problem-solving process.

Initial due date: Sunday, April 9 at 11:59pm ET Overview Our final miniproject reaches back into linear algebra to look at diagonalizable matrices and their uses in solving systems of differential equations. Prerequisites: You'll need to be able to solve basic systems of differential equations and find the eigenvalues and eigenvectors for a small matrix. You'll also need a basic comfort level with concepts of linear independence and matrix arithmetic from earlier in the course. Background This entire problem comes from Section 3.9.1 in your textbook. Here is a rephrased version of the introduction to that section.

3/29/2023Initial due date: Sunday, April 9 at 11:59pm ET Overview This miniproject will teach you about the Runge-Kutta method, a standard numerical solution technique for differential equations. Prerequisites: A strong grasp of Euler's Method for single DE's is needed. You will also need to be comfortable using a spreadsheet. Miniproject 6 (Euler's Method for systems) is also recommended. Background A description of the Runge-Kutta method along with an example is given in this tutorial. Read it carefully and make sure you can work along with the example before proceeding.

3/29/2023Initial due date: Sunday, April 9 at 11:59pm ET Overview This miniproject introduces a version of Euler's Method as a numerical solution technique for systems. Prerequisites: You will need to be comfortable with using Euler's method for single differential equations. You'll also benefit from some familiarity with spreadsheets or Python in order to automate the calculations. Background This tutorial gives you the background you need for this assignment. Please read it and make sure you understand the concepts and the example: https://github.com/RobertTalbert/linalg-diffeq/blob/main/assignments/Euler's_Method_for_Systems.ipynb

3/22/2023Initial due date: Sunday, March 26 at 11:59pm ET Overview Eigenvalues of a matrix are incredibly useful and important for many applications. (Some of these applications are in Miniprojects 1-3.) But computing eigenvalues of a matrix, even of relatively small size, can be difficult or impossible to do exactly. So we need numerical approximation methods for most practical uses of eigenvalues. This miniproject will teach you one such method. Prerequisites: You'll need to know what an eigenvalue and eigenvector for a matrix are, and how to find these using SymPy. You'll also need to know how to multiply matrices and vectors. Background Complete the following warmup exercises first. These don't go in your writeup. They are just here to teach you some terminology you'll need in the main assignment.

3/3/2023
Published on ** HackMD**