Andy Rundquist | arundquist@hamline.edu | Robbins Science 124 | 651-252-1778 |

Math Methods Lab: Fall 2016

Goals: To introduce and demonstrate the use of mathematical and computational methods important in physics and engineering.

Content: Physics and engineering applications associated with ordinary and partial differential equations, Laplace transforms, linear algebra, vector calculus, Fourier analysis, complex analysis, numeric analysis, probability & statistics.

Taught: Fall term

Prerequisites: MATH 3720 and PHYS 3540 or consent of instructor

Credits: 4

These are all of the outcomes. Those in bold are what are introduced/reinforced/assessed in this course

Students will demonstrate a thorough understanding of general and modern physics. |

(BS only) Students will demonstrate a fundamental understanding of advanced physics topics. |

Students will design, perform and interpret an insightful physics experiment. |

Students will communicate physical concepts and experimental details. |

Students will collaborate as part of a scientific team. |

Students will apply math and technology tools to problem solving. |

(BS only) Students will demonstrate the ability to model a physical system using current computational and analytical techniques. |

Every day (of new material) will have its own learning outcome (called “standard” in this document). To see them, click on the dates to the right.

- good MMA introduction
- list of Wolfram-generated mma tutorials
- screencast on how to use NonlinearModelFit

See empty space on my calendar between 8 and 4

Ways to contact me:

- twitter (@arundquist)
- phone/text: 651-252-1778

Lab plays two major roles in this course:

- Learn how to use Arduinos for computer-based experimental control and data collection
- Learn how to use Mathematica as a tool to further explore the mathematical and computational methods we’ll be studying in class.

On these days we’ll develop syntax to do numerical work that augments the analytical things we’ll be studying in the lecture portion of the class. We’ll use screen sharing software so that everyone will be able to diagnose problems with everyone else’s code. There will not be different standards for each of these days. Rather, everyone will get a new score for the “I can diagnose and correct coding problems in Mathematica” standard. I fully expect everyone to get 4’s on this towards the end of the semester. If the last score is unsatisfactory to you, there will be further opportunities to improve it.

The goal is to get you comfortable with using computers to control experiments and collect data. Arduinos are inexpensive microprocessors that can facilitate this. We’ll use them to both control devices (LEDs, motors, etc) and to record and process data (temperature, humidity, voltage, etc). Every day you’ll get a new score for the “I can interface a computer to an Arduino” standard.

Working with the Sustainability office on campus, we’ve developed a project where students in this class install arduino-based devices around campus to record longitudinal data that can help the campus make decisions to help us be more sustainable. Here’s a blog post about the project. You will:

- Find a campus “client” who needs something measured.
- Determine the appropriate probes and software to achieve the result desired.
- Build, characterize, and optimize the hardware and software necessary to collect the data into my HU IOT database.
- Model the physical situation to make predictions about trends in the data.
- Provide a report to the client indicating how the data is being collected and how to access it.

We will be using a very different assessment approach this semester. It is called "Standards-Based Grading" and it addresses the following issues I've had with students in the past:

- Students cram for an exam but sometimes don't retain the information
- Students can sometimes be more focussed on points than learning
- If a student doesn't "get it" at the time of homework being due or the exam, they lose the points, even if they clearly learn it by the final.

The basic idea is that there are certain things the department thinks you should learn in this class. Those are what I'll call the "standards." Typically every chapter we cover will have around 3 standards and there will also be a few holistic standards as well. For each standard you will be assessed many times. An assessment might cover 2 or 3 standards but you can also come up with your own ways to assess your learning. Every time a standard is assessed, the score for that standard is updated in the gradebook. The score might go up and it might go down. You can reassess any standard often, at least within reason.

- I can interface a computer to an Arduino
- I can provide a campus client with a full solution to a recurring measurement problem.
- I can diagnose and correct coding problems in Mathematica (and Python?)

- We’ll add a new one every day. They will start with one of the following:

- I can calculate . . .
- I can model (using Mathematica) . . .
- I can discuss the foundations of, usefulness of, and ramifications of . . .
- I can do an interesting problem on . . .

Much of this was inspired by/copied from Frank Noschese's work on SBG

Note: Not assessed: 0

- Doesn't meet expectations: 1

- I need lots of help from my instructor (one-on-one).
- I have low confidence on how to do the skills and need more instruction.
- I need my textbook/notes at all times.
- I do not understand the concept/skills.
- I cannot correctly identify concepts and/or define vocabulary.
- I cannot make connections among ideas or extend the information.
- My responses lack detail necessary to demonstrate basic understanding.
- Cannot articulate most of the main ideas involved in the standard

- Approaches expectations: 2

- I have a general understanding of the content/skills, but I'm also confused about some important parts.
- I need some help from my instructor (one-on-one or small group) to do the skills correctly
- I do not feel confident enough to do the skills on my own
- I need my textbook/notes most of the time.
- I can correctly identify concepts and/or define vocabulary; however I cannot make connections among ideas and/or independently extend my own learning.
- My responses demonstrate basic understanding of some main ideas, but significant information is missing.

- Meets expectations: 3

- I understand the important things about the content/skills.
- I have confidence on how to do the skills on my own most of the time, but I need to continue practicing some parts that still give me problems.
- I need my handouts and notes once in a while.
- I am proficient at describing terms and independently connecting them with concepts.
- I understand not just the "what," but can correctly explain the "how" and "why" of scientific processes.
- My responses demonstrate in-depth understanding of main ideas.

- Exceeds expectations: 4

- I understand the content/skills completely and can explain them in detail.
- I can explain/teach the skills to another student.
- I have high confidence on how to do the skills.
- I can have a conversation about the skills.
- I can independently demonstrate extensions of my knowledge.
- I can create analogies and/or find connections between different areas within the sciences or between science and other areas of study.
- My responses demonstrate in-depth understanding of main ideas and of related details.

We will be using a very different assessment approach this semester. It is called "Standards-Based Grading" and it addresses the following issues I've had with students in the past:

- Students cram for an exam but sometimes don't retain the information
- Students can sometimes be more focussed on points than learning
- If a student doesn't "get it" at the time of homework being due or the exam, they lose the points, even if they clearly learn it by the final.

The basic idea is that there are certain things the department thinks you should learn in this class. Those are what I'll call the "standards." Every day of new content will have a new standard associated with it.

Each standard will be accompanied by three rich problems. These will be used for every assessment (quizzes, oral exams, student-submitted videos, office visits). Here’s a blog post of mine about this approach.

For each standard you will be assessed many times. Every time a standard is assessed, the score for that standard is updated in the gradebook. The score might go up and it might go down. You can reassess any standard often, at least within reason.

Here are some of the types of assessments we'll use:

- Screencasts

- you can use Jing to record your screen.

- you can do this for a Mathematica document

- You walk me through your calculation
- you can use pre-approved "cut and paste" materials/functions. Everything else has to be typed in real time

- Exams

- There are a few times in the semester where I've scheduled breaks for review and assessment. Here we can do oral testing in class for particular standards.
- You should bring your whole portfolio to these as we may reference work on other standards. In the exam we’ll randomly select one standard and then one of the three problems for the standard.
- The exam will be 10 minutes long in my office.

- For the first minute, I will silently review your work on the problem and frame my questions
- You will spend the next 8 minutes answering my questions.
- Together we will spend 1 minute determining your score.

- Note that these show up in the gradebook just like any other assessment. In other words, if you do poorly you are free to do a reassessment.

- Office visits

- If you schedule it in advance (including mentioning the standard you want assessed), you can come to my office where I will randomly pick one of the three problems to assess. The process will be just like the oral exam (the only difference being you can pick the standard).

- Online office hours

- We can use my online office hours in the same way (again, with some advanced notice)

95% of your grade depends on how you do on the standards assessment. I will simply add up your points and divide by the total. We will also have a final in this class. On the final you will make a mind-map of the standards and discuss several of the important connections. This will represent the final 5% of your grade.

Every day with new material three problems will be assigned. The next class period will have a 10 minute quiz where one of those problems will be chosen. We will work together to “turn the problem inside out” so that you shouldn’t just memorize how to do that problem as it’s stated. Here’s a blog post of mine about this. Wednesday’s material will be quizzed on Friday. Friday’s material will be quizzed on Monday. There is no new material on Monday so the Wednesday quiz will be chose from one of the 6 most recent problems. This allows for some cycling through the material, where we go back as a class to review some older ideas. You should endeavor to really understand every problem assigned, as they can also act as context for oral exams and for office visits.

I will not provide solutions to these problems, as they will continue to be viable for oral exams and office visits.

If a standard is not selected as a quiz question you will need to either submit a screencast or come to my office within 2 weeks of the standard being assigned. The same happens after every other assessment (2 weeks later it becomes frozen). The only way to unfreeze a score is an instructor-initiated reassessment (most likely an oral exam).

Being able to show your understanding of material efficiently is a sign of deeper understanding. It shows that you know the priority of the important concepts, as you don't spend too much time on less important ones. You will not receive a 4 (see scale above) for a technically correct assessment, even one whose content is "brag-worthy," if it is deemed to be too long. A good rule of thumb for the duration of a typical assessment is ten minutes.

If you get a 0-3 on a standard, you can, of course, redo it, but you must do a different problem. Note that I'll give you copious feedback on what went wrong. If you get what's called a "3 improvable" I'll indicate that there's something to be fixed but I won't tell you what. You can resubmit just that fix to get up to a 4.

letter grade: | A | A- | B+ | B | B- | C+ | C | C- | D+ | D | D- | F |

rounded score >= | 94 | 90 | 87 | 84 | 80 | 77 | 74 | 70 | 67 | 64 | 60 | 0 |

- Wed Sep 7: Probability
- Thu Sep 8: LAB: Probability
- Fri Sep 9: Probability 2
- Mon Sep 12: Review
- Wed Sep 14: Complex numbers 1
- Thu Sep 15: LAB: Arduino intro
- Fri Sep 16: Complex numbers 2
- Mon Sep 19: Review
- Wed Sep 21: Linear Algebra 1
- Thu Sep 22: LAB: Linear Algebra
- Fri Sep 23: Linear Algebra 2
- Mon Sep 26: Review
- Wed Sep 28: Eigenvectors and eigenvalues
- Thu Sep 29: LAB: Arduino project
- Fri Sep 30: Diagonalization
- Mon Oct 3: Review
- Wed Oct 5: First order ODE's
- Thu Oct 6: LAB: ODEs
- Fri Oct 7: 2nd order ODE's
- Mon Oct 10: Review
- Wed Oct 12: systems of ODEs
- Thu Oct 13: LAB: ODEs
- Fri Oct 14: ODE series solution
- Mon Oct 17: Review
- Wed Oct 19: Oral
- Thu Oct 20: LAB: Oral
- Fri Oct 21: Oral
- Mon Oct 24: Oral
- Wed Oct 26: Laplace solutions of ODEs
- Thu Oct 27: LAB: Arduino project
- Fri Oct 28: MIDTERM BREAK
- Mon Oct 31: vectors, dot, and cross
- Wed Nov 2: (Andy gone)
- Thu Nov 3: LAB: vector calculus
- Fri Nov 4: grad, div, curl
- Mon Nov 7: Review
- Wed Nov 9: fundamental theorems of calculus
- Thu Nov 10: LAB: Arduino project
- Fri Nov 11: Fourier analysis
- Mon Nov 14: Review
- Wed Nov 16: Fourier analysis
- Thu Nov 17: LAB: Fourier
- Fri Nov 18: Andy gone
- Mon Nov 21: Fourier Transform applications
- Wed Nov 23: PDEs: 1D wave equation
- Thu Nov 24: THANKSGIVING BREAK
- Fri Nov 25: THANKSGIVING BREAK
- Mon Nov 28: Review
- Wed Nov 30: PDEs: Heat equation
- Thu Dec 1: LAB: PDEs
- Fri Dec 2: PDEs: 2D wave equation
- Mon Dec 5: Review
- Wed Dec 7: Oral
- Thu Dec 8: Lab: oral
- Fri Dec 9: oral
- Mon Dec 12: oral
- Thu Dec 15: FINAL 10AM - NOON